Connecting IB to the Core: Mathematics Relationship Studies to Inform Curriculum Alignment

7/27/2019 Connecting IB to the Core: Mathematics Relationship Studies to Inform Curriculum Alignment

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International Baccalaureate Organization 2013nternational Baccalaureate | Baccalaurat International | Bachillerato Internacional

IB and the Common Core State StandardsRelationship studies: Resources to inorm curriculum alignment

Mathematics

standards


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What is an IB education?

IB and the Common Core State StandardRelationship studies: Resources to inorm curriculum alignme

Mathematic

standards


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Table o Contents

Foreword ..............................................................................................i

Introduction ........................................................................................iii

About the IB....................................................................................iii

About these resources ................................................................iii

The Primary Years Programme and the Common Core

State Standards or mathematics ................................................1

The Middle Years Programme and the Common Core

State Standards or mathematics ................................................13

The Diploma Programme and the Common Core State

Standards or mathematics............................................................23

The IB Career-related Certicate and the Common Career

Technical Core ....................................................................................33

IB programmes and the Common Core State Standards

Application to Students with Disabilities ....................................39

Appendices ..........................................................................................44

Bibliography ........................................................................................51

IB reerences ........................................................................................52

Common Core State Standards or mathematics

Published July 2013

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Common Core State Standards for mathematics

Foreword

Since 1968 the small group o international school edu-cators who ounded the International Baccalaureate(IB) have been analysing best practices in the ield oeducation rom around the world. They drew uponthese best practices in order to build what wouldbecome the IBs Diploma Programme (DP). Today,over one million IB students rom over 140 countriesare held to the s ame rigorous academic expectationsthat ormed the building blocks o the DP 45 years

ago. The IBs experience working lexibly within thediversity o national education systems and curricu-lums across a global platorm make it a senior states-man in the ield o broad, standards-based academicreorm movements such as the Common Core StateStandards initiative (CCSS).

The IB and the CCSS share many goals, the oremost owhich is their mutual emphasis on career and collegereadiness. An IB education not only holds students tothe highest academic standards but also incorporatesan understanding and appreciation o other culturesand points o view, and world language compe-tencyprecisely the sot skills in demand by the globaleconomy. IB students demonstrate a strong compe-tency in the context o global readiness and are, notsurprisingly, sought ater by colleges and universi-ties or their sot skills as well as their hard-earnedacademic achievements.

IB World Schools have an advantage when adoptingthe CCSS. IB standards were selected as one o iveinternational benchmarks against which to comparethe CCSS in an inluential study conducted by theEducational Policy Improvement Center (EPIC). TheCCSS represents a shit in teaching rom covering awide breadth o content to a greater ocus on deptho understanding and interdisciplinary approaches toteaching and learning. These very characteristics de-ine what makes an IB education so eective. The shitin thinking and practice that many IB schools made

on their journey to becomeIB World Schools are otenthe same shits schools willneed to make in transition-ing to the CCSS.

Our goal in undertaking these relationship studieto support IB educators in their eorts to align thcurriculum to the CCSS. We are conident that th

studies will provide a starting point to begin the iportant work o curriculum alignment in your owschools and serve as a touchstone to reassure you ttransitioning to the CCSS will be that much easier dto the hard work that you and your colleagues haalready done to meet the rigorous standards requito oer an IB education.

Although the CCSS initiative is unique to the UniStates, it will impact standards-based reorm moments everywhere. The IB contributes a long-respecvoice in the ield o international education, addinglobal dimension to the discussion around the CCThe IB will continue to draw upon school reorm tiatives around the world, such as the CCSS, to ensuthat it remains a leader in providing a pedagogiccurrent international education based on research abest practices.

As always, we welcome your ideas and want to heyour relections and eedback. All materials relato the IB and the CCSS will be posted and can accessed through a dedicated webpage on thepublic website: http://www.ibo.org/iba/commoncoAll eedback related to the CCSS can be sent to a mbox especially created to respond quickly to inqui([email protected]).

Warm regards

Drew Deutsch

Director, IB Americas

Artwork by: Eleazar Mendoza

Dwight D. Eisenhower High School

11th Grade


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Introduction

About the IB

The IB continuum o international education or 3 to19-year-olds is unique because o its academic andpersonal rigour. Teaching and learning in all IB pro-grammes the Primary Years Programme (PYP),the Middle Years Programme (MYP), the DiplomaProgramme (DP) and the IB Career-related Certiicate(IBCC)grows rom an understanding o educationthat celebrates the many ways people work togetherto construct meaning and make sense o the world.

An IB education is or the whole person, providing a

well-rounded experience anchored by values and out-comes described in the IB learner proile. IB learnersstrive to become inquirers, knowledgeable, thinkers,communicators, principled, open-minded, caring, risk-takers, balanced and relective. These attributes o inter-nationally minded people represent a broad range ohuman capacities and responsibilities that go beyondintellectual development and academic success.

The IBs student-centred philosophy, with its ocus onthe interplay between inquiry, action and relection,empowers students or a lietime o learning, both in-dependently and in collaboration with others. An IBeducation centres on learners, develops eective ap-proaches to teaching and learning, and explores sig-niicant content within global contexts.

IB World Schools undertake rigorous authorizationand evaluation processes to oer one or more IB pro-grammes. The IB Programme standards and practices is adocument that provides a set o criteria against whichboth the IB World School and the IB can evaluatesuccess in the implementation o the our programmes.This ound ation al docum ent or scho ols and the

IB ensures quality and idelity in the implementation oIB programmes.

About these resources

The IB re cognizes that the implemen tation o tCommon Core State Standards (CCSS) will have a sniicant impact on public schools in the US and inWorld Schools around the globe that ollow a US criculum. In order to support IB World Schools as tprepare or the CCSS, the IB commissioned studiesidentiy the broad relationships that exist between toverall expectations in the PYP mathematics scoand sequence, the MYP and DP aims and objectivor mathematics and the K12 CCSS or mathematic

The IB developed these studies in collaboration wIB educators, a hallmark o its relationship with its comunity. Educators with specialized knowledge ocurriculums and the CCSS or mathematics workclosely with IB academic sta to produce these sources or the PYP, MYP and DP.

The CCSS deine what students in mathematics shounderstand and be able to do by the end o eagrade. The PYP and MYP provide curriculum ramworks that are designed to meet the developmenneeds o students. These curriculum rameworks athe DP mathematics courses oer schools the lexiity to accommodate the demands o national or lorequirements or mathematics.

Studies were commissioned to educators with specized knowledge o IB curriculums and CCSS or maematics. The purpose o these studies is to provschools with a lexible resource to inorm their ocurriculum alignment. The studies employ the strture o the eight common core standards or maematical practice to highlight the broad relationswith teaching and learning about mathematics in t

PYP, MYP and DP. They provide a snapshot o the retionships and are not intended to be comprehensin nature.

The IB anticipates that these resources will evolve wurther implementation o the CCSS. IB educators no doubt discover other aspects o the relationsbetween teaching and learning in IB programmes athe CCSS as they relect upon their teaching and sdents learning.Artwork by: Alexandra Philco

FDR American School o Lima

12th Grade


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The Primary Years Programmeand the

Common Core State Standardsor mathematics


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The Primary Years Programme and the Common Core State Standardsor mathematics

The PYP is designed or students

3 to 12. It ocuses on the developm

the whole child as an inquirer, both

classroom and in the world outside

It is a ramework guided by six tra

ciplinary themes o global signi

explored using knowledge and

derived rom six subject areas, as w

approaches to learning with a po

emphasis on inquiry.

