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Stepanek, Jennifer; Jarrett, DeniseAssessment Strategies To Inform Science and MathematicsInstruction: It's Just Good Teaching.Northwest Regional Educational Lab., Portland, OR.Department of Education, Washington, DC.1997-06-0040p.

RJ96006501Northwest Regional Educational Laboratory, 101 S.W. MainStreet, Suite 500, Portland, OR 97204-3297.Guides General (050) Reports Evaluative (142)MF01/PCO2 Plus Postage.Educational Change; Elementary Secondary Education;Evaluation Criteria; *Learning Strategies; *MathematicsInstruction; *Performance Based Assessment; *PortfolioAssessment; *Science Instruction; *Self Evaluation(Individuals); Student Evaluation; Teaching Methods

Changes in assessment practices are central to ongoingreform efforts in science and mathematics education. The education communityis currently focused on new ways to measure, evaluate, and report students'progress toward standards and learning goals. The focus of this publication,using assessment for informing and improving instruction is not only key toeffective teaching and learning but also serves as a fundamental buildingblock for other evaluation activities. Embedded in instruction, assessmentfor this purpose requires a simultaneous focus on what students are doing andlearning, and how teachers are guiding the students and facilitatinglearning. This document includes a summary of research and current literatureon the topic, a discussion of effective strategies, an annotated listing oforganizations, and print and electronic resources. Contains 34 references.(Author/ASK)

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Assessment Strategiesto Inform Science andMathematics Instruction

It's Just Good TeachingPERMISSION TO REPRODUCE AND

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TO THE EDUCATIONAL RESOURCESINFORMATION CENTER (ERIC)

U S DEPARTMENT OF EDUCATIONOffice of Educational Research and Improvement

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Points of view or opinions stated in thisdocument do not necessarily representofficial OERI position or policy

This publication is based on work supported wholly or in part both by agrant and contract number RJ96006501 from the U.S. Department of Edu-cation. The content of this document does not necessarily reflect the viewsof the department or any other agency of the United States government.Permission to reproduce this publication in whole or in part is grantedwith the acknowledgment of the Northwest Regional Educational Labo-ratory as the source on all copies.

Comments or queries may be directed to Kit Peixotto, Director,Mathematics and Science Education Center (formerly Science andMathematics Education), Northwest Regional Educational Laboratory,101 S.W. Main Street, Suite 500, Portland, Oregon 97204,(503) 275-9594 or (800) 547-6339, ext. 594.

Appreciation is extended to the many educators who provided informa-tion and guidance in the development of this publication. Acknowledg-ments also go to the panel of reviewers and contributors for their valu-able input: Jane Braunger, Cheyenneh King, Dylan King, Karma Nelson,Sue Pack, Richard Petersen, Judy Snider, and Judy Vose. In addition, sever-al individuals made special contributions to the development of thisproduct, including:

Jennifer StepanekResearch and writingDenise JarrettResearch and writingKit PeixottoConceptual support and guidanceDawn DzubayResource research and compilationDenise CrabtreeDesktop publishing and proofreadingLee ShermanEditorial reviewPhotographyCatherine Paglin: front cover; Rick Stier: pages 2, 3, 4, 5, 6, 7,12, 14, 16, 18, 20; Susan Dunn: pages 15, 21, back cover;Denise Jarrett: pages 17, 19, 22

Assessment Strategiesto Inform Science andMathematics InstructionIt's Just Good Teaching

June 1997

&, Northwest Regional Educational Laboratory

Table of ContentsIntroduction 2

Using assessment to inform instruction 2

Diagnostic assessment 3

Formative assessment 3

Sum mative assessment 3

Target assessments to obtain specific information 3

Choose the appropriate assessment format 4

Integrate assessments into instruction 4

Make appropriate decisions about instruction 6

Assessment strategies 7

Concept maps 8

Writing activities 10

Performance assessment 11

An era of standardized testing 12

Interviews and conferences 14

Debriefing 17

Observations 18

Portfolios 19

Student self-assessment 20

Student assessment of instruction 21

Conclusion 22

Resources and bibliography 23

Prefacechanges in assessment practices arecentral to ongoing reform effortsin science and mathematics educa-

tion. Currently, the education communi-ty is focused on new ways to measure,evaluate, and report students' progresstoward standards and learning goals.While attention to assessment for thispurpose is important and necessary, anequally significant and essential goal isoften overshadowed by the flurry ofactivity surrounding accountabilityreforms. Using assessment for informingand improving instructionthe focus ofthis publicationis not only key to effec-tive teaching and learning but also servesas a fundamental building block forother evaluation activities.

Assessment Strategies to Inform Scienceand Mathematics Instruction follows aformat similar to the other documentsin the It's Just Good Teaching series pro-duced by the Northwest Regional Educa-tional Laboratory's Mathematics andScience Education Center. Intended foruse by K-12 teachers, each includes asummary of the research and currentliterature on the topic, a discussion ofeffective strategies, and an annotatedlisting of organizations and resources,both print and electronic. In each publi-cation an attempt is made to contextual-ize the information for Northwest class-rooms. Research in the preparation ofAssessment Strategies to Inform Scienceand Mathematics Instruction includedinterviews with Northwest teachers.Their comments serve to illustrate howteachers are thinking about and usingassessment strategies to strengthenteaching and improve student learning.

Using assessment to inform and improveinstruction provides teachers with apowerful tool as they explore the alter-

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native assessment arena. Embedded ininstruction, assessment for this purposerequires a simultaneous focus on whatstudents are doing and learning, andhow teachers are guiding them and facil-itating learning. Students' learning andteachers' instruction are mutually depen-dentaction in one aspect should informand affect the other. The NorthwestRegional Educational Laboratory offersthis publication as a resource to supportand assist practitioners in their pursuitof effective science and mathematicsteaching and learning. Similar to theprocess described in this document, yourassessment informs our actions. We lookforward to your continued feedback toguide our efforts to provide meaningfuland useful products in support of quali-ty science and mathematics educationfor all Northwest students.

Kit PeixottoDirectorMathematics and Science Education CenterJune 1997

IntroductionAssessment to inform instruc-tion means that you're usingstudent assessments to make

decisions about teaching, to adjustand monitor your teaching style oryour activities.

Judy Vose, teacher,Ferndale, Washington

Using assessment to inform instructionis one of the most powerful tools a teach-er has to improve her teaching. It is alsoone of the most overlooked. Teachersroutinely use assessments for a varietyof reasons, most often to assign gradesand to report students' progress to theirparents. However, assessment's real powerits ability to shape and direct class-room instructionis frequentlyuntapped.

A teacher can learn valuable informa-tion about her students' progress and theeffectiveness of her teaching methods byexamining students' work or products.She can also gain insights into her stu-dents' thinking and understanding by

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observing them both informally (whilethey are engaged in activities) and for-mally (during student presentations andconferences between student andteacher).

Although large-scale standardized testsusually in the form of multiple-choiceexamshave dominated the realm ofassessment for most of this century,this practice is changing. Today's empha-sis on what students are able to do aswell as what they know, together with anew understanding of how people learn,has caused educators to look for alterna-tive methods of evaluating studentachievement.

Using assessment toinform instruction

Teachers use assessments for vari-ous reasons. In the book, Assess-ment Standards for School Mathe-

matics, the National Council of Teachersof Mathematics (1995) identifies severalkey purposes for using assessment. Thesepurposes include:

Monitoring students' progress towardlearning goalshow is each student pro-gressing in relation to learning goals?

