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2003TIMSS Assessment Frameworksand Specifications 20032nd Edition

Ina V. S. Mullis

Michael O. Martin

Teresa A. Smith

Robert A. Garden

Kelvin D. Gregory

Eugenio J. Gonzalez

Steven J. Chrostowski

Kathleen M. O’Connor

Trends in Mathematicsand Science Study

The International Study CenterLynch School of Education

The International Association for theEvaluation of Educational Achievement

© 2003 International Association for theEvaluation of Educational Achievement (IEA)

TIMSS Assessment Frameworksand Specifications 2003 2nd Edition

February 2003

Publisher: International Study Center,Lynch School of Education, Boston College

Library of CongressCatalog Card Number: 2003101238

ISBN: 1–889938–30–0

For more information aboutTIMSS contact:

TIMSS International Study CenterLynch School of EducationManresa HouseBoston CollegeChestnut Hill, MA 02467United States

tel: +1-617-552-1600fax: +1-617-552-1203

e-mail: [email protected]

http: //timss.bc.edu

Boston College is an equal opportunity,affirmative action employer.

Printed and bound in the United States.

Preface i

Introduction 1Overview 3

The TIMSS Curriculum Model 3

The Development Process for theTIMSS Assessment Frameworksand Specifications 4

The TIMSS Tests 5

Student Populations Assessed 6

Mathematics Framework 7Overview 9

Mathematics Content Domains 11

a Number 12

b Algebra 14

c Measurement 16

e Geometry 18

d Data 21

Mathematics Cognitive Domains 25

f Knowing Facts and Procedures 27

g Using Concepts 28

h Solving Routine Problems 30

i Reasoning 32

Communicating Mathematically 34

Guidelines for Calculator Use 34

Contents

Science Framework 35Overview 37

Science Content Domains 38

a Life Science 40

c Chemistry 47

b Physics 50

d Earth Science 54

e Environmental Science 58

Science Cognitive Domains 61

f Factual Knowledge 63

g Conceptual Understanding 64

h Reasoning and Analysis 66

Scientific Inquiry 69

Contextual Framework 71Overview 73

The Curriculum 73

The Schools 75

Teachers and Their Preparation 76

Classroom Activities and Characteristics 78

The Students 81

Assessment Design 83Scope of the Assessment 85

Dividing up the Item Pool 85

Block Design for Student Booklets 86

Question Types and Scoring Procedures 88

Scales for Reporting Student Achievement 89

Releasing Assessment Materialto the Public 90

Background Questionnaires 90

Endnotes 93

Appendix A 97National Research Coordinators

Appendix B 103Example Mathematics Items

Appendix C 121Example Science Items

Background

Advancing science and mathematics education has long been the focus ofstudies by the IEA, the International Association for the Evaluation ofEducational Achievement. Reflecting the seminal place that these two keycurriculum areas hold in all educational systems as fundamental to devel-oping technologically proficient societies, IEA has been measuring studentachievement and collecting contextual information to facilitate studentlearning in mathematics and science for nearly 40 years.

The conduct of the First International Mathematics Study (FIMS)dates back to 1964, and science first was assessed as part of the Six SubjectStudy in 1970-71. Mathematics and science were again the focus of majorresearch efforts in 1980-82 and 1983-84, respectively. In 1990, the IEAGeneral Assembly determined to assess science and mathematics togetheron a regular basis every four years. This decision marked the first of thelarge-scale international studies to measure trends in student performance,beginning with the original TIMSS (the Third International Mathematicsand Science Study) conducted in 1995, TIMSS-Repeat in 1999, and nowTIMSS 2003 (renamed the Trends in International Mathematics andScience Study), also known as TIMSS Trends.

Frameworks for TIMSS 2003

A particular challenge for TIMSS 2003 was developing this set of frame-works articulating important content for students to have learned in math-ematics and science, as well as describing important home and schoolcontexts influencing achievement in these subjects. It is important thatthese frameworks capture important issues for mathematics and scienceeducation today, while providing the vision necessary to take the TIMSScycle of studies beyond the 2003 assessment. The frameworks, producedat the beginning of the new millennium, are designed to shape future IEAassessments in mathematics and science so that they can evolve with thetimes, while recognizing the axiom – If you want to measure change, do notchange the measure.

The TIMSS International Study Center at Boston College preparedthis second edition of the frameworks to provide examples of the types ofassessment questions contained in the TIMSS 2003 assessment. The exam-ple items for mathematics are presented in Appendix B and for science inAppendix C. The second edition also contains some minor revisions, inparticular to the section on the assessment design.

TIMSS 2003 i

Preface

Acknowledgments

The IEA was founded in 1959 for the purpose of conducting comparativeresearch studies on educational policies, practices, and outcomes. Sincethen, IEA studies have contributed a deeper understanding of the educa-tional process both within and among the nearly 60 member countries.The IEA has a permanent Secretariat in Amsterdam, the Netherlands, anda Data Processing Center in Hamburg, Germany. TIMSS is directed by IEA’sInternational Study Center at Boston College. The strength, quality, andsuccess of IEA’s studies, however, derive from the expertise among itsmembers in curriculum, measurement, and education and their collabora-tion in conducting the research.

Also, extremely crucial to success is securing the funding necessary tocarry out the extensive development and review work required by inter-national projects of this magnitude. Without such support a project likeTIMSS is not possible. The IEA is deeply grateful to the U.S. NationalScience Foundation, the U.S. National Center for Education Statistics, andfor the fees paid by participating countries for helping to fund the develop-ment of the TIMSS frameworks presented herein.

The TIMSS frameworks are the result of considerable collaborationamong individuals from around the world, most notably the specialistscomprising the TIMSS Expert Panel in Mathematics and Science, theNational Research Coordinators from the participating countries, staff fromIEA’s International Study Center at Boston College, and staff from IEA’sSecretariat and Data Processing Center. I am extremely grateful for the con-tribution of each person who devoted his or her energy and time to thisimportant and comprehensive effort. In particular, I would like to acknowl-edge the work of the TIMSS Mathematics Coordinator Robert Garden andthe Science Coordinator Teresa Smith. Kelvin Gregory, the TIMSSCoordinator at the time the frameworks were developed, had specialresponsibility for the contextual framework. The Director of Operations andAnalysis of the International Study Center and TIMSS, Eugene Gonzalez,oversaw development of the assessment design.

Without a dedicated, continuing center from which to coordinateprojects like TIMSS and the experienced staff from the consortium oforganizations that implements the studies, success would be limited. Iwould like to express my thanks to the staff at the International StudyCenter at Boston College, the IEA Secretariat, the IEA Data ProcessingCenter, Statistics Canada, and Educational Testing Service. Finally, I wouldlike to especially thank the Co-Directors of the International Study Centerand TIMSS, Ina V.S. Mullis and Michael O. Martin, for their leadership anddedication to this project.

Hans WagemakerIEA Executive Director

TIMSS 2003ii

TIMSS 2003 iii

The International Study Center at Boston College

The International Study Center (ISC) at Boston College is dedicated toconducting comparative studies in educational achievement. Principally, itserves as the International Study Center for IEA’s studies in mathematics,science, and reading – the Trends in International Mathematics andScience Study (TIMSS), and the Progress in International Reading LiteracyStudy (PIRLS). The staff at the ISC is responsible for the design and imple-mentation of these studies. In developing and producing the TIMSS frame-works, ISC staff conducted a collaborative effort involving a series ofreviews by an Expert Panel and the National Research Coordinators. Thefollowing individuals were instrumental in this process.

Ina V.S. MullisCo-Director, TIMSS

Eugenio J. GonzalezDirector of Operations and Data Analysis

Teresa A. SmithScience Coordinator

Steven J. ChrostowskiDevelopment Specialist

Christine O’SullivanScience Consultant

Michael O. MartinCo-Director, TIMSS

Kelvin D. GregoryTIMSS Coordinator (2000-2001)

Robert A. GardenMathematics Coordinator

Kathleen M. O’ConnorDevelopment Specialist

Eugene JohnsonPsychometric/Methodology Consultant

Hans WagemakerExecutive Director

Dirk HastedtIEA Data Processing Center

Barbara MalakManager, Membership Relations

Oliver NeuschmidtIEA Data Processing Center

TIMSS 2003iv

International Association for the Evaluation ofEducational Achievement (IEA)

In developing the TIMSS Assessment Frameworks and Specifications, theIEA has provided overall support in coordinating TIMSS with IEA’s mem-ber countries and reviewing all elements of the design. The following per-sons are closely involved with TIMSS.

Statistics Canada

Statistics Canada is responsible for collecting and evaluating the sample inTIMSS, and helping participants to adapt the TIMSS sampling design tolocal conditions. Senior methodologists Pierre Foy and Marc Joncasreviewed the frameworks from a sampling perspective, and made manyhelpful suggestions.

Educational Testing Service

Educational Testing Service conducts the scaling of the TIMSS achievementdata. Researchers Matthias Von Davier, Edward Kulick, and KentaroYamamoto reviewed the frameworks from a design perspective.

National Research Coordinators

The TIMSS National Research Coordinators (NRCs) work with internation-al project staff to ensure that the study is responsive to their concerns,both policy-oriented and practical, and are responsible for implementingthe study in their countries. NRCs reviewed successive drafts of the frame-works, and made numerous suggestions that greatly benefited the finaldocument. A list of the NRCs appears in Appendix A.

TIMSS 2003 v

International Expert Panel in Mathematicsand Science

The Expert Panel worked with staff from the International Study Center indeveloping all aspects of the frameworks and particularly the mathematicsand science frameworks. They made recommendations for the contentareas, cognitive domains, problem-solving and inquiry tasks, and focusareas for policy-orientated research.

Mathematics

Khattab Abu-LibdehJordan

Anica AleksovaRepublic of Macedonia

Kiril BankovBulgaria

Aarnout BrombacherSouth Africa

Anna Maria CaputoItaly

Joan Ferrini-MundyUnited States

Jim FeyUnited States

Derek HoltonNew Zealand

Jeremy KilpatrickUnited States

Pekka KupariFinland

Mary LindquistUnited States

David RobitailleCanada

Graham RuddockUnited Kingdom

Hanako SenumaJapan

Science

K.Th. (Kerst) BoersmaThe Netherlands

Rodger BybeeUnited States

Audrey ChampagneUnited States

Reinders DuitGermany

Martin HollinsUnited Kingdom

Eric JakobssonUnited States

Galina KovalyovaRussian Federation

Svein LieNorway

Jan LokanAustralia

Francisco MazzitelliArgentina

Gabriella NoveanuRomania

Margery OsborneUnited States

Jana PaleckovaCzech Republic

Hong Kim TanSingapore

Khadija Zaim-Idrissi Morocco

TIMSS 2003vi

Funding

Funding for the development of the TIMSS Assessment Frameworks andSpecifications was provided by the U.S. National Science Foundation, theU.S. National Center for Education Statistics, and participatingcountries. In particular, much of the work was made possible by a grantfrom the U.S. National Science Foundation. Janice Earle, Finbarr Sloane,Elizabeth Vander Putten, and Larry Suter each played crucial roles inmaking the frameworks possible.

Introduction

Introduction 3

1 Originally named the Third International Mathematics andScience Study.

2 Robitaille, D. F., Beaton, A. E., and Plomp, T., eds. (2000), TheImpact of TIMSS on the Teaching and Learning of Mathematicsand Science, Vancouver, BC: Pacific Educational Press.

Overview

The Trends in International Mathematics andScience Study (TIMSS1) is a project of theInternational Association for the Evaluation ofEducational Achievement (IEA). The IEA is anindependent international cooperative of nation-al research institutions and government agenciesthat has been conducting studies of cross-nation-al achievement since 1959.

TIMSS 2003 is the most recent in theseries of IEA studies to measure trends in stu-dents’ mathematics and science achievement.Offered first in 1995 and then in 1999, the reg-ular cycle of TIMSS studies provides countrieswith an unprecedented opportunity to measureprogress in educational achievement in mathe-matics and science.

Additionally, to provide each participatingcountry with a rich resource for interpreting theachievement results and to track changes ininstructional practices, TIMSS asks students, theirteachers, and their school principals to completequestionnaires about the contexts for learningmathematics and science. Trend data from thesequestionnaires provide a dynamic picture ofchanges in the implementation of educationalpolicies and practices and help to raise new issuesrelevant to improvement efforts. TIMSS datahave had an enduring impact on reform anddevelopment efforts in mathematics and scienceeducation around the world, leading on onehand to continuing demand for trend data tomonitor developments and on the other to aneed for more and better policy-relevant infor-mation to guide and evaluate new initiatives.2

This publication, the TIMSS AssessmentFrameworks and Specifications, serves as the basisof TIMSS 2003 and beyond. It describes insome detail the mathematics and science con-tent to be assessed in future assessments inmathematics and science. Topic areas are elabo-rated with objectives specific to grades 4 and 8.The TIMSS frameworks document alsodescribes the contextual factors associated withstudents’ learning in mathematics and sciencethat will be investigated. Finally, it provides anoverview of the assessment design and theguidelines for item development.

The TIMSS Curriculum Model

Building on earlier IEA studies of mathematicsand science achievement, TIMSS uses the cur-riculum, broadly defined, as the major organiz-ing concept in considering how educationalopportunities are provided to students, and thefactors that influence how students use theseopportunities. The TIMSS curriculum model hasthree aspects: the intended curriculum, theimplemented curriculum, and the achieved cur-riculum (see Exhibit 1). These represent, respec-tively, the mathematics and science that societyintends for students to learn and how the educa-tion system should be organized to facilitate this

National Socialand Educational

Context

School, Teacherand Classroom

Context

StudentOutcomes andCharactertistics

IntendedCurriculum

ImplementedCurriculum

AttainedCurriculum

Exhibit 1: TIMSS Curriculum Model

learning; what is actually taught in classrooms,who teaches it, and how it is taught; and, finally,what it is that students have learned, and whatthey think about these subjects.

Working from this model, TIMSS usesmathematics and science achievement tests todescribe student learning in the participatingcountries, together with questionnaires to pro-vide a wealth of information. The questionnairesask about the structure and content of theintended curriculum in mathematics and sci-ence, the preparation, experience, and attitudesof teachers, the mathematics and science contentactually taught, the instructional approachesused, the organization and resources of schoolsand classrooms, and the experiences and atti-tudes of the students in the schools.

The Development Process for theTIMSS Assessment Frameworksand Specifications

Developing this document began by updatingthe Curriculum Frameworks for Mathematics andScience3 used as the basis for the 1995 and 1999assessments. This process involved widespreadparticipation and reviews by educators aroundthe world. To permit the content assessed byTIMSS to evolve, the frameworks were revisedto reflect changes during the last decade in cur-ricula and the way mathematics and science aretaught. In particular, the frameworks wereexpanded to provide specific objectives forassessing students at grades 4 and 8, resulting inthe specifications for the assessments in mathe-matics and science contained in this document.

To provide the basis for valid internationaltests, assessment frameworks require extensiveinternational input. They must be appropriatefor the levels of mathematics and science learn-ing of the populations studied in the manyTIMSS countries, and hence representativesfrom national centers were asked to play animportant role in contributing critiques andadvice as the frameworks were developed.

An international panel of mathematics andscience education and testing experts providedguidance for the general form the assessmentframeworks should take. The U.S. NationalScience Foundation provided support for themeetings and the work of the expert panel.Using an iterative process, successive drafts werepresented for comment and review by NationalResearch Coordinators (NRCs), national commit-tees, and expert panel members. A detailedquestionnaire to participating countries about

Introduction4

3 Robitaille, D.F., et al (1993), TIMSS Monograph No. 1:Curriculum Frameworks for Mathematics and Science,Vancouver, BC: Pacific Educational Press.

topics included in their curricula provided valu-able feedback on the suitability of assessing indi-vidual mathematics and science topics at thefourth and eighth grades.

The frameworks do not consist solely ofcontent and behaviors included in the curriculaof all participating countries. The aim of theextensive consultation on curriculum was toensure that goals of mathematics and scienceeducation regarded as important in a significantnumber of countries are included. The ability ofpolicy makers to make sound judgments aboutrelative strengths and weaknesses of mathemat-ics and science education in their systemsdepends on achievement measures being based,as closely as possible, on what students in theirsystems have actually been taught. This is also aprerequisite for valid use of the measures inmany potential secondary analyses.

The following factors were considered infinalizing the content domains and the topicsand objectives of the assessment frameworks:

• Inclusion of the content in the curricula of a significant number of participating countries

• Alignment of the content domains withthe reporting categories of TIMSS 1995and TIMSS 1999

• The likely importance of the content tofuture developments in mathematics andscience education

• Appropriateness for the populations ofstudents being assessed

• Suitability for being assessed in a large-scale international study

• Contribution to overall test balance and coverage of content and cognitive domains.

The TIMSS Tests

The overriding principle in constructing tests forthe upcoming cycles of the study is to produceassessment instruments that will generateachievement data that are valid for the purposesthey are to be used for, and are reliable. Basedon the frameworks, the TIMSS tests are devel-oped through an international consensus-build-ing process involving input from experts ineducation, mathematics, science, and measure-ment. The tests contain questions requiring stu-dents to select appropriate responses or to solveproblems and answer questions in an open-ended format. With each cycle, TIMSS releasestest questions to the public and then replacesthese with newly developed questions. As inearlier phases of TIMSS, most test items, whilefocusing on a particular content element, willalso assume knowledge or skills from one ormore other content areas. Additionally, sometopics have been stated more broadly, and it isexpected that a number of the newly developeditems will require students to synthesize knowl-edge and skills from more than one topic. From2003 on, TIMSS will gradually place moreemphasis on questions and tasks that offer bet-ter insight into students’ analytical, problem-solving, and inquiry skills and capabilities. Tofacilitate innovations in assessment instrumenta-tion, the plan calls for incorporating investigative-or production-based tasks into the tests to theextent possible.

TIMSS test results can be used for a varietyof purposes. Policy makers and researchers canlook forward to achievement data in mathemat-ics and science overall and in major contentareas that:

Introduction 5

• Extend and strengthen measurement oftrends in mathematics and sciencebegun in TIMSS 1995 and continued inTIMSS 1999

• Allow informed between-countrycomparisons of achievement and, inconjunction with other TIMSS data,suggest reasons for differences

• Enhance evaluation of the efficacy ofmathematics and science teaching andlearning within each country

• Highlight aspects of growth inmathematical and scientific knowledgeand skills from grade 4 to grade 8

• Provide data for secondary analysesconcerned with raising achievementlevels through better-informed policymaking in education systems andschools, and improved teaching practice.

Student Populations Assessed

TIMSS 2003 will assess the mathematics and sci-ence achievement of children in two target pop-ulations. One target population, sometimesreferred to as Population 1, includes childrenages 9 and 10. It is defined as “the upper of thetwo adjacent grades with the most 9-year-olds.”In most countries, this is the fourth grade. Theother target population, sometimes referred to asPopulation 2, includes children ages 13 and 14,and is defined as “the upper of the two adjacentgrades with the most 13-year-olds.” In mostcountries, this is the eighth grade. Thus, throughthe remainder of this document, the gradesassessed will be described as the fourth andeighth grades.

By assessing these grades using the sametarget populations as in 1995 and 1999, TIMSS2003 can provide trend data at three points overan eight-year period. In addition, TIMSS datawill complement IEA’s Progress in InternationalReading Literacy Study (PIRLS) being conductedin 2001 at the fourth grade. By participating inPIRLS and TIMSS, countries will have informa-tion at regular intervals about how well theirstudents read and what they know and can doin mathematics and science. TIMSS also comple-ments another international study of studentachievement, the OECD’s Programme forInternational Student Achievement (PISA),which assesses the mathematics and science lit-eracy of 15-year-olds.

Introduction6

Mathematics Framework

1 Similarly, the curriculum frameworks for TIMSS 1995 and 1999assessments included content areas and performance expecta-tions (Robitaille, D.F., et al, (1993), TIMSS Monograph No.1:Curriculum Frameworks for Mathematics and Science,Vancouver, BC: Pacific Educational Press).

2 More information about the factors considered in finalizing thetopics and assessment objectives is provided in the Introduction.

Overview

The mathematics assessment framework forTIMSS 2003 is framed by two organizing dimen-sions, a content dimension and a cognitivedimension, analogous to those used in the earli-er TIMSS assessments.1 As outlined below, eachdimension has several domains:

Mathematics Content Domains

a Number

b Algebra

c Measurement

e Geometry

d Data

Mathematics Cognitive Domains

f Knowing Facts and Procedures

g Using Concepts

h Solving Routine Problems

i Reasoning

The two dimensions and their domains arethe foundation of the mathematics assessment.The content domains define the specific mathe-matics subject matter covered by the assessment,and the cognitive domains define the sets ofbehaviors expected of students as they engagewith the mathematics content. Each contentdomain has several topic areas (i.e., number isfurther categorized by whole numbers, fractionsand decimals, integers, and ratio, proportion,and percent). Each topic area is presented as alist of objectives covered in a majority of partici-pating countries, at either grade 4 or grade 8.2

Exhibit 2 shows the target percentages oftesting time devoted to each content and cogni-tive domain for both the fourth and eighthgrade assessments. The content and cognitivedomains for the mathematics assessment arediscussed in detail in the following sections.Example mathematics items and tasks are pre-sented in Appendix B.

Mathematics Framework 9

FourthGrade

EighthGrade


Number 40% 30%

Algebra* 15% 25%

Measurement 20% 15%

Geometry 15% 15%

Data 10% 15%


Knowing Facts and Procedures 20% 15%

Using Concepts 20% 20%

Solving Routine Problems 40% 40%

Reasoning 20% 25%

*At fourth grade, the Algebra content domain is calledPatterns, Equations, and Relationships.

Exhibit 2: Target Percentages of TIMSS 2003 MathematicsAssessment Devoted to Content and Cognitive Domains byGrade Level

Mathematics Framework10



As mentioned earlier, the five content domainsdescribed in the mathematics framework, withassessment objectives defined that are appropri-ate for either the fourth or eighth grade, are:

• Number• Algebra• Measurement• Geometry• Data

The structure of the content dimension ofthe TIMSS framework reflects the importance ofbeing able to continue comparisons of achieve-ment with previous assessments in these contentdomains. The organization of topics across thecontent domains reflects some minor revision inthe definition of the reporting categories used inthe 1995 and 1999 assessments, particularly forthe fourth grade.3 The current structure, howev-er, permits the direct mapping of trend itemsfrom 1995 and 1999 into the content domainsdefined for 2003. Thus, each mathematics con-tent domain is considered as an analysis andreporting category.

The grade-specific assessment objectivesindicated by topic areas within content domainsdefine the assessment areas appropriate for eachmathematics reporting category. These grade-specific objectives are written in terms of studentunderstandings or abilities that items alignedwith these objectives are designed to elicit. Therange of behaviors assessed to measure studentunderstandings and abilities is discussed in thesection of the mathematics framework describingthe cognitive domains. While the assessment of

abilities such as solving non-routine problemsand reasoning with mathematics will be of spe-cial interest, the factual, procedural, and concep-tual knowledge that form the initial base for thedevelopment and implementation of these skillswill also be assessed.

Problem solving and communication arekey outcomes of mathematics education thatare associated with many of the topics in thecontent domains. They are regarded as validbehaviors to be elicited by test items in mosttopic areas.

The categorization by mathematics topic areawithin content domains at the fourth grade paral-lels that used at the eighth grade. Not all of thetopic areas, however, are appropriate for thefourth grade. Also, the mathematical and cogni-tive levels of items developed according to theassessment objectives in the frameworks will beappropriate for the grade/age group. For example,at the fourth grade, there is a greater emphasis onnumber relative to the other major domains.