The design o the PYP is suic iently lexibl e to

modate the demands o national or local curric

schools develop their own programme o inquir

ollows thereore, that as a lexible and rigorou

lum ramework, the PYP oers teachers the oppo

develop learning experiences or students that demands set out by the CCSS.

The CCSS or mathematics do not dictate curri

teaching methods (NGA Center 2010: 5). The PY

inquiry-based pedagogy, provides an eective r

or teaching and learning the CCSS.



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Common Core State Standards for mathematicsPrimary Years Programme (PYP)4

The CCSS deine what students should understand and be able to do by the end o each grade and the CCSS

or mathematics place an emphasis on applying mathematics to the real world. Mathematical instruc-

tion in the CCSS includes both the proiciency in, and processes o, mathematics.

This ollowing study employs the structure o CCSS to relate the eight standards or mathematical

practice or kindergarten through grade ive to a speciic component o the PYP: the overall expect-

ations and learning outcomes o the PYP Mathematics scope and sequence. The purpose is to provide

schools with a resource to support their own curriculum alignment. The study demonstrates that the

curriculum ramework o the PYP supports the implementation o the CCSS in mathematics or kinder-

garten through grade ive.

Introductory observations

The CCSS are a shit in the direction o mathematics education. They move beyond traditional stand-

ards to a ocus on applying mathematics to real-lie situations. Students are no longer learning con-

tent as isolated acts, but rather as tools to solve a wide range o problems. This shit resonates withthe PYP Changes in mathematics practices (Appendix 2), which notes an increased emphasis on real-lie

problem solving using mathematics.

Both the PYP and the CCSS use strands o mathematics to structure learning progression. In the PYP

Mathematics scope and sequence the strands are: data handling, measurement, shape and space,

pattern and function and number (Appendix 1).

The strands are divided into our phases. Each phase urther identiies the ollowing stages students

typically ollow when learning mathematics: constructing meaning,transferring meaning into

symbols, and applying with understanding. The our phases orm a developmental learning

continuum detailing how students might move through the phases as they become more pro-

icient in mathematics. It is important to note that these phases are not to be identiied as grade

equivalents and should allow or developmental dierences. This will enable teachers to more

accurately identiy current levels o each students development and plan learning experiences

accordingly. The PYP Mathematics scope and sequence document states in the section The structure o

the PYP Mathematics scope and sequence that the evidence o mathematical understandings are

described in the behaviours or learning outcomes associated with each phase and these learning

outcomes relate speciically to mathematical concepts, knowledge and sk ills. The learning outcomes

have been written to relect the stages a learer goes through when developing conceptual under-

standing in mathematicsconstructing meaning, transerring meaning into symbols and applying

with understanding.

The CCSS are a shit in the direction o mathematics education.

They move beyond traditional standards to a ocus on

applying mathematics to real-lie situations.

The CCSS or mathematics set grade-speciic standards (NGA Center 2010: 4) o what students should

understand and be able to do. The CCSS or mathematical content are divided into domains which

are larger groups o related standards (NGA Center 2010: 5) identiied as operations and alge-

braic thinking, number and operations in base 10, measurement and data and geometry.

Kindergarten also includes the domain ocounting and cardinality.

Both the CCSS and PYP identiy the importance o conceptual

learning in mathematics. The conceptual ramework o the PYP

promotes a deep understanding o mathematical principles

and the use o transdisciplinary themes ensures that con-

nections with the real world are made.

In the PYP, mathematics is viewed as a tool to sup-

port inquiry and provides a global language through

which students make sense o the world around them.

Mathematics helps explain the why and how, and is a

process o thinking. The overall expectations o PYP

mathematics include processes and proiciency, as doesthe CCSS.

The comprehe nsive philosophy and approach o the PYP s

written, taught and assessed curriculum is highly visible within

the eight Standards or mathematical practice as evidenced in the

ollowing section.

Constructingmeaning Transferring

meaning

Applying with

understanding

How children learn mathematics

Figure 1


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Standards for mathematical practice

1. Make sense o problems and persevere in solving them.

Mathematically procient students start by explaining to themselves the meaning o a prob-

lem and looking or entry points to its solution(NGA Center 2010: 6).

Both the PYP Mathematics scope and sequence and the Standards or mathematical practice

recognize the many ways in which s tudents construct mathematical understandings.

Students learn mathematics by constructing meaning through ever-increasing levels o

abstraction, starting with exploring their own personal experiences, understandings and

knowledge. The PYP Mathematics scope and sequence identies constructing meaning as the

rst stage in all our phases in every strand. The PYP recognizes the need or students to learn

using concrete problems beore they can work at an abstract level. The nature o learning

through inquiry in the PYP naturally promotes making sense o problems and persevering insolving them.

The PYP recognizes the need or students to learn using concrete

problems beore they can work at an abstract level. The nature o

learning through inquiry in the PYP naturally promotes making

sense o problems and persevering in solving them.

2. Reason abstractly and quantitatively.

Mathematically procient students make sense o quantities and their relationships in prob-

lem situations(NGA Center 2010: 6). When students truly understand mathematics conceptu-

ally, they can apply their mathematical understanding to a new problem and use mathemati-

cal symbols and language to explain their thinking. While the CCSS or mathematics explicitly

reer to the ability to decontextualizeand contextualize, development o this ability is implicit

in all PYP mathematical strands and phases. Both the PYP Mathematics scope and sequence

and the Standards or mathematical practicehave similar expectations o students to reason

abstractly and quantitatively.

In order to be able to use mathematics as a tool, students need to be able to go rom thespecics o the situation to the more abstract mathematics underlying the problem. The PYP

Mathematics scope and sequence identies the second stage in all our phases o every strand

as transerring meaning into symbols. The third stage is to apply with understanding. These

two stages in every strand move studentsunderstanding rom the concrete to the abstract.

3. Construct viable arguments and critiqu e the reasoning o others.

Mathematically procient students understand and use stated assumptions, denitions, and

previously established results in constructing arguments (CCSS 2010: 6).

Both the PYPMathematics scope and sequenceand the CCSS or mathematical practice encourage

not only that students are able to comprehend mathematical concepts and content, but also

exhibit and demonstrate the processes and new understandings developed. Students explain

their thinking using numbers, models, graphs, words and relationships. In addition, students

should then be able to apply new knowledge and understandings in a variety o situations that

allow or urther understanding as well as the development o multiple perspectives.

The PYP Mathematics scope and sequence encourages students and teachers to use certain

processes o mathematical reasoning as they progress through the three stages o learning

mathematics. These processes include:

using patterns and relationships to analyse the problem situations upon which theyare working

making and evaluating their own and each others ideas

using models, acts, properties and relationships to explain their thinking

justiying answers and the processes by which they arriveat solutions.

In this way, students validate the meaning they construct rom their experiences with mathe-

matical situations. By explaining their ideas, theories and results, both orally and in writing, they

invite constructive and critical eedback, as well as lay out alternative models

o thinking or the class (see the section What the PYP believes about

learning mathematics).

The IB learner prole attributes o communicator and thinker

urther reinorce the construction o viable arguments and

the ability to critique the reasoning o others. The ability to

conjecture and justiy conclusions is essential i students

are to be able to ully experience mathematics.

4. Model with mathematics.

Mathematically procient students can apply the

mathematics they know to solve problems arising in

everyday lie, society, and the workplace (NGA Center

2010: 7).