Making instructional decisionshowcan a teacher use evidence about hisstudents' progress to make instructionaldecisions?

Evaluating students' achievementhow does each student's understandingat this time compare with the goals thatstudent was expected to achieve?

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Evaluating programshow well is theprogram working in relation to goalsand expectations for the students?

Generally, assessment purposes fall intothree broad categories: diagnostic, forma-tive, and summative.

Diagnostic assessment. The pur-pose of diagnostic assessment is to deter-mine, prior to instruction, the student'sbackground experiences, skills, attitudes,and misconceptions. This will help theteacher to evaluate each student's learn-ing needs before instruction begins(Meng & Doran, 1993).

Formative assessment. Formativeassessments are often administered dur-ing a lesson. They help teachers to ascer-tain how students are progressing intheir learning. Formative assessmentsoften include student demonstrations,written projects, and interviews betweenteacher and student. Formative assess-ments are not used for grading purposes,but provide both teacher and studentwith valuable feedback about the stu-dent's progress. Teachers can use thisinformation to make informed decisionsabout their teaching, such as adjustingthe rate of instruction, assigning remedi-al activities, and planning alternativeexperiences (Meng & Doran, 1993).

Summative assessment. Summa-tive assessments are most often adminis-tered at the conclusion of a lesson, unit,or grading period. They provide a sum-mation of what a student knows at thatpoint in time. Summative assessmentsare often used for reporting studentachievement levels to districts and states,for assigning grades, and for determiningwhether to place a student in anadvanced or remedial class.

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Target assessments to obtainspecific information. In addition toidentifying what students know and cando before instruction begins, and how wellthey are progressing toward learninggoals during instruction, teachers cantarget assessments to determine specificinformation, such as (Kober, 1993):

How they are progressing towardlearning goals

Which strategies and thinking pro-cesses students use to reach answers orconclusions

How well students are integrating newinformation

What motivates students

How effective are special interventions

Whether a teacher needs to alter herteaching

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here is absolutely no way thatI can be an effective teacherfor each one of my children if

I don't know where each one is in hisor her learning. I have tounderstand the child's thinking inorder to provide the right kinds ofexperiences.

Sue Pack, teacher,Twin Falls, Idaho

Choose the appropriate assess-ment format. The challenge for teach-ers is to use the most appropriate assess-ment format for obtaining informationthat will serve the desired purpose. Tradi-tional formats of assessment, such asstandardized tests and paper-and-pencilexams, will continue to be useful toolsfor measuring specific educational out-comes. They will be, however, only one ofmany instruments teachers will use toimprove student learning and to adjusttheir instructional strategies to meet theneeds of all students.

Assessments can take many forms, frominformal observations and interviews, tostudent-led conferences and portfolios. Ateacher might use checklists to documentstudents' progress, or periodically reviewstudents' portfolios and journals to ascer-tain the progress of their learning.

Some of the methods for collecting infor-mation for assessment purposes arefamiliar activities in the classroom: writ-ten tests; observations and interviews;and projects. According to the authors ofImproving Instruction and LearningThrough Evaluation: Elementary SchoolScience (Meng & Doran, 1993), all of thesemethods are useful and appropriate forsome objectives. None are both appropri-ate and useful for all objectives.

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The written test is particularly usefulfor assessing student achievement oncontent objectives, the authors say. Per-formance-based assessments are usefulto assess process and/or problem-solvingobjectives, as well as to assess contentknowledge. When administered andrecorded in a structured fashion, observa-tions and interviews also provide valu-able information about students' processand problem-solving skills, and some ofthe content objectives. Student projectsand reports can be used to evaluate stu-dents' knowledge and skills, and theirability to plan, conduct, and report oninvestigations (Meng & Doran, 1993).

Integrate assessments intoinstruction. Teachers have alwaysused diagnostic, formative, and summa-tive methods to determine how to helpstudents learn, but with today's empha-sis on standards-based instruction, teach-ers will want to use assessments in aparticularly purposeful way by integrat-ing assessments into instruction. Byassessing a student's progress before,

during, and after a lesson, a teacher hasopportunities to adjust her teachingstrategies to meet the immediate needsof her students. By evaluating her stu-dents' learning during instruction, ateacher gains insight into the effective-ness of her teaching and obtains valu-able information about specific areas ofher teaching. Using assessment to informinstruction is an integral process in sci-ence and mathematics classrooms whereinquiry and teaching for depth ofunderstanding are the focus.

As a scientist you don't plan thenext experiment withoutincluding information from

the previous experiment, and withoutcarefully and thoughtfully design-ing that experiment. It's the samewith planning your instruction.

Richard Petersen, teacher,Beaverton, Oregon

The national standards for both scienceand mathematics emphasize the impor-tance of using assessment to guideinstruction and to improve teaching,expanding the purpose of assessmentbeyond accountability and assigninggrades. The standards depict assessmentas an opportunity for learningfor bothteachers and studentsrather than aninterruption of the learning process. Inaddition to monitoring student progressand evaluating mathematics and scienceprograms, the standards call upon teach-ers to use assessment data to plan curric-ula and improve classroom practices.Teachers use the information for deci-sions about classroom interactions, howto modify activities to meet the diverselearning approaches of the students, andhow to design activities that build onstudent experiences, cultures, and priorknowledge (National Council of Teach-

5

10

ers of Mathematics [NCTM], 1995; Nation-al Research Council [NBC], 1996).

To use assessments to inform his deci-sions about instruction, a teacher willwant to monitor his students' under-standing and progress in order to designand facilitate instructional activities. Hecan determine where the gaps are in hisstudents' learning, or where mispercep-tions are interfering with students'understanding, and he can adjust histeaching methods to rectify these prob-lems (Kober, 1993).

According to Nancy Kober (1993), assess-ments that are particularly useful forinforming instruction have the followingfeatures: They measure the processesstudents use as well as the answers theyreach; they measure all of the goals ofthe curriculum; they address both groupand individual activities; they are devel-oped by teachers and include a teacher'sprofessional observation and judgment;and they draw information from multi-ple assessment sources. Finally, assess-

444111110.,..

ments should have a self-evaluation com-ponent for both students and teachers.

Make appropriate decisionsabout instruction. Learning activi-ties that engage students in solving non-standard problems, and require them tojustify their strategies and solutions, canprovide teachers with strong evidence ofstudents' learning. Based on this evi-dence, teachers can then make appropri-ate instructional decisions that respondto the specific needs of their students(NCTM, 1995).

6

The Assessment Standards for SchoolMathematics (NCTM, 1995) state thatsuch decisions include:

Identifying appropriate content,sequencing, and pacing of lessons

Modifying or extending activities

Choosing effective teaching methods

Examining the effects of the tasks, dis-course, and learning environment onstudents' knowledge, skills, and disposi-tions

Making instruction more responsive tostudents' needs

Ensuring that every student is gainingmathematical [and scientific] power

According to the Standards, "The qualityof teachers' instructional decisionsdepends, in part, on the quality of theirassessment and their purposeful sam-pling of evidence during instruction."Teachers will want to blur the linesbetween instruction and assessmentbecause assessment is an opportunityfor learning rather than an interruptionin the learning process.