The following sections describe each of themathematics content domains. They give anoverview of the topic areas to be covered in theTIMSS assessment, focusing on the difference instudent understandings expected at the fourthand eighth grades. Following the generaldescription of each content domain is a tableindicating a set of assessment outcomes for eachmain assessment topic area. These assessmentoutcomes are written in terms of behaviors to beelicited by items that exemplify the understand-ings and abilities expected of students at eachgrade level.

3 The five reporting categories used in the TIMSS 1999 interna-tional report for eighth grade were Fractions and NumberSense; Measurement; Data Representation, Analysis, andProbability; Geometry; and Algebra. The six reporting categoriesused in the TIMSS 1995 international report for fourth gradewere Whole Numbers; Fractions and Proportionality;Measurement, Estimation, and Number Sense; DataRepresentation, Analysis, and Probability; Geometry;and Patterns, Relations, and Functions.

aMathematics Framework12

a Number

Grade 4

• Represent whole numbers using words, diagrams,or symbols, including recognizing and writingnumbers in expanded form.

• Demonstrate knowledge of place value.

• Compare and order whole numbers.

• Identify sets of numbers according to commonproperties such as odd and even, multiples,or factors.

• Compute with whole numbers.

• Estimate computations by approximating thenumbers involved.

• Solve routine and non-routine problems, includingreal-life problems.

Grade 8

• Demonstrate knowledge of place value and of thefour operations.

• Find and use factors or multiples of numbers, andidentify prime numbers.

• Express in general terms and use the principles ofcommutativity, associativity, and distributivity.

• Evaluate powers of numbers, and square roots ofperfect squares to 144.

• Solve problems by computing, estimating, orapproximating.

Number: Whole Numbers

The number content domain includes under-standing of counting and numbers, ways of rep-resenting numbers, relationships amongnumbers, and number systems. At the fourthand eighth grades, students should have devel-oped number sense and computational fluency,understand the meanings of operations and howthey relate to one another, and be able to usenumbers and operations to solve problems.

The number content domain consists ofunderstandings and skills related to:

• Whole numbers• Fractions and decimals• Integers• Ratio, proportion, and percent

In this domain, there is more emphasis oncomputing with whole numbers at the fourthgrade than at the eighth grade. Since wholenumbers provide the easiest introduction tooperations with numbers that are basic to thedevelopment of mathematics, working withwhole numbers is the foundation of mathemat-ics in the primary school. Most children learn tocount at a young age and can solve simple addi-tion, subtraction, multiplication, and division

problems during the first few years of school.Grade 4 students should be able to computewith whole numbers of reasonable size, estimatethe sums, differences, products, and quotients,and use computation to solve problems.

In the area of common fractions and deci-mal fractions, the emphasis is on representationand translation between forms, understandingwhat quantities the symbols represent, and com-putation and problem solving. At the fourthgrade, students should be able to compare famil-iar fractions and decimals. By the eighth grade,they should be able to move flexibly amongequivalent fractions, decimals, and percentsusing a range of strategies.

Although the integer topic area is notappropriate for grade 4, students in the middlegrades of schooling should extend their mathe-matical understanding from whole numbers tointegers, including order and magnitude as wellas operations with integers.

Assessing students’ ability to work withproportions is an important component. Aspectsof proportional reasoning can include numericaland qualitative comparison problems as well asthe more traditional missing value problems(i.e., presenting three values and asking studentsto find the fourth or missing value).

aMathematics Framework 13

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Grade 4

• Recognize fractions as parts of unit wholes, partsof a collection, locations on number lines, divisionsof whole numbers.

• Identify equivalent fractions.

• Compare and order fractions.

• Show understanding of decimals.

• Represent fractions or decimals using words,numbers, or models.

• Add and subtract fractions with the samedenominator.

• Add and subtract with decimals.Notes: Grade 4 fractions items will involve denominators of 2, 3, 4, 5, 6, 8,

10, or 12.

Grade 4 decimals items will involve decimals to tenths and/or hundredths.

Grade 8

• Compare and order fractions.

• Compare and order decimals.

• Demonstrate knowledge of place valuefor decimals.

• Represent decimals and fractions using words,numbers, or models (including number lines).

• Recognize and write equivalent fractions.

• Convert fractions to decimals and vice versa.

• Relate operations with fractions or decimals tosituations and models.

• Compute with fractions and decimals, including useof commutativity, associativity, and distributivity.

• Approximate decimals to estimate computations.

• Solve problems involving fractions.

• Solve problems involving decimals.

Number: Fractions and Decimals

Grade 4

• Not assessed.

Grade 8

• Represent integers using words, numbers,or models (including number lines).

• Compare and order integers.

• Show understanding of addition, subtraction,multiplication, and division with integers.

• Compute with integers.

• Solve problems using integers.

Number: Integers

Grade 4

• Solve problems involving simple proportionalreasoning.

Grade 8

• Identify and find equivalent ratios.

• Divide a quantity in a given ratio.

• Convert percents to fractions or decimals, andvice versa.

• Solve problems involving percents.

• Solve problems involving proportions.

Number: Ratio, Proportion, and Percent

bMathematics Framework14

b AlgebraWhile functional relationships and their usesfor modeling and problem solving are of primeinterest, it is also important to assess how wellthe supporting knowledge and skills have beenlearned. The algebra content domain includespatterns and relationships among quantities,using algebraic symbols to represent mathemat-ical situations, and developing fluency in pro-ducing equivalent expressions and solvinglinear equations.

Because algebra is generally not taught as aformal subject in primary school, this contentdomain will be identified as Patterns, Equations,and Relationships at the fourth grade. In contrast,at the eighth grade the algebra reporting catego-ry will reflect understandings across all of thetopic areas below.

The major topic areas in algebra are:

• Patterns• Algebraic expressions• Equations and formulas• Relationships

Students will be asked to recognize andextend patterns and relationships. They will alsobe asked to recognize and use symbols to repre-sent situations algebraically. At the fourth grade,understandings related to patterns, simple equa-tions, and the idea of functions as they apply topairs of numbers are included. Algebraic con-cepts are more formalized at the eighth grade,and students should focus on understanding lin-ear relationships and the concept of variable.Students at this level are expected to use andsimplify algebraic formulas, solve linear equa-tions and inequalities and pairs of simultaneousequations involving two variables, and use arange of linear and nonlinear functions. Theyshould be able to solve real-world problemsusing algebraic models and to explain relation-ships involving algebraic concepts.

Grade 4

• Extend and find missing terms of numeric andgeometric patterns.

• Match numeric and geometric patterns withdescriptions.

• Describe relationships between adjacent terms in asequence or between the number of the term andthe term.

Grade 8

• Extend numeric, algebraic, and geometric patternsor sequences using words, symbols, or diagrams;find missing terms.

• Generalize pattern relationships in a sequence, orbetween adjacent terms, or between the numberof the term and the term, using words or symbols.

Algebra: Patterns

bMathematics Framework 15

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Grade 4

• Not assessed.

Grade 8

• Find sums, products, and powers of expressionscontaining variables.

• Evaluate expressions for given numeric values ofthe variable(s).

• Simplify or compare algebraic expressions todetermine equivalence.

• Model situations using expressions.

Algebra: Algebraic Expressions

Grade 4

• Show understanding of equality using equations,areas, volumes, masses/weights.

• Find the missing number in an equation (e.g., if 17 + __ = 29, what number would go in the blankto make the equation true?).

• Model simple situations involving unknowns withan equation.

• Solve problems involving unknowns.

Grade 8

• Evaluate formulas given values of the variables.

• Use formulas to answer questions about givensituations.

• Indicate whether a value, or values, satisfies agiven equation.

• Solve simple linear equations and inequalities, andsimultaneous (two variables) equations.

• Write linear equations, inequalities, orsimultaneous equations that model givensituations.

• Solve problems using equations or formulas.

Algebra: Equations and Formulas

Grade 4

• Generate pairs of numbers following a given rule(e.g., multiply the first number by 3 and add 2 toget the second number).

• Write, or select, a rule for a relationship givensome pairs of numbers satisfying the relationship.

• Graph pairs of numbers following a given rule.

• Show why a pair of numbers follows a given rule.(E.g., a rule for a relation between two numbers is“multiply the first number by 5 and subtract 4 toget the second number.” Show that when the firstnumber is 2 and the second number is 6 the ruleis followed.)

Grade 8

• Recognize equivalent representations of functionsas ordered pairs, tables, graphs, words, orequations.

• Given a function in one representation, generate adifferent but equivalent representation.

• Recognize and interpret proportional, linear, andnonlinear relationships (travel graphs and simplepiecewise functions included).

• Write or select a function to model a givensituation.

• Given a graph of a function, identify attributessuch as intercepts on axes, and intervals where thefunction increases, decreases, or is constant.

Algebra: Relationships

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c MeasurementMeasurement involves assigning a numericalvalue to an attribute of an object. The focus ofthis content domain is on understanding meas-urable attributes and demonstrating familiaritywith the units and processes used in measuringvarious attributes. Measurement is important tomany aspects of everyday life.

The measurement content domain is com-prised of the following two main topic areas:

• Attributes and units• Tools, techniques, and formulas

A measurable attribute is a characteristicof an object that can be quantified. For exam-ple, line segments have length, plane regionshave area, and physical objects have mass.Learning about measurement begins with arealization of the need for comparison and thefact that different units are needed to measure

different attributes. The types of units that stu-dents use for measuring and the ways they usethem should expand and shift as students movethrough the curriculum.

At both the fourth and eighth grades, age-appropriate performances expected of studentsinclude the use of instruments and tools tomeasure physical attributes, including length,area, volume, weight/mass, angle, temperature,and time, in standard or non-standard unitsand converting between systems of units.Students at the fourth grade are expected touse approximation and estimation, and simpleformulas, to calculate areas and perimeters ofsquares and rectangles. At the eighth grade, themeasurement domain is expanded to includethe measurement of rate (such as speed or den-sity) as well as the application of more complexformulas to measure compound areas and thesurface areas of solids.

Grade 4

• Use given non-standard units to measure length,area, volume, and time (e.g., paper clips forlength, tiles for area, sugar cubes for volume).

• Select appropriate standard units to measurelength, area, mass/weight,* angle, and time (e.g., kilometers for car trips, centimeters forhuman height).

• Use conversion factors between standard units(e.g., hours to minutes, grams to kilograms).

• Recognize that total measures of length, area,volume, angle, and time do not change withposition, decomposition into parts, or division.

* More properly mass, but weight expressed in grams or kilograms is thecommon usage at these levels. Countries in which mass is the commonusage for grades 4 and/or 8 will frame items accordingly.

Grade 8

• Select and use appropriate standard units to findmeasures of length, area, volume, perimeter,circumference, time, speed, density, angle,mass/weight.*

• Use relationships among units for conversionswithin systems of units, and for rates.

Measurement: Attributes and Units

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Grade 4

• Use instruments with linear or circular scales tomeasure length, weight, time, and temperature inproblem situations (e.g., dimensions of a window,weight of a parcel).

• Estimate length, area, volume, weight, and time inproblem situations (e.g., height of a building,volume of a block of material).

• Calculate areas and perimeters of squares andrectangles of given dimensions.

• Compute measurements in simple problemsituations (e.g., elapsed time, change intemperature, difference in height or weight).

Grade 8

• Use standard tools to measure length, weight,time, speed, angle, and temperature in problemsituations and to draw line segments, angles, andcircles of given size.

• Estimate length, circumference, area, volume,weight, time, angle, and speed in problemsituations (e.g., circumference of a wheel, speedof a runner).

• Compute with measurements in problemsituations (e.g., add measures, find average speedon a trip, find population density).

• Select and use appropriate measurement formulasfor perimeter of a rectangle, circumference of acircle, areas of plane figures (including circles),surface area and volume of rectangular solids,and rates.

• Find measures of irregular or compound areas bycovering with grids or dissecting and rearrangingpieces.

• Give and interpret information about precision ofmeasurements (e.g., upper and lower bounds of alength reported as 8 centimeters to the nearestcentimeter).

Measurement: Tools, Techniques, and Formulas

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e GeometryEven at the fourth grade, the geometry contentdomain extends well beyond identification ofgeometric shapes. At both the fourth and eighthgrades, students should be able to analyze theproperties and characteristics of a variety of geo-metric figures, including lines, angles, and two-and three-dimensional shapes, and to provideexplanations based on geometric relationships.The focus should be on geometric properties andtheir relationships. The geometry content areaincludes understanding coordinate representa-tions and using spatial visualization skills tomove between two- and three-dimensionalshapes and their representations. Studentsshould be able to use symmetry and apply trans-formation to analyze mathematical situations.

The major topic areas in geometry are:

• Lines and angles• Two- and three-dimensional shapes• Congruence and similarity• Locations and spatial relationships• Symmetry and transformations

Spatial sense is an integral component ofthe study and assessment of geometry. The cog-nitive range extends from making drawings andconstructions to mathematical reasoning about

combinations of shapes and transformations. Atboth the fourth and eighth grades, students willbe asked to describe, visualize, draw, and con-struct a variety of geometric figures, includingangles, lines, triangles, quadrilaterals, and otherpolygons. Students should be able to combine,decompose, and analyze compound shapes. Bythe middle grades, they should be able to inter-pret or create top or side views of objects anduse their understanding of similarity and con-gruence to solve problems. They should be ableto make use of grids, find distances betweenpoints in the plane, and apply the Pythagoreantheorem to solve real-world problems.

At both the fourth and eighth grades, stu-dents should be able to recognize line symmetryand draw symmetrical figures. They should beable to determine the effects of transformation.In the middle grades, students should under-stand and be able to describe rotations, transla-tions, and reflections in mathematical terms(e.g., center, direction, and angle). As studentsprogress through school, using proportionalthinking in geometric contexts is important, as ismaking some initial links between geometry andalgebra. Students should be able to solve prob-lems using geometric models and explain rela-tionships involving geometric concepts.

Grade 4

• Classify angles as greater than, equal to, or lessthan a right angle (or 90°).

• Identify and describe parallel and perpendicularlines.

• Compare given angles and place them in orderof size.

Grade 8

• Classify angles as acute, right, straight, obtuse,reflex, complementary, and supplementary.

• Recall the relationships for angles at a point,angles on a line, vertically opposite angles, anglesassociated with a transversal cutting parallel lines,and perpendicularity.

• Know and use the properties of angle bisectorsand perpendicular bisectors of lines.

Geometry: Lines and Angles

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Grade 4

• Know and use vocabulary associated with familiartwo- and three-dimensional shapes.

• Identify common geometric shapes in theenvironment.

• Classify two- and three-dimensional shapesaccording to their properties.

• Know properties of geometric figures and usethem to solve routine problems.

• Decompose shapes and rearrange the parts toform simpler shapes.

Grade 8

• Recall properties of geometric shapes: triangles(scalene, isosceles, equilateral, right-angled) andquadrilaterals (scalene, trapezoid, parallelogram,rectangle, rhombus, square).

• Use properties of familiar geometric shapes in acompound figure to make conjectures aboutproperties of the compound figure.

• Recall properties of other polygons (regularpentagon, hexagon, octagon, decagon).

• Construct or draw triangles and rectangles ofgiven dimensions.

• Apply geometric properties to solve routine andnon-routine problems.

• Use Pythagorean theorem (not proof) to solveproblems (e.g., find the length of a side of a right-angled triangle given the lengths of the othertwo sides; or, given the lengths of three sides of atriangle, determine whether the triangle isright-angled).

Geometry: Two- and Three-dimensional Shapes

Grade 4

• Identify triangles that have the same size andshape (congruent).

• Identify triangles that have the same shape butdifferent sizes (similar).

Grade 8

• Identify congruent triangles and theircorresponding measures.

• Identify congruent quadrilaterals and theircorresponding measures.

• Consider the conditions of congruence todetermine whether triangles with givencorresponding measures (at least three) arecongruent.

• Identify similar triangles and recall their properties.

• Use properties of congruence in mathematical andpractical problem situations.

• Use properties of similarity in mathematical andpractical problem situations.

Geometry: Congruence and Similarity

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Grade 4

• Use informal coordinate systems to locate pointsin a plane.

• Relate a net to the shape it will make.

• Recognize relationships between two-dimensionaland three-dimensional shapes when shown netsand different two-dimensional views of three-dimensional objects.

Grade 8

• Locate points using number lines, coordinategrids, maps.

• Use ordered pairs, equations, intercepts,intersections, and gradient to locate points andlines in the Cartesian plane.

• Recognize relationships between two-dimensionaland three-dimensional shapes when shown netsand different two-dimensional views of three-dimensional objects.

Geometry: Locations and Spatial Relationships

Grade 4

• Recognize line symmetry.

• Draw two-dimensional symmetrical figures.

• Recognize translation, reflection, and rotation.

Grade 8

• Recognize line and rotational symmetry for two-dimensional shapes.

• Draw two-dimensional symmetrical figures.

• Recognize, or demonstrate by sketching,translation, reflection, rotation, and enlargement.

• Use transformations to explain or establishgeometric properties.

Geometry: Symmetry and Transformations

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dd DataThe data content domain includes understandinghow to collect data, organize data that havebeen collected by oneself or others, and displaydata in graphs and charts that will be useful inanswering questions that prompted the data col-lection. This content domain includes under-standing issues related to misinterpretation ofdata (e.g., about recycling, conservation, ormanufacturers’ claims).

The data content domain consists of the fol-lowing four major topic areas:

• Data collection and organization• Data representation• Data interpretation• Uncertainty and probability

At the fourth and eighth grades, studentscan engage in simple data-gathering plans orwork with data that have been gathered by oth-ers or generated by simulations. They shouldunderstand what various numbers, symbols, andpoints mean in data displays. For example, theyshould recognize that some numbers representthe values of the data and others represent the

frequency with which those values occur.Students should develop skill in representingtheir data, often using bar graphs, tables, or linegraphs. They should be able to compare the rela-tive merits of various types of displays.

Students at grades 4 and 8 should be ableto describe and compare characteristics of data(shape, spread, and central tendency). Theyshould be able to draw conclusions based ondata displays. In the eighth grade, studentsshould be able to identify trends in data, makepredictions based on data, and evaluate the rea-sonableness of interpretations.

Probability will not be assessed at thefourth grade, and at the eighth grade the proba-bility items will focus on assessing studentunderstandings of the concept.4 By the eighthgrade students’ appreciation of probabilityshould have increased beyond being able to des-ignate the occurrence of familiar events as cer-tain; as having greater, equal, or less likelihood;or as impossible, and they should be able tocompute probabilities for simple events, or esti-mate probabilities from experimental data.

4 The original data representation, analysis, and probability category defined in the 1995 and 1999 assessments included asmall number of items related to uncertainty and probability,but these depended heavily on knowledge of whole numbers,fractions, and proportionality.

Grade 4

• Match a set of data with appropriatecharacteristics of situations or contexts (e.g., outcomes from rolling a die).

• Organize a set of data by one characteristic (e.g., height, color, age, shape).

Grade 8

• Match a set of data, or a data display, withappropriate characteristics of situations or contexts(e.g., monthly sales of a product for a year).

• Organize a set of data by one or morecharacteristics using a tally chart, table, or graph.

• Recognize and describe possible sources of error incollecting and organizing data (e.g., bias,inappropriate grouping).

• Select the most appropriate data collectionmethod (e.g., survey, experiment, questionnaire) toanswer a given question, and justify the choice.

Data: Data Collection and Organization

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Grade 4

• Compare characteristics of related data sets (e.g., given data or representations of data onstudent heights in two classes, identify the classwith the shortest/tallest person).

• Draw conclusions from data displays.

Grade 8

• Compare characteristics of data sets, using mean,median, range, and shape of distribution (ingeneral terms).

• Interpret data sets (e.g., draw conclusions, makepredictions, and estimate values between andbeyond given data points).

• Evaluate interpretations of data with respect tocorrectness and completeness of interpretation.

• Use and interpret data sets to answer questions.

Data: Data Interpretation

Grade 4

• Not assessed.

Grade 8

• Judge the likelihood of an event as certain, morelikely, equally likely, less likely, or impossible.

• Use data from experiments to estimateprobabilities for favorable outcomes.

• Use problem conditions to calculate theoreticalprobabilities for possible outcomes.

Data: Uncertainty and Probability

Grade 4

• Read data directly from tables, pictographs, bargraphs, and pie charts.

• Display data using tables, pictographs, andbar graphs.

• Compare and match different representationsof the same data.

Grade 8

• Read data from charts, tables, pictographs, bargraphs, pie charts, and line graphs.

• Display data using charts, tables, pictographs, bargraphs, pie charts, and line graphs.

• Compare and match different representations ofthe same data.

Data: Data Representation



To respond correctly to TIMSS test items, stu-dents will need to be familiar with the mathe-matics content of the items. Just as important,items will be designed to elicit the use of particu-lar cognitive skills. Many of these skills and abili-ties are included with topics in the lists ofassessable topics that comprise the contentdomains. However, as an aid in developing bal-anced tests in which appropriate weight is givento each cognitive domain across all topics, a fullset of the learning outcomes mathematics educa-tors would wish to see demonstrated is indispen-sable. Thus, descriptions of skills and abilitiesthat make up the cognitive domains and will beassessed in conjunction with content are pre-sented in the framework in some detail. Theseskills and abilities should play a central role indeveloping items and achieving a balance acrossthe item sets at grades 4 and 8.

The student behaviors used to define themathematics frameworks have been classifiedinto the following four cognitive domains thatare described in this section:

• Knowing Facts and Procedures• Using Concepts• Solving Routine Problems• Reasoning

The specific student behaviors included ineach cognitive domain comprise the outcomessought by educational planners and practitionersaround the world. Different groups within asociety, and even among mathematics educators,have different views about the relative values ofthe cognitive skills, or at least about the relativeemphases that should be accorded them inschools. For TIMSS they are all regarded asimportant, and a variety of test items will beused to measure each of them.

The skills and abilities included in each cog-nitive domain exemplify those that studentscould be expected to demonstrate in the TIMSSachievement tests. They are intended to apply toboth grades 4 and 8, even though the accepteddegree of sophistication in demonstrating behav-iors will vary considerably between the two. Thedistribution of items over knowing facts and proce-dures, using concepts, solving routine problems, andreasoning also differs slightly between the twopopulations in accord with the mathematicalexperience of the target age/grade groups (seeExhibit 2).

As students’ mathematical proficiencydevelops with the interaction of experience,instruction, and maturity, curricular emphasismoves from relatively straightforward problemsituations to more complex tasks. In general, thecognitive complexity of tasks increases from onebroad cognitive domain to the next. The intent isto allow for a progression from knowing a fact,procedure, or concept to using that knowledgeto solve a problem, and from use of that knowl-edge in uncomplicated or familiar situations tothe ability to engage in systematic reasoning.

Nevertheless, cognitive complexity shouldnot be confused with item difficulty. For nearlyall of the cognitive skills listed, it is possible tocreate relatively easy items as well as very chal-lenging items. In developing items aligned withthe skills, it is expected that a range of item diffi-culties will be obtained for each one, and thatitem difficulty should not affect the designationof the cognitive skill.

The following sections further describe thestudent behaviors, skills, and abilities used todefine each cognitive domain with respect to thegeneral capabilities expected of students. A tableindicating specific behaviors to be elicited byitems that are aligned with each skill in adomain follows the general descriptions, withexamples of test items provided in some casesfor illustration.