Both the PYP Mathematics scope and sequence and the CCSS or

mathematical practice require students to explain their answers

both by the use o estimation and by precise computation.


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The PYP Mathematics scope and sequence reinorces that modelling using manipulatives pro-

vides a valuable scaold or constructing meaning about mathematical concepts. It identies

modelling as one o the processes students and teachers use throughout the three stages o

learning mathematics. It is specically mentioned as a way to develop conceptual understand-

ing in the ollowing strands: data-handling, shape and space and number.

In the pattern and function strand, students progress in phase one to understand patterns

and sequences in everyday situations. In phase two, they represent patterns using numbers

and other symbols. In phase three, they sense real-lie situations using mathematical represen-

tations. In phase our, symbolic rules are used to analyse and represent patterns.

In the shape and space strand, students to use two-dimensional and three-dimensional models

to explain properties o various shapes. In the number strand, students use ractions in real-lie

situations and use estimation to check the reasonableness o their answers.

PYP educators provide regular opportunities or students to use a range o manipulatives as

well as discuss and negotiate their developing understanding with others.

PYP educators provide regular opportunities or studentsto use a range o manipulatives as well as discuss and

negotiate their developing understanding with others.

5. Use appropriate tools strategically.

Mathematically procient students consider the available tools when solving a mathemati-

cal problem(NGA Center 2010: 7). Mathematics has always relied on tools o some orm, or

example, paper and pencil, slide rule or computer sotware. The goal is to help students know

when and how to use tools appropriately. Both the PYP Mathematics scope and sequence and

the CCSS standards or mathematical practice encourage students to employ appropriate

tools. This includes using technology to solve real-lie problems in a strategic and meaningul

manner that will assist with the development o mathematical concepts within a relevant context.

Learners are asked to integrate new mathematical knowledge in a variety o situations that

require in-depth understanding and application o new learning.

Use o mathematical tools is evident throughout the PYP, and provides authentic opportunities

or students to interact in realistic contexts with mathematical tools playing a key role. The use

o tools is encouraged and evident in the PYP Mathematics scope and sequence strands and

is particularly emphasized in the data handling and measurement strands. For example,in the measurement strand in phase three, students select and use appropriate tools and

units o measurement and in phase our learners develop and describe ormulas to nd area,

perimeter and volume(see the section Learning continuum or measurement). In the data

handling strand, students in all phases learn how to sort, categorize and interpret data with a

variety o charts and graphs. By phase three and our, students are able to choose which type

o graph best depicts the data or representation (see the section Learning continuum or data

handling).

The PYP Mathematics scope and sequence notes that while tools commonly used should be

utilized in authentic ways to solve problems, care should be taken to ensure that students

have a strong understanding o the concepts embedded in the problem to ensure meaningul

engagement with the tools and develop a uller understanding o the solution posed. Doing

so ensures that students use appropriate tools strategically.

The goal is to help students know when and how to use tools

appropriately. Both the PYP Mathematics scope and sequence

and the CCSS standards or mathematical practice encourage

students to employ appropriate tools. This includes using

technology to solve real-lie problems in a strategic and

meaningul manner that will assist with the development o

mathematical concepts within a relevant context.

6. Attend to precision.

Mathematically procient students try to communicate precisely to others(NGA Center 2010: 7).

Both PYP mathematics and the CCSS or mathematics recognize the importance o commu-

nicating mathematical concepts and understandings in an eective, knowledgeable manner.

The two mathematics courses also require students to communicate precisely using

mathematical terminology, including labels and notation. Attention to detail when recording

mathematical data and solutions is essential to both, and students are provided

with multiple opportunities to ensure attention to the recording and

reporting o data and inormation.

The PYP Mathematics scope and sequence recognizes that in

order to be useul, number acts (or addition, subtraction,

multiplication and division) must be recalled automatically

with precision. The PYP notes that the degree o precision

needed when calculating depends on how the result

will be used. In the PYP data handling strand, as early

as phase one, students use tally marks or pictographs to

accurately depict data. Phase our o the measurement

strand addresses precision in the degree o accuracy or

their measurements as well as their mathematical notation.

In thenumber strand, students have automatic recall o acts

and use strategies to solve problems and check or accuracy.

Phase our o the shape and space strand requires stu-

dents to use scale accurately to enlarge and reduce shapes

as well as encouraging them to create and manipulate shapes.

By doing this, students align their natural vocabulary with more

ormal mathematical vocabulary and begin to appreciate the need or

this precision.

Artwork by: Emma Downey

Caldwell Heights Elementary

2nd Grade


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Primary Years Programme (PYP)10 Common Core State Standards for mathematics

Summary

The areas o convergence bet ween the re quirements o the CCSS or mathematical practice and

the PYP Mathematics scope and sequence are evident upon review. While the phases o learning that

exist within the PYP are more developmental in nature, both the PYP and the CCSS require attention to

the important processes o learning and the ability to communicate new understandings.

The study also highlights some areas o distinction in the PYP that are identiied by commitment to

the development o international-mindedness and student-led inquiry, which are essential to the PYP

and provide opportunities or students and teachers to appreciate the global dimension o mathemat-

ics. The IB learner proile, together with the ive essential elements o the PYPknowledge, concepts,

skills, attitudes and actioninorms all planning, teaching and assessing in the PYP. The PYP approach-

es to learning coupled with the learner proile promote the qualities expected in 21st century learners

and international-mindedness.

As students investigate mathematics and its application to the real world, the PYP provides an

authentic ramework or exploring the CCSS or mathematical practice. The PYP Mathematics scope and

sequence purports, The power o mathematics or describing and analysing the world around us is

such that it has become a highly eective tool or solving problems. It is also recognized that students can

appreciate the intrinsic ascination o mathematics and explore the world through its unique

perceptions (2009: 1).

With the implementation o the CCSS or mathematical practice, IB practitioners will discover other

aspects o the relationship between the PYP Mathematics scope and sequence and the CCSS as they

relect upon their teaching and students learning.

The power o mathematics or describing and analysing

the world around us is such that it has become a highly

eective tool or solving problems.

7. Look or and make use o structure.

Mathematically procient students look

closely to discern a pattern or structure

(NGA Center 2010). Both the PYP

Mathematics scope and sequence and

the CCSS or mathematical practice

require students to utilize patterns to

explain mathematical thinking in geom-

etry and with numbers. The pattern and

function strand in the PYP Mathematics

scope and sequence sets expectations in

each phase that students will look or, and

make use o, structure. The guide also notes

that By analysing patterns and identiying rules or

patterns it is possible to make predications (see the

section Learning continuum or pattern and unction).

In the number strand, students use operations and the order ooperations to solve problems. In the data handling strand, students gather and display

various types o data, seek ways in which best to represent that data and learn to identiy

patterns in order to analyse data.

In the PYP Mathematics scope and sequence shape and space strand, students learn the prop-

erties o regular and irregular polyhedra and can use models to visualize real world situations

by phase our. Students are able to use ratios and scale to create models to explain larger or

smaller shapes.

8. Look or and express regularity in repeated reasoning.

Mathematically procient students notice i calculations are repeated, and look both or general

methods and or shortcuts(NGA Center 2010: 8).

Both the PYP Mathematics scope and sequence and the CCSS or mathematical practice require

students to have a strong number sense so that they can determine patterns caused by re-

peated numbers and justiy the relationship between the numbers.