Observing, listening, and questioningare the most common methods for gath-ering evidence of learning duringinstruction, and teachers may elect tomodify their instruction based on thatevidence, state the Standards:

Questioning a few students oftenleads to a redirection of the les-son for all. The justification forchanging the direction of a les-son could come from the confu-sion ensuing as third-gradersattempt to measure their heightswith metersticks or from the

excited conversation of highschool juniors exploring expo-nential functions on a graphingcalculator. Similarly, a teachermight adjust plans for the weekas a result of recognizing thatstudents' responses to a problemare far richer than expected,musing, 'Terrific! I hadn'tthought of so many ways to dothis problem. I wonder if thereare even more. Maybe we shouldspend some more time on ittomorrow'

As teachers integrate instruction andassessment, they will want to identifyplaces in the lesson where they cancheck for specific types of understand-ing, ask specific questions, or collectwork to inform themselves as they makeinstructional decisions. By combiningwritten products with documented evi-dence from observations and questions, ateacher will have a more complete pic-ture of students' knowledge and abilities

7

than can be revealed by relying only ontests, quizzes, and assignments that focuson the mastery of procedures or skills(NCTM, 1995).

Assessmentstrategies

The following assessment strategiesare not new, and many teacherswill recognize techniques they are

already using to evaluate students'achievement. Using these methods toinform instruction often requires just aslight shift in current thinking andpractice. When teachers are consideringhow to provide effective instruction, theywill approach assessment with differentquestions: "What does this tell me aboutmy students' learning? How can I adjustmy instruction to address their difficul-ties and build on their strengths?"

In this approach, assessment does nottake place only at the end of a unit butis an ongoing, cyclical process. Teachersmonitor student development andrespond to the results by adjusting theirinstruction. Before beginning a unit orlesson, teachers can use assessment datato determine a starting pointwhatprior knowledge needs to be addressed,what types of activities are required, andhow to group students for cooperativelearning activities. During a unit, teach-ers will use assessment to monitor thesuccess of the activities, to diagnose mis-conceptions that students may be form-ing, and to determine if students areacquiring the necessary level of under-standing and the ability to apply theirknowledge. The final assessment activi-

ties help teachers identify areas for fur-ther study and plan upcoming units.

ou can't get all the informa-tion you need from justpaper-and-pencil activities.

Over the years, I've learned to do dif-ferent kinds of assessment to obtainmore information about the kidsand their learning.

Judy Snider, teacher,Filer, Idaho

Teachers are encouraged to choose thestrategies from the following sectionsthat seem to meet their needs and inter-ests. They may want to select one or twomethods to investigate and implement(See "Resources" section). As always, eachteacher will need to evaluate the activi-ties and adjust them to fit her studentsand classroom.

Concept maps. Students create con-cept maps to demonstrate their reason-ing and understanding (Stiggins, 1997).Ideas are placed in a diagram and linkedby lines and words that indicate relation-ships between the concepts (see Figures 1and 2). Other terms for this strategyinclude mental mapping, concept web-bing, and clustering.

Concept maps can be "windows into theminds" of learners, providing a richerview of students' knowledge than tests(Dana, Lorsbach, Hook, & Briscoe, 1992).Concept maps help students organizeand represent concepts in a meaningfulway. They are also valuable because theyare a visual tool for depicting ideas andconnections.

Teachers can use concept maps in sever-al different ways. Students can createtheir own maps individually, which canbe useful for identifying individual

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needs and learning styles and for moni-toring each student's understanding.

Concept mapping can be a small groupactivity with students collaborating andthen discussing and comparing howthey designed their diagrams. Thisapproach is useful for determiningthemes and shared misunderstandings.It gives students a chance to sort outtheir ideas and clarify their thinkingtogether, and it is also an opportunity forpeer teaching.

Another approach to concept mapping isas a whole class-activity. Students pro-vide and discuss ideas and the teacherfills in the map. This process is especial-ly useful with students whose writingabilities are not yet well developed.Teachers can use this activity to identi-fy students' questions and areas of inter-est, a good starting point for a new unitor an inquiry activity.

With modifications, concept maps canbe appropriate at all grade levels. Mathe-matics teacher Bobbye Hoffman Bartelssuggests several activities with varyinglevels of difficulty. Teachers can givestudents a list of concepts and a map tofill in with the connections and linkingwords already provided. For a more diffi-cult task, students create their own mapsfrom a list of concepts, determining theconnections and the linking words forthemselves. Even more challenging is atask in which students generate theirown lists of concepts and create theirown map (Bartels, 1995).

Teachers can use concept maps as anongoing assessment of students' learn-ing. They allow teachers and students toexchange ideas about why a linkage isvalid or invalid, and to identify linksthat are missing. The maps help teachersidentify misunderstandings about con-

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What does this student's map tell you about his understandingof the "food chain?"

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Figure 1Reproduced with permissionfrom Dylan King.

cepts and the connections between ideas.Teachers can then address students'incorrect conclusions and identify areasfor new learning.

At the beginning of a unit, teachers canuse concept maps to determine waysthat they can connect material to stu-dents' prior knowledge and directlyaddress their misconceptions (Novak &Gowin, 1984). In the middle of a unit,concept maps can be used to determineareas that may need additional empha-sis, reteaching, or a different approach.Having students complete maps at thebeginning and the end of a unit pro-vides documentation of their growth.

Writing activities. Writing activitiesprovide teachers with a variety of infor-mation to guide their instruction. Stu-dents can express their attitudes and

feelings, as well as identify areas theyare having difficulty with or particular-ly enjoy. Teachers can use writingassignments to examine their students'thinking processes and conceptualunderstanding (Carter, Ogle & Royer,1993; Kulm, 1994).

Writing about mathematics and sciencerequires students to focus on and inter-nalize important ideas (Miller, 1991) .

Therefore, writing tasks are a way todetermine when students have under-stood a concept. In addition, the processof writing may help students come to abetter understanding of a topic or idea.Teachers may want to extend theseactivities by having students read andrespond to each other's writing.

What insights can a teacher gain by examining this concept map?

Figure 2Reproduced with permission from Mathematics Teaching in the Middle School ("Promoting Mathemat-ics Connections with Concept Mapping," by Bobbye Hoffman Bartels), copyright 1995 by the NationalCouncil of Teachers of Mathematics.

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The thing that struck me themost about using writingassessments was how much

students clarify the concept whenthey write.

Judy Vose, teacher,Ferndale, Washington

Teachers can incorporate writing intomathematics and science in a variety ofways. Journals and notebooks can be adaily or weekly part of class or can beassigned as homework. Individual writ-ing assignments can be used as follow-ups to an activity or a cooperative learn-ing experience.

Journal writing can be free-form or theteacher can provide specific questions orprompts. Teachers might also ask stu-dents to keep a notebook for an extendedproject or investigation, documentingtheir activities. Students should beencouraged to write thoughtfully todemonstrate their understanding of theactivities and concepts. The studentsshould also raise questions, identify prob-lems or concerns, and propose solutions.Notebooks can include an element ofself-assessment, allowing students toreflect and evaluate their progress (Cuoz-zo, 1996).

math journals are very effec-tive assessments of studentlearning and are helpful to

the teacher in establishing the paceof instruction. At the end of the peri-od I ask students to explain a con-cept or give them a problem to solveand then have them justify theirsolutions in their journal. It's like amath diary where students can keeptrack of their own progress.

Judy Snider, teacher,Filer, Idaho

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Journals can be used to uncover miscon-ceptions or areas of weakness that teach-ers need to address. It is important forteachers to be able to determine if stu-dents are merely manipulating symbolsand following rules without really under-standing them (Miller, 1991). Journalsprovide information about areas of diffi-culty, helping teachers identify studentswho are having similar problems in orderto adjust their plans according to stu-dent needs (Potter, 1996).