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resff Knowing Facts and Procedures

Facility in using mathematics, or reasoningabout mathematical situations, depends primari-ly on mathematical knowledge. The more rele-vant knowledge a student is able to recall, thegreater the potential for engaging a wide rangeof problem-solving situations. Without access toa knowledge base that enables easy recall of thelanguage and basic facts and conventions ofnumber, symbolic representation, and spatialrelations, students would find purposeful mathe-matical thinking impossible. Facts encompass thefactual knowledge that provides the basic lan-guage of mathematics, and the essential mathe-matical facts and properties that form thefoundation for mathematical thought.

Procedures form a bridge between morebasic knowledge and the use of mathematics forsolving routine problems, especially thoseencountered by many people in their daily lives.In essence a fluent use of procedures entailsrecall of sets of actions and how to carry themout. Students need to be efficient and accuratein using a variety of computational proceduresand tools. They need to see that particular pro-cedures can be used to solve entire classes ofproblems, not just individual problems.

Recall Recall definitions; vocabulary; units; number facts; numberproperties; properties of plane figures; mathematical conventions(e.g., algebraic notation such as a × b = ab, a + a + a = 3a, a × a × a = a3, a/b = a ÷ b).

Recognize/Identify Recognize/identify mathematical entities that are mathematicallyequivalent, i.e., areas of parts of figures to represent fractions,equivalent familiar fractions, decimals, and percents; simplifiedalgebraic expressions; differently oriented simple geometric figures.

Compute Know algorithmic procedures for +, –, ×, ÷, or a combination ofthese; know procedures for approximating numbers, estimatingmeasures, solving equations, evaluating expressions and formulas,dividing a quantity in a given ratio, increasing or decreasing aquantity by a given percent. Simplify, factor, expand algebraic andnumerical expressions; collect like terms.

Use Tools Use mathematics and measuring instruments; read scales; drawlines, angles, or shapes to given specifications. Use straightedgeand compass to construct the perpendicular bisector of a line, anglebisector, triangles, and quadrilaterals, given necessary measures.

Knowing Facts and Procedures

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g Using Concepts

Familiarity with mathematical concepts is essen-tial for the effective use of mathematics for prob-lem solving, for reasoning, and thus fordeveloping mathematical understanding.

Knowledge of concepts enables students tomake connections between elements of knowl-edge that, at best, would otherwise be retainedas isolated facts. It allows them to make exten-

sions beyond their existing knowledge, judge thevalidity of mathematical statements and meth-ods, and create mathematical representations.Representation of ideas forms the core of mathe-matical thinking and communication, and theability to create equivalent representations isfundamental to success in the subject.

Know Know that length, area, and volume are conserved under certainconditions; have an appreciation of concepts such as inclusion andexclusion, generality, equal likelihood, representation, proof,cardinality and ordinality, mathematical relationships, place value.

Grade 4 example: Decide whether area of paper is greater, the same, or less after asheet of paper has been cut into strips (diagram shows completesheet and separated strips).

Grade 8 example: Know that if five successive tosses of a fair coin come up “heads,”the outcome of the next toss is as likely to be “tails” as “heads.”

Classify Classify/group objects, shapes, numbers, expressions, and ideasaccording to common properties; make correct decisions aboutclass membership; order numbers and objects by attributes.

Grade 4 example: Select the triangles from a set of geometric figures having variousshapes and numbers of sides.

Grade 8 example: Group pairs of quantities (lengths, weights, costs, etc.) in which thefirst quantity is greater than the second quantity.

Represent Represent numbers using models; display mathematical informationor data in diagrams, tables, charts, graphs; generate equivalentrepresentations for a given mathematical entity or relationship.

Grade 4 example: Shade areas of figures to represent given fractions.

Grade 8 example: Given a function rule, generate ordered pairs that describe the function.

Using Concepts

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Formulate Formulate problems or situations that could be modeled by givenequations or expressions.

Grade 4 example: Jane has read 29 pages of her book. If the book has 87 pages, in theequation 87 – _ = 29 the blank would contain the number of pagesJane still has to read. Make up another situation that this equationcould be used for.

Grade 8 example: The equation 4x + 3 = 51 could be used to solve the followingproblem: Four boxes are filled with golf balls, and 3 golf balls are leftover. If there are 51 balls altogether, how many does each box hold?Make up a problem that the equation 25 – 3x = 1 could be used tosolve. (Do not solve the equation.)

Distinguish Distinguish questions that can be addressed by given information,such as a data set, from those that cannot.

Grade 4 example: Given a bar graph, select from a set of questions those for whichanswers can be obtained from the graph.

Grade 8 example: The weights of boys in a class are <weights given>. Answers towhich of the following questions can be found? What is the averageweight of boys in the class? On average, do boys in the class weighmore than girls in the class? How many boys weigh more than 70kg? What is the grade level of the class?

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h Solving Routine ProblemsStudents should be educated to recognize math-ematics as an immense achievement of humani-ty, and to appreciate its nature. Nevertheless,mathematical knowledge for its own sake isprobably not the most compelling reason foruniversal inclusion of mathematics in schoolcurricula. Prime reasons for inclusion of mathe-matics are the increasing awareness that effec-tiveness as a citizen and success in the workplaceare greatly enhanced by knowing and, moreimportant, being able to use mathematics. Thenumber of vocations that demand a high level ofproficiency in the use of mathematics, or mathe-matical modes of thinking, has burgeoned withthe advance of technology, and with modernmanagement methods.

Problem solving is a central aim, and oftenmeans, of teaching school mathematics, andhence this and supporting skills (e.g., manipulateexpressions, select, model, verify/check) featureprominently in the solving routine problemsdomain. In items aligned with this domain, theproblem settings are more routine than thosealigned with the reasoning domain. The routineproblems will have been standard in classroomexercises designed to provide practice in particularmethods or techniques. Some of these problems

will have been in words that set the problem situ-ation in a quasi-real context. Solution of othersuch “textbook” type problems will involveextended knowledge of mathematical properties(e.g., solving equations). Though they range indifficulty, each of these types of “textbook” prob-lems is expected to be sufficiently familiar to stu-dents that they will essentially involve selectingand applying learned procedures.

Problem solving is a desired outcome ofmathematics instruction linked with manymathematics topics in the TIMSS framework.Problems may be set in real-life situations, ormay be concerned with purely mathematicalquestions involving, for example, numeric oralgebraic expressions, functions, equations, geo-metric figures, or statistical data sets. Therefore,problem solving has been included not only insolving routine problems but also in reasoning,depending on whether students are asked tosolve routine problems or more non-routineproblems (see following).

Select Select/use an efficient method or strategy for solving problemswhere there is a known algorithm or method of solution, i.e., analgorithm or method students at the target level could be expectedto be familiar with. Select appropriate algorithms, formulas, or units.

Grade 4 example: A class is presenting a class concert and the 28 members of the classeach have 7 tickets to sell. To find the total number of tickets youshould: divide 28 by 7; multiply 28 by 7; add 7 to 28; etc.

Grade 8 example: Given a problem that can be modeled by a simple equation, selectthe appropriate equation.

Solving Routine Problems

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Model Generate an appropriate model, such as an equation or diagram,for solving a routine problem.

Interpret Interpret given mathematical models (equations, diagrams, etc.);follow and execute a set of mathematical instructions.

Grade 4 example: Given an unfamiliar (but not complex) figure or procedure, write theverbal instructions you would give to another student to havehim/her reproduce the figure.

Grade 8 example: Given a set of expressions including 4(3 + 2) = 4 × 3 + 4 × 2, whichone can the diagram be used to show?

Apply Apply knowledge of facts, procedures, and concepts to solve routinemathematical (including real-life) problems, i.e., problems similar tothose target students are likely to have encountered in class.

Verify/Check Verify/check the correctness of the solution to a problem; evaluatethe reasonableness of the solution to a problem.

Grade 4 example: Mario estimates the area of a room in his house in square meters.His estimate is 1300 square meters. Is this likely to be a goodestimate? Explain.

Grade 8 example: Jack wants to find how far an airplane will travel in 3.5 hours at itstop speed of 965 kph. He uses his calculator to multiply 3.5 by 965and tells his friend Jenny that the answer is 33,775 km. Jenny says“that can’t be right.” How does she know?

iMathematics Framework32

i ReasoningReasoning mathematically involves the capacityfor logical, systematic thinking. It includes intu-itive and inductive reasoning based on patternsand regularities that can be used to arrive atsolutions to non-routine problems. Non-routineproblems are problems that are very likely to beunfamiliar to students. They make cognitivedemands over and above those needed for solu-tion of routine problems, even when theknowledge and skills required for their solutionhave been learned. Non-routine problems maybe purely mathematical or may have real-lifesettings. Both types of items involve transfer ofknowledge and skills to new situations, andinteractions among reasoning skills are usuallya feature.

Most of the other behaviors listed within thereasoning domain are those that may be drawnon in thinking about and solving such problems,but each by itself represents a valuable outcomeof mathematics education, with the potential toinfluence learners’ thinking more generally. Forexample, reasoning involves the ability to observeand make conjectures. It also involves makinglogical deductions based on specific assumptionsand rules, and justifying results.

Hypothesize/Conjecture/ Make suitable conjectures while investigating patterns, discussing Predict ideas, proposing models, examining data sets; specify an outcome

(number, pattern, amount, transformation, etc.) that will result fromsome operation or experiment before it is performed.

Grade 8 example: Twin primes are prime numbers with one other number betweenthem. Thus, 5 and 7, 11 and 13, and 17 and 19 are pairs of twinprimes. Make a conjecture about the numbers between twin primes.

Analyze Determine and describe or use relationships between variables orobjects in mathematical situations; analyze univariate statisticaldata; decompose geometric figures to simplify solving a problem;draw the net of a given unfamiliar solid; make valid inferences fromgiven information.

Evaluate Discuss and critically evaluate a mathematical idea, conjecture,problem solving strategy, method, proof, etc.

Grade 4 example: Two painters use three tins of paint in painting a fence. They thenhave to use the same kind of paint to paint a similar fence that istwice as long and twice as high. One of the painters said that theywould need about twice as much paint to paint the wall. Indicatewhether the painter was right and support your answer with reasons.

Grade 8 example: Comment on a survey with obvious flaws (too small a sample,non-representative sample, etc.).

Reasoning

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Generalize Extend the domain to which the result of mathematical thinkingand problem solving is applicable by restating results in moregeneral and more widely applicable terms.

Grade 4 example: Given the pattern 1, 4, 7, 10, …, describe the relationship betweeneach term and the next, and give the next term after 61.

Grade 8 example: Given that the sum of the angles of a triangle is 2 right angles, andgiven diagrams of 4-, 5-, and 6-sided polygons divided into triangles,describe the relationship between the number of sides of anypolygon and the sum of its angles in right angles.

Connect Connect new knowledge to existing knowledge; make connectionsbetween different elements of knowledge and relatedrepresentations; make linkages between related mathematical ideasor objects.

Grade 8 example: A triangle ABC has sides AB = 3cm, BC = 4cm, and CA = 5 cm.Which of these is the area of the triangle: 6 cm2, 7.5 cm2, 10 cm2,or 12 cm2?

Synthesize/Integrate Combine (disparate) mathematical procedures to establish results;combine results to produce a further result.

Grade 4 example: Solve a problem for which one of the key pieces of information mustfirst be obtained from a table.

Grade 8 example: Combine results obtained from two distinct graphs to solve a problem.

Solve Non-routine Solve problems set in mathematical or real-life contexts whereProblems target students are very unlikely to have encountered closely similar

items; apply mathematical procedures in unfamiliar contexts.

Grade 4 example: In a certain country the people write numbers as follows: 11 iswritten as ∇∇Φ, 42 is ❑❑ΦΦ, and 26 is ❑∇Φ. How do people inthis country write 37?

Grade 8 example: Given data and conditions in advertisements for competing products,select relevant data and find ways to make value comparisons validin determining which product is most suitable in a particular context.

Justify/Prove Provide evidence for the validity of an action or the truth of astatement by reference to mathematical results or properties;develop mathematical arguments to prove or disprove statements,given relevant information.

Grade 4 example: 50 + 30 = 80. Use the number line below to show that thissentence is true. (Students to put in links or mark appropriately insome other way.)

Grade 8 example: Show that the sum of any two odd numbers is an even number.

Communicating Mathematically

Communicating mathematical ideas and process-es is another set of skills that is seen as impor-tant for many aspects of living and fundamentalto the teaching and learning of the subject.Representing, modeling, and interpreting, forexample, are aspects of communication. Whilecommunication is an important outcome ofmathematics education, it is not included as aseparate cognitive domain. Rather, it may bethought of as an overarching dimension acrossall mathematics content areas and processes.Communication is fundamental to each of theother categories of knowing facts and procedures,using concepts, solving routine problems, and reason-ing, and students’ communication in and aboutmathematics should be regarded as assessable ineach of these areas.

Students in TIMSS may demonstrate com-munication skills through description and expla-nation, such as describing or discussing amathematical object, concept, or model.Communication also occurs in using mathemati-cal terminology and notation; demonstrating theprocedure used in simplifying, evaluating, orsolving an equation; or using particular repre-sentational modes to present mathematical ideas.Communication is involved in explaining why aparticular procedure or model has been used,and the reason for an unexpected or anomalousresult. While describing and explaining are notexplicitly listed as behaviors in the frameworkdocument, items across a wide range of contentand processes will require these communicationskills. Students could be asked to describe orexplain why they chose a particular method,why they made a particular response, and so on.

Guidelines for Calculator Use

Although technology in the form of calculatorsand computers can help students learn mathe-matics, it should not be used to replace basicunderstanding and competencies. Like any teach-ing tool, calculators need to be used appropriately,and policies for their use differ across the TIMSScountries. Also, the availability of calculatorsvaries widely. It would not be equitable to requirecalculator use when students in some countriesmay never have used them. Similarly, however, itis not equitable to deprive students of the use of afamiliar tool. Thus, after considerable debate onthis issue, beginning with TIMSS 2003 calculatorsare permitted but not required for newly devel-oped grade 8 assessment materials.

The aim of the TIMSS guidelines for calcu-lator use is to give students the best opportunityto operate in settings that mirror their classroomexperience. Thus, if students are used to havingcalculators for their classroom activities, then thecountry should encourage students to use themduring the assessment. On the other hand, ifstudents are not used to having calculators orare not permitted to use them in their dailymathematics lessons, then the country need notpermit their use. In developing the new assess-ment materials, every effort will be made toensure that the test questions do not advantageor disadvantage students either way – with orwithout calculators.

Students at grade 4 will not be permitted touse calculators. Since calculators were not per-mitted at grade 8 in the 1995 and 1999 assess-ments, test administration procedures willensure that they are not available for items fromthose assessments used to measure trends.


Science Framework

1 These two dimensions are comparable to the content and per-formance expectations aspects defined in the TIMSS curriculumframeworks for the 1995 and 1999 assessments (Robitaille,D.F., et al (1993), TIMSS Monograph No.1: CurriculumFrameworks for Mathematics and Science, Vancouver, BC:Pacific Educational Press.)

2 More information about the factors considered in finalizing thetopics and assessment objectives is provided in the Introduction.

Overview

In parallel with mathematics, the science assess-ment framework for TIMSS 2003 is based on twomain organizing dimensions, a content dimensionand a cognitive dimension.1 Each of these twodimensions has several domains:

Science Content Domains

a Life Science

c Chemistry

b Physics

d Earth Science

e Environmental Science

Science Cognitive Domains

f Factual Knowledge

g Conceptual Understanding

h Reasoning and Analysis

The content domains define the specific sciencesubject matter covered by the assessment, andthe cognitive domains define the sets of behav-iors expected of students as they engage withthe science content. Each content domain hasseveral main topic areas (e.g., the earth sciencedomain is comprised of the topic areas of theearth’s structure and physical features; theearth’s processes, cycles and history; and theearth in the solar system and the universe). Eachtopic area is presented as a list of specific assess-

ment objectives that are appropriate for eitherthe fourth or eighth grade and reflect what iscovered in the science curriculum in a majorityof participating countries by those grade levels.2

Exhibit 3 shows the target percentages oftesting time devoted to each science content andcognitive domain for both the fourth and eighthgrade assessments, and indicates the contentreporting categories for each grade level. At theeighth grade, the reporting categories correspondto the five content domains of Life Science,Chemistry, Physics, Earth Science, andEnvironmental Science. At the fourth grade,only three reporting categories are planned dueto the combined reporting of chemistry andphysics topics as Physical Science and a reducedemphasis on topics in Environmental Science.

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FourthGrade

EighthGrade


Life Science 45% 30%Physical Science 35% *

Chemistry * 15%

Physics * 25%

Earth Science 20% 15%

Environmental Science * 15%


Factual Knowledge 40% 30%

Conceptual Understanding 35% 35%

Reasoning and Analysis 25% 35%

*At fourth grade, Physical Science will be assessed as onecontent area including both physics and chemistry topics.Some understandings related to Environmental Science willbe assessed as part of the Life Science and Earth Sciencecontent domains at fourth grade.

Exhibit 3: Target Percentages of TIMSS 2003 ScienceAssessment Devoted to Content and Cognitive Domainsby Grade Level

In addition to the content and cognitivedomains, the TIMSS 2003 science frameworkalso includes Scientific Inquiry as a separateassessment strand. Scientific inquiry is treated asan overarching dimension that includes knowl-edge, skills, and abilities assessed by items ortasks set in different content-related contextsthat cover a range of cognitive demands. Theitems and tasks developed to assess understand-ings and abilities related to scientific inquiry will,therefore, be associated with both a content anda cognitive domain as well as with assessmentareas related specifically to scientific inquiry.From the entire set of items and tasks developedto draw on understandings and abilities acrossthe content and cognitive domains, a portionalso will engage students in the process of scien-tific inquiry and permit the assessment of theirperformance in this area. Many of the outcomesrelated to scientific inquiry will be assessed pri-marily in the problem solving and inquiry tasksand will represent up to 15 percent of the totalassessment time.3 The content domains, cognitivedomains, and scientific inquiry assessment strandfor the science assessment are discussed in detailin the following sections. Example science itemsand tasks are presented in Appendix C.


While TIMSS recognizes the importance of theteaching and learning of unified concepts andtopics that bridge the domains of science, thefollowing major content domains are used todefine the science content covered in the fourthand eighth grade assessments in TIMSS 2003:

• Life Science• Chemistry• Physics• Earth Science• Environmental Science

The organization of topics across these domainsis in general the same as that used to define thereporting categories in the 1995 and 1999 assess-ments, although there are some differences inthe definition of the areas of environmental sci-ence and scientific inquiry.4 Direct mapping ofthe trend items from 1995 and/or 1999 onto thescience content domains defined in this frame-works document will permit the analysis andreporting of content domains appropriate foreach grade level. It is important to note that inan international assessment such as TIMSS theorganization of science topics into these contentdomains may not correspond to the structure ofscience instruction in all countries. In fact, someof the topics included in the TIMSS 2003 scienceframework may be taught in some countries inother courses, such as health education, socialstudies, or geography.

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3 See the Assessment Design chapter for further discussion of theassessment design and the allocation of items/tasks and assessment time to blocks.

4 In TIMSS 1995, a combined reporting category of EnvironmentalIssues and the Nature of Science was included at both thefourth and eighth grades. In the 1999 eighth grade assessment,this combined category was replaced with two reporting categories: Environmental and Resource Issues, and ScientificInquiry and the Nature of Science. Trend items in these categories will be mapped to the appropriate content domain in the science framework for 2003.

The following sections describe each of thescience content domains. They give an overviewof the topics to be covered in the TIMSS assess-ment, focusing on the difference in studentunderstandings expected at the fourth andeighth grades. In defining the assessment out-comes expected at the two grade levels, TIMSSassumes a development of conceptual under-standing across the grades, progressing from theobservable at the fourth grade to somewhatmore abstract concepts by the eighth grade.Understandings specified at the eighth grade arefocused on describing what the students at thatlevel know and can do beyond what is expectedat the fourth grade.

Following the general description of eachcontent domain is a table indicating a set ofassessment outcomes for the fourth and eighthgrades. The assessment outcomes are organizedinto main topic areas and then into a set ofsubtopics defining specific understandings andabilities in conceptually related areas. Theseassessment outcomes are written in terms ofbehaviors to be elicited by items that exemplifythe understandings and abilities expected of stu-dents at each grade level. The main topic areasin each content domain are basically the same atthe fourth and eighth grades, but the specificassessment outcomes are appropriate for eachgrade level, and some of the more advanced top-ics are not assessed at the fourth grade. Furtherdiscussion of the range of behaviors assessed tomeasure student understandings and abilities isincluded in the section of the science frameworkdescribing the cognitive domains.


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a Life ScienceThe life sciences include understandings of thenature and function of living organisms, therelationships between them, and their interac-tion with the environment. At the fourth andeighth grades, it is expected that in some curric-ula, many of the essential biological conceptsmay be approached through a study of humanbiology. While TIMSS recognizes the importanceof human biology in the science curriculum offourth- and eighth-grade students, a separatehuman biology topic area is not specified in thescience framework. Rather, understandings relat-ed to human biology are included within the fol-lowing major life science topic areas that addressboth humans and other organisms and include aseparate topic area devoted to human health:

• Types, characteristics, and classification ofliving things

• Structure, function, and life processesin organisms

• Cells and their functions• Development and life cycles of organisms• Reproduction and heredity• Diversity, adaptation, and natural selection• Ecosystems• Human health

The classification of organisms by physical andbehavioral characteristics is fundamental to lifescience, and is expected of both fourth- andeighth-grade students. At the fourth grade, stu-dents may be assessed on their understanding ofgeneral characteristics that distinguish betweenliving and nonliving things, and their ability tocompare and contrast characteristics of majorgroups of common organisms, including

humans. At the eighth grade, students areexpected to know the defining characteristics ofmajor taxonomic groups and classify organismsaccording to these characteristics.

Understanding of structure and function inorganisms at the fourth grade begins with knowl-edge of the basic bodily functions and relatingmajor body structures in humans and otherorganisms to their functions. By the eighth grade,students should have developed an understandingof tissues, organs, and organ systems, and be ableto explain how certain biological processes arenecessary to sustain life. Basic understanding ofcells and their functions is expected at the eighthgrade but not the fourth grade.

Understandings in development, reproduc-tion, and heredity are expected to increase sub-stantially from the fourth to eighth grade. At thefourth grade, students are expected to know andcompare the life cycles of familiar organisms.Knowledge of reproduction and heredity at thisgrade level is restricted to a very basic under-standing that organisms of the same kind repro-duce and that offspring closely resemble theirparents. By the eighth grade, students shouldstart developing a more mechanistic understand-ing that includes the comparison of growth anddevelopment in different organisms. They alsoare expected to compare sexual and asexualreproduction in terms of biological processes atthe cellular level, including ideas about hereditythat involve the passing of genetic material fromparent(s) to offspring.

The development of some understandingsrelated to diversity, adaptation, and naturalselection among organisms is expected at boththe fourth and eighth grades. At the fourth

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grade, students are expected to provide exam-ples of physical and behavioral characteristicsthat make some plants and animals better suitedfor different environments. At the eighth grade,it is expected that students are beginning todevelop an understanding of populations and aworking definition of modern species in terms ofsimilarity of characteristics and reproductioncapabilities in a population of related organisms.They are making more connections, relating thediversity of characteristics to the survival orextinction of species in changing environments.It is not until the eighth grade that students areexpected to start considering evidence for thehistory and changes in the earth’s life forms overtime by the comparison of living species and fos-sil records.