In the PYP Mathematics scope and sequencepattern and function strand, repeated reasoning

is clearly evident in all phases. Although not explicitly stated, the number strand incorporates

repeated reasoning in that estimation, order o ractions, equivalent ractions to percentages

and actors are all examples o repeated reasoning. When students are using algebra to solve

problems, they utilize patterns and number sense.

Both the PYPMathematics scope and sequence andthe CCSS or mathematical practice require students

to have a strong number sense.


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The Middle Years Programmeand the

Common Core State Standards

or mathematics


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The Middle Years Programme and the Common Core State Standards or mathem

The MYP is designed or students aged

11 to 16. It provides a coherent and com-

prehensive curriculum ramework o

learning. The MYP encourages studentsto become creative, critical and reective

thinkers. The MYP emphasizes intellec-

tual challenge, encouraging students to

make connections between their stud-

ies in traditional subjects and to the real

world. It osters the development o

skills or communication, intercultural

understanding and global engagement,

qualities that are essential or lie in the

21st century.

Th e MYP is l exi ble en oug h to acc omm oda te thedemands o national and local curriculums. It builds on the

knowledge, skills and attitudes developed in the PYP and

prepares students to meet the challenges o the DP and

the IBCC. The MYPs rigorous curriculum ramework, within

which schools develop their own units o study, ensures

that students can meet the learning objectives demanded

in the CCSS.

Common Core State Standards or Mathematics

First teaching rom September 2014


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Common Core State Standards for mathematicsMiddle Years Programme (MYP)16

o learning outcomes or the 21st century, promoting lie-long learning and international-mindedness.

The IB learner proile is integral to teaching and learning in the MYP because it represents the qualities

o eective learners and internationally minded students. The MYP approaches to learning (ATL) are

organized into ive skill areas: thinking, communication, social, self-management and research.

The ATL, coupled with the learner proile, promote the qualities expected in 21st century learners and

promote international-mindedness. As students explore mathematics and its application to the real

world as promoted by the CCSS, these undamental components o all IB programmes provide an

authentic ramework or exploring the CCSS standards o mathematical practice.

Standards for mathematical practice


Mathematically procient students start by explaining to themselves the meaning o a

problem and looking or entry points to its solution(NGA Center 2010: 6).

A main goal o mathematics education is to help students use it as a tool to solve problems. In

order to do so, they must be willing to persist rom the initial introduction to the problem to

its eventual solution. This requires students to have at their disposal a wide range o strategies

and a willingness to constantly evaluate their work in case they need to change their approach.

Two o the stated aims o MYP mathematics are to develop logical, critical and creative think-

ingand to develop perseverance in problem solving. Both the CCSS and the MYP encourage

the use o appropriate technology in the solution o problems. Students in MYP Common

Core State Standards or mathematics classes are assessed on their ability to select and apply

problem-solving techniques in a wide variety o contexts including unamiliar situations

(objective A). Students are also required to identiy relevant elements o real-lie problems,

select and apply appropriate mathematics correctly and reect on whether their answer makes

sense in the context o the problem (objective D). The use o investigations (objective B) and

the use o inquiry as a teaching method help students to develop that perseverance since they

are accustomed to looking or and nding relationships in mathematics without direct dis-

semination rom the teacher. All o these are supported and urther developed by the ATL skill

othinking as well as the learner prole characteristics o being inquirers, thinkers, reective

and knowledgeable.

Mathematically profcient students start by

explaining to themselves the meaning o a problem

and looking or entry points to its solution

The CCSS or mathematics do not dictate curr iculum

or teaching methods (NGA Center 2010: 5). The MYP,

thereore, is an eective ramework or teaching and

learning or the CCSS. MYP schools develop their

own units o study incorporating the content o

the CCSS using the MYP philosophy o teaching

and learning.

The CCSS deine what students should under-

stand and be able to do by the end o each grade

and the CCSS or mathematics place an emphasis

on applying mathematics to the real world. These

standards set out to develop a clear deinition o

what students need to know to succeed in university

and in their uture careers.

Studies demonstrating the broad relationship between the over-

all expectations in the PYP Mathematics scope and sequence, the aims

and objectives o mathematics in the MYP and DP with the CCSS standards o mathematical practice

were commissioned to educators with specialized knowledge o IB curriculums and CCSS. The purpose

o these studies is to provide schools with resources to inorm their own curriculum alignment.

The ollowing relationship study employs the structure o the CCSS to relate the eight standards or

mathematical practice in grades 6 to 10 to speciic components o the MYP mathematics as identiied

in the Mathematics guide (2013).


This study demonstrates that the aims and objectives o MYP mathematics or years 1 to 5 clearly sup-

port the implementation o the CCSS in mathematics grades 6 to 10.

The emphasis on both application and inquiry are tenets o the MYP. The conceptual ramework o the

MYP promotes that deep understanding o mathematical principles and the global contexts inuse

the realworld in mathematics education. From the aims o MYP mathematics to its objectives and cri-

teria, together with its stance on the use o technology, students in MYP classrooms are experiencing

the type o learning described by the CCSS.

The CCSS are a shit in the direction o mathematics education. They move beyond traditional stand-

ards to a ocus on applying mathematics to real-lie situations. Students are no longer learning con-tent as isolated acts, but rather as tools to solve a wide range o problems (both mathematical and

real-world). At the same time, the CCSS ocus more on students understanding o mathematical prin-

ciples and involvement in the exploration o mathematical concepts to grasp better the mathematics

they are learning. The IB learner proiles ten attributes are the IB mission statement translated into a set


15/33



Mathematically procient students can apply the mathematics they k now to solve problems

arising in everyday lie, society, and the workplace (NGA Center 2010: 7).

In order or students mathematical knowledge and understanding to be useul (as well as to

motivate them to want to learn more), they need to be able to apply mathematics in authentic

ways to problems in the real world. It is no longer enough to simply be skilled in procedures.

As stated in the MYP mathematics aims, students need to be able to apply and transer skills

to a wide range o situations, including real lie, other areas o knowledge and uture develop-

ments. Through the MYP global contexts, the undamental concept oholistic learning and

in developing the ATL thinking skill otransfer, students explore how content relates to other

courses and the world around them. Students in MYP mathematics seldom ask the question

When am I ever going to use this? because they know the answer will be evident throughout

the unit. Objective D (applying) clearly outlines the expectation that all students should be able

to model authentic real-lie problems using mathematics and that they should be assessed

on their ability to do so. It also requires students to analyse whether or not their answer makes

sense in real-lie as well as justiy their degree o accuracy. By pairing this objective with objective C

(communicating) students are then pushed to be able to use the multiple representations

described in the CCSS and move eectively between them.

Mathematically profcient students can apply the

mathematics they know to solve problems arising

in everyday lie, society, and the workplace


Mathematically procient students consider the available

tools when solving a mathematical problem(NGA Center

2010: 7).

Mathematics has always relied on tools o some orm,

or example, paper and pencil, a slide rule or computer

sotware. The goal is to help students know when and

how to use tools appropriately.

The CCSS and the MYP promote the use o technologyin the application o mathematics and the MYP goes one

step urther to also promote its use in the communication

o mathematics. Inormation and communication technology

(ICT) is useul not just when considering complex calculations, but

also to investigate data and mathematical concepts; obtaining rapid

eedback when testing out solutions; [and] observing patterns and making



lem situations. (NGA Center 2010: 6)

In order to be able to use mathematics as a tool, students need to be able to go rom the

specics o the situation to the more abstract mathematics underlying the problem. They then

must be able to manipulate symbols in order to come to a solution.