Writing activities give students who arereticent about speaking in class an oppor-tunity to communicate that is more com-fortable for them and therefore moreeffective (Miller, 1991). Journal writingallows students to express their anxietiesabout a topic and explain problems theyare having.

Although monitoring student journalsdoes take time, journals can be a veryefficient way for teachers and studentsto interact and communicate with oneanother. They are a form of indirectpersonal attention. Teachers can come toknow their students better as people andas learners, identifying their needs andinterests. Teachers who are short on timemight respond indepth to several stu-dents per week on a rotating basis. Inthis case, it is important for the studentsto know that their writing is valued andthat the teacher will read their journals,even though he may not respond inwriting every week.

Performance assessment. Perfor-mance assessments typically focus onthe process of solving problems or com-pleting complex tasks. The emphasis ison what students can do, not just whatthey know. Performance assessmentsallow students to show how they reachtheir solutions, explain their answers,and demonstrate their ability to synthe-

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boo cwm off

emndudik@di aer-ncoiAs the importance of classroomassessments increases, andthe heavy reliance on multiple-

choice standardized testing lessens, itis helpful to understand how and whythe practice of large-scale testingbegan. In his book, Student-CenteredClassroom Assessment (1997), RichardJ. Stiggins identifies a period in Ameri-can history that shaped the philosophyof testing that has prevailed in theUnited States throughout most of the20th century. After World War I, immi-grants flooded into the United States.As Americans, we wished for a commonculture in which we all spoke the samelanguage and shared a national expe-rience. We believed that schools pro-vided the best means for assimilatingnewcomers into American society, sowe created a standard curriculum andmade school attendance compulsory.

Students in unparalleled numbersshowed up at school doorsteps, andeducators scrambled to devise a wayto educate them as efficiently andeconomically as possible. The "assem-bly line school" was created in whichstudents moved annually from onelevel to the next. Over time, some stu-dents fell behind, creating a growingachievement gap. This practice con-tributed to the sorting of young peopleinto social and economic segments.

This principle of sorting students wassolidified with the invention of a newkind of achievement test: the objective-ly scored paper-and-pencil test thatwas used to separate students based

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on their test score. Because it wasthought to eliminate teacher bias andcould be mass produced, adminis-tered, and scored efficiently, the testwas believed to be "scientific." Thus,the realm of assessment was left toscientists or statisticians, and not toteachers.

[Editor's note: This reliance on stan-dardized testing to sort students rest-ed on an assumption that achieve-ment was based on a student's abilityand not on a student's effort. One ofthe most valuable attributes of class-room assessment is that it allows

1?

teachers to understand their students'learning processes, including both theconcepts and misconceptions thatunderlie students' thinking.]

In the 1960s, states began passinglegislation that held schools account-able for raising student achievement(Rothman, 1995). Educators turned tostandardized tests as a source of rela-tively reliable data on which to evalu-ate student achievement. Though pub-lishers indicated in their test guidesthat the tests were intended tosupplement teachers' classroomassessments, standardized testsbecame the principal measure ofeducational excellence for decades.

Today, most people believe that aschool's mission should be to ensurethat students attain core competen-cies, rather than sorting them. Schoolsmust ensure that students becomecompetent in those skills that willenable them to thrive and to contributeto society.

Research in cognitive psychology hasalso influenced educators' search foralternative testing methods. Accordingto research, learning is not linear butadvances in many directions at thesame time and at an uneven pace(Dietel, Herman, & Knuth, 1991). To bea competent thinker or problem solver,people need more than the simpleacquisition of knowledge. They needthe ability to use skills and strategies,as well as the understanding of whenand how to apply them.

Today, many believe that classroomteachers can provide some of the mostaccurate and appropriate measures oftheir students' abilities. Large-scale

i.

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standardized tests will continue to playan important role in assessment.Classroom assessment and alternativeformats will contribute additional infor-mation about what students know andare able to do. Finally, assessment toinform instruction is another powerfultool for teachers to use to guide theirteaching and improve student learning(Stiggins, 1997; Herman, Aschbacher,& Winters, 1992; Mathematical Sci-ences Education Board, 1993).

(Unless otherwise noted, text is adapt-ed with permission from Stiggins, R.(1997). Student-Centered ClassroomAssessment (2nd Ed.). Upper SaddleRiver, NJ: Prentice-Hall.)

t S

size. This assessment strategy providesteachers with information about stu-dents' thinking and reasoning (Parke &Lane, 1996).

Performance assessments can provideinformation that is more instructionallyrelevant than paper-and-pencil tests.Teachers gain a more complete pictureof students' understandings and abili-ties. This in turn leads to better decisionsabout student misconceptions and errors,and provides better assessment of theinstructional process (Stenmark, 1991).

In order to understand how to help stu-dents improve their work, teachers needinformation on the processes that stu-dents use. It is impossible to determinewhat elements of a teacher's instructionlead to which student results. However,teachers can use performance assess-ments to develop hypotheses about howtheir students go about creating an ade-quate or superior product or performance(Herman, Aschbacher, & Winters, 1992).Using this information, they can modifyor develop instructional practices tofacilitate growth among all students.

Teachers obtain information on theprocesses that students use by observingthem as they work, by interviewingthem about their work, and by examin-ing products that students produce(Stenmark, 1991). Paper-and-pencil tasksthat require students to show their workor describe their procedures will alsogive teachers insights into students'problem-solving tactics.

Teachers can get valuable informationabout how to help students improve byanalyzing how students complete tasksand looking for patterns related to out-comes. Did successful students use adifferent approach than less successfulstudents? Were the less successful per-

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formers hindered by misconceptionsand how might they have developedthese misconceptions? Where in theprocess did students run into difficulty?What kinds of errors did they make?Teachers can use this important infor-mation to plan future lessons and activi-ties (Herman, Aschbacher, & Winters,1992).

Interviews and conferences.Interviews help teachers identify whatstudents have learned and what theyhave yet to learn. Whether formal orinformal, they provide students withpersonal attention and an avenue fortwo-way communication. Students candescribe what is and is not working forthem (Spandel & Stiggins, 1990). Inter-views also send the message to studentsthat their thinking is valued by theteacher (Huinker, 1993).

During an interview, teachers can askstudents directly about their comfortlevel, needs, and interests. Interviews arean excellent way for teachers and stu-dents to gain an understanding of how

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to work together most effectively (Stig-gins, 1997). At the beginning of a unit,teachers can use interviews to help iden-tify, select, and organize the content andactivities. At the midpoint or end of aunit, interviews provide feedback andhelp teachers determine if they havesuccessfully fostered student understand-ings and abilities (Novak & Gowin, 1984).

2- think that a teacher will veryquickly learn that one form ofinstruction does not fit all. If

you use your assessment wisely, itcan become one of the many strate-gies that you can use to provide anopportunity for students to beengaged in meaningful thoughtprocesses related to curriculum, con-tent, and skills.

Richard Petersen, teacher,Beaverton, Oregon

In order to conduct interviews, teacherscan set up a formal time, calling a stu-dent aside as the class is involved inother activities. Or the interviews can beinformal, asking a student or groupsome specific questions as they work.The questions should draw the studentsinto thinking out loud, explaining howthey arrived at solutions or what conclu-sions they can make based on collecteddata and observations (Huinker, 1993).