The study of ecosystems is essential tounderstanding the interdependence of livingorganisms and their relationship to the physicalenvironment. Basic concepts related to ecosys-tems, including energy flow and the interaction ofbiotic and abiotic factors, are expected to be intro-duced in the primary school science curriculumand further developed throughout middle andsecondary school. At the fourth grade, students’understandings may be demonstrated throughdescriptions of specific relationships between

plants and animals in common ecosystems. At theeighth grade, students should show introductory-level understanding of the interdependencebetween populations of organisms that maintainsbalance in an ecosystem. They are expected torepresent the flow of energy in an ecosystem, rec-ognize the role of organisms in the cycling ofmaterials, and predict the effects of changes inecosystems. The effect of human activity onecosystems is an important aspect of understand-ing the interdependence of living organisms andthe environment. Students’ understandings relat-ed to the impact of humans are described in theEnvironmental Science section.

Both fourth- and eighth-grade students areexpected to demonstrate understandings relatedto human health, nutrition, and disease. At thefourth grade, students should demonstrate famil-iarity with common communicable diseases andrelate diet and personal habits to their effect onhealth. At the eighth grade, students are expect-ed to know some causes of disease, communi-cate more in-depth knowledge about themechanisms of infection and transmission, andknow the importance of the immune system.They should also be able to describe the role ofspecific nutrients in the normal functioning ofthe human body.

Grade 4

• Explain differences between living and nonlivingthings based on common features (movement,basic needs for air/food/water, reproduction,growth, response to stimuli).

• Compare and contrast physical and behavioralcharacteristics of humans and other major groupsof organisms (e.g., insects, birds, mammals,plants), and identify/provide examples of plantsand animals belonging to these groups.

Grade 8

• State the defining characteristics that are used todifferentiate among the major taxonomic groupsand organisms within these groups, and classifyorganisms on the basis of a variety of physicaland behavioral characteristics.

Life Science: Types, Characteristics, and Classification of Living Things


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Grade 4

• Relate major body structures in humans and otherorganisms (plants and animals) to their functions(e.g., digestion takes place in the stomach, plantroots absorb water, teeth break down food, bonessupport the body, lungs take in oxygen).

• Demonstrate knowledge of bodily actions inresponse to outside conditions (e.g., heat, cold,danger) and activities (e.g., exercise).

Grade 8

• Locate major organs in the human body; identifythe components of organ systems; andcompare/contrast organs and organ systems inhumans and other organisms.

• Relate the structure and function of organs andorgan systems to the basic biological processesrequired to sustain life (sensory, digestive,skeletal/muscular, circulatory, nervous, respiratory,reproductive).

• Explain how biological actions in response tospecific external/internal changes work to maintainstable bodily conditions (e.g., sweating in heat,shivering in cold, increased heart rate duringexercise).

Life Science: Structure, Function, and Life Processes in Organisms

Grade 4

• Not Assessed

Grade 8

• Describe the cellular make-up of all livingorganisms (both single-celled and multi-cellular),demonstrating knowledge that cells carry out lifefunctions and undergo cell division duringgrowth/repair in organisms, and that tissues,organs, and organ systems are formed fromgroups of cells with specialized structures andfunctions.

• Identify cell structures and some functions of cellorganelles (cell wall, cell membrane, nucleus,cytoplasm, chloroplast, mitochondria, vacuoles),including a comparison of plant and animal cells.

• Provide a general description of the process ofphotosynthesis that takes place in plant cells (the need for light, carbon dioxide, water, andchlorophyll, production of food, and release of oxygen).

• Describe the process of respiration that takes placein plant and animal cells (the need for oxygen,breaking down of food to produce energy, andrelease of carbon dioxide).

Life Science: Cells and Their Functions

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Grade 4

• Associate physical features and patterns ofbehavior of plants and animals with theenvironments in which they live; identify/provideexamples of certain physical or behavioralcharacteristics of plants/animals that makethem better suited for survival in differentenvironments and explain why (e.g., camouflage,color change, fur thickness).

Grade 8

• Relate the survival/extinction of different species tovariation in physical/behavioral characteristics in apopulation and reproductive success in changingenvironments.

• Demonstrate knowledge of the relative time majorgroups of organisms have existed on the earth(e.g., humans, reptiles, fish, plants); describe howsimilarities and differences among living speciesand fossils provide evidence of the changes thatoccur in living things over time.

Life Science: Diversity, Adaptation, and Natural Selection

Grade 4

• Recognize that plants and animals reproducewith their same kind to produce offspring withfeatures that closely resemble those of the parents.

Grade 8

• Explain that reproduction (asexual or sexual)occurs in all living organisms and is important forthe survival of species; compare/contrast biologicalprocesses in asexual and sexual reproduction ingeneral terms (e.g., cell division to produce anidentical offspring versus combination of egg andsperm from female/male parents to produceoffspring that are similar but not identical to eitherparent); state advantages and disadvantages ofeach type of reproduction.

• Relate the inheritance of traits to the passing onof genetic material contained in the cells of theparent(s) to their offspring; distinguish inheritedcharacteristics from physical/behavioral featuresthat are acquired/learned.

Life Science: Reproduction and Heredity

Grade 4

• Trace the general steps in the life cycle oforganisms (birth, growth and development,reproduction, and death); know and compare lifecycles of familiar organisms (e.g., humans,butterflies, frogs, plants, mosquitos).

Grade 8

• Compare and contrast how different organisms growand develop (e.g., humans, plants, birds, insects).

Life Science: Development and Life Cycles of Organisms


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Grade 4

• Explain that all plants and animals need food toprovide fuel for activity and material for growthand repair; understand that plants need the sun tomake their own food, while animals consumeplants and/or other animals as food.

• Explain relationships in a given community (e.g., forest, tidepool) based on simple foodchains, using common plants and animals andpredator/prey relationships.

Grade 8

• Demonstrate knowledge of the flow of energy inan ecosystem (the role of photosynthesis andrespiration and the storage of food/energyproducts in organisms); identify differentorganisms as producers, consumers, anddecomposers; draw/interpret food pyramidsor food web diagrams.

• Describe the role of organisms in the cycling ofmaterials through the earth’s surface (e.g., oxygen/carbon dioxide, water) and thedecomposition of organisms and recycling ofelements back into the environment.

• Discuss the interdependence of populations oforganisms in an ecosystem in terms of the effectsof competition and predation; identify factors thatcan limit population size (e.g., disease, predators,food resources, drought); predict effects ofchanges in an ecosystem (e.g., climate, watersupply, food supply, population changes,migration) on the available resources and thebalance among populations.

Life Science: Ecosystems5

Grade 4

• Recognize ways that common communicablediseases (e.g., colds, influenza) are transmitted;identify signs of health/illness and some methodsof preventing and treating illness.

• Describe ways of maintaining good health,including the need for a balanced/varied diet,identification of common food sources (e.g., fruitsand vegetables, grains), and the effect of personalhabits on health (e.g., using sunscreen, preventinginjury, personal hygiene, exercise, drug, alcohol,and tobacco use).

Grade 8

• Describe causes of common infectious diseases,methods of infection/transmission, prevention, andthe importance of the body’s natural resistance(immunity) and healing capabilities.

• Explain the importance of diet, hygiene, exercise,and lifestyle in maintaining health and preventingillness (e.g., heart disease, diabetes, skin cancer,lung cancer); identify the dietary sources and roleof nutrients in a healthy diet (vitamins, minerals,proteins, carbohydrates, fats).

Life Science: Human Health

5 Assessment objectives related to the effects of human behavioron environments are described in the Environmental Sciencesection. At grade 4 these objectives may be reported in LifeScience.

Science Framework46

Physical Sciences

The physical sciences include concepts related tomatter and energy and cover topics in the areasof both chemistry and physics. At the eighthgrade, these two main content areas will beassessed and reported separately, although thereis overlap of some of the understandings relatedto chemical and physical properties and changesin matter. While some of the physical sciencetopics are appropriate in either physics or chem-istry courses in different science curricula, theTIMSS 2003 science framework treats topicsrelated to the properties, composition, classifica-tion, and particulate structure of matter as partof the chemistry domain and topics related togeneral physical states of matter and their trans-formation as part of the physics domain. Theorganization of topics in the assessment frame-work for 2003 is consistent with the classifica-tion of items in the reporting categories for theearlier TIMSS assessments. At the fourth grade,where the understandings of both chemical andphysical concepts are considerably less devel-oped, physical science will be reported as a sin-gle content domain combining understandingsrelated to both chemical and physical concepts,with less emphasis on chemistry topics.Although the reporting of the physical scienceswill differ for the fourth and eighth grades, stu-dent understandings and abilities related to thetopics in each of the physical science contentareas are specified separately at both grade levels.

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In the area of chemistry, students will beassessed on their understanding of conceptsrelated to the following topic areas:

• Classification and composition of matter• Particulate structure of matter• Properties and uses of water• Acids and bases• Chemical change

At the fourth grade, understandings related tothe classification, composition, and properties ofmatter are focused on comparing or classifyingobjects and materials on the basis of observablephysical properties and relating these propertiesto their uses. Students at the fourth grade arealso expected to have a beginning practicalknowledge of the formation of mixtures andwater solutions. At the eighth grade, studentsshould be able to classify substances on the basisof characteristic properties and differentiatebetween elements, compounds, and mixtures interms of their composition. Their understandingof mixtures and solutions is expected to be moresophisticated, including ideas related to hetero-geneous and homogeneous mixtures and the

preparation, concentration, and components ofsolutions. They are also expected to have abeginning understanding of the particulate struc-ture of matter in terms of atoms and molecules;this area is not assessed at the fourth grade.While students at both grades may be assessedon their knowledge of some properties and usesof metals and water, by the eighth grade abeginning knowledge of acids and bases is alsoexpected.

At the fourth grade, students should identi-fy some familiar changes in materials that pro-duce other materials with different properties,but they are not expected to know how thesechanges are related to chemical transformations.At the eighth grade, students should have a clearunderstanding of the difference between physi-cal and chemical changes and demonstrate basicknowledge of conservation of matter duringthese changes. Eighth-grade students are alsoexpected to recognize the need for oxygen inrusting and burning and the relative tendency offamiliar substances to undergo these types ofreactions, and to identify common reactions thatabsorb or give off heat/energy.

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Grade 4

• Compare/classify/order different objects andmaterials on the basis of observable physicalproperties (e.g., weight/mass, shape, volume,color, hardness, texture, odor, taste, magneticattraction).

• Identify some properties of metals and relate themto their use (e.g., conduct heat and electricity, arehard, are shiny, can be molded).

• Identify/describe mixtures on the basis of physicalappearance; demonstrate understanding thatmixtures can be separated based on theobservable properties of their parts (e.g., particlesize, shape, color, magnetic attraction).

• Give examples of some materials that willdissolve in water and some that will not, andidentify common conditions that increase theamount of material that will dissolve or the speedat which materials dissolve (hot water, stirring,small particles).

Grade 8

• Classify/compare substances on the basis ofcharacteristic physical properties that can bedemonstrated or measured (e.g., density,thermal/electrical conductivity, solubility,melting/boiling point, magnetic properties).

• Recognize that substances may be groupedaccording to similar chemical and physicalproperties; describe properties of metals thatdistinguish them from other common substances(nonmetals).

• Differentiate between pure substances (elementsand compounds) and mixtures (homogeneous andheterogeneous) on the basis of their formationand composition, and provide/identify examples ofeach (solid, liquid, gas).

• Select/describe physical methods for separatingmixtures into their components (e.g., filtration,distillation, sedimentation, magnetic separation,flotation, dissolution).

• Define solutions in terms of substance(s) (solid,liquid, or gas solutes) dissolved in a solvent; applyknowledge of the relationship betweenconcentration/dilution and the amounts ofsolute/solvent and the effect of factors such astemperature, stirring, and particle size.

Chemistry: Classification and Composition of Matter

Grade 4

• Not Assessed

Grade 8

• Describe the structure of matter in terms ofparticles, including molecules as combinations ofatoms and atoms as being composed of subatomicparticles (electrons surrounding a nucleuscontaining protons and neutrons).

Chemistry: Particulate Structure of Matter

Grade 4

• Identify common uses of water in each of itsforms (e.g., solvent, coolant, heat source).

Grade 8

• Identify water as a compound with moleculescomposed of one oxygen atom and two hydrogenatoms; relate the behavior/uses of water to itsphysical properties (e.g., melting point and boilingpoint, ability to dissolve many substances, thermalproperties, expansion upon freezing).

Chemistry: Properties and Uses of Water

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Grade 4

• Not Assessed

Grade 8

• Compare the properties and uses of commonacids and bases (acids have a sour taste and reactwith metals; bases usually have a bitter taste andslippery feel; strong acids and bases are corrosive;both acids and bases dissolve in water and reactwith indicators to produce different color changes;acids and bases neutralize each other).

Chemistry: Acids and Bases

Grade 4

• Identify some familiar changes in materials thatproduce other materials with differentcharacteristics (e.g., decaying of animal/plantmatter, burning, rusting, cooking).

Grade 8

• Differentiate chemical from physical changes interms of the transformation (reaction) of one ormore substances (reactants) into differentsubstances (products); provide evidence that achemical change has taken place based oncommon examples (e.g., temperature change, gasproduction, color change, light emission).

• Recognize that although matter changes formduring chemical change, its total amount isconserved.

• Recognize the need for oxygen in commonoxidation reactions (combustion, rusting); comparethe relative tendency of familiar substances toundergo these reactions (e.g., combustion ofgasoline versus water, corrosion of steel versusaluminum).

• Demonstrate understanding that some chemicalreactions give off while others absorb heat/energy;classify familiar chemical transformations as eitherreleasing or absorbing heat/energy (e.g., burning,neutralization, cooking).

Chemistry: Chemical Change

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b PhysicsIn physics, students’ understandings of conceptsrelated to energy and physical processes will beassessed in the following topic areas:

• Physical states and changes in matter• Energy types, sources, and conversions• Heat and temperature• Light• Sound and vibration• Electricity and magnetism• Forces and motion

At the fourth grade, students have a limitedunderstanding of physical states and changesbased on observable differences between matterin its three forms – solid, liquid, and gas. Whilegeneral knowledge about changes of state is notexpected at the fourth grade, students at thislevel are expected to know that water can existin all three forms and can change from one formto another by being heated or cooled. In con-trast, by the eighth-grade students should beable to describe processes involved in changes ofstate and begin to relate the states of matter tothe distance and movement among particles.They also demonstrate understanding that mat-ter is conserved during physical changes.

Concepts related to energy, heat, and tem-perature are assessed at some level at both thefourth and eighth grade, but these concepts aremore formalized at the higher grade. While stu-dents at the fourth grade are able to identify com-mon energy sources, those at the eighth grade areexpected to compare different forms of energy,describe simple energy transformations, and applythe principle of conservation of total energy inpractical situations. Eighth-grade students are alsoexpected to recognize heat as the transfer of ener-gy, and to relate temperature to the movement orspeed of particles. At the fourth grade, assessmentof students’ understandings about heat is restrict-ed to observable physical processes.

Understandings of light and sound areexpected to develop substantially from fourth toeighth grade. Fourth-grade students’ knowledgeof light includes the identification of commonsources and recognition of some familiar physi-cal phenomena related to light. Students at theeighth grade are expected to know some basicproperties/behavior of light and its interactionwith matter; to use simple geometrical optics tosolve practical problems; and to relate theappearance and color of objects to light proper-ties. Students at the eighth grade also areexpected to demonstrate practical knowledge ofthe nature/source of sound as caused by vibra-tions, while fourth-grade students will not beassessed in this area.

In the area of electricity and magnetism,fourth-grade students are expected to have someexperience with the idea of a complete electricalcircuit and practical knowledge of magnets andtheir uses. At the eighth grade, assessment ofstudents’ understanding of electricity is expand-ed to include the idea of current flow in com-plete circuits, simple circuit diagrams, and therelationship between current and voltage in cir-cuits. They can also describe properties andforces of permanent magnets, as well as theessential features and uses of electromagnets.

Students at the fourth grade are expectedto have an intuitive grasp of the idea of forces asthey relate to movement, such as gravity actingon falling objects and push/pull forces.Knowledge about the measurement of theweight of objects may also be assessed at thefourth grade in the context of floating objects orobjects on a scale. At the eighth grade, morequantitative knowledge of mechanics is expect-ed. At this level, students are expected to repre-sent motion, compute speed, interpret/usedistance versus time graphs, and predict changesin the motion of an object based on the forcesacting upon it. They should also demonstratecommonsense understanding of density andpressure as they relate to familiar physical phe-nomena, although more formalized knowledgeis not expected.

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Grade 4

• Describe that all objects/materials are made up ofmatter that exists in three major states (solid,liquid, gas), and describe differences in theobservable physical properties of solids, liquids,and gases in terms of shape and volume.

• Demonstrate knowledge that water exists indifferent physical states and can be changed fromone state to another by heating or cooling, anddescribe these changes in familiar terms (melting,freezing, boiling).

Grade 8

• Use knowledge about the movement of anddistance between particles to explain differences inthe physical properties of solids, liquids, and gases(volume, shape, density, compressibility).

• Describe the processes of melting, freezing,evaporation, and condensation as changes of stateresulting from the supplying or removing ofheat/energy; relate the rate/extent of theseprocesses to common physical factors (surfacearea, dissolved substances, temperature,altitude/pressure).

• Demonstrate understanding of the melting/boilingpoint of substances; explain why temperatureremains constant during phase change (melting,boiling, freezing).

• Illustrate understanding that matter (mass) isconserved during familiar physical changes (e.g., change of state, dissolving solids, thermalexpansion).

Physics: Physical States and Changes in Matter

Grade 4

• Identify common energy sources and forms (e.g., wind, sun, electricity, burning fuel, waterwheel, food); know some practical uses of energy.

Grade 8

• Identify different forms of energy (e.g., mechanical,light, sound, electrical, thermal, chemical); describesimple energy transformations (e.g., combustion inan engine to move a car, electrical energy to powera lamp, hydroelectric power, changes betweenpotential and kinetic energy); and apply knowledgeof the concept of conservation of total energy.

Physics: Energy Types, Sources, and Conversions

Grade 4

• Demonstrate knowledge that heat flows from ahot object to a cold object and causes materials tochange temperature and volume; identify commonmaterials that conduct heat better than others;recognize the relationship between temperaturemeasurements and how hot/cold an object is.

Grade 8

• Relate heat to the transfer of energy from anobject at a high temperature to one at a lowertemperature; compare the relative thermalconductivity of different materials; andcompare/contrast methods of heat transfer(conduction, convection, and radiation).

• Explain thermal expansion in terms of changein volume and/or pressure (e.g., thermometers,balloons).

• Relate temperature and changes in volume and/orpressure to the movement/speedof particles.

Physics: Heat and Temperature

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Physics: Light

Grade 4

• Not assessed.

Grade 8

• Explain how sound with varying loudness(intensity) and pitch is produced by vibrations withdifferent properties (amplitude, frequency);*recognize that sound is transmitted away from asource through different materials and can bereflected by surfaces.

* Knowledge/use of the specific terms amplitude and frequency is notexpected at grade 8.

Physics: Sound and Vibration

Grade 4

• Know common uses of electricity; identify a completeelectrical circuit using batteries, bulbs, wires, andother common components that conduct electricity.

• Know that magnets have north and south poles,that like poles repel and opposite poles attract,and that magnets can be used to attract someother materials/objects.

Grade 8

• Describe the flow of current in an electrical circuit;draw/identify diagrams representing completecircuits (series and parallel); classify materials aselectrical conductors or insulators; and recognizethat there is a relationship between current andvoltage in a circuit.

• Demonstrate knowledge of the properties ofpermanent magnets and the effects of magneticforce; identify essential features and practical usesof electromagnets.

Physics: Electricity and Magnetism

Grade 4

• Identify common sources of light (e.g., bulb, flame,sun); and relate familiar physical phenomena to thepresence/absence and behavior of light (e.g., appearance of rainbows; colors producedfrom prisms, oil slicks, soap bubbles, etc.; formationof shadows; visibility of objects; mirrors).

Grade 8

• Describe/identify some basic properties/behaviorsof light (transmission from a source throughdifferent media; speed of light compared tosound; reflection, refraction (bending), absorption,and transmission by different materials; splitting ofwhite light into its component colors by prismsand other dispersive media).

• Relate the appearance/color of objects to theproperties of reflected/absorbed light.

• Solve practical problems involving the reflection oflight from plane mirrors and the formation ofshadows; use/interpret ray diagrams to identify thepath of light and locate reflected/projected images.

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Grade 4

• Identify familiar forces that cause objects tomove (e.g., gravity acting on falling objects,push/pull forces).

• Describe how the relative weight of objects can bedetermined using a balance; relate the weight* ofdifferent objects to their ability to float or sink.

* Although buoyancy is a function of density, knowledge of the term andconcept of density and the distinction between weight and mass is notexpected at grade 4. At this level, students may be assessed on theirknowledge of flotation using objects of comparable size but differentweight/mass.

Grade 8

• Represent the motion of an object in terms of itsposition, direction, and speed in a given referenceframe; compute speed from time and distanceusing standard units; and use/interpret informationin distance versus time graphs.

• Describe general types of forces (e.g., weight as aforce due to gravity, contact force, buoyant force,friction); predict changes in motion (if any) of anobject based on the forces acting on it;demonstrate basic knowledge of work and thefunction of simple machines (e.g., levers) usingcommon examples.

• Explain observable physical phenomena in terms ofdensity differences (e.g., floating/sinking objects,rising balloons, ice layers).

• Demonstrate knowledge of effects related topressure (e.g., atmospheric pressure as a functionof altitude, ocean pressure as a function of depth,evidence of gas pressure in balloons, spreadingforce over a large/small area, fluid levels).

Physics: Forces and Motion

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d Earth ScienceEarth science is concerned with the study of theearth and its place in the solar system and theuniverse. Topics covered in the teaching andlearning of earth science draw on the fields ofgeology, astronomy, meteorology, hydrology, andoceanography, and are related to concepts inbiology, physics, and chemistry. Although sepa-rate courses in earth science covering all of thesetopics are not taught in all countries, it is expect-ed that understandings related to earth sciencetopic areas will have been included in a sciencecurriculum covering the physical and life sci-ences or in separate courses such as geographyand geology. While there is no single picture ofwhat constitutes an earth science curriculum atdifferent grade levels that applies to all countries,the TIMSS framework identifies the followingtopic areas that are universally considered to beimportant for students at the fourth and eighthgrades to understand about the planet on whichthey live and its place in the universe:

• Earth’s structure and physical features(lithosphere, hydrosphere and atmosphere)

• Earth’s processes, cycles, and history• Earth in the solar system and the universe

Both fourth- and eighth-grade students areexpected to have some general knowledge aboutthe structure and composition of the earth. Atthe fourth grade, students should know thatsolid earth is composed of rocks, sand, and soil,and that most of the earth’s surface is covered bywater. At this level, assessment of students’understandings of the atmosphere is limited toevidence for the presence of water and theimportance of air for the survival of livingthings. Eighth-grade students’ understandings inthese areas are more directly connected tounderlying concepts in the life and physical sci-ences. Students are expected to compare physi-

cal characteristics of the earth’s crust, mantle,and core, and to describe the distribution ofwater on the earth, including comparisons withrespect to physical state, composition, and move-ment. Their understanding of the atmosphereincludes the relative abundance of the maincomponents of air, and changes in atmosphericconditions in relation to altitude. While studentsat the fourth grade are expected to know com-mon features of the earth’s landscape, those atthe eighth grade should be able to use/interprettopographic maps and diagrams representingthese structural features.