The aims o MYP mathematics include helping students develop powers o generalization and

abstractionas well as develop an understanding o the principles and nature o mathematics.

While the MYP does not explicitly separate abstract and quantitative reasoning, the use o

investigations (objective B) allows students to study and manipulate quantities in order to

establish the relationships between them. The ocus on applying mathematics to the real

world (objective D) aords students the opportunity to move between decontextualizing and

contextualizing a situation. They do much the same as they develop the ATL skill othinking.

Mathematically profcient students make sense o quantitiesand their relationships in problem situations.

3. Construct viable arguments and critique the reasoning o others.


previously established results in constructing arguments (NGA Center 2010: 6).

The ability to conjecture and justiy conclusions is essential i students are to be able to ully ex-

perience mathematics. They need to be able to communicate and logically deend their own

conclusions as well as evaluate those o others.

These are ideals that are clearly reected in the MYP mathematics aims o helping students

to develop the ability to reect critically upon their own work and the work o others and

communicate clearly and condently in a variety o contexts. Objective C (communicating)

helps students develop their abilities to communicate complete, coherent and concise lines o

reasoning as well moving between dierent representations and it also promotes presenting

work using a logical structure. Once again, objective B (investigating) is assessed and holds

students accountable or nding patterns, representing them and justiying their conclusions.

With logic as one o three key concepts, and a ocus on inquiry-based learning, MYP math-

ematics students are exposed to a wide range o opportunities and content where they willdevelop their powers o argumentation and justication.


16/33


be attending to the structure o an entity to discern its properties and any inherent patterns.

Furthermore, objective B (investigating) also requires students to take part in investigations

where they are then assessed on their ability to discern patterns and describe them as general

rules. This puts the student in the position o creating knowledge rather than simply being a

recipient o someone elses k nowledge.


Mathematically procient students notice i calculations are repeated, and look both or gen-

eral methods and or shortcuts (NGA Center 2010: 8).

Students are asked to look or patterns themselves in order to establish rules. Rather than sim-

ply giving students the ormula, they will understand it better when they are involved in its

ormulation or discovery. The MYP ocus on inquiry and objective B (investigating) promotes

this important ability. Students are regularly looking or patterns in data and then commu-

nicating their ndings to an audience. In an MYP mathematics classroom, students are chal-

lenged to discover concepts on their own or in groups and then extend their knowledge to

other situations.

Mathematically profcient students notice i calculations are

repeated, and look both or general methods and or shortcuts

Summary

MYP mathematics is not a set o mandatory tasks but rather a philosophy o teaching that exempliies

what the CCSS are attempting to accomplish. With a ocus on concepts and applications, students

learn not only where the mathematics comes rom, but where it can be used in the real world. By pro-

moting a student-centred approach based on inquiry, action and relection in the MYP, students can

experience mathematics as described by the CCSS.

The Standards or mathematical content give speciic objectives or student learning, while the MYP

has a suggested mathematical ramework that describes the types o topics that students might

learn in a MYP mathematics classroom (without prescribing them). The ramework includes the our

branches o number, algebra, geometry and trigonometry, and statistics and probability, very similar

to the number system, expressions and equations, geometry, and statistics and probability clusters

described or CCSS grades 6 through 8. Some grades also include the clusters o ratio and proportionalrelationships (grades 6 and 7) that then develop into unctions in grade 8. The se topics are speciically

suggested in the number and algebra branches in the MYP. Once in high school, students develop the

8th grade clusters urther, though now algebra and modelling have been added. These two clusters

are also evident in the mathematics ramework provided by the MYP.

generalizations (Mathematics guide 2013: 9).

These are not just tools or doingmathematics,

but also or teaching and learning it.

All o the objectives (A, B and D) that require

students to select and apply problem-

solving strategies recognize that students

may also select various tools in order

to implement their plan. The ATL skill o

research is urther evidence o the MYPs

commitment to helping students learn to

use responsibly all o the strategies available

to them.


Mathematically procient students try to communicate

precisely to others (NGA Center 2010: 7).

Both communicating and calculating in mathematics require students to take care in choosing

their words and symbols and in the execution o operations. To not do so would hinder both

the students success and their ability to transmit what they know to someone else.

With a undamental concept ocommunication, and a learner prole characteristic and ATL

skill ocusing on communicating, MYP students learn the necessity or communicating pre-

cisely to others. The aims o MYP mathematics include the ability to communicate clearly,

something also evident in the MYP mathematics objective C (communicating) where students

improve their ability to be clear, concise and coherent. Objective D (applying) also requires

students to attend to accuracy by asking them to justiy their level o precision.

Mathematically profcient students try

to communicate precisely to others


Mathematically procient students look closely to discern a pattern or structure (NGA Center

2010: 8).

Whereas traditional state standards would have required students to simply know how to ac-

tor a trinomial, or example, the CCSS now want students to be involved in discovering its pat-

terns, in understanding what makes something actorable. Students, then, need practice at

arriving at these conclusions, something the MYPs ocus on inquiry-based learning promotes.

The MYP conceptual ramework also contributes to this type o learning as it orces teachers

and students to go beyond the mere acquisition o skills and reach or an understanding o the

mathematics underlying those skills. With one o three key concepts being form, students will


17/33

The Diploma Programmeand the


or mathematics

Middle Years Programme (MYP)22

Reading through the Standards or mathematical content, the MYP philosophy is very apparent. All o

the elements o the MYP, including aims, objectives, assessment criteria, conceptual ramework, ocus

on inquiry and approaches to learning, support the implementation o the one element that is not

explicitly given in MYP mathematics: content. That content and its accompanying practices are clearly

laid out in the CCSS.

This study also highlights some areas o distinction in the MYP that are identiied by a commitment

to the development o international-mindedness and the IB learner proile attributes that provide

opportunities or students and teachers to appreciate the global dimension o mathematics. MYP

mathematics also promotes that students will enjoy mathematics, develop curiosity and begin to ap-

preciate its elegance and power (MYP Mathematics guide 2013).

Teaching MYP mathematics clearly supports and extends the teaching o the CCSS or mathematics.

Students will enjoy mathematics, develop curiosity

and begin to appreciate its elegance and power.

Artwork by: Aiden Malcolm Rose

Park IB School

2nd Grade


18/33

The Diploma Programme and the Common Core State Standards or mathematics

The DP is an academically challenging

and balanced programme o education

with internal assessment and nal exam-

inations that prepares students, aged

16 to 19, or success at university and

lie beyond. It has been designed to ad-

dress the intellectual, social, emotional

and physical well-being o students.

The programme has gained recognition

and respect rom the worlds leading

universities.

DP students must choose one subject rom each o ive

groups, ensuring breadth o knowledge and understand-

ing in their best language (language A), additional lan-

guages (language B), the social s ciences, the experimentalsciences and mathematics. Students may choose either an

arts subject rom group 6, or a second subject rom groups

15. DP subjects can be taken at higher level (HL) or stand-

ard level (SL). In addition to disciplinary and interdisciplinary

study, the DP eatures three core elements that broaden

students educational experience and challenge them to

apply their knowledge and skills.



19/33

Common Core State Standards for mathematicsDiploma Programme (DP)26


Both the DP and the CCSS expect a high degree o skills development and content knowledge

in mathematics. The DP mathematics courses provide opportunities or students to develop

mathematical concepts in a coherent manner while applying their mathematical knowledge to solve

realistic problems in context.