It is important for students to feel com-fortable with the interview process. Stu-dents should understand the objective ofthe interviews and should be aware thatthe teacher will be taking notes. Stu-dents will accept interviews as unobtru-sive, routine classroom experiences ifthey are conducted regularly (Kulm,1994). Teachers can write down a few keyideas and observations as the studentspeaks and then expand on their notesimmediately after the session is over. For

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more accuracy, a tape recorder or videocamera can be used.

Although teachers will want to establisha list of questions in advance, interviewsneed not be uniform for all. Teachers donot have to talk about the same thingswith all students. Teachers will want tocustomize their questions based on howa student responds. This means that theycan gain information not normallyavailable from a less flexible strategy(Moon & Schulman, 1995). It is also notnecessary to interview all students aboutthe same lesson or during the same unit.The sessions can be spread out over thecourse of a grading period or the school

20

year. Teachers can also use focus-grouptechniques and interview three or fourstudents together, rather than individu-ally (Ku lm, 1994).

have to keep reminding myself,'Be realistic here: Just work onthese three or four kids today,

and do a good job with them. Thenyou can get the next three or fourtomorrow."

Judy Snider, teacher,Filer, Idaho

Interviews can be better sources ofinformation than tests for a number ofinstructional purposes. They are betterfor determining students' reasoning andlevel of understanding; for diagnosingtheir misconceptions and missed connec-tions; for identifying areas of strength;for discovering students' attitudes towardthe subject; and for assessing their abili-ty to communicate verbally about math-ematics and science (Huinker, 1993; Moon& Schulman, 1995). Teachers can useinterviews to respond directly to

16

students' misconceptions and errors(Thompson & Briars, 1989).

Interviews provide an opportunity forstudents to think at a high cognitivelevel. It is suggested that teachers begin aquestioning sequence with general ques-tions and proceed to increasingly specificquestions. It is important to give studentsenough time to think through theiranswers, to reconsider them, and torespond to additional probes (Kulm, 1994).

DeAnn Huinker (1993) of the Universityof Wisconsin, Madison, suggests thatteachers follow up students' responseswith probing questions to clarify whatthey said or did. However, she empha-sizes that teachers should do very littletalking during the interview. They willneed to resist the urge to teach, to givestudents answers or suggestions, or topose leading questions.

In her book, Mathematics Assessment:Myths, Models, Good Questions, and Prac-tical Suggestions (1991), Jean Kerr Sten-mark provides an extensive list of possi-ble interview questions. The questionsare formulated to provide specific infor-mation about student abilities such asapproaches and strategies (What stepsdid you take?), hypotheses (What do youpredict will happen?), communication(How would you explain what you knowright now?), flexibility (Have you triedmaking a guess?), and examining results(How would your method work withother problems?).

Conferences are an opportunity for stu-dents to present their work and to gainfirsthand knowledge about how theirwork is assessed. Any disagreementsbetween the student's self-assessmentand his or her formal grade can be clari-fied. Conferences provide importantinformation for instruction because they

set the course for future improvementand growth. Teachers can provide stu-dents with strategies that will improvetheir performance and help them togenerate goals and next steps (Darling-Hammond, Ancess, & Falk, 1995).

Debriefing. In debriefing activities,teachers ask students to report extendedproblem-solving activities or investiga-tions. The students prepare and presentreports and then respond to questionsfrom the teacher or classmates. Theseactivities are similar to the processesthat mathematicians and scientists usein working together. Debriefings involvemore than just reporting answers: Stu-dents are required to justify their con-clusions and talk about their processes,mistakes or wrong turns, areas of diffi-culty, and remaining questions.

This information about students' trial-and-error process can provide importantinformation for guiding instruction(Raizen, et al., 1989). "Debriefings enableteachers to see what students know, tounderstand how they got to know whatthey know, and to get to know the stu-dents as individuals and learners" (Dar-ling-Hammond, Ancess, & Falk, 1995).

The feedback I got from myclassroom assessments wasthat I needed to readjust my

teaching in some areas. That is valu-able information, but it can be frus-trating, too, because I never do any-thing the same way twice anymore._Pm constantly getting new informa-tion, so I'm constantly adjusting andmonitoring my teaching methods.

Judy Vose, teacher,Ferndale, Washington

Debriefings are appropriate as whole-class activities, or teachers can work with

students individually or in small groups.The sessions can take place in the middleof an activity, allowing teachers to checkprogress and redirect the students if nec-essary. A debriefing may also identifyneeds for additional background infor-mation or skill development.

5 4 2

111116L,- "

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Debriefings are usually more formalthan interviews because students preparefor them in advance. However, teacherscan also conduct debriefings as the stu-dents work, a technique similar to inter-viewing. The teacher circulates throughthe classroom watching students andasking them questions about what theyare doing and why: What did you do toget to this point? Why did you do that?What are you planning to do next? (Her-man, Aschbacher, & Winters, 1992).

Debriefings help ensure that activitiesprovide students with opportunities forhigh-quality learning experiences ratherthan merely a chance to apply roteskills. The students are called upon to

reflect on what they have learned, aswell as how they learned it (Darling-Hammond, Ancess, and Falk, 1995).Debriefings require students to putmathematics and science concepts andprocesses into their own words. They canprovide evidence of higher-level think-ing skills and depth of understanding.

Observations. Teachers can use theinformation they obtain from observa-tions to judge students' progress, as wellas the success of their instructionalapproaches. Students' language andbehaviors provide information abouttheir interests and their thinking. Obser-vations are also useful for diagnosingdifficulties, allowing teachers to designlearning experiences that address prob-lems (Moon & Schulman, 1995).

Observing students is a natural part ofteaching, but teachers may not have asystem in place for documenting theirobservations. There are a variety of effec-tive methods to accomplish this task:rating forms, narrative descriptions,checklists, and logs. It is recommended

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that teachers try a variety of formats,adapting the preferred one to their needs(Chittenden, 1991). Teachers can findexamples of a variety of tools in the pub-lications listed in the "Resources" section,which begins on page 23.

Teachers will want to have specific ideasabout what they are looking for in theirobservations: levels of understanding,skills and abilities, or types of thinking.Small cooperative groups can be observedas they are engaged in a problem-solvingactivity or investigation. The teachermoves from group to group as the stu-dents work and listens to their conversa-tions, determining what they do and donot understand (Johnson & Johnson,1990).

This method will not be effective to usewith every student every day. Moon andSchulman (1995) suggest that teachersfocus on five or six students at a timewhen opportunities arise. Teachers canthen rotate through the whole class overthe course of a unit or grading period.Depending on what abilities or qualitiesare being assessed, teachers may be ableto observe students during differentactivities.

Any good teacher is going tointegrate assessment withinstruction. Making informal

observations while students areactually working can tell the tea-cher if they are doing the work cor-rectly and, even more importantly, itshows her how they are doing it. Themore she studies her students inaction, the more she will learnabout their growing understandingof the concepts involved.

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Sue Pack, teacher,Twin Falls, Idaho

Less formally, teachers may also want torecord anecdotes and memorable inter-actions with or between students as theyhappen. In listening to students talkwith each other, teachers gain informa-tion about how students make sense ofnew information and ideas. They canidentify patterns in students' learningpreferences that may otherwise go unno-ticed (Moon & Schulman, 1995). Teacherscan then use this information for ideason how to present material.

As the kids arc working on agroup activity, they're inter-acting with each other, so I

listen to what they're saying and Itake notes. If I wonder what a stu-dent understands or why he didsomething, then I ask a question, butmuch of the time I'm just listeningto what they're saying and learningfrom that.