An understanding of the earth’s processes,cycles, and history is expected at substantiallydifferent levels for fourth- and eighth-grade stu-dents. At the fourth grade, students are expectedto be able to describe some of the earth’sprocesses in terms of observable changes, includ-ing the movement of water, cloud formation,and changes in daily or seasonal weather condi-tions. In comparison, eighth-grade students areexpected to provide more complete descriptionsbased on the concept of cycles and patterns.They use words and/or diagrams to describe therock and water cycle, and interpret/use data ormaps related to global and local factors affectingweather patterns. They can also differentiatebetween daily weather changes and general cli-mate in different regions of the world. Assessingthe understanding of the earth’s history is fairlylimited at the fourth grade. Students at that levelshould know that the earth is quite old and thatfossils of plants and animals that lived a longtime ago can be found in rocks. By the eighthgrade, students are expected to start to develop asense of the magnitude of time scales, and to beable to describe some physical processes andgeological events that have taken place on theearth over billions of years.

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By the fourth grade, students are expectedto demonstrate some understandings about theearth’s place in the solar system based on obser-vations of changes in the earth and sky. In par-ticular, they should be familiar with the motionsof the earth, and relate daily changes on theearth to its rotation on its axis and relationshipto the sun. By the eighth grade, students areexpected to have a more complete knowledge ofthe solar system in terms of the relative dis-tances, sizes, and motions of the sun, the plan-ets, and their moons, and of how phenomena onthe earth relate to the motion of bodies in the

solar system. Students at the eighth grade arealso expected to compare the physical features ofthe earth, the moon, and the other planets withrespect to their ability to support life.

Assessment of knowledge of the universeoutside the solar system is focused on a develop-ing understanding of stars by the eighth grade.Eighth-grade students are expected to identifythe sun as an “average” star and recognize thatbillions of other stars are observed in the nightsky that are outside and very distant from oursolar system. This area is not assessed at thefourth grade.

Grade 4

• Know that the surface of the earth is composedof rocks, minerals, sand, and soil; and comparephysical properties, locations, and uses of thesematerials.

• Recognize that most of the earth’s surface iscovered with water; describe the locations/types of water found on the earth (e.g., salt water inoceans, fresh water in lakes and rivers, clouds,snow, ice caps, icebergs).

• Provide evidence for the existence/nature of air,including the fact that air contains water (e.g., cloud formation, dew drops, evaporation ofponds), examples of the uses of air, and theimportance of air for supporting life.

• Identify/describe common features of the earth’slandscape (e.g., mountains, plains, rivers, deserts)and relate them to human use (e.g., farming,irrigation, land development).

Grade 8

• Demonstrate knowledge of the structure andphysical characteristics of the earth’s crust, mantle,and core; use/interpret topographic maps; describethe formation, characteristics, and/or uses of soil,minerals, and basic rock types.

• Compare the physical state, movement,composition and relative distribution of water onthe earth (e.g., oceans, rivers, ground water,glaciers, ice caps, clouds).

• Know that the earth’s atmosphere is a mixture ofgases, and identify the relative abundance of itsmain components; relate changes in atmosphericconditions (temperature, pressure, composition)to altitude.

Earth Science: Earth’s Structure and Physical Features6

6 Assessment objectives related to the use and conservation ofearth’s natural resources are described in the EnvironmentalScience section. At grade 4, these objectives may be reported inEarth Science.

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Grade 4

• Draw/describe the movement of water on theearth’s surface (e.g., flowing in rivers/streamsfrom mountains to oceans/lakes); relate theformation of clouds and rain/snow to a changeof state of water.

• Describe changes in weather conditions from dayto day or over the seasons in terms of observableproperties such as temperature, precipitation(rain/snow), clouds, and wind.

• Recognize that fossils of animals and plants thatlived on the earth a long time ago can be found inrocks and provide evidence that the earth is very old.

Grade 8

• Demonstrate knowledge of the general processesinvolved in the rock cycle (weathering/erosion,deposition, heat/pressure, melting/cooling, lavaflow) resulting in the continuous formation ofigneous, metamorphic, and sedimentary rock.

• Diagram/describe the steps in the earth’s watercycle (evaporation, condensation, andprecipitation), referencing the sun as the source ofenergy and the role of cloud movement and waterflow in the circulation and renewal of fresh wateron the earth’s surface.

• Interpret weather data/maps, and relate changingweather patterns to global and local factors interms of temperature, pressure, precipitation,wind speed/direction, cloud types/formation, andstorm fronts.

• Compare seasonal climates of major regions onthe earth, considering effects of latitude, altitudeand geography (e.g., mountains and oceans);identify/describe long- and short-term climaticchanges (e.g., ice ages, global warming trends,volcanic eruptions, changes in ocean currents).

• Identify/describe physical processes and majorgeological events that have occurred over billionsof years (e.g., weathering, erosion, deposition,volcanic activity, earthquakes, mountain building,plate movement, continental drift); explain theformation of fossils and fossil fuels.

Earth Science: Earth’s Processes, Cycles, and History

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Grade 4

• Describe the solar system as a group of planets(including earth) each revolving around the sun,and identify the sun as the source of heat andlight for the solar system.

• Relate daily patterns observed on the earth to theearth’s rotation on its axis and its relationship tothe sun (e.g., day/night, appearance of shadows).

• Draw/describe the phases of the moon.

Grade 8

• Explain phenomena on the earth (day/night, tides,year, phases of the moon, eclipses, seasons in thenorthern/southern hemisphere, appearance of sun,moon, planets, and constellations) in terms of therelative movements, distances, and sizes of theearth, moon, and other bodies in and outside thesolar system.

• Recognize the role of gravity in the solar system(e.g., tides, keeping the planets and moons inorbit, pulling us to the earth’s surface).

• Compare and contrast the physical features of theearth with the moon and other planets (e.g., atmosphere, temperature, water, distancefrom sun, period of revolution/rotation, ability tosupport life).

• Recognize the sun as an “average” star, and knowthat there are billions of other stars in the universeoutside and very distant from the earth’s solar system.

Earth Science: Earth in the Solar System and the Universe

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e Environmental ScienceEnvironmental science is a field of applied sci-ence concerned with environmental andresource issues. As such, it involves conceptsfrom the life, earth, and physical sciences, andconsiderable overlap with these content areas.While environmental science typically is notoffered as a separate science course until at leastthe upper secondary or post-secondary level, itsinclusion in the TIMSS framework as a separatecontent domain reflects the relative importanceplaced internationally on educating studentsabout factors affecting the environment andecosystems. Both fourth- and eighth-grade stu-dents are expected to have attained some under-standings related to environmental science.However, because these are more limited at thefourth grade, environmental science will bereported separately at the eighth grade but notthe fourth, where items measuring these under-standings will be included in the Earth Scienceor Life Science reporting categories as indicatedbelow. In addition, a number of assessmentobjectives appropriate to each grade level thatare related to a basic understanding of the func-tioning of and relationships in ecosystems, fun-damental to environmental science, aredescribed in the Life Science section.

The environmental science category inTIMSS is defined primarily by understandingsrelated to the interaction of humans withecosystems, changes in the environment frommanmade or natural events, and protection ofthe environment. An underlying themethroughout is the roles and responsibilities ofscience, technology, and society in maintainingthe environment and conserving resources. Themain topic areas in environmental science are:

• Changes in population• Use and conservation of natural resources• Changes in environments

Eighth-grade but not fourth-grade students areexpected to demonstrate some understanding ofthe consequences of rapid growth in the human

population. They should be able to analyzetrends in world population, and be able to dis-cuss some effects of increasing population on theenvironment, demonstrating a link to underly-ing science concepts related to biodiversity, sus-tainable populations, and carrying capacity ofenvironments.

Fourth-grade students are expected to havepractical knowledge of human use of the earth’snatural resources and may identify some physi-cal resources used in everyday life, their com-mon sources, and the need to conserve theseresources. At the eighth grade, students areexpected to demonstrate an increased under-standing of limiting resources in environmentsand the impact of science and technology on theuse and conservation of these resources.

As described in the Life Science section, stu-dents at the fourth and eighth grades are expect-ed to have some understanding of balance inecosystems in terms of interactions betweenorganisms and their relationship to the physicalenvironment. An important understanding inenvironmental science is how changes in environ-ments, whether resulting from natural processesor from human activity, can affect both living andnonliving components and shift this balance. Atboth grade levels, students are expected todemonstrate understanding that human activitycan affect the environment positively or negative-ly and to cite examples. At the eighth grade, it isexpected that students will be able to discuss bothshort- and long-term effects and the role of sci-ence and technology in environmental issues.Students at the fourth grade are expected toknow the effects of some common types of pollu-tion and how humans can prevent or reducethem. At the eighth grade, a broader knowledgeof pollution is expected, and students should beable to relate some global environmental concernsto their possible causes and/or effects. Theyshould be able to discuss the impact of environ-mental changes in terms of changes to habitat,resources, food webs, and life cycles.

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Grade 4

• Not Assessed.

Grade 8

• Analyze trends in human population, identifyingthat the world population is growing at anincreasing rate, and comparing the populationdistribution, growth rate, andconsumption/availability of resources in differentregions.

• Discuss effects of population growth on theenvironment (e.g., use of natural resources, foodsupply/demand, health, water supply/demand,growth of cities/suburbs, land use/development,hunting/fishing).

Environmental Science: Changes in Population

Grade 4

• Identify some of the earth’s physical resources thatare used in everyday life and their commonsources (e.g., water, soil, wood, minerals, fuel,food); explain the importance of using theseresources wisely.

Note: Environmental Science is not reported separately at Grade 4. Itemsmeasuring understandings related to the use and conservation of natural resources are reported in Life Science or Earth Science.

Grade 8

• Know common examples of renewable andnonrenewable resources; discuss advantages anddisadvantages of different types of energy sources(e.g., fossil fuels, wood, solar, wind, geothermal,nuclear, hydroelectric, chemical batteries); anddescribe methods of conservation and wastemanagement (e.g., recycling/reuse, use ofbiodegradable materials).

• Relate effects of human use of land/soil resources(e.g., farming, ranching, mining, tree harvesting)to methods used in agriculture and landmanagement (e.g., crop rotation,terracing/contour farming, fertilization, irrigation,pest control, grazing management,reclamation/recycling, reforesting).

• Discuss factors related to the supply/demand offresh water and use of water resources (e.g., renewable but limited supply of fresh water,purification, desalination, irrigation, watertreatment/reuse, conservation, use of dams,fishing practices).

Environmental Science: Use and Conservation of Natural Resources

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Grade 4

• Present ways in which human behavior can have apositive or a negative effect on environments;provide general descriptions and examples of theeffects of pollution on humans, plants, animals,and their environments, and ways of preventing orreducing pollution.

Note: Environmental Science is not reported separately at grade 4. Itemsmeasuring understandings related to changes in environments arereported in Life Science or Earth Science.

Grade 8

• Discuss ways in which human activity can bothcontribute to and help solve environmentalproblems, including both short- and long-termeffects on ecosystems; describe sources, effects,and ways of preventing/reducing air, water, andland pollution; and explain the role of science andtechnology in addressing environmental issues.

• Relate some global environmental concerns totheir possible causes and/or effects (e.g., globalwarming, acid rain, depletion of the ozone layer,deforestation, desertification); present ways inwhich science and technology can be used toaddress these concerns.

• Describe some natural hazards and their impact onhumans, wildlife, and the environment in terms ofchanges to habitat, resources, food webs, and lifecycles (e.g., earthquakes, landslides, wildfires,volcanic eruptions, floods, storms).

Environmental Science: Changes in Environments


The TIMSS science framework is based on theidea of science as a process used to learn aboutthe physical world that involves observation,description, investigation, and explanation ofnatural phenomena. As such, it includes bothdemonstration of content knowledge and theability to apply and communicate understandingof concepts in solving problems, developingexplanations, and conducting and reportingresults of investigations. In addition to definingthe specific science topics that will be assessed,the assessment outcomes for each science con-tent domain include descriptions of illustrativeskills and cognitive abilities that the items on theTIMSS test are designed to assess. In this section,the cognitive dimension is further described, andthe skills and abilities that illustrate studentunderstandings are classified into three broadcognitive domains that will be assessed acrossthe science content domains:

• Factual Knowledge• Conceptual Understanding• Reasoning and Analysis

The development of scientific understanding andreasoning builds on previous knowledge,expanding and revising the knowledge base as itprogresses. It requires the ability to determinehow facts and concepts are related to each other.In order to participate in the scientific endeavor,it is important to have a firm grasp of basic sci-ence concepts and be able to support them withfacts. Therefore, in TIMSS it is relevant toinclude a measure of the extent and accuracy ofstudents’ factual knowledge base as well as theirunderstanding, use, and application of scienceconcepts in problem situations. In a problem-solving situation, students may fail to solve theproblem either because they lack the factual or

procedural knowledge required or because theyare unable to analyze the problem to identify therelevant facts and concepts to apply and/or todevelop an effective strategy. Determining theimpact of each of these factors is important inidentifying areas where education and learningcan be improved.

Including the cognitive dimension in theframeworks will ensure that balanced tests areproduced that provide adequate coverage ofeach cognitive domain at each grade level. Thedistribution of items across factual knowledge, con-ceptual understanding, and reasoning and analysiswill vary between fourth and eighth grade inaccordance with the increased cognitive ability,maturity, instruction, experience, and breadthand depth of conceptual understanding of stu-dents at the higher grade level (see Exhibit 3).While some hierarchy is imposed in the divisionof behaviors into the three cognitive categories,there is still a range of complexity in the cogni-tive skills elicited by items aligned with each cat-egory. In addition, a range of difficulty levels isexpected for items developed in each of the cog-nitive domains. While an individual item mayelicit behaviors that correspond to more thanone cognitive domain, an item will be catego-rized into a cognitive domain on the basis of themost complex cognitive ability required and theprimary contribution of the item to the interpre-tation of results from the assessment. The fol-lowing sections further describe the studentskills and abilities defining the cognitivedomains. The general descriptions are followedby tables indicating specific behaviors to be elicit-ed by items that are aligned with each category.


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f Factual KnowledgeThe cognitive domain of factual knowledge refersto students’ knowledge base of relevant sciencefacts, information, tools, and procedures. In orderto solve problems and develop explanations inscience, students must possess a strong knowl-edge base. Accurate and broad-based factualknowledge enables students to engage successful-ly in the more complex cognitive activities essen-tial to the scientific enterprise. Demonstratingfactual knowledge involves more than just rotememorization and recall of isolated bits of infor-mation. For example, being able to make com-parisons, classify/order, and differentiate amongmaterials and organisms hinges on basic knowl-

edge of physical characteristics and the applica-tion of science concepts. In addition, students’knowledge and use of the definitions of scientificterms is linked to their understanding of underly-ing concepts and relationships. Knowledge ofvocabulary, facts, information, symbols, units,and procedures may be assessed through theirproper usage in a given context. The selection ofthe appropriate apparatus, equipment, measure-ment devices, and experimental operations to usein conducting investigations also depends on stu-dents’ basic knowledge of the tools and proce-dures of science.

Recall/Recognize Make or identify accurate statements about science facts,relationships, processes, and concepts; identify the characteristics orproperties of specific organisms, materials, and processes.

Define Provide or identify definitions of scientific terms; recognize and usescientific vocabulary, symbols, abbreviations, units, and scales inrelevant contexts.

Describe Recognize or describe organisms, physical materials, and scienceprocesses that demonstrate knowledge of properties, structure,function, and relationships.

Use Tools Demonstrate knowledge of the use of science apparatus, and Procedures equipment, tools, procedures, and measurement devices/scales.

Factual Knowledge

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g Conceptual UnderstandingConceptual understanding in science means havinga grasp of the relationships that explain thebehavior of the physical world and relating theobservable to more abstract or more general sci-entific concepts. It increases in sophistication asstudents progress through school and developcognitively, and the evidence of understandingwill vary across grades. Conceptual understand-ing, then, is not something that will be meas-ured directly. Rather, students must showevidence of it through its use and application inperforming specific tasks appropriate for eachgrade level. To measure conceptual understand-ing, TIMSS items will be included that requirestudents to extract and use scientific informationand use and apply their understanding of scienceconcepts and principles to find solutions anddevelop explanations. This cognitive domain also

includes the selection of illustrative examples insupport of statements of facts or concepts. Itemsaligned with this cognitive domain will involvethe direct application or demonstration of rela-tionships, equations, and formulas in contextslikely to be familiar in the teaching and learningof science concepts. Both quantitative problemsrequiring a numerical solution and qualitativeproblems requiring a written descriptiveresponse are included. In providing explana-tions, students should be able to use models toillustrate structures and relationships anddemonstrate knowledge of scientific concepts.The problems in this cognitive domain aredesigned to involve more straightforward appli-cations of concepts and require considerably lessanalysis and integration than the items alignedwith the reasoning and analysis domain.

Illustrate with Examples Support or clarify statements of facts/concepts with appropriateexamples; identify or provide specific examples to illustrateknowledge of general concepts.

Compare/Contrast/ Identify or describe similarities and differences between groups of Classify organisms, materials, or processes; distinguish, classify, or order

individual objects, materials, organisms, and processes based oncharacteristics and properties.

Represent/Model Use/draw diagrams and/or models to demonstrate understanding ofscience concepts, structures, relationships, processes, and biological/physical systems and cycles (e.g., food webs, electrical circuits, water cycle, solar system, atomic structure).

Relate Relate knowledge of underlying biological and physical concepts tothe observed or inferred properties/behaviors/uses of objects,organisms, and materials.

Extract/ Identify/extract/apply relevant textual, tabular, or graphicalApply Information information in light of science concepts/principles.

Conceptual Understanding

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Find Solutions Identify/use science relationships, equations, and formulas to findqualitative or quantitative solutions involving the direct application/demonstration of concepts.

Explain Provide or identify reasons/explanations for observations or naturalphenomena, demonstrating understanding of the underlyingscience concept, principle, law, or theory.

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h Reasoning and AnalysisReasoning and analysis is involved in all of themore complex tasks related to science. A majorpurpose of science education is to prepare stu-dents to engage in scientific reasoning to solveproblems, develop explanations, draw conclu-sions, make decisions, and extend their knowl-edge to new situations. In addition to the moredirect applications of science concepts exempli-fied in the conceptual understanding domain,some problem-solving situations involve unfa-miliar or more complicated contexts that requirestudents to reason from scientific principles toprovide an answer. Solutions may involve break-ing down the problem into component parts,each involving the application of a science con-cept or relationship. Students may be required toanalyze the problem to determine what underly-ing principles are involved; interpret/use dia-grams and graphs; devise and explain strategiesfor problem solving; select and apply the appro-priate equations, formulas, relationships, andanalytical techniques; and evaluate their solu-tions. Correct solutions to such problems maystem from a variety of approaches or strategies,and developing the ability to consider alternativestrategies is an important educational goal in theteaching and learning of science.

Students may be required to draw conclu-sions from scientific data and facts, providingevidence of both inductive and deductive rea-soning and an understanding of the investigationof cause and effect. They are expected to evalu-ate and make decisions based on conceptualunderstanding, including weighing advantages

and disadvantages of alternative materials andprocesses, considering the impact of different sci-entific endeavors, and evaluating solutions toproblems. By the eighth grade, in particular,they also start to consider and evaluate alterna-tive explanations, extend conclusions to new sit-uations, and justify explanations based onevidence and scientific understanding.Considerable scientific reasoning is also involvedin developing hypotheses and designing scientificinvestigations to test them, and in analyzing andinterpreting data. Abilities in this area are intro-duced at a very basic level in primary school andthen further developed throughout students’ sci-ence education in middle and secondary school.

Some items in this cognitive domain mayfocus on unified concepts and major conceptualthemes, requiring students to bring togetherknowledge and understanding from differentareas and apply it to new situations. As such,they may involve the integration of mathematicsand science and/or the integration and synthesisof concepts across the domains of science.Fourth-grade students may be expected todemonstrate some of the abilities needed for sci-entific reasoning, but at a less sophisticated levelthan eighth-grade students. Items included toassess these areas at the fourth grade will bemore structured and less open-ended than itemsfor eighth-grade students. Due to the moresophisticated cognitive abilities required, lessweight will be placed on this cognitive domainat the fourth grade.

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Analyze/Interpret/ Analyze problems to determine the relevant relationships, concepts, Solve Problems and problem-solving steps; develop/explain problem-solving

strategies; interpret/use diagrams and graphics to visualize and/or solve problems; give evidence of deductive and inductive reasoningprocesses used to solve problems.

Integrate/Synthesize Provide solutions to problems that require consideration of anumber of different factors or related concepts; makeassociations/connections between concepts in different areas ofscience; demonstrate understanding of unified concepts andthemes across the domains of science; integrate mathematicalconcepts/procedures in the solutions to science problems.

Hypothesize/Predict Combine knowledge of science concepts with information fromexperience or observation to formulate questions that can beanswered by investigation; formulate hypotheses as testableassumptions using knowledge from observation and/or analysis ofscientific information and conceptual understanding; makepredictions about the effects of changes in biological or physicalconditions in light of evidence and scientific understanding.

Design/Plan Design/plan investigations appropriate for answering scientificquestions or testing hypotheses; describe/recognize thecharacteristics of well-designed investigations in terms of variablesto be measured and controlled and cause-and-effect relationships;make decisions about measurements/procedures to use inconducting investigations.

Collect/Analyze/ Make and record systematic observations and measurements,Interpret Data demonstrating appropriate applications of apparatus, equipment,

tools, procedures, and measurement devices/scales; representscientific data in tables, charts, graphs, and diagrams using appropriate format, labeling, and scales; select/apply appropriatemathematical computations/techniques to data to obtain derivedvalues necessary to draw conclusions; detect patterns in data,describe/summarize data trends, and interpolate/extrapolate fromdata or given information.

Draw Conclusions Make valid inferences on the basis of evidence and/orunderstanding of science concepts; draw appropriate conclusionsthat address questions/hypotheses, and demonstrate understandingof cause and effect.

Reasoning and Analysis

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Generalize Make/evaluate general conclusions that go beyond theexperimental or given conditions, and apply conclusions tonew situations; determine general formulas for expressingphysical relationships.

Evaluate Weigh advantages and disadvantages to make decisions aboutalternative processes, materials, and sources; consider scientific andsocial factors to evaluate the impact/consequences of science andtechnology in biological and physical systems; evaluate alternativeexplanations and problem-solving strategies and solutions; evaluateresults of investigations with respect to sufficiency of data tosupport conclusions.

Justify Use evidence and scientific understanding to justify explanationsand problem solutions; construct arguments to support thereasonableness of solutions to problems, conclusions frominvestigations, or scientific explanations.

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Reasoning and Analysis

Scientific Inquiry

In the contemporary science curricula of manycountries, considerable emphasis is placed onengaging students in scientific inquiry. The goalof scientific inquiry is to provide explanations ofscientific phenomena that help us understandthe underlying principles governing the naturalworld. At the fourth- and eighth-grade level,students are not expected to be formulating andtesting fundamental theories, but they should beable to pose scientific questions or hypotheses oflimited scope that can be investigated. At thesegrade levels, scientific inquiry involves studentsin the process of questioning, planning, and con-ducting investigations to gather evidence, andformulating explanations based on observationsand in light of scientific understanding. Theunderstandings and abilities required to engagein this type of scientific investigation are impor-tant in developing citizens that are literate in themethods, processes, and products of science.They are also precursors of the more advancedtypes of inquiry directed at furthering scientificknowledge that are important in preparingfuture scientists. Given that the scientific inquiryprocess is an integral part of learning and doingscience, it is important to assess students’ under-standings and abilities required to engage in thisprocess successfully.