The CCSS or mathematics do p rovide clear signposts along the way to the goal o co llege and

career-readiness or all students. They are designed to be relevant to the real world, representing the

knowledge and skills students need to be prepared or college and a career. The CCSS or mathematics

were developed to help mathematics education become more ocused and coherent, allowing or

more clarity and speciicity. They include consistent rigorous content and application o knowledge

through higher-order skills, so all students are prepared to succeed in our global economy and society.

The three main mathematics courses in the DP identiied below support the CCSS goals noted above.

Mathematical studies SL: A standard level course designed or students with a wide range o

abilities. This course concentrates on the applications o mathematics, notably statistics.

Mathematics SL: A standard level course designed or students who have achieved reasonable

prociency in mathematical techniques and who may require the use o some mathematics

in urther study.

Mathematics HL: A higher level course designed or students with good prociency in

mathematics.

These three main DP courses represent a progression o understanding and application o mathematical

concepts and skills.

The aims or DP mathematics (Appendix 4) are broader than the CCSS and include reerences to ethics

and international-mindedness, but in general terms have similar aspirations. The DP assessment objec-

tives or mathematics (Appendix 4) meanwhile provide explicit expectations or students and teachers

related to knowledge and understanding, problem-solving, communication and interpreta-

tion, technology, reasoning, inquiry and investigative approaches. Furthermore, the internal

assessment component o each DP course provides an opportunity or s tudents to use higher-order

reasoning skills while communicating in a clear and coherent manner.

The CCSS deine what students should understand and be able to do by the end o each grade and

include detailed expectations or students. Appendix A: Designing high school mathematics courses

based on the Common Core State Standards identiies our model course pathways in mathematics

based on the CCSS. These can be a useul oundation or discussing how best to organize the highschool standards into courses.

As students explore mathematics and its application to the real world as promoted by the CCSS, these

undamental components o all IB programmes provide an authentic ramework or exploring the CCSS

or mathematics.

Students take written examinations at the end o the

programme, which are marked by external IB examin-

ers. Students also complete assessment tasks in the

school, which are either initially marked by teach-

ers and then moderated by external moderators

or sent directly to external examiners. Assessment

is criterion-related, which means student per-

ormance is measured against pre-speciied as-

sessment criteria based on the aims and objec-

tives o each subject curriculum, rather than the

perormance o other students taking the same

examinations.

The IB learner proiles ten attr ibutes are the IB mis-

sion statement translated into a set o learning out-

comes or the 21st century. The IB learner proile is integral to

teaching and learning in IB programmes as it represents the quali-

ties o eective learners and internationally minded students.

The CCSS or mathematics deine what students should understand and be able to do in their study

o mathematics (CCSS 2010: 4) and place an emphasis on applying mathematics to the real world.

These standards set out to develop a clear deinition o what students need to know to succeed in

university and in their uture careers.

The ollowing relationship study employs the structure o the CCSS to relate the CCSS or mathemat-

ics or grades 11 to 12 to speciic components o the DP mathematics aims and assessment objectives

identiied in the DP mathematics subject guides.

The CCSS defne what students should understand

and be able to do in their study o mathematics.


20/33

Common Core State Standards for mathematicsDiploma Programme (DP)28

Standards or mathematical practice


Mathematically procient students start by explaining to themselves the meaning o a

problem and looking or entry points to its solution (NGA Center 2010: 6).

This mathematical practice provides opportunities or students to struggle with problems,

search or strategies and solutions on their own and learn to evaluate their own results. DP

mathematics courses aim to develop logical, critical and creative thinking, and patience and

persistence in problem-solving(aim 4) which closely relates to this rst mathematical practice.

In the DP, students seek ways to justiy and explain their solutions to problems. These explan-

ations allow opportunities to observe studentsmathematical thinking.

The assessment objectives or DP mathematics courses clearly show that problem-solving is

central to learning mathematics and students need to persevere when learning concepts and

skills through non-routine and open-ended problems. This is evident in assessment objective

2, which states students need to recall, select and use their knowledge o mathematical skills,results and models in both real and abstract contexts to solve problems.

The internal assessment provides an opportunity or students to understand a problem, de-

velop and carry out a plan to solve the problem then end with an opportunity to reect back

on what worked and did not work while making use o dierent approaches including the use

o technology. This mathematical practice is urther developed through the IB learner prole

attributes o being inquirers, thinkers, reective and knowledgeable.

Mathematically profcient students start by explaining

to themselves the meaning o a problem and

looking or entry points to its solution



lem situations (CCSS 2010: 6). In order to be able to use mathematics as a tool, students need

to be able to go rom the specics o the situation to the more abstract mathematics underly-

ing the problem.

The intention o this standard or mathematical practice is or students to reason with models

or pictorial representations to solve problems, convert situations into symbols to appropriately

solve problems as well as convert symbols into meaningul situations. This mathematical prac-

tice is clearly addressed in the aims and assessment objectives o DP mathematics courses.

One o the s tated aims o all DP mathematics courses is that students employ and rene their

powers o abstraction and generalization (aim 5). At the same time, one o the assessment

objectives requires students to use reasoning skills to manipulate mathematical expressions

and modelling in real and abstract contexts. Another clearly states that students are able to

construct mathematical arguments through use o precise statements, logical deduction and

inerence, and by the manipulation o mathematical expressions(assessment objective 5).

3. Construct viable arguments and critiqu e the reasoning o others.


previously established results in constructing arguments (NGA Center 2010: 6).

The ability to conjecture and justiy conclusions is essential i students are to be able to ully

experience mathematics. They need to be able to communicate and logically deend their

own conclusions as well as evaluate those o others.

Students learn to create arguments that rely on logical thinking and reasoning skills. This is

central to all o the DP mathematics courses, as illustrated in the aim to communicate clearly

and condently in a variety o contexts (aim 3). Several assessment objectives also relate tothis mathematical standard, as in assessment objective 3 where students should be able to

transorm common realistic contexts into mathematics; comment on the context; sk etch or

draw mathematical diagrams, graphs or constructions both on paper and using technology;

record methods, solutions and conclusions using standardized notation.

Another dimension to this mathematical standard is its relationship to the IB learner prole. The

attribute o thinking promotes critical and creative thinking to approach complex problems,

and the attribute ocommunicators promotes the expression o ideas condently in a variety

o modes o communication. Developing a classroom culture that supports and nurtures

mathematical discourse provides an environment or constructing arguments

and critiquing the reasoning o others.

Mathematically profcient students

understand and use stated

assumptions, defnitions, and

previously established results in

constructing arguments


Mathematically procient students can apply the math-

ematics they know to solve problems arising in everyday lie,

society, and the workplace(NGA Center 2010: 7).


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Diploma Programme (DP)30 Common Core State Standards for mathematics

Throughout the aims and objectives o the DP

mathematics courses, students are expected

to demonstrate an inquiry and modelling

approach by using their knowledge o

mathematics to model both real and

abstract contexts to solve problems.

Apply and transer skills to alternative

situations, to other areas o knowledge

and to uture developments (aim 3) is

particularly relevant to this mathematical

standard.

As specically stated in DP mathematics HL

and SL, students should be able to investigate

unamiliar situations, both abstract and real world,

involving organising and analyzing inormation, mak-

ing conjectures, drawing conclusions and testing their

validity(assessment objective 6). In mathematical stud-ies students should be organizing and analysing inor-

mation or measurements, drawing conclusions, testing

their validity, and considering their scope and limita-

tions (assessment objective 6). Students have oppor-

tunities to explore mathematical relationships in real world contexts through regular class-

room assignments and mini projects or explorations.