Judy Snider, teacher,Filer, Idaho

Teachers can also focus their observa-tions on finding out more about theirstudents, using an inquiry approachrather than just checking on studentprogress. Observations allow teachers toexplore the needs, interests, and relation-ships of their students, as well as gaininsights into how individuals learn(Chittenden, 1991).

Portfolios. Portfolios are an effectivetool for collecting a variety of studentwork, including the products from mul-tiple assessment strategies. By theirnature, they will include different kindsof indicators of what students know andcan do, as well as how they think. As anoverall picture of learning, portfoliosdocument conceptual understanding,problem solving, reasoning, and commu-nication abilities. The evidence from

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portfolios is especially rich because itgives an overview of students' progressover an extended period of time (Dar-ling-Hammond, 1996).

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_ITn reading what they have writ-ten and chosen to put in theirportfolios, it gives me informa-

tion not just on what they like, butwhat they've learned wellwhatthey've conquered that they didn'tknow before.

Judy prose, teacher,Ferndale, Washington

Portfolios also help teachers to knowtheir students better. When portfoliosinclude open-ended tasks and self-assess-ments, they become a means of individ-ual expression, and teachers learn moreabout their students and their preferredlearning styles (Moon & Schulman, 1995).More generally, portfolios are a way forteachers to construct their own knowl-edge of children, how they learn, and

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how to evaluate that learning (Herbert,1992).

The process of deciding what to includein portfolios also informs instruction.Teachers must clarify what is valuablefor students to learn and what activitiesare most worthwhile (Collins, 1992; Moon& Schulman, 1995) and therefore mustreflect on their teaching practice.

Portfolios are valuable as a way for teach-ers to share information with each other.At the beginning of the year, teacherscan examine the portfolios of their newstudents to inform their planning process.The portfolios can provide informationabout students' areas of strength andweakness, interests, and attitudes. Theyare useful for planning activities andthemes for the year, and may help teach-ers estimate how much time they willneed to spend on certain units.

Student self-assessment. Manyof the strategies outlined in this publica-tion (journals, interviews, debriefings,and portfolios) incorporate an elementof self-assessment for students. Self-assessment allows students to reflect ontheir learning experiences. Through thisprocess, they become more conscious oftheir own learning and gain an under-standing of their own strengths andweaknesses. They become active partici-pants in evaluation (Moon & Schulman,1995; Zessoules & Gardner, 1991).

Students' self-assessments help teachersmake sense of student efforts andachievements and are an essential partof guiding instruction. Self-assessmentsimprove communication because stu-dents become aware of areas in whichthey are having difficulties and thus areable to articulate their needs to theteacher.

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Self-assessment activities are also anopportunity for teachers to gain knowl-edge of student attitudes. This enablesteachers to address the dispositions oftheir students through their interactionsand instruction. They can also help stu-dents see how their attitudes affect theirperformances (Ku lm, 1994).

When students reflect on tasks that theyenjoyed and tasks that they found diffi-cult it can help teachers understandstudent learning preferences. Thus,teachers can design activities thataddress the students' preferences, as wellas tasks to build their confidence andcomfort level in areas where they havemore difficulty.

Teachers can ask students to discuss orwrite about their experiences as a clos-ing activity: What did you learn today?What were the main points of today'slesson? What are you still confusedabout? This provides teachers with feed-back on the effectiveness of the activi-ties and their instruction. They can alsodetermine what points they need to .

emphasize and address in upcominglessons (Kenney & Silver, 1993).

Student assessment of instruc-tion. Another way for students to pro-vide teachers with direct information isthrough student assessment of instruc-tion. Student input provides teacherswith additional evidence in evaluatingtheir effectiveness, identifying strengths,and recognizing areas for improvement.Students can suggest how the teachercan help them learn and indicate whatactivities or instructional strategies havebeen most effective (Roscoe, 1992).

my students give me feedbackon my teaching. For exam-ple, I was talking with some

students who thought math wasreally hard this year. I asked themwhat made it hard, and they saidthe most difficult thing had beenthe vocabulary because it was allnew. That is really helpful for me toknow. I thought they would be morefamiliar with it. Sometimes youmake assumptions and if the stu-dents don't say anything, you don'tknow the real cause of the difficul-ties. I found out that it was thevocabulary and not the concept thatthe students didn't understand.That was really helpful to me.

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26

Judy Snider, teacher,Filer, Idaho

Students' assessment of instruction pro-vides much of the same informationthat students provide in self-assessments,and can result in the same benefits. Inaddition, students are empowered andbecome more actively engaged whenthey are involved in determining thedirection and atmosphere of the class.

As a closing activity for a lesson or unit,teachers can ask students to identifywhat they enjoyed most or least, whatthey liked and didn't like, and why. Stu-dents can explain what activities helpedto build their understanding and whichones were least useful. Teachers can alsoask students about their suggestions forfuture learning activities.

In addition, teachers can ask students forcritiques of their instruction. Some possi-ble questions include: What are examplesof things I do or say that make it easier ormore interesting for you to learn? Whatare things that make it harder or less

interesting? What might make me a bet-ter teacher for you? (Cross & Angelo,1988).

These activities can be done for individ-ual lessons and units, and at the end ofgrading periods. Students will becomemore adept and thoughtful in theiranswers if this type of assessment is aregular part of class. Teachers must alsodecide if they want students to producetheir evaluations anonymously, individ-ually, in small groups, or as a class.

This type of assessment requires anatmosphere of trust between teacher andstudents. The teacher must be open tothe students' feedback and willing tomake changes. The students must feelcomfortable about honestly expressingtheir opinions.

ConclusionWhen assessment is used to guideinstruction, it becomes anotheropportunity for learning, rather

than an interruption. Drawing on infor-mation from a variety of appropriatesources, teachers make decisions aboutinstruction as learning proceeds. Thiscomplex process calls for advance plan-ning and an approach that includesinquiry and reflection. The followingpages contain a list of resources thatteachers can use to help them imple-ment assessment to inform theirinstruction.

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Resources &Bibliography

Os

Note: All books listed in this section areavailable through NWREL's Mathemat-ics and Science Education Center lendinglibrary.

Resources forfurther readingDarling-Hammond, L., Ancess, J., & Falk,B. (1995). Authentic assessment in action:Studies of schools and students at work.New York, NY: Teachers College Press.

Case studies depict how five schoolshave developed "authentic" perfor-mance-based assessments and howthis has influenced teaching andlearning experiences.

Herman, J.L., Aschbacher, P.R., & Winters,L. (1992). A practical guide to alternativeassessment. Alexandria, VA: Associationfor Supervision and Curriculum Devel-opment.

This guide offers ideas on the creationand use of alternative assessments,with a process model that links assess-ment to curriculum and instruction.

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Huinker, D.M. (1993). Interviews: A win-dow to students' conceptual knowledgeof the operations. In N.L. Webb & A.F.Coxford (Eds.), Assessment in the mathe-matics classroom: 1993 yearbook (pp. 80-86). Reston, VA: National Council ofTeachers of Mathematics.

A collection of articles addressingassessment techniques, managingassessment, and issues pertinent toclassroom assessment.

Kulm, G. (1994). Mathematics assessment:What works in the classroom. San Fran-cisco, CA: Jossey-Bass.

This book is designed to help teachersplan and implement alternativeassessment in the classroom.

Moon, J., & Schulman, L. (1995). Findingthe connections: Linking assessment,instruction, and curriculum in elemen-tary mathematics. Portsmouth, NH:Heinemann.

This book provides a model for inte-grating assessment with instructionand guided opportunities to practiceand reflect on the assessment process.