Scientific inquiry is treated as an overarch-ing assessment strand in the TIMSS frameworkthat overlaps all of the fields of science and hasboth content- and skills-based components.Assessment of scientific inquiry includes itemsand tasks requiring students to demonstrateknowledge of the tools, methods, and proce-dures necessary to do science, to apply thisknowledge to engage in scientific investigations,and to use scientific understanding to propose

explanations based on evidence. These processesof scientific inquiry promote a broader under-standing of science concepts as well as reasoningand problem-solving skills.

It is expected that students at both gradelevels will possess some general knowledge ofthe nature of science and scientific inquiry,including the fact that scientific knowledge issubject to change, the importance of using dif-ferent types of scientific investigations in verify-ing/testing scientific knowledge, the use of basic“scientific methods,” communication of results,and the interaction of science, mathematics, andtechnology. In addition to this general knowl-edge, students are expected to demonstrate theskills and abilities involved in the following fivemajor phases of the scientific inquiry process:7

• Formulating questions and hypotheses• Designing investigations• Collecting and representing data• Analyzing and interpreting data• Drawing conclusions and developing

explanations

These phases of scientific inquiry are appropriatefor both fourth- and eighth-grade students, butthe understandings and abilities to be demon-strated increase in complexity across grades,reflecting the cognitive development of students.The learning of science in the fourth grade isfocused on observing and describing, and stu-dents at this level are expected to be able to for-mulate questions that can be answered based onobservations or information obtained about thenatural world. To obtain evidence to answerthese questions, they should demonstrate agrasp of what constitutes a “fair test,” and beable to describe and conduct an investigationbased on making systematic observations or


7 The order of the phases of scientific inquiry is imposed primarilyfor organizational purposes, reflecting the logical sequence con-sistent with the convention used in reporting the results ofinvestigations. While real scientific inquiry may not proceed in astrict order, some aspect of each of these phases will be part ofany scientific investigation.

measurements using simple tools, equipment,and procedures. They are also expected to repre-sent their findings using simple charts and dia-grams, apply routine mathematical computationsof measured values, identify simple relation-ships, and briefly describe the results of theirinvestigations. Conclusions drawn from investi-gations at the fourth grade are expected to bewritten as an answer to a specific question.

By the eighth grade, students shoulddemonstrate a more quantitative and formalizedapproach to scientific investigation that involvesmore evaluation and decision-making. They areexpected to be able to formulate a hypothesis orprediction based on observation or scientificknowledge that can be tested by investigation.They are expected to demonstrate an under-standing of cause and effect and the importanceof specifying variables to be controlled and var-ied in well-designed investigations. They mayalso be required to make more decisions aboutthe measurements to be made and the equip-ment and procedures to use. In collecting andrepresenting data, students at this level areexpected to use appropriate terminology, units,precision, format, and scales. They should alsodemonstrate more advanced data analysis skillsin selecting and applying appropriate mathemat-ical techniques and describing patterns in data.Eighth-grade students may be expected to evalu-ate the results of their investigation with respectto the sufficiency of their data for supportingconclusions that address the question or hypoth-esis under investigation.

The assessment of both fourth- and eighth-grade students’ ability to provide explanationsbased on evidence from scientific investigationsprovides another measure of their understandingand application of related science concepts. Bythe eighth grade, it is expected that students willbe able to formulate explanations in terms ofcause-and-effect relationships between variables

and in light of scientific understanding. At thislevel, students may also begin to consider alter-native explanations and apply/extend their con-clusions to new situations.

Students’ understandings and abilities relat-ed to scientific inquiry will be assessed primarilythrough items or tasks that require students toapply knowledge and process skills in a practicalcontext. The tasks, while not intended to be fullscientific investigations, will be designed torequire a basic understanding of the processes ofscientific investigation and elicit some of theskills that are essential to the scientific inquiryprocess. As such, they will be used to assesswhether students have some of the key under-standings and abilities necessary to engage in sci-entific inquiry.

Science Framework70

Contextual Framework

Contextual Framework 73

Overview

For a fuller appreciation of what the TIMSSachievement results mean and how they may beused to improve student learning in mathematicsand science, it is important to understand thecontexts in which students learn. In addition totesting students’ achievement in mathematicsand science, TIMSS collects a range of informa-tion about the contexts for learning these sub-jects. The Contextual Frameworks encompassesfive broad areas:

• Curriculum• Schools• Teachers and Their Preparation• Classroom Activities and Characteristics• Students

In particular, TIMSS examines the curricu-lar goals of the education system and how thesystem is organized to attain those goals; theeducational resources and facilities provided; theteaching force and how it is educated, equipped,and supported; classroom activities and charac-teristics; home support and involvement; andthe knowledge, attitudes, and predisposition thatstudents and teachers themselves bring to theeducational enterprise. Just as the mathematicsand science frameworks describe what should beassessed in those areas, the contextual frame-work identifies the major characteristics of theeducational and social contexts that will be stud-ied with a view to improving student learning.

The Curriculum

Building on IEA experience, the TIMSS contex-tual framework addresses five broad aspects ofthe intended curriculum in mathematics and sci-ence, from its formulation to its implementation.

Curriculum development involves consider-ation of the society which the education systemserves, the needs and aspirations of the students,the nature and function of learning, and the for-mulation of statements on what learning isimportant. In understanding the intended cur-riculum, it is important to know who makes thecurricular decisions, what types of decisions aremade, and how decisions are communicated tothe education community.

Formulating the Curriculum. When formulatinga curriculum, developers take its situational con-text into account. Contextual considerationsinclude the resources – national, regional, andlocal – available for education; the value societyplaces on mathematics and science education;societal attitudes towards mathematics and sci-ence; and the degree to which educationalattainment, broadly or narrowly defined, islinked to societal well-being and the nation’seconomic health.

Scope and Content of the Curriculum. Curriculardocuments define and communicate expecta-tions for students in terms of the knowledge,skills, and attitudes to be acquired or developedthrough their formal education. The nature andextent of the mathematics and science goals tobe attained in school are important to policymakers and curriculum specialists in all coun-tries. Also important is how these goals are keptcurrent in the face of scientific and technologicaladvances, and how the demands and expecta-tions of society and the workplace change.

Although mastery of the subject is a majorfocus of mathematics and science curricula inmost countries, countries differ considerably inhow the curriculum specifies that masteryshould be achieved. For example, acquiring basicskills, applying mathematics to “real-life” situa-tions, communicating mathematically, and prob-lem solving in novel situations are approaches toteaching mathematics that have been advocatedin recent years and are used to varying degreesin different countries.1 In science, focus on theacquisition of basic scientific facts, the under-standing and application of scientific concepts,emphasis on designing and conducting investiga-tions, communicating scientific explanations,and the adoption of a thematic approach areteaching strategies that are recommended insome countries more so than in others.2

Organization of the Curriculum. The way theeducation system – national, regional, and local– is organized has a significant impact on stu-dents’ opportunities to learn mathematics andscience. At the school level, the relative empha-sis on and amount of time specified for mathe-matics, science, and other subjects up throughvarious grade levels can greatly affect suchopportunities. Practices such as tracking, stream-ing, or setting can expose students to differentcurricula. In science, teaching the major compo-nents of science as separate subjects can result indifferent experiences for students compared withthe science-as-single-subject approach.

Monitoring and Evaluating the ImplementedCurriculum. Many countries have systems inplace for monitoring and evaluating the imple-mentation of curriculum and for assessing thestatus of their education systems. Commonlyused methods include standardized tests, schoolinspection, and audits. Policy makers may useinfluences external to the school, for examplenational or regional standardized tests, to pre-scribe the implementation of the curriculum.Policy makers may also work collaborativelywith the school community (or selected sub-populations) to develop, implement, and evalu-ate the curriculum.

Curricular Materials and Support. Apart from theuse of standardized tests, inspections, and audits,countries can employ a range of other strategiesto facilitate the implementation of the intendedcurriculum. These include training teachers in thecontent and pedagogic approaches specified in thecurriculum. Such training may be an integral partof the teacher education curriculum, or it may beincluded in professional development programs.The implementation of the curriculum can be fur-ther supported through the development and useof teaching materials, including textbooks,instructional guides, and ministerial notes, thatare specifically tailored to the curriculum.

Contextual Framework74

1 Mullis, I.V.S., et al (2000), TIMSS 1999 InternationalMathematics Report: Findings from IEA’s Repeat of the ThirdInternational Mathematics and Science Study at the EighthGrade, Chestnut Hill, MA: Boston College.

2 Martin, M.O., et al (2000), TIMSS 1999 International ScienceReport: Findings from IEA’s Repeat of the Third InternationalMathematics and Science Study at the Eighth Grade, ChestnutHill, MA: Boston College.

The Schools

In the TIMSS contextual model, the school is theinstitution through which the goals of the cur-riculum are implemented. Accepting that a high-quality school is not simply a collection ofdiscrete attributes but rather a well-managedintegrated system where each action or policydirectly affects all other parts, TIMSS focuses ona set of indicators of school quality that researchhas shown to characterize such schools.

School Organization. Whether as part of a largernational, regional, or local education system orbecause of decisions made at the school level,science and mathematics instruction is carriedout within certain organizational constraints. Forexample, the time in terms of days per years andminutes per day allotted for schooling, and inparticular for mathematics and science instruc-tion, can influence achievement. It is also impor-tant to know about different types of schools,since some schools may specialize. For example,in countries with tracking, the school may bedesignated to emphasize either an academic or avocational curriculum.

School Goals. Research on effective schools sug-gests that successful schools identify and com-municate ambitious but reasonable goals andwork towards implementing them. Commonlyarticulated school goals include literacy, academ-ic excellence, personal growth, good workhabits, and self-discipline.

Roles of the School Principal. The school princi-pal typically fulfills multiple leadership roles.These include ensuring that the school, its oper-ation, and its resources are managed optimally.The principal may guide the school in settingdirections, seeking future opportunities, andbuilding and sustaining a learning environment.

He or she can facilitate the development, articu-lation, implementation, stewardship, and evalua-tion of a model of learning that is shared andsupported by the school community. The princi-pal may actively advocate, nurture, and sustain apositive school culture and an education pro-gram conducive to student learning and teach-ers’ professional growth. The primary roles thatthe principal fulfills provide a useful indicationof the administrative and educational structureof the school.

Resources to Support Mathematics and ScienceLearning. Curriculum implementation can befacilitated by allocating the facilities, materials,and equipment necessary to achieve the specifiedlearning goals. Results from TIMSS indicate thatstudents in schools that are well-resourced gener-ally have higher achievement than those inschools where shortages in resources affect capac-ity to implement the curriculum. Two types ofresources affect implementation of the curricu-lum. General resources include teaching materi-als, budget for supplies, school buildings andsupplies, heating/cooling and lighting systems,and classroom space. Subject-specific resourcesmay include computers, computer software, cal-culators, laboratory equipment and materials,library materials, and audio-visual resources.


Parental Involvement. Research has shown thateffective schools have a high degree of congru-ence between parental, student, and schoolexpectations. Parental involvement in schoolactivities can be an important source of support inworking to achieve student and school goals, andin forming positive student attitudes. Data fromTIMSS reveal that schools with a high degree ofparental involvement, particularly in the areas ofchecking homework, volunteering for field trips,and fund raising, generally have higher academicperformance than those that do not.

Disciplined School Environment. Although asafe and orderly school environment does notitself guarantee high levels of student achieve-ment, student learning can be more difficult inschools where student discipline is a problem,where students are regularly absent or late toclass, or where they fear injury or loss of per-sonal property.

Teachers and Their Preparation

Teachers are the primary agents of curriculumimplementation. Regardless of how closely pre-scribed the curriculum, or how explicit thetextbook, it is the actions of the teacher in theclassroom that most affect student learning.What teachers know and are able to do is ofcritical importance. A recent review suggeststhat to ensure excellence, teachers should havehigh academic skills, teach in the field in whichthey received their training, have more than afew years of experience, and participate inhigh-quality induction and professional devel-opment programs.3

Academic Preparation and Certification. Awareof the key role played by the teacher in imple-menting the curriculum, many countries arefocusing on improving education for aspiringteachers, particularly the mathematics and sci-ence prerequisites necessary for effective teach-ing in these subject areas.

The methods by which teachers are certi-fied to practice vary widely across countries.They include the completing of specified courses,passing exams, and serving a probation period.In some countries there may be alternativemethods of being certified, especially in subjectareas with a shortage of teachers.

The relative emphasis on content knowl-edge and pedagogic approach of trainee teachers,and how teacher education programs keepabreast of the changes brought about by rapidadvances in science and technology, are impor-tant features of teacher preparation programs.Methods used to enable teachers to becomebroadly educated, reflective, professional educa-tors with a lifelong positive attitude toward


3 Mayer, D.P., Mullens, J.E., and Moore, M.T. (2000), MonitoringSchool Quality: An Indicators Report, NCES 2001-030,Washington, DC: National Center for Education Statistics.

learning may also be an important facet ofteacher education. Collaboration between uni-versities and schools and the use of teacher com-petency standards may also contribute to goodacademic preparation to teach. Innovativeapproaches to teacher education that capitalizeon the opportunities provided by the Internetand modern information technology in generalmay also be important in preparing teachers.

Teacher Recruitment. The growth of technologyin recent years has meant that education sys-tems must compete with industry for the bestmathematics and science candidates. The rapidadvancement of mathematics and science neces-sitates that prospective teachers be capable ofkeeping pace with these fast-evolving fields. Thiscalls for the attraction of top-level applicantswho are capable of adjusting their teaching tothe evolving demands of modern education.Employment contracts, incentives such as freecollege education, and other benefits are somemethods used to recruit suitable candidates.

Teacher Assignment. TIMSS has shown thatthere is considerable variation across countries inthe percentage of students taught mathematicsor science by teachers with a major in the sub-ject. While there can be both problems and ben-efits associated with teachers teaching “out offield,” of interest is how such teachers acquirethe subject-specific knowledge they need inorder to teach effectively.

Teacher Induction. The transition from universityto a school teaching position can be difficult.Consequently, in many countries a large per-centage of new teachers leave the professionafter only a few years of teaching.4 The extent towhich schools take an active role in the accul-turation and transition of the new teacher may

be important. Mentoring, the modeling of goodteacher practice by peers, professional develop-ment activities, and induction programs designedby experienced teachers within the school maybe important to aid the beginning teacher.

Teacher Experience. Studies have suggested thatstudents learn more when taught by experi-enced teachers than they do when taught byteachers with just a few years’ experience.However, the relationship between experienceand achievement may be affected by many fac-tors. For example, assignment policies withinschools may result in the more highly skilledteachers getting specific classes, or older teachersgetting higher-tracked classes. The need for long-serving teachers to engage in professional devel-opment, and the extent to which they do so, canalso impact their effectiveness.

Teaching Styles. Researchers have identified anumber of teaching styles.5 Information on howteachers allot their time to such activities as lec-ture-style presentation, teacher-guided studentpractice, re-teaching and clarifying content andprocedures, small group work, and independentpractice, for example, provides useful evidenceabout the predominant pedagogic approaches inthe classroom. Student reports of how muchtime they spend being shown how to do mathe-matics and science, working from worksheets ortextbooks, working on projects, or discussinghomework are also important indicators ofteaching style.

TIMSS international reports have shownthat the use of the board was an extremely com-mon presentation mode in both mathematicsand science classes. Other presentation modes,including teacher use of an overhead projector,teacher use of a computer to demonstrate ideas,student use of the board, and student use of anoverhead projector are less frequent.


4 Moskowitz, J. and Stephens, M., eds. (1997), From Students ofTeaching to Teachers of Students: Teacher Induction Around thePacific Rim, Washington, DC: U.S. Department of Education.

5 Grasha, A. (1996), Teaching with Style, Pittsburgh, PA: AlliancePublishers.

Professional Development. Although investmentin pre-service education of prospective mathe-matics and science teachers will likely pay divi-dends in the long run, efforts to strengthen theknowledge and skills of existing teachers mustrely on professional development opportunities.Unless teachers participate in ongoing profession-al development activities, they risk being unin-formed about key developments in educationand in their subject areas that have occurredsince they received their initial training. There isspecial concern that without access to high-quali-ty professional development, teachers will beunable to benefit from the advances made ininformation technology. Consequently, teachersneed to learn how to use computers and theInternet in their classrooms to good advantage.

The professional development of teachers isof central importance to any attempts to changeor reform an education system. Teacher develop-ment activities include expanding an individual’srepertoire of well-defined and skillful classroompractices through training, observation of or byother teachers, immersion or internship activi-ties, teacher task forces, teacher collaboratives,subject-matter associations, collaborations target-ed at specific initiatives, and special institutesand centers.6 The frequency and type of devel-opment activities, the level of intellectual, social,and emotional engagement, and the degree towhich the program is grounded in the largercontexts of school practice and the educationalneeds of the students are important indicators ofsuccessful teacher development programs.7

Classroom Activities andCharacteristics

Although the school provides the general con-text for learning, it is in the classroom settingand through the guidance of the teacher thatmost teaching and learning take place. The class-room setting here is taken to include workassigned in the classroom but completed else-where, such as homework, library assignments,or field work. Aspects of the implemented cur-riculum that are most readily studied in theclassroom include the curriculum topics that areactually addressed, the pedagogic approachesused, the materials and equipment available, andthe conditions under which learning takes place,including the size and composition of the classand the amount of classroom time devoted tomathematics and science education.

Curriculum Topics Taught. A major focus of theimplemented curriculum is the extent to whichthe mathematics and science topics in the TIMSSframeworks are covered in the classroom. TIMSSaddresses this question by asking the mathemat-ics and science teachers of the students assessedto indicate whether each of the topics tested hadbeen covered in class, either in the current orprevious years, and how many class periodswere devoted to the topic. TIMSS characterizesthe coverage and level of rigor of the mathemat-ics and science courses taught in participatingcountries by describing the main focus of thework in the classes being tested.


6 Mullis, I.V.S., et al (2001), Mathematics Benchmarking Report,TIMSS 1999 – Eighth Grade: Achievement for U.S. States andDistricts in an International Context (pp. 237-244), ChestnutHill, MA: Boston College; Martin, M.O., et al (2001), ScienceBenchmarking Report, TIMSS 1999 – Eighth Grade:Achievement for U.S. States and Districts in an InternationalContext (pp. 253-260), Chestnut Hill, MA: Boston College.

7 Little, J. W. (1993), “Teachers’ Professional Development in aClimate of Educational Reform,” Educational Evaluation andPolicy Analysis, 15(2), 129-51, Washington, DC: AmericanEducational Research Association.

Time. The amount of classroom instructionaltime devoted to mathematics and science is animportant aspect of curricular implementation.TIMSS has shown that the efficient use of thattime and the disruptive effects of outside inter-ruptions are aspects related to effective teaching.

Homework. The reasons for assigning homeworkas well as the amount and types assigned areimportant pedagogic considerations. Homeworkserves to increase the time devoted to a subject.It can be used to reinforce and/or extend theconcepts developed in a lesson.

Assessment. TIMSS results show that teachersdevote a fair amount of time to student assess-ment, whether as a means of gauging what stu-dents have learned to guide future learning, orfor providing feedback to students, teachers, andparents. The frequency of various types ofassessment and the weight given to each areimportant indicators of teaching and school ped-agogy. Types of assessment include external stan-dardized tests, teacher-made tests requiringexplanations, teacher made objective tests,homework assignments, projects or practicalexercises, students’ responses in class, and obser-vations of students.

Classroom Climate. Classroom climate, or envi-ronment, characterizes the ambience, tone,atmosphere, and ethos of the classroom.8 Studentand teacher perceptions of the classroom envi-ronment influence learning behaviors and out-comes.9 The extent to which students participateactively and attentively in class, the degree towhich they like and interact positively with eachother, the relationship between students andteacher, and the organizational clarity of the classare all important facets of classroom climate.

Information Technology. The computer is rapidlytransforming education as students prepare toenter the technological workforce. Informationtechnology saves time and, more important,gives students access to powerful new ways toexplore concepts at a depth that has not beenpossible in the past. Computers can trigger anew enthusiasm and motivation for learning,enable students to learn at their own pace, andprovide students with access to vast informationsources via the Internet.

While computers are undoubtedly changingthe educational landscape, schools operate withfinite resources, and the allocation of money,time, and space for technology may divert scarceresources from other priorities, such as increas-ing teacher salaries, teachers’ professional devel-opment, lowering student-teacher ratios, and theprovision of teaching resources including labora-tory equipment and space. Further, the sustain-ability of school computer systems and thecontinuity of support staffing may be as impor-tant as the acquisition of the computers.

The effective and efficient use of comput-ers requires suitable training of teachers, stu-dents, and school staff. Factors limitingcomputer use include the lack of appropriatesoftware and hardware, software not congruentwith the curriculum, lack of teacher trainingand support, and lack of funding for computerrepair and maintenance.

The rapid growth in access by students inschools and at home to the informationalresources of the Internet has the potential torevolutionize mathematics and science learninglike nothing before. There is evidence to showthat multiple layers of access to the Internet, forexample at schools, in libraries, and at home, isimportant. For countries in which students dohave ready access to the Internet, it is importantthat they be taught how to use the information,and how to evaluate its truth or worth.


8 Fraser, B.J. and Walberg, H.J. (1991), Educational Environments:Evaluation, Antecedents and Consequences, New York, NY:Pergamon Press.

9 Lorsbac, A. W. and Jinks, J. L. (1999), “Self-Efficacy Theory andLearning Environment Research,” Learning EnvironmentsResearch, 2, 157-167, Boston, MA: Kluwer Academic Publishers.

Besides giving students access to theInternet, computers can serve a number of othereducational purposes. While initially limited tolearning drills and practice, they are now used ina variety of ways including tutorials, simulations,games, and applications. New software enablesstudents to pose their own problems and exploreand discover mathematics and scientific proper-ties on their own. Computer software for model-ing and visualization of ideas can open a wholenew world to students and help them connectthese ideas to their language and symbol systems.

Calculator Use. Calculator use varies widelyamong, and even within, countries, but general-ly is increasing steadily as cost becomes less ofan impediment and mathematics curriculumevolves to take calculators into account. Manycountries have policies regulating the access toand use of calculators, especially at the earliergrade levels. What those policies are and howthey change over the grades can be important inunderstanding the curriculum.

Calculators can be used in exploring num-ber recognition, counting, and the concepts oflarger and smaller. They can allow students tosolve numerical problems faster by eliminatingtedious computation and thus become moreinvolved in the learning process. Graphing calcu-lators make it possible to switch from equationsto graphs to data analysis, enabling problems tobe approached either visually or numerically.How best to make use of calculators, and whatrole they should have, continue to be questionsof importance to mathematics curriculum spe-cialists and teachers.

Emphasis on Investigations. The emphasis onconducting projects and investigations varieswidely across countries. An exploration of thefrequency and the nature of a task can illumi-nate the learning at issue. In science, practicalinvestigations are often an integral part of thelearning process. The extent to which theseactivities are demonstrated by the teacher andconducted by the students also shows variationacross countries.

Class Size. Class size can serve as an economicindicator, with smaller classes signifying greaterwealth. However, smaller class sizes may be theresult of government policies that cap class size.Further, class size may reflect selective resourceallocation to, for example, special needs or prac-tical classes. Whatever the reason for the classsize, there is little doubt that it affects howteachers implement the curriculum.