Mathematically procient students consider the available tools when solving a mathematical

problem (CCSS 2010: 7).

Mathematics has always relied on tools o some orm, or example, paper and pencil, slide

rule or computer sotware. The goal is to help students know when and how to use tools

appropriately.

The aim o this mathematical practice is or a student to select and use a combination o tools,

including technology, to explore and solve a problem as well as justiy their tool selection and

problem solution. Students in the DP mathematics courses are expected to use technology

accurately, appropriately and efciently both to explore new ideas and to solve problems as

stated in the DP aim to appreciate how developments in technology and mathematics have

inuenced each other(aim 7).

Students are encouraged to demonstrate the proper uses o technology through the internal

assessment component o all DP mathematics courses in order to explore and deepen their

understanding o mathematical concepts. Students have opportunities to choose and use a

variety o tools to solve problems through investigative tasks. There are extensive reerences in

all the DP mathematics guides on the use o technology or teaching and learning.


Mathematically procient students try to communicate precisely to others(NGA Center 2010:

7). The intent o this mathematical practice is or a mathematically procient student to be

able to communicate mathematics precisely in a clear and coherent manner. This includes the

proper use o mathematical terminology and symbols. Within the DP mathematics courses,

students are expected to communicate and interpret mathematics. Specically stated in the

assessment objectives, students will demonstrate the ability to: transorm common realistic

contexts into mathematics, comment on the context, sketch or draw mathematical diagrams,

graphs or constructions both on paper and using technology and record methods, solutions

and conclusions using standardized notation. Additionally, one o the DP mathematics aims is

to enable students to communicate clearly and condently in a variety o contexts (aim 5).

Students are provided with multiple opportunities to practice precision through mini explora-

tions or projects in preparation or the internal assessment.


Mathematically procient students look closely to discern a pattern or structure (NGA Center

2010: 8). Students have to be inquirers and use their knowledge o mathematical acts, con-

cepts and techniques to discover how some c omplicated concepts are a composition o sev-

eral other concepts. Students discover patterns, unctions and general ormulas through inves-

tigative tasks. Students are expected to discuss the reasonableness o their results as part o

these investigative tasks.

Mathematically procient students are able to compose and decompose number situations

and relationships through observed patterns in order to simpliy solutions.


Mathematically procient students notice i calculations are repeated, and look both or gen-

eral methods and or shortcuts (NGA Center 2010: 8).

Students not only need to be able to look or obvious patterns but also use reasoning strat-

egies or obvious patterns. They need to be able to discover deep, underlying relationships, or

example, uncover a model or equation that unies the various aspects o a problem such as

a discovery o an underlying unction. DP students are required to apply and transer skills to

alternative situations, to other areas o knowledge and to uture developments(aim 6).

Students in the DP mathematics courses develop an appreciation o the elegance and

power o mathematics(aim 1) while employing and rening their powers o abstraction and

generalization.

Mathematically profcient students notice i calculations are

repeated, and look both or general methods and or shortcuts

Artwork by: Rosana PozoEscuela Bella Vista

18 Years Old


22/33

The IB Career-related Certifcateand the

Common Career Technical Core

Diploma Programme (DP)32

Summary

The DP mathematics courses and the CCSS mathematical standards ocus on preparing students

or college and career readiness by developing thinkers, inquirers and communicators through

mathematics. The DP assessment objectives or mathematics: knowledge and understanding,

problem-solving, communication and interpretation, technology, reasoning and inquiry or investigative

approaches are clearly relected in the CCSS eight mathematical practices.

The study also highlights some areas o distinction in the DP, as identiied by commitment to the

development o international-mindedness and attributes o the IB learner proile. This provides a

strong oundation or students and teachers to appreciate the global dimension o mathematics.

Furthermore, DP mathematics aims to enable students to enjoy mathematics, develop curiosity

and begin to appreciate its elegance and power (aim 1). This is a powerul testament to the role o

mathematics in education and the impact it can have on the lives o students.

The three main DP mathematics courses clearly support and provide oppor tunities to extend the

teaching o the CCSS o mathematical practice in grades 11 to 12. With the implementation o the

CCSS mathematics, IB practitioners will discover other aspects o the relationship between the

DP courses and the CCSS as they relect upon their own teaching and their students learning.


23/33

The IB Career-related Certifcate and the Common Career Technical Core

The IB has developed a ramework o

international education that incorporates

the vision and educational principles o

the IB into local programmes, addressingthe needs o students engaged in career-

related studies. The IBCC is an academic

educational ramework designed to sup-

port schools and colleges that also ofer

career-related studies to their students.

A unique oering, the IBCC speciically addresses the needs

o students who wish to engage in career-related educa-

tion. The IBCC prepares students or lexibility and mobility

in a range o employment opportunities as well as continu-

ing lielong learning through the integration o broad, gen-

eral learning areas and speciic career-related content in a

ramework o education.

The IBCC encourages these students to beneit rom ele-

ments o an IB education through a selection o two or

more DP courses in addition to a unique IBCC core, com-

prised o courses in: approaches to learning, community

and service, a relective project, and language develop-ment. The core ramework is at the heart o the IBCC and

enables students to enhance their personal and inter-

personal development, with an emphasis on experiential

learning.

This document brie ly outlines the relationship between

the IBCC and the career ready practices o the Common

Career Technical Core (CCTC).



24/33

Career-related Certicate (IBCC)36 Common Core State Standards for mathematics

Relationship between the CCTC and the IBCC

The CCTC career ready practices are ound predominantly within the IBCC core elements o approaches

to learning, community and service, language development and relective project. By examining both

the stated aims and the deined content o each component, the 12 CCTC career ready practices are

ound to be explicitly embedded in the IBCC core.

The ollowing table provides a brie overview o the overlap between the IBCC and the 12 CCTC career

ready practices.

CCTC career ready practices Corresponding IBCC core elements

1. Act as a responsible and contributingcitizen and employee.

Community and service

2. Apply appropriate academic and technicalskills.

Approaches to learning: personaldevelopment, thinking

3. Attend to personal health and inancialwell-being.


Approaches to learning:personal development

4. Communicate clearly, eecti vely and withreason.

Approaches to learning: thinking, personaldevelopment, communication

Language development

5. Consider the environmental, social andeconomic impacts o decisions.

Approaches to learning: thinking,personal development, communication,intercultural understanding

Relective project


6. Demonstrate creativity and innovation. Approaches to learning: thinking,communication

Relective project

7. Employ valid and reliable researchstrategies.

Relective project

Approaches to learning: thinking

8. Utilize critical thinking to make sense oproblems and persevere in solving them.

Relective project

Approaches to learning: thinking

9. Model integrity, ethical leadership andeective management.


Approaches to learning

10. Plan education and career path aligned

to personal goals.

Approaches to learning: personal

development, thinking

11. Use technology to enhance productivity. Approaches to learning: communication

12. Work productively in teams while usingcultural global competence.


Approaches to learning: interculturalunderstanding, communication

Summary

The IBCC is a cha llenging and r ewarding educatio nal ramework that de mands the b est rom

motivated students. It is evident that the IBCC clearly delivers the CCTC career ready practices through

the broad and comprehensive IBCC core. Furthermore, the 10 attributes o the IB learner proile also

support the application and development o the skills outlined in the 12 CCTC career ready practices.