National Council of Teachers of Mathe-matics. (1995). Assessment standards forschool mathematics. Reston, VA: Author.

Four purposes of assessment are dis-cussed, including making instructiondecisions. Vignettes and student worksamples provide useful examples andillustrations of the assessment stan-dards in practice.

National Research Council. (1996).National science education standards.Washington, DC: National Academy Press.

The standards identify essential char-acteristics of exemplary assessmenttasks, practices, and policies.

Raizen, S.A., Baron, J.B., Champagne, A.B.,Haertel, E., Mullis, I.V.S., & Oakes, J. (1989).Assessment in elementary school scienceeducation. Washington, DC: NationalCenter for Improving Science Education.

This report addresses issues in assess-ment: assessment of student learning,assessment of programs, and improve-ment of assessment.

Regional Educational Laboratory Net-work Program. (1994). Tool kit for profes-sional developers: Alternative assessment.Portland, OR: Northwest Regional Educa-tional Laboratory.

This collection of professional devel-opment activities and support materi-als focuses on alternative assessment.

Romberg, T.A. (Ed.). (1995). Reform inschool mathematics and authenticassessment. Albany, NY: State Universityof New York Press.

This book proposes models that giveteachers a wealth of nontraditionalassessment strategies and concreteways to obtain measures of bothgroup and individual growth.

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Stenmark, J.K. (1991). Mathematics assess-ment: Myths, models, good questions, andpractical suggestions. Reston, VA: Nation-al Council of Teachers of Mathematics.

This resource is a collection of exam-ples of various assessment techniquesthat focus on student thinking.

Stiggins, R. (1997). Student-centered class-room assessment (2nd Ed.). Upper SaddleRiver, NJ: Prentice-Hall.

This book includes step-by-step meth-ods for developing effective assess-ments, integrating assessment intothe teaching/learning process, andinvolving students productively inthe assessment process.

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OrganizationsAmerican Association for theAdvancement of Science (AAAS)1200 New York Avenue, N.W.Washington, DC 20005(202) 326-6400http://www.aaas.org/

A nonprofit, professional society thatprovides a variety of programs, publica-tions, and resources, including informa-tion on alternative assessment and cur-riculum standards in science.

Assessment Training Institute50 S.W. Second Avenue, Suite 300Portland, OR 97204-2636(503) 228-3060(800) 480-3060Fax: (503) 228-3014E-mail: ati@assessmentinst.com

The institute offers guidance in soundassessment practices through consulta-tion, regional seminars, national confer-ences, and print and video trainingmaterials.

Association for Supervision andCurriculum Development (ASCD)1250 N. Pitt StreetAlexandria, VA 22314(703) 549-9110(800) 933-2723http: / /wwwascd.org/

ASCD coordinates, develops, and publish-es print and video resources related toassessment.

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The Center on Learning, Assessment,and School Structure (CLASS)65 S. Main Street, Building BPennington, NJ 08534(609) 730-1199Fax: (609) 730-1488E-mail: classnj@aol.comhttp://www.classnj.org/

CLASS helps educators build schoolsaround students' needs. The center pro-vides consultations, professional develop-ment activities, and a variety of resourceson student assessment and curriculumdesign.

Eisenhower National Clearinghousefor Mathematics and ScienceEducationThe Ohio State University1929 Kenny RoadColumbus, OH 43210-1079(614) 292-7784(800) 621-5785E-mail: info@enc.orghttp://www.enc.org/

The clearinghouse is a national informa-tion source for K-12 mathematics andscience teachers, providing curriculumresources, a monthly list of outstandingInternet sites, thousands of classroom-ready lessons and activities, and links toother Web sites.

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EXEMPLARS: A Teacher's SolutionRR1 Box 7390Underhill, VT 05489(800) 450-4050http://www.exemplars.com/index.html

Exemplars assists teachers in imple-menting authentic assessment andmathematics and science standards intheir classrooms.

Lawrence Hall of ScienceUniversity of CaliforniaBerkeley, CA 94720(510) 642-4193

This center for teacher education,research, and curriculum developmentpublishes materials and assessmentinstruments in science.

National Council for Teachers ofMathematics (NCTM)1906 Association DriveReston, VA 20191-1593(703) 620-9840(800) 235-7566Fax: (703) 476-2970http: / /wwwnctm.org/

A nonprofit professional associationdedicated to the improvement of mathe-matics education for all students. NCTMregularly publishes information onalternative assessment and curriculumresources.

National Science TeachersAssociation (NSTA)1840 Wilson BoulevardArlington, VA 22201-3000(703) 243-7100Fax: (703) 243-7177http://www.nsta.org/

A professional organization committedto promoting excellence and innovationin science teaching and learning for all,NSTA publishes journals and books, andconducts conventions.

Northwest Regional EducationalLaboratory (NWREL)101 S.W. Main Street, Suite 500Portland, OR 97204-3297(503) 275-9500

The Northwest Regional EducationalLaboratory provides leadership, exper-tise, and services to education, govern-ment and community agencies, andbusiness and labor, primarily in thestates of Alaska, Idaho, Montana, Oregon,and Washington.

Assessment & Accountability ProgramJudy Arter, Unit Manager(503) 275-9562E-mail: arterj@nwrel.orghttp://www.nwrel.org/eval/

The Assessment & Accountability Pro-gram collects, reviews, and offers instru-ments for alternative assessment in sci-ence and mathematics. Its database ofalternative assessment instruments,resources, procedures, and annotatedbibliographies is offered online.

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3 2

Mathematics and ScienceEducation CenterKit Peixotto, Director(503) 275-9594E-mail: peixottkOnwrel.orghttp://www.nwrel.org/psc/same/

The center provides resources and ser-vices in support of effective curriculum,instruction, and assessment. A lendinglibrary of books, videos, and other mate-rials on a variety of topics, includinginquiry-based teaching, equity issues,education reform, standards and assess-ment, and effective instructional prac-tices complements other products andservices.

Science and MathematicsConsortium for Northwest Schools(SMCNWS)171 N.E. 102ndPortland, OR 97220-4169(503) 760-2346http://www.col-ed.org/smcnws

One of 10 regional Eisenhower consortia,the SMCNWS disseminates promisingprograms, practices, and materials, andprovides technical assistance and train-ing in support of state and local initia-tives for quality science and mathemat-ics education. For a list of assessmentresources, see: http://www.col-ed.org/smcnws/assessment.html.

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Online resourcesClassroom CompassAssessmentA Window to Learninghttp://diogenes.sedl.org/scimath/compass/v02n02/welcome.html

Southwest Educational DevelopmentLaboratory's online newsletter includesexamples of activities that illustrate eachissue's theme. The spring 1996 issueexamines assessment as an integral partof the learning cycle. A resource listcompletes the issue.

ERIC Clearinghouse on Assessmentand Evaluationhttp://ericae2.educ.cua.edu/main.htm

This site contains links to other Websites, a listsery on assessment and evalua-tion, and allows searching of the ERICdatabase and three assessment instru-ment databases.

Math Forum Assessment inMathematics Teachinghttp://forum.swarthmore.edu/mathed/assessment.html

The forum supports teachers, students,and others with an interest in mathe-matics. The site provides extensive linksto books, articles, and other Web sitesrelated to mathematics assessment.