The Students

Home Background. Students come to schoolfrom different backgrounds and with differentexperiences. The number of books in the home,availability of a study desk, the presence of acomputer, the educational level of the parents,and the extent to which students speak the lan-guage of instruction have been shown to beimportant home background variables, indicativeof the family’s socio-economic status, that arerelated to academic achievement. Also importantare the attitudes of parents and their involve-ment in their child’s education. The extent towhich employment, sports and recreational pas-times, and other activities occupy the student’stime may also affect learning.

Prior Experiences. Students engage with mathe-matics and science with a host of prior experi-ences that affect their preparedness to learn.These include past learning in the subject, posi-tive or negative interactions with past teachers,and the difficulty or ease with which the subjectmatter was learned.

Attitudes. Creating a positive attitude in stu-dents toward mathematics and science is animportant goal of the curriculum in many coun-tries. Students’ motivation to learn can be affect-ed by whether they find the subject enjoyable,place value on the subject, and think it is impor-tant in the present and for future career aspira-tions. In addition, students’ motivation can beaffected by the degree to which they attributesuccess and failure in the subject to internal orexternal factors.


Assessment Design

Scope of the Assessment

To measure students’ achievement in mathemat-ics and science at the fourth and eighth gradesand gather information about the contexts forachievement, the TIMSS 2003 assessmentincludes written tests of mathematics and sci-ence and a series of questionnaires focusing oncontexts for student learning in those subjects.This chapter describes the design of the assess-ment and specifications for operationalizing thecomponents of the study. A characteristic ofTIMSS is that it includes both mathematics andscience, with each student completing parts ofthe assessment in both subjects.

The TIMSS frameworks have broad cover-age goals, and consequently the TIMSS ExpertPanel found that a valid assessment of the math-ematics and science described in the frameworkswould require a substantial pool of assessmentitems and extensive testing time – at least sevenhours at eighth grade (mathematics and sciencetogether) and more than five and one half hoursat fourth grade. While the assessment materialthat can be presented in that time should pro-vide good coverage of the mathematics and sci-ence students encounter at schooland in their everyday lives, it is notreasonable to expect each student toanswer the entire pool of test items.

Dividing up the Item Pool

Since the testing time required bythe entire assessment item poolgreatly exceeds the time available fortesting individual students, TIMSSdivides the assessment materialamong students. The TIMSSapproach, based on matrix samplingtechniques, involves dividing theitem pool among a set of studentbooklets, with each student complet-ing just one booklet. Items areassigned to booklets in such a way

that a comprehensive picture of the achieve-ment of the entire student population can beassembled from the combined responses ofindividual students to individual booklets.

Based on past experience with TIMSS,National Research Coordinators from participat-ing countries agreed that the testing time for anyone student should not be increased from previ-ous assessments. Thus, as in the past, the assess-ment time for each student booklet needed to fitinto approximately 90 minutes for eighth gradeand approximately 65 minutes for fourth grade.An additional 15-30 minutes for a student ques-tionnaire is also planned at each grade level.

To facilitate the creation of the studentbooklets, the items in the assessment pool arefirst grouped into clusters or blocks of items.These then become the building blocks fromwhich the student booklets will be assembled. InTIMSS 2003, the total item pool at each gradelevel (seven hours of testing at eighth grade andmore than five and one half hours at fourthgrade) will be divided into 28 blocks, 14 inmathematics and 14 in science, as shown inExhibit 6. Each block will contain mathematicsitems only or science items only. Eighth-grade

Assessment Design 85

Source of Items MathematicsBlocks

Trend Items (TIMSS 1995 or 1999) M1 S1



Trend Items (TIMSS 1999) M4 S4



New Replacement Items M7 S7








ScienceBlocks

Exhibit 6: General Design of the TIMSS 2003 Matrix-Sampling Blocks

blocks will contain 15 minutes of assessmentitems and fourth-grade blocks 12 minutes; oth-erwise the general design is identical at bothgrade levels. The blocks containing mathematicsitems will be labeled M1 through M14 and thescience items S1 through S14.

Since TIMSS in 2003 and in later cyclesplans to provide an up-to-date assessment ofstudent achievement in mathematics and sci-ence while also measuring trends in achieve-ment since 1995 and 1999,1 the TIMSS designfor 2003 includes items from earlier assessmentsto measure trends as well as innovative newproblem-solving and inquiry items and replace-ment items for those released into the publicdomain. Of the 14 item blocks in each subject,six (blocks 1 through 6) contain secure itemsfrom earlier TIMSS assessments to measuretrends,2 and eight (blocks 7 through 14) containnew replacement items.

Although calculators were not permitted in1995 or 1999, calculators may be used in theeighth-grade assessment at the discretion of eachparticipating country.3 Calculators will not bepermitted in the fourth-grade assessment.

Block Design for Student Booklets

In choosing how to distribute assessment blocksacross student booklets, the major goal was tomaximize coverage of the framework whileensuring that every student responded to suffi-cient items to provide reliable measurement oftrends in both mathematics and science. A furthergoal was to ensure that trends in the mathematicsand science content areas could be measured reli-ably. To enable linking among booklets, at leastsome blocks had to be paired with others. Sincethe number of booklets can become very large ifeach block is to be paired with all other blocks, itwas necessary to choose judiciously among possi-ble block combinations to keep the number ofstudent booklets to a minimum.

The decision to allow calculator use at theeighth grade for the first time in 2003 also hadan impact on the booklet design. Since calcula-tors were not allowed in 1995 or 1999 but willbe permitted in the eighth-grade assessment in2003, it was necessary in order to safeguard themeasurement of trend to arrange the item blocksin the booklets so that calculators could be usedfor the new assessment items, but not for thetrend items. Accordingly, the trend blocks wereplaced in the first part of each booklet, to becompleted without calculators before the break.However, two mathematics trend blocks (M5and M6) and two science trend blocks (S5 andS6) also were placed in the second part of onebooklet each.

In the TIMSS 2003 design, the 28 assess-ment blocks will be distributed across 12 studentbooklets (see Exhibit 7). The same bookletdesign will be used at both fourth and eighthgrade, although the eighth-grade blocks willcontain 15 minutes of assessment items and thefourth grade blocks 12 minutes. Each studentbooklet will consist of six blocks of items. Halfthe booklets will contain four mathematics

Assessment Design86

1 TIMSS will measure trends at the eighth grade from 1995 and1999, but at the fourth grade from 1995 only, since the TIMSS1999 assessment was conducted at the eighth grade but notthe fourth grade.

2 The six trend blocks for the TIMSS 2003 eighth-grade assess-ment will contain secure items from both the 1995 and 1999TIMSS assessments, with all trend items from 1995 being placedin blocks 1 through 3. Because there are no fourth-grade itemsfrom 1999, trend blocks 4 through 6 for the fourth-gradeassessment will consist of new items. In order to create balanced blocks, some new items are also included in blocks 1 through 6 at the eighth grade.

3 To avoid introducing bias into the measurement of trends, calculators will be used only with items new in 2003, and notwith items measuring trends.

blocks and two science blocks,and the other half will containfour science blocks and twomathematics blocks. All studentbooklets will contain at least twoblocks of mathematics items andtwo blocks of science items, sothat all students will respond toenough items to provide reliablemeasurement of trends in bothsubjects. In addition, the stu-dents that are assigned bookletswith four mathematics blocks(half of the student sample) willprovide sufficient data to meas-ure trends in the mathematicscontent areas, and the studentsassigned the booklets with four science blockswill provide data on trends in the science con-tent areas.

As may be seen from Exhibit 7, studentsassigned Booklet 1 will complete four blocks ofmathematics items, M1, M2, M5, and M7, andtwo blocks of science items, S6 and S7. Theitems in blocks M1, M2, M5, and S6 will betrend items from earlier TIMSS assessments,while those in M7 and S7 will be new items.Students assigned Booklet 2, 3, 4, 5, or 6 willalso have four mathematics blocks and two sci-ence blocks, although the blocks will vary frombooklet to booklet, as shown in Exhibit 7.Students assigned Booklets 7 through 12 eachwill complete four blocks of science and twoblocks of mathematics items. To enable linkingbetween booklets, all blocks will appear in atleast two of the 12 booklets, with the trendblocks appearing in three or four of the book-lets. Countries participating in TIMSS will aimfor a sample of at least 4,500 students to ensurethat there are enough respondents for eachitem. The 12 student booklets will be rotatedamong the students in each sampled class, so

that approximately equal proportions of stu-dents respond to each booklet.

As summarized in Exhibit 8, each studentwill complete just one of the 12 student bookletsand a student questionnaire. The individual stu-dent response burden for the assessment is simi-lar to TIMSS in 1995 and 1999, i.e., 72 minutesfor the assessment and 30 minutes for the ques-tionnaire at fourth grade (slightly more than the65 minutes for the assessment in 1995), and 90minutes and 30 minutes, respectively, at eighthgrade. Students may not use calculators whileworking on Part 1 of the student booklet, as this


Student Booklet

Booklet 1 M1 M2 S6 S7 M5 M7

Booklet 2 M2 M3 S5 S8

Booklet 3 M3 M4 S4 S9 M11

Booklet 4 M4 M5 S3 S10

Booklet 5 M5 M6 S2 S11 M9 M13

Booklet 6 M6 M1 S1

Booklet 7 S1 S2 M6 M7 S5 S7

Booklet 8 S2 S3 M5 M8

Booklet 9 S3 S4 M4 S11

Booklet 10 S4 S5 M3

Booklet 11 S5 S6 M2 S9 S13

Booklet 12 S6 S1 M1

Assessment Blocks

M6 M8

M13

M14 M12

M14

S8S6

S12S14

S10 S14

S12

M9

M10

M12

M10

S13

M11

Exhibit 7: TIMSS 2003 Booklet Design – Fourth and Eighth Grade

Activity FourthGrade

EighthGrade

Student Booklet – Part 1(Calculators Not Permitted) 36 minutes 45 minutes

Student Booklet – Part 2(Calculators Permitted –8th grade only)

36 minutes 45 minutes

Student Questionnaire 30 minutes 30 minutes

Break

Break

Exhibit 8: TIMSS 2003 Student Testing Time

contains the trend items. Calculators may beused for Part 2 of the student booklet, but onlyby eighth-grade students. Calculators are notpermitted in the fourth-grade assessment.

Question Types and ScoringProcedures

Students’ knowledge and understanding of math-ematics and science will be assessed through arange of questions in each subject. Two questionformats will be used in the TIMSS assessment –multiple-choice and constructed-response. Eachmultiple-choice question will be worth one point.Constructed-response questions generally will beworth one, two, or three points, depending onthe nature of the task and the skills required tocomplete it. Extended problem-solving andinquiry tasks may require students to work withmaterials and manipulatives and to provide oneor more extended constructed responses. Up totwo-thirds of the total number of points repre-sented by all the questions will come from multi-ple-choice questions. In developing assessmentquestions, the choice of item format will dependon the mathematics or science being assessed,and the format that will best enable students todemonstrate their proficiency.

Multiple-Choice Questions. Multiple-choicequestions provide students with four or fiveresponse options, of which only one is correct.These questions can be used to assess any of thebehaviors in the cognitive domains. However,because they do not allow for students’ explana-tions or supporting statements, multiple-choicequestions may be less suitable for assessing stu-dents’ ability to make more complex interpreta-tions or evaluations.

In assessing fourth- and eighth-grade stu-dents, it is important that linguistic features ofthe questions be developmentally appropriate.Therefore, the questions are written clearly and

concisely. The response options are also writtensuccinctly in order to minimize the reading loadof the question. The options that are incorrectare written to be plausible, but not deceptive.For students who may be unfamiliar with thistest question format, the instructions given atthe beginning of the test include a sample multi-ple-choice item that illustrates how to select andmark an answer.

Constructed-Response Questions. For this type oftest item students are required to construct a writ-ten response, rather than select a response from aset of options. Constructed-response questions areparticularly well suited for assessing aspects ofknowledge and skills that require students toexplain phenomena or interpret data based ontheir background knowledge and experience.

In the TIMSS assessment, constructed-response questions will be worth one, two, orthree points, depending on the nature of thetask and the extent of the explanation thequestion requires. In these questions, it isimportant to provide enough information tohelp students understand clearly the nature ofthe response expected.

Scoring guides for each constructed-response question describe the essential featuresof appropriate and complete responses. Theguides focus on evidence of the type of behaviorthe question assesses. They describe evidence ofpartially correct and completely correct respons-es. In addition, sample student responses ateach level of understanding provide importantguidance to those who will be rating the stu-dents’ responses. In scoring students’ responsesto constructed-response questions, the focus issolely on students’ achievement with respect tothe topic being assessed, not on their ability towrite well. However, students need to commu-nicate in a manner that will be clear to thosescoring their responses.

Assessment Design88

In addition, scoring guides are designed toenable, for each item, identification of the vari-ous successful, partially successful, and unsuc-cessful approaches. Diagnosis of commonlearning difficulties in mathematics and scienceas evidenced by misconceptions and errors is animportant aim of the study.

Since constructed-response questions con-stitute an important part of the assessment andare an integral part of the measurement oftrends, it is very important for scoring guides tobe implemented consistently in all countries andin each data collection year. To ensure consistentapplication of the scoring guides for trend itemsin the 2003 assessment, IEA has archived sam-ples of student responses from each country;these will be used to train scorers in 2003 and tomonitor consistent application.

Score Points. In developing the assessment,the aim is to create blocks of items that eachprovide, on average, about 15 score points ateighth grade and about 12 score points at fourthgrade. For example, at eighth grade blocks 1through 14 in each subject could be made up ofapproximately 8 multiple-choice items (1 pointeach), 2 or 3 short constructed-response items (1or 2 points each), and 1 extended constructed-response item (3 points). The exact number ofscore points and the exact distribution of ques-tion types per block will vary somewhat. Sincethe blocks for the fourth-grade assessment willbe designed to yield 12 rather than 15 scorepoints, there will be fewer items but the relativeproportions of different item types will beapproximately the same.

Scales for Reporting StudentAchievement

TIMSS will report trends in student achievementin both the general areas of mathematics andscience and in the major subject matter contentareas. As each student will respond to only partof the assessment, these parts must be combinedfor an overall picture of the assessment resultsfor each country. Using item response theory(IRT) methods,4 individual student responses tothe items related to mathematics and sciencewill be placed on common scales that link toTIMSS results from 1995 and 1999. At theeighth grade, there will be an overall mathemat-ics scale that will allow countries that participat-ed in TIMSS in 1995 or 1999 to track theirprogress in mathematics achievement since then,and a similar scale in science overall that willprovide the same information for science. At thefourth grade, the overall mathematics and sci-ence scales will link to 1995 only, since theTIMSS 1999 assessment did not include fourthgrade. All students will have overall mathemat-ics and science scores.

All student responses will contribute to themeasurement of achievement in each of themathematics and science content areas. In addi-tion, those students assigned booklets with fourblocks of mathematics items (half of the studentsample) will provide the data to report on trendsin mathematics content areas, while thoseassigned booklets with four blocks of scienceitems (the other half) will provide data on trendsin science content areas.


4 For a description of the TIMSS scaling techniques as applied tothe 1999 data, see Yamamoto, K. and Kulick, E. (2000),“Scaling Methods and Procedures for the TIMSS Mathematicsand Science Scales” in M.O. Martin, K.D. Gregory, andS.E. Stemler (eds.), TIMSS 1999 Technical Report, Chestnut Hill,MA: Boston College.

In mathematics at the eighth grade therewill be five content reporting categories in 2003:

• Number • Algebra• Measurement• Geometry• Data

At fourth grade there also will be five con-tent reporting categories in mathematics:

• Number • Patterns, Equations, and Relationships• Measurement• Geometry• Data

Eighth-grade science will have five contentreporting categories:

• Life Science • Chemistry• Physics• Earth Science• Environmental Science

At fourth grade, science will have just threecontent reporting categories:

• Life Science • Physical Science• Earth Science

Results will be reported separately for eachcontent area and grade level.

In addition to the IRT scales that will beused to summarize achievement in mathematicsand science content areas and in these subjectsoverall, TIMSS will report on performance in

each of the cognitive domains in terms of theaverage percentage of students answering itemscorrectly in each domain. This approach mayalso be used to report student performance inscientific inquiry.

Releasing Assessment Material tothe Public

The data collection in 2003 will be the third inthe TIMSS series of regular four-year studies,and will provide data on trends in mathematicsand science achievement since 1995 and 1999.TIMSS will be administered again in 2007, 2011,and so on into the future. The design providesfor releasing many of the items into the publicdomain as the international reports are pub-lished, while safeguarding the trend data bykeeping secure a substantial proportion of theitems. As items are released, new items will bedeveloped to take their place.

According to the TIMSS design, half of the14 assessment blocks in each subject will bereleased when the assessment results for 2003 arepublished, and half will be kept secure for use inlater assessments. The released blocks will includethe three blocks containing trend items from1995, one block of trend items from 1999, andthree blocks of items used for the first time in2003.5 The released items will be replaced withnew items before the next survey cycle, in 2007.

Background Questionnaires

An important purpose of TIMSS is to study theeducational context within which students learnmathematics and science. To that end, TIMSSwill administer questionnaires to curriculumspecialists, and to the students in participatingschools, their mathematics and science teachers,

Assessment Design90

5 Since there are no 1999 trend items at fourth grade, four blocksof 2003 items will be released at this grade level.

and their school principals. The questions aredesigned to measure key elements of the cur-riculum as it is intended, as it is implemented,and as it is learned.

Curriculum Questionnaires. The curricu-lum questionnaires, one for mathematics andone for science, are designed to collect basicinformation about the organization of the math-ematics and science curriculum in each country,and about the content in these subjects intendedto be covered up to and including the fourthgrade and between fourth and eighth grades.The National Research Coordinator in eachcountry will be responsible for completing thequestionnaires, drawing upon the knowledgeand expertise of curriculum specialists and edu-cators as necessary.

Student Questionnaire. This question-naire will be completed by each student whotakes the TIMSS assessment. It asks aboutaspects of students’ home and school lives,including classroom experiences, self-perceptionand attitudes about mathematics and science,homework and out-of-school activities, comput-er use, home educational supports, and basicdemographic information. The questionnairerequires 15-30 minutes to complete.

Teacher Questionnaires. In each schoolparticipating at the eighth grade, a single eighth-grade mathematics class will be sampled to takepart in the TIMSS testing. The mathematicsteacher of that class will be asked to complete amathematics teacher questionnaire, providinginformation on the teacher’s background, beliefs,attitudes, educational preparation, and teachingload, as well as details of the pedagogic approachused in that class. The science teacher (or teach-ers) of the students in that class will be asked tocomplete a science teacher questionnaire, whichin many respects will parallel the mathematicsquestionnaire. Both questionnaires ask aboutcharacteristics of the class tested in TIMSS;

instructional time, materials, and activities forteaching mathematics and science and promot-ing students’ interest in the subjects; use of com-puters and the Internet; assessment practices;and home-school connections. They also askteachers their views on their opportunities forcollaboration with other teachers and profession-al development, and for information aboutthemselves and their education and training.

At the fourth grade, there will be a singleteacher questionnaire containing questions aboutmathematics and science instruction and aboutthe teachers’ background that will be completedby the classroom teacher of the sampled fourth-grade class. The teacher questionnaires require30-45 minutes of the teacher’s time.

School Questionnaire. The principal ofeach school in TIMSS will be asked to respond tothis questionnaire. It asks about enrollment andstaffing; resources available to support mathe-matics and science instruction, such as the avail-ability of instructional materials and staff; schoolgoals and the role of the principal; instructionaltime; home-school connections; and school cli-mate. It is designed to take about 30 minutes.


The following is a partial list of works that wereconsulted in the preparation of the mathematics,science, and contextual frameworks. Althoughnot cited, additional curriculum materials pro-vided by a number of TIMSS 1999 countrieswere also consulted.

Mathematics

Beaton, A., Mullis, I.V.S., Martin, M.O.,Gonzalez, E.J., Kelly, D.L., and Smith, T.A.(1996), Mathematics Achievement in the MiddleSchool Years: IEA’s Third InternationalMathematics and Science Study, Chestnut Hill,MA: Boston College.

Confrey, J. (1990), “A Review of the Researchon Student Conceptions in Mathematics,Science, and Programming,” in C.B. Cazden(ed.), Review of Research in Education 16,Washington DC: American EducationalResearch Association.

Hiebert, J. and Carpenter, T.P. (1992), “Learningand Teaching with Understanding,” in D.A.Grouws (ed.), Handbook of Research onMathematics Teaching and Learning, NewYork, NY: MacMillan Publishing Company.

Howard, P.J. (2000), The Owner’s Manual for theBrain: Everyday Applications of Mind-BrainResearch (2nd edition), Austin, TX: Bard Press.

Kulm, G. (ed.) (1990), Assessing Higher OrderThinking in Mathematics, Washington, DC:American Association for the Advancementof Science.

Ministry of Education (1992), Mathematics in theNew Zealand Curriculum, Wellington, NewZealand: Learning Media.

Mullis, I.V.S., Martin, M.O., Gonzalez, E.J.,Gregory, K.D., Garden, R.A., O’Connor,K.M., Chrostowski, S.J., and Smith, T.A.(2000), TIMSS 1999 International MathematicsReport: Findings from IEA’s Repeat of the ThirdInternational Mathematics and Science Study atthe Eighth Grade, Chestnut Hill, MA: Boston College.

Mullis, I.V.S., Martin, M.O., Gonzalez, E.J.,O’Connor, K.M., Chrostowski, S.J.,Gregory, K.D., Garden, R.A., and Smith,T.A. (2001), Mathematics BenchmarkingReport, TIMSS 1999 – Eighth Grade:Achievement for U.S. States and Districts in anInternational Context, Chestnut Hill, MA:Boston College.

NAEP Mathematics Assessment Project (1996),Mathematics Framework for the 1996 NationalAssessment of Educational Progress,Washington DC: U.S. Government Printing Office.

National Council of Teachers of Mathematics(2000), Principles and Standards for SchoolMathematics, Reston, VA: NCTM.

Nickersen, R.S. (1988), “On Improving Thinkingthrough Instruction,” in E.Z. Rothkopf(ed.), Review of Research in Education 15,Washington, DC: American EducationalResearch Association.

Endnotes 93

Endnotes

OECD Programme for International StudentAssessment (1999), Measuring StudentKnowledge and Skills: A New Framework forAssessment, Paris, France: Organisation forEconomic Co-operation and Development.

Putnam, R.T., Lampert, M., and Peterson, P.L.(1990), “Alternative Perspectives onKnowing Mathematics in ElementarySchools,” in C.B. Cazden (ed.), Review ofResearch in Education 16, Washington, DC:American Educational Research Association.

Robitaille, D.F., McKnight, C.C., Schmidt, W.H.,Britton, E., Raizen, S., and Nicol, C. (1993),TIMSS Monograph No 1: CurriculumFrameworks for Mathematics and Science,Vancouver, BC: Pacific Educational Press.

Science

American Association for the Advancement ofScience (1993), Benchmarks for ScienceLiteracy, Oxford, England: Oxford University Press.

Beaton, A., Martin, M.O., Mullis, I.V.S.,Gonzalez, E.J., Smith, T.A., and Kelly, D.L.(1996), Science Achievement in the MiddleSchool Years: IEA’s Third InternationalMathematics and Science Study, Chestnut Hill,MA: Boston College.