The IBCC is an academic educational ramework

designed to support schools and colleges that also

oer career-related studies to their students.

CCTC career ready practices Corresponding IBCC core elements


25/33

IB programmesand the


Application to Students with Disabilities


26/33


IB programmes and the Common Core State StandardsApplication to students with disabilit

Both the IB and the CCSS provide state-

ments on access to the curriculum or

all students. The IB states that difer-

ence and diversity are central in IB World

Schools where all students enrolled in IB

programmes should receive meaningul

and equitable access to the curriculum ...

and access to an appropriate education

that afords students the opportunity to

achieve personal potential (Learning di-

versity in the International Baccalaureate

programmes/Special educational needs

within the International Baccalaureate

programmes 2010: 2).

The CCSS documentApplication to Students with Disabilities

states that the common core standards provide an his-toric opportunity to improve access to rigorous academic

content standards or students with disabilities. The CCSS

notes that students with disabilities must be challenged

to excel within the general curriculum and be prepared or

success in their post-school lives, including college and/or

careers.

Artwork by: Helen Marcella Stritzel

William Palmer High School

11th Grade


27/33

Learning Diversity42 Common Core State Standards for mathematics

The CCSS sets expectatio ns or schools to incorpo rate suppor t and accommodations to enable

students with disabilities to meet high academic standards and to ully demonstrate their conceptual

and procedural knowledge and skills in mathematics, reading, writing, speaking and listening.

While the IB cannot be as explicit in its demands due to the legal and contextual issues o schools in

such a wide range o countries, student access is supported through the ollowing standards as de-

tailed in the IB Programme standards and practices (2010).

Standard A.9: The school supports access or students to the IBprogramme(s) and philosophy.

Standard B2.8 The school provides support or its students with learningand/or special educational needs and supports their teachers.

Standard C1.6: Collaborative planning and reection incorporatesdiferentiation or students learning needs and styles.

Standard C3.10: Teaching and learning diferentiates instruction to meetstudents learning needs and styles.

To urther support schools in meeting these standards, the IB has identiied our principles o good

practice or promoting and supporting equal access: airming identity and building sel-esteem, valu-

ing prior knowledge, scaolding and extending learning. While supporting the Programme standards

and practices, these principles also allow schools to use the learning approaches and strategies that are

appropriate, or are legal requirements, within their own contexts.

The IB document Candidates with assessment access requirements/special educational needs outlines the

principles and guidelines or applying access arrangements so that all DP

examination candidates are allowed to demonstrate their ability

under assessment conditions that are as air as possible.

Inclusive assessment arrangements allow all learners

air access to assessment without changing the

demand and without devaluing the qualiication.

Arrangements may include additional time/rest,

assistive technologies, scribes, readers, commu-

nicators, prompters, modiications (Braille, print

sizes, coloured paper), audio recordings,

transcriptions and assistance with practical work.

It is expected that reasonable adjustments andinclusive access arrangements as outlined above

will be respected in the PYP, MYP and the IBCC, and

these principles can be ound in the programme

guidelines.

IB programmes and the CCSS both promote a culture o high expectations or all students. Additional

supports and services are suggested by the IB and CCSS; or example: instructional supports such as

those based on the principles o Universal Design or Learning (http://www.udlcenter.org/aboutudl) as

well as instructional accommodations or which standards remain unchanged yet there are changes

in materials or procedures. Through the supports, accommodations and inclusive arrangements

identiied above, students receive access to multiple means o learning and opportunities to

demonstrate their knowledge, while the rigour and high expectations o the CCSS and IB programmes

are maintained.

dierence and diversity are central in IB World Schools where all

students enrolled in IB programmes should receive meaningul

and equitable access to the curriculum

Artwork by: Madison Graber

Hutchinson High School

11th Grade

Artwork by: Camille Jackson

FDR American School o Lima

12th Grade


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Appendices44 Common Core State Standards for mathematics

Appendix 2: How mathematics practices are changing(Making the PYP happen: 84)

How are mathematics practices changing?

Increased emphasis on: Decreased emphasis on:

connecting mathematical concepts and

applications to learning

treating mathematics as isolated concepts

and acts

manipulatives, to make mathematics

understandable to students

rote learning, memorization and symbol

manipulation

real-lie problem solving using mathematics word problems as problem solving

instruction built on what students know,

what they want to know, and how they best

might ind out

instruction ocused on what students do

not know

a variety o strategies or possible multiple

solutionsemphasis on process

one answer, one method, emphasis

on answer

students being encouraged to speculate and

pursue hunches

the teacher as the sole authority or

right answers

a broad range o topics regardless o

computational skills

computational mastery beore moving on

to other topics

mathematics as a means to an end teaching mathematics disconnected rom

other learning

the use o calculators and computers or

appropriate purposes

a primary emphasis on pencil and paper

computations

programme o inquiry as the context or

learning

the textbook as the context or learning

students investigating, questioning,

discussing, justiying and journaling

their mathematics

the use o worksheets

students and teachers engaged in

mathematical discourse.

teacher telling about mathematics.

Appendix 1: PYP mathematical strands(Making the PYP happen: 86)

What do we want students to know?

Data handling Data handling allows us to make a summary o what we know about the worldand to make inerences about what we do not know.

Data can be collected, organized, represented and summarized in a varietyo ways to highlight similarities, dierences and trends; the chosen ormatshould illustrate the inormation without bias or distortion.

Probability can be expressed qualitatively by using terms such as unlikely,certain or impossible. It can be expressed quantitatively on a numericalscale.

Measurement To measure is to attach a number to a quantity using a chosen unit. Since the

attributes being measured are continuous, ways must be ound to deal with

quantities that all between numbers. It is important to know how accurate a

measurement needs to be or can ever be.

Shape and space The regions, paths and boundaries o natural space can be described by shape.

An understanding o the interrelationships o shape allows us to interpret,

understand and appreciate our two-dimensional (2D) and three dimensional

(3D) world.

Pattern and unction To identiy pattern is to begin to understand how mathematics applies to the

world in which we live. The repetitive eatures o patterns can be identiied and

described as generalized rules called unctions. This builds a oundation or the

later study o algebra.

Number Our number system is a language or describing quantities and the relationshipsbetween quantities. For example, the value attributed to a digit depends on its

place within a base system.

Numbers are used to interpret inormation, make decisions and solve problems.

For example, the operations o addition, subtraction, multiplication and division

are related to one another and are used to process inormation in order to solve

problems. The degree o precision needed in calculating depends on how the

result will be used.

Appendices


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Appendices46 Common Core State Standards for mathematics

Appendix 3: MYP mathematics aims and objectives (2013)

The aims o the teaching and learning o MYP mathematics are to en-courage and enable students to:

enjoy mathematics, develop curiosity and begin to appreciate its elegance and power

develop an understanding o the principles and nature o mathematics

communicate clearly and condently in a variety o contexts

develop logical, critical and creative thinking

develop perseverance in problem solving

develop powers o generalization and abstraction

apply and transer skills to a wide range o situations, including real lie, other areas o

knowledge and uture developments

appreciate how developments in technology and mathematics have inuenced each

other

appreciate the moral, social and ethical implications arising rom the work o

mathematicians and the applications o mathematics

appreciate the international dimension in mathematics through an awareness o the

universality o mathematics and its multicultural and historical perspectives

appreciate the contribution o mathematics to other areas o knowledge

develop the knowledge, skills and attitudes necessary to pursue