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Pathways to School Improvementhttp://www.ncrel.org/sdrs/pathwayg.htm

The North Central Regional EducationalLaboratory produces "Critical Issues"sections that provide practical, action-oriented summaries of best practices,research, descriptions of schools thathave successfully addressed criticalissues, and lists of materials to supportchange. For "Integrating Assessment andInstruction in Ways that Support Learn-ing," see Critical Issues in Assessment athttp://www.ncrel.org/sdrs/areas/asOcont.htm

The Regional Alliance forMathematics and Science EducationReform Hub Assessmenthttp://ra.terc.edu/hub/regional_networks/cia/assessment.html

The Regional Alliance's assessment pageprovides links to resources for alterna-tive assessment.

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Resources forspecific strategies

Concept maps

The Concept Mapping Home Pagehttp://www.to.utwente.nl/user/ism/lanzing/cm_home.htm

This site explains how concept mappingcan be used for many purposes, includ-ing assessment. Illustrations, conceptmapping software, additional links, andnumerous references are provided.

Problem Solving: Concept Mapshttp://cotf.edu/ETE/concept.html

The Exploring the Environment (ETE)site outlines the steps to constructing aconcept map, and provides examples anda list of other resources.

Writing activities

Countryman, J. (1992). Writing to learnmathematics: Strategies that work.Portsmouth, NH: Heinemann.

This book describes writing activitiesteachers can use to enhance the learn-ing and teaching of mathematics.

Saul, W, Reardon, J., Schmidt, A., Pearce, C.,Blackwood, D., & Bird, M.D. (1993). Scienceworkshop: A whole language approach.Portsmouth, NH: Heinemann.

Dana Blackwood's chapter, "ConnectingLanguage and Science Assessment,"covers a variety of assessment strate-gies and instruments.

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Scott, J. (Ed.). (1993). Science & languagelinks: Classroom implications. Ports-mouth, NH: Heinemann.

This book examines the links thatexist between science and languagelearning and teaching. The book alsoprovides teachers with suggestionsand ideas for using differenttechniques.

Performance assessment

Blum, R.E., & Arter, J.A. (Eds.). (1996).Handbook for student performanceassessment in an era of restructuring.Alexandria, VA: Association for Supervi-sion and Curriculum Development.

Section IV, 'Aligning Assessment withCurriculum and Instruction," presentspapers on what it means to integrateassessment and instruction.

McCain, R. (1997). Assessment practicesin mathematics: Outdated assessmenttools are simply not good enough. TheJournal of the New England League ofMiddle Schools, 9(4), 33-36.

The article explores various strategies,including interviews, observations,portfolios, performance assessment,self-assessment, and student writing.

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OERI Consumer Guide:Performance Assessmenthttp://inet.ed.gov/pubs/OR/ConsumerGuides/perfasse.html

This Consumer Guide is produced by theOffice of Educational Research andImprovement (OERI) of the U.S. Depart-ment of Education for teachers, parents,and others interested in current educa-tion themes.

Interviews & conferences

Corwin, R.B. (1996). Talking mathematics:Supporting children's voices. Portsmouth,NH: Heinemann.

This book includes materials to supportteachers in developing a culture ofinquiry and communication in theirclassrooms, including how talk caninform instruction and practical waysto encourage and support discussion.

Garland, C. (1988). Mathematics theirway: Summary newsletter. Saratoga, CA:Center for Innovation in Education.

This newsletter includes Teacher Ref-erence Cards which list materialsneeded for assessments, any prepara-tion necessary, suggested questions,procedures, and possible extensions.

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Observations

Baratta-Lorton, M. (1976). Mathematicstheir way: Black-line masters. Palo Alto,CA: Addison-Wesley.

This resource contains numerous"observation sheets," informal record-keeping devices used to documentchildren's progress.

Portfolios

Electronic Portfolios:A New Idea in Assessmenthttp://ericir.syr.edu/ithome/digests/portfolio.html

Anna Maria D. Lankes describes theelements of portfolios and how technolo-gy is helping with the creation andmanagement of this form of alternativeassessment.

NEA Professional Library. (1993). Studentportfolios. West Haven, CT: National Edu-cation Association.

This collection of articles discusseshow teachers changed their assess-ment practices by using student port-folios in their classrooms.

Resources addressingmultiple strategiesHein, G.E., & Price, S. (1994). Active assess-ment for active science: A guide for ele-mentary school teachers. Portsmouth,NH: Heinemann.

This resource encourages teachers touse a range of assessment approachesand describes specific methods.

Parker, R.E. (1993). Mathematical power:Lessons from a classroom. Portsmouth,NH: Heinemann.

The author describes methods for inte-grating the National Council of Teach-ers of Mathematics standards intoclassroom practice, including assess-ment, and addresses observations,learning logs, rubrics, and portfolios.

Rowan, T.E., & Bourne, B. (1994). Think-ing like mathematicians: Putting the K-4NCTM standards into practice. Ports-mouth, NH: Heinemann.

This book applies NCTM goals tomathematics instruction. Three spe-cific methods of informal assessmentare presented: anecdotal records, port-folios, and journals.

Tsuruda, G. (1994). Putting it together:Middle school math in transition.Portsmouth, NH: Heinemann.

The chapter on "Assessment Alterna-tives" presents writing and talking asthe core of alternative assessment.Student presentations, portfolios, anda variety of ways to record observa-tions of groups are discussed.

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36

BibliographyBartels, B.H. (1995). Promoting mathemat-

ics connections with concept map-ping. Mathematics Teaching in theMiddle School, 1(7), 542-549.

Carter, EL., Ogle, P.K., & Royer, L.B. (1993).Learning logs: What are they and howdo we use them? In N.L. Webb & A.F.Coxford (Eds.), Assessment in themathematics classroom (pp. 87-96).Reston, VA: National Council of Teach-ers of Mathematics.

Chittenden, E. (1991). Authentic assess-ment, evaluation, and documentationof student performance. In V. Perrone(Ed.), Expanding student assessment(pp. 22-31). Alexandria, VA: Associationfor Supervision and CurriculumDevelopment.

Collins, A. (1992). Portfolios for assessingstudent learning in science: A newname for a familiar idea? In G. Ku lm &S.M. Malcolm (Eds.), Science assessmentin the service of reform (pp. 291-300).Washington, DC: American Associationfor the Advancement of Science.

Cross, K.P. & Angelo, T.A. (1988). Class-room assessment techniques: A hand-book for faculty. Ann Arbor, MI:National Center for Research toImprove Postsecondary Teaching andLearning, University of Michigan.

Cuozzo, C.C. (1996). What do lepidopteristsdo? Educational Leadership, 54(4), 34-37.

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Dana, T.M., Lorsbach, A.W., Hook, K., &Briscoe, C. (1992). Students showingwhat they know: A look at alternativeassessment. In G. Ku 1m & S.M. Mal-colm (Eds.), Science assessment in theservice of reform (pp. 331-337). Wash-ington, DC: American Association forthe Advancement of Science.

Darling-Hammond, L., Ancess, J., & Falk,B. (1995). Authentic assessment inaction. New York, NY: Teachers CollegePress.

Darling-Hammond, L. (1996). Foreword:On assessment and accountability. InK. Jervis (Ed.), Eyes on the child: Threeportfolio stories (pp. ix-xi). New York,NY: Teachers College Press.

Dietel, R., Herman, J., & Knuth, R. (1991).What does research say about assess-ment? [Online]. Available:http://www.ncrel.org/sdrs/areas/stw_esys/4assess.htm

Herbert, E.A. (1992). Portfolios invitereflectionfrom students and staff.Educational Leadership, 49(8), 58-61.

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