Champagne, A.B., Kouba, V.L., and Hurley, M.(2000), “Assessing Inquiry,” in J. Minstrelland E.H. Van Zee (eds.), Inquiring intoInquiry Learning and Teaching in Science (pp.447-470), Washington, DC: AmericanAssociation for the Advancement of Science.

International Association for the Evaluation ofEducational Achievement (1992), The IEAStudy of Science III, Changes in ScienceEducation and Achievement: 1970 to 1984, J.P.Keeves (ed.), Oxford, England: Pergamon Press.

Martin M.O., Mullis, I.V.S., Gonzalez, E.J.,Gregory, K.D., Smith, T.A., Chrostowski,S.J., Garden, R.A., and O’Connor, K.M.(2000), TIMSS 1999 International ScienceReport: Findings from IEA’s Repeat of the ThirdInternational Mathematics and Science Study atthe Eighth Grade, Chestnut Hill, MA: Boston College.

Martin, M.O., Mullis, I.V.S., Gonzalez, E.J.,O’Connor, K.M., Chrostowski, S.J. Gregory,K.D., Smith, T.A., and Garden, R.A. (2001),Science Benchmarking Report, TIMSS 1999 –Eighth Grade: Achievement for U.S. States andDistricts in an International Context, ChestnutHill, MA: Boston College.

Endnotes94

NAEP Science Consensus Project (1996), ScienceFramework for the 1996 National Assessment ofEducational Progress, Washington, DC:National Assessment Governing Board, U.S.Department of Education.

NAEP Science Consensus Project (1994), ScienceAssessment and Exercise Specifications for the1994 National Assessment of EducationalProgress, Washington, DC: NationalAssessment Governing Board, U.S.Department of Education.

National Center on Education and the Economy(1995), New Standards: Performance Standardsin English Language Arts, Mathematics, Science,Applied Learning, Volume 2, Middle School,Pittsburgh, PA: University of Pittsburgh.

National Research Council (1995), NationalScience Education Standards, Washington, DC:National Academy Press.

National Research Council (2000), Inquiry andthe National Science Education Standards: AGuide for Teaching and Learning, Washington,DC: National Academy Press.

National Science Foundation (1995), Innovatingand Evaluating Science Education: NSFEvaluation Forums 1992-94, Arlington, VA:National Science Foundation.

National Science Teachers Association (1997),Pathways to the Science Standards: Guidelinesfor Moving the Vision into Practice (elementaryschool edition), Arlington, VA: NSTA Press.

National Science Teachers Association (1998),Pathways to the Science Standards: Guidelinesfor Moving the Vision into Practice (middleschool edition), Arlington, VA: NSTA Press.

Orpwood, G. and Garden, R.A. (1999), TIMSSMonograph No 4: Assessing Mathematics andScience Literacy, Vancouver, BC: PacificEducational Press.

Robitaille, D.F., McKnight, C.C., Schmidt, W.H.,Britton, E., Raizen, S., and Nicol, C. (1993),TIMSS Monograph No 1: CurriculumFrameworks for Mathematics and Science,Vancouver, BC: Pacific Educational Press.

Schmidt, W.H., Raizen, S.A., Britton, E.D.,Bianchi, L.J., and Wolfe, R.G. (1997), ManyVisions, Many Aims, Volume 2: A Cross-NationalInvestigation of Curricular Intentions in SchoolScience, Dordrecht, The Netherlands: KluwerAcademic Publishers.

Endnotes 95

Contextual

Fraser, B.J. and Walberg, H.J. (1991), EducationalEnvironments: Evaluation, Antecedents andConsequences, New York, NY: Pergamon Press.

Grasha, A. (1996), Teaching with Style, Pittsburgh,PA: Alliance Publishers.

Little, J.W. (1993), “Teachers’ ProfessionalDevelopment in a Climate of EducationalReform,” Educational Evaluation and PolicyAnalysis, 15(2), 129-51, Washington, DC:American Educational ResearchAssociation.

Lorsbac, A.W. and Jinks, J.L. (1999), “Self-Efficacy Theory and Learning EnvironmentResearch,” Learning Environments Research,2, 157-167 Boston, MA: Kluwer AcademicPublishers.

Martin, M.O., Mullis, I.V.S., Gonzalez, E.J.,Gregory, K.D., Smith, T.A., Chrostowski,S.J., Garden, R.A., and O’Connor, K.M.(2000), TIMSS 1999 International ScienceReport: Findings from IEA’s Repeat of the ThirdInternational Mathematics and Science Study atthe Eighth Grade, Chestnut Hill, MA: Boston College.

Martin, M.O., Mullis, I.V.S., Gregory, K.D.,Hoyle, C., and Shen, C. (2000), EffectiveSchools in Science and Mathematics, ChestnutHill, MA: Boston College.

Mayer, D.P., Mullens, J.E., and Moore, M.T.(2000), Monitoring School Quality: AnIndicators Report, NCES 2001-030,Washington, DC: National Center forEducation Statistics.

Moskowitz, J. and Stephens, M. (eds.) (1997),From Students of Teaching to Teachers ofStudents: Teacher Induction Around the PacificRim, Washington, DC: U.S. Department of Education.

Mullis, I.V.S., Martin M.O., Gonzalez, E.J.,Gregory, K.D., Garden, R.A., O’Connor,K.M., Chrostowski, S.J., and Smith, T.A.(2000), TIMSS 1999 International MathematicsReport: Findings from IEA’s Repeat of the ThirdInternational Mathematics and Science Study atthe Eighth Grade, Chestnut Hill, MA: Boston College.

Endnotes96

Appendix A

National Research Coordinators

National ResearchCoordinators

Appendix A 99

Argentina

Silvia MontoyaVeronica ParrenoLilia ToranzosMinisterio de Educacion

Carlos Alfredo Rondon CardosoUniversidad del Valle

Armenia, Republic of

Arsen BaghdasaryanYerevan State University

Australia

Susan ZammitAustralian Council for Education Research

Bahrain

Ahmad Muhammad RafeaMinistry of Education

Belgium (Flemish)

Jan van Damme Ann Van Den BroeckKatholieke Universiteit Leuven

Christiane Brusselmans-DehairsVakgroep Onderwijskunde Universiteit Gent

Botswana

Cyprian Ismael CeleDorcas K. MorakeOthusitse M. Siele Ministry of Education

Bulgaria

Kiril BankovUniversity of Sofia

Canada

Alan TaylorMichael MarshallUniversity of British Columbia

Louis-Philippe GaudreaultMeq. Direction de la Sanction d’Etudes

Francine JaquesOntario Ministry of Education

Chile

Leonor Cariola HuertaMinisterio de Educacion

Chinese Taipei

Chu-Nan ChangMei-Hung ChiuTein-Ying LeePi-Jen LinHak-Ping TamPo-Son Dennis TsaoNational Taiwan Normal University

Cyprus

Constantinos PapanastasiouUniversity of Cyprus

Denmark

Peter AllerupDanish University of Education

Egypt

Sulaiman Al-Khodry Al-SheikMinistry of Education

England

Graham RuddockNational Foundation for Educational Research

Appendix A100

Estonia

Kristi MereMinistry of Education

Ghana

Aba Mansa FolsonMinistry of Education

Greece

Georgia PolydoridesUniversity of Athens

Hong Kong, SAR

Frederick LeungThe University of Hong Kong

Hungary

Peter VariNational Institute of Public Education

Indonesia

Jahja UmarMinistry of National Education

Iran, Islamic Republic of

Ali Reza KiamaneshInstitute for Educational Research

Israel

Ruth ZuzovskyTel Aviv University

Italy

Anna Maria CaputoIstituto Nazionale per la Valutazione del Sistemadell’Istruzione

Japan

Yuji SarutaHanako SenumaNational Institute for Educational Policy Research

Jordan

Tayseer Al-NharNational Center for Human Resources Development

Korea, Republic of

Gwisoo NaChung ParkKorea Institute of Curriculum & Evaluation

Latvia

Andrejs GeskeUniversity of Latvia

Lebanon

Leila Maliha FayadMinistry of Education

Lithuania

Algirdas ZabulionisMinistry of Education and Science

Macedonia, Republic of

Anica AleksovaMinistry of Education and Science

Malaysia

Azmi ZakariaMinistry of Education

Moldova

Ilie NasuMinistry of Education and Science

Appendix A 101

Morocco

Mohammed SassiMinistiere de l’Education Nationale

Netherlands

Klaas BosMartina MeelissenUniversity of Twente

New Zealand

Megan ChamberlainMinistry of Education

Norway

Svein LieLiv Sissel Gr nmoUniversity of Oslo

Pakistan

Hafiz Muhammad IqbalUniversity of the Punjab

Palestinian National Authority

Said AssafOla KhaliliMinistry of Education

Philippines

Vivien TalisayonUniversity of the Philippines

Romania

Gabriela NoveanuInstitute for Educational Sciences

Russian Federation

Galina KovalyovaInstitute for General Secondary Education

o

Saudi Arabia

Ali AlhakamiMinistry of Education

Scotland

Liz LevyBrian SempleScottish Office Education and Industry Department

Singapore

Seau-Fah FooMinistry of Education

Slovak Republic

Maria BerovaJozef KurajSPU-National Institute for Education

Slovenia

Barbara JapeljEducational Research Institute

South Africa

Anil KanjeeHuman Sciences Research Council

Spain

Ramon Pajares-BoxInstituto Nacional de Calidad y Evaluación

Sweden

Jan-Olof LindströmWidar HenrikssonUmeå University

Anita WesterNational Agency for Education

Appendix A102

Syria

Faisal WahbehMinistry of Education

Tunisia

Nejib AyedCentre National d’Innovation Pédagogique et de Recherche en Education

Ktari MohsenMinistere de l’Education

United Arab Emirates

Nagib Mahfood BalfakihUnited Arab Emirates University

United States

Patrick GonzalesNational Center for Education Statistics

Yemen, Republic of

Omar Ba-FadhelMinistry of Education

Yugoslavia

Djordje KadijevichSlobodanka Milanovic-NahoInstitute for Educational Research

Appendix B

Example Mathematics Items

Grade 4 and Grade 8

Example Mathematics Items: Grade 4

Appendix B 105

*Correct Answer

Which two of these lines are parallel?

a 1 and 2

b 1 and 3

c 2 and 3

d 2 and 4

Line 1 Line 2 Line 3 Line 4

*

Brad thought of a number. He then multiplied it by 2 and added 4. Theanswer Brad obtained was 16. What was the number he firstthought of?

Answer: _______________

1

2


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Appendix B106

*Correct Answer

Ana placed 12 identical blocks on the scale as shown in the figure.How many blocks should be removed to reduce the weight to 1000 grams?

a 1

b 2

c 3

d 4

1200 grams

SCALE

*

On the number line, which of these numbers would be closest to 1?

a 0.1

b 0.9

c 1.2

d 1.9

0 1 2

*

3

4


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Appendix B 107

The chart above shows the eye color of all students in Ms. Hagan’s choir.

A. How many students are in Ms. Hagan's choir?

Answer: _______________

B. What fraction of Ms. Hagan's choir has blue eyes?

Answer: _______________

8

6

4

2

0Green Blue Brown

Student’s Eye Color

Num

ber

of Stu

den

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Eye Color

5


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Appendix B108

MapInstructions: Questions 6 and 7 are about using a map.

For these questions, you have been given a cardboard ruler.If you do not have the cardboard ruler raise your hand.

Use the map below and your ruler to answer this set of questions.

Emory

Smithville

Brown

Easton

Mott

Scale: 1 cm represents 4 km

4 km

1 cm

Questions for Map begin on the next page.

Rosetown


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Appendix B 109

Traveling Between Towns

A. How many centimeters is it between Mott and Brown on the map?

Answer: ______________________centimeters (cm)

B. How many kilometers is it between Mott and Brown on the road?

Answer: ______________________kilometers (km)

C. It takes one hour to drive from Mott through Easton to Brown. At thesame speed, how much time would it take to travel from Mott to Easton?

Answer: ______________________

Distances From Rosetown

A. Is Emory or Smithville closer to Rosetown?

Answer: ______________________

B. How many centimeters closer is it on the map?

Answer: _____________________centimeters (cm)

C. Another town called Marytown is the same distance from Rosetown as itis from Smithville. Show on the map where Marytown might belocated. Mark it with an X and write Marytown below it.

End of Map section.

6

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Appendix B 111

Type of Item Percent Increase

CDs 80%

Food 15%

Toys 25%

TVs 40%

Clothes 120%

Use the data in the table above to construct a bar graph using the axisbelow. Indicate the scale for the percent increase and label each bar.

Perc

ent

Incr

ease

Sales Increases at Super Value Stores2000 to 2001

Sales Increases at Super Value Stores 2000 to 2001

Type of Item

1


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Appendix B112

*Correct Answer

In the coordinate plane above, what are the coordinates of vertex P ?

a (2,7)

b (2,8)

c (3,7)

d (3,8)

(3,2) (8,2)

45˚

xO

y

P

45˚

*

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Appendix B 113

Row Terms Sum

Row 1 1 1

Row 2 1 + 3 4

Row 3 1 + 3 + 5 9

Row 4 1 + 3 + 5 + 7 16

Row 7

A. Enter the terms and sum for Row 7 in the table.

B. Without writing out all the terms, what is the sum for Row 20?

Answer: _______________

C. What is the value of the sum for Row n?

Answer: _______________

......

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Appendix B114

*Correct Answer

If 81 < n < 144 , then n could be which of the following numbers?

a 9

b 11

c 12

d 13

*

Write an equation to represent the following sentence.

“When half of x is added to 10, the result is 24.”

Answer: _____________________________________________________________

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Appendix B 115

BirdhouseInstructions: Questions 6 and 7 are about building a bird house. Toanswer these questions you may refer to any information shown onthe pages in the Birdhouse section.

For these questions you have been given a cardboard ruler.If you do not have the cardboard ruler raise your hand.

As a class project, students in Ms. Grant’s eighth grade class are makingsmall birdhouses out of wood. Chris receives a paper pattern to build asmall birdhouse that looks like the one shown below.

picture not to scale

right roofpanel

right sidewall panel

front wallpanel

Questions for Birdhouse begin on the next page.


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Appendix B116

Chris has the pattern for 6 pieces: 4 wall pieces and 2 roof pieces. The sheetwith the pattern for the floor is lost. Chris’ pattern pieces are shown inFigure 1 below. The directions state that 1 centimeter in the patternrepresents 3 centimeters for the actual birdhouse.

Figure 1

backwall

panel

left sidewall panel


frontwall

panel

leftroof

panel

rightroof

panel

5.0 cm3.0

cm

length

length

3.0

cm

3.0

cm

3.0

cm

widthwidth

3.2 cm3.2 cm

5.0 cm

2.3 cm 2.3 cm 2.3 cm 2.3 cm

This Birdhouse question continues on the next page.

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Appendix B 117

A. Figure 1 shows the dimensions of the pattern pieces for the four wallpanels. Use your ruler to measure the dimensions of the pattern piecesfor the two roof panels, to the closest millimeter.

What is the length and width of the pattern for the left roof panel?

The length of the left roof panel is _________cm.

The width of the left roof panel is _________cm.

What is the length and width of the pattern for the right roof panel?

The length of the right roof panel is _________cm.

The width of the right roof panel is _________cm.

B. What needs to be done to the measurements in the pattern to find themeasurements in centimeters for the actual birdhouse?

Answer: _________________________________________________________

C. What will be the actual measurements of the left side wall panel of thebirdhouse?

Answer: _________________________________________________________

D. Since some of the pattern pieces in Figure 1 are exactly the same in sizeand shape, Chris does not need to find the actual measurements forevery piece.

What is the least number of the 6 pattern pieces Chris needs to find theactual measurements for the birdhouse?

Answer: _________________

Questions for Birdhouse continue.


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Appendix B118

Figure 2 below shows how the birdhouse should look when the front panel,back panel, side panels, and floor are assembled using glue and nails.

Since the pattern for the floor piece is lost, Chris must use this figure todetermine the measurements for the floor. To do this, Chris needs to knowthe thickness of the wood used to build the birdhouse.

The thickness of the wood is 1.2 cm.

A. What is the length (longer side) and width (shorter side) of the piece ofwood Chris would need for the birdhouse floor?

Length: ____________ cm

Width: ____________ cm

Figure 2

picture not to scale

left sidewall panel

backwall panel


frontwall panel

floor

This Birdhouse question continues on the next page.

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Appendix B 119

B. In the space below make a drawing of the actual size of the floor of thebirdhouse using your ruler. Indicate the length, in centimeters, of thelonger and shorter sides.

End of Birdhouse section.


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Appendix B120

Appendix C

Example Science Items

Grade 4 and Grade 8

Example Science Items: Grade 4

Appendix C 123

*Correct Answer

Magnet 1 is hanging by two strings. Magnet 2 is moved towardsMagnet 1 as shown in the picture. What will happen to Magnet 1?

a Magnet 1 will swing away from Magnet 2.

b Magnet 1 will swing towards Magnet 2.

c Magnet 1 will swing back and forth.

d Magnet 1 will not move.

Magnet 1

N S

Magnet 2

N S

*

Describe two ways people can help to reduce air pollution in a city.

1.

2.

1

2


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Appendix C124

You are given a mixture of sawdust, pebbles, and iron filings.You must separate the mixture into its parts.

A. What things would you need to separate this mixture?

B. Write down the steps you would take to separate the mixture.

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Appendix C 125

The picture below shows clothes drying outside on two different days in thesame month. On Day 1 it is raining. On Day 2 the sun is shining.The clothes are protected from the rain by the hut.

On Day 1 the clothes dry in 24 hours. On Day 2 they dry in 8 hours.Explain why it takes longer to dry clothes on Day 1 than on Day 2.

Day 1 Day 2

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Appendix C126

Ocean Food Chain

The picture below shows part of an ocean and some of the organisms(plants and animals) that live in and around the ocean.

Look at the list of living organisms (plants and animals) below. The tablegives information about what each organism in the picture of the oceanneeds for food.

Name of Organism What the Organism Needs for Food

Seaweed Sunlight to make its own food

Limpet Seaweed

Crab Limpets

Octopus Limpets, crabs, and fish

Seagull Crabs and fish

Seal Crabs, octopus and fish

Questions for Ocean Food Chain begin on the next page.

The Ocean andRocky Shore

seagulls

rocks

seaweed

seals limpets

crab

octopus

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Appendix C 127

The diagram below shows part of a food chain. The arrows go from oneorganism to another organism that eats it. In this food chain, the limpetseat seaweed.

A. Complete the food chain above by writing the names of two otherorganisms from the table in the blank spaces. Use the information in thetable about what each organism needs for food.(There is more than one correct food chain. You need to show just one.)

B. One year a disease causes many limpets to die. What would happen tothe seaweed in your food chain when the limpets die?

C. Choose another organism in your food chain (not seaweed or limpet).

Name of organism: ______________________________

What would happen to this organism when the limpets die?

D. What would happen to the other organisms in your food chain if theseaweed does not grow well?

seaweed limpet

End of Ocean Food Chain questions.


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Appendix C 129

Your skin and your hair are both made up of cells. When you cut your skin,it hurts. When you cut your hair, it does not hurt.

Explain why.

The human population of the world has grown rapidly over the past 200years. Describe one way the increased world population has affected theenvironment.

1

2


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Appendix C130

*Correct Answer

A metal was heated for several minutes at a constant rate. It melted andthen boiled. The graph below shows how the temperature changed as heatwas added over time.

From the graph, what is the melting point of the metal?

a 200°C

b 400°C

c 800°C

d 1200°C

0 1 2 3 4 5 6 7 8 9 10

1400

1200

1000

800

600

400

200

0

Time (minutes)

Tem

per

ature

(ºC

)

*

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Appendix C 131

A ship is built mostly of metal. Metal usually sinks when put into water,but a ship does not sink. Explain why.

How was the oil formed that is found in the rock layers beneath theocean floor?

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Appendix C132

Emile and Andre went to a clothing store. They bought an orange shirt. Onthe way home, they opened up the bag to show a friend the new orangeshirt. They noticed, however, that the shirt looked red instead of orange.

Emile thought that they were given the wrong shirt. Andre thought thatthey had the right shirt. He said that the color of a material can changeunder different light conditions. They decided to conduct an investigation totest Andre’s ideas about light and color.

Questions for Light Filters begin on the next page.

Light FiltersInstructions: Questions 6, 7, 8, 9, and 10 are about light filters. Toanswer these questions you may refer to any information shown onthe pages in the Light Filters section.


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Appendix C 133

Emile and Andre got a flashlight, some transparent sheets of colored plasticto use as light filters, and some colored paper. They used these materials fortheir investigation. First they looked at the different pieces of paper insunlight. They recorded what they saw.

Paper 1 Paper 2 Paper 3 Paper 4

Appearance in sunlight White Red Green Black

A. Andre said that sunlight is made up of a mixture of different colors. Healso said that the papers looked the way they did because they reflectonly part of the sunlight to the eye and absorb the rest. What colors thatmake up sunlight are reflected to the eye by papers 1, 2, 3, and 4?

Paper 1: _______________________________________________________

Paper 2: _______________________________________________________

Paper 3: _______________________________________________________

Paper 4: _______________________________________________________

B. Andre said that sunlight can be separated into its different colors.Give an example of how this can be demonstrated.

Questions for Light Filters continue.

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Appendix C134

Emile and Andre took the colored papers, the colored sheets of plastic, andthe flashlight into a dark room. First they shined the flashlight onto eachpiece of paper. Then they put each sheet of colored plastic (light filter) overthe flashlight and shined the flashlight onto the papers.

They recorded all of their results in a table.

Light ConditionAppearance of Paper

Paper 1 Paper 2 Paper 3 Paper 4

Sunlight White Red Green Black

Flashlight(without a filter) White Red Green Black

Red light(red filter placed Red Red Black Blackover flashlight)

Green light(green filter placed Green Black Green Blackover flashlight)


FilterPapers

Flashlight


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Appendix C 135

*Correct Answer

Look at the results shown in the table. How does the light coming from theflashlight compare to the light coming from the sun? Explain your answerbased on the results of Emile’s and Andre’s investigation.

Light filters transmit (pass through) only part of the light and absorb therest. Which of the following statements is true about how the red filteraffects the color of light from the flashlight?

a The red filter absorbs the red part of light and transmits thegreen part of light.

b The red filter transmits the red part of light and absorbs the greenpart of light.

c The red filter absorbs both the red and green part of light

d The red filter transmits both the red and green part of light.

*


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Appendix C136

Green paper appears black when viewed in red light. Red paper appearsblack when viewed in green light. Explain why this happens in terms of thelight that is transmitted by the filters and the light that is reflected by thepapers.



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Appendix C 137

Light filters have a number of uses. For example, color photographs canfade over time if they are exposed to bright sunlight.

Light filters can be placed over color photographs to reduce the amount offading that occurs in sunlight.

Plan an investigation using light filters that could be used to test howdifferent colors of light affect the fading of color photographs. Describe thematerials you would use and the procedures you would follow. Include inyour plan a description of the variable that you would change and thevariable(s) that you would keep constant.

End of Light Filters section.

BEFORE fading AFTER fading

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TypographyText and headings set in Meridien and Frutiger, designed by Adrian Frutiger.

Book Design and Original IllustrationsJosé R. Nieto

Layout and ProductionJosé R. Nieto and Mario Pita

Cover DesignChristine Conley

T03 AF FrontMatterarchivos.agenciaeducacion.cl/4_Marco_de_evaluacion_TIMSS_2003.… · Science...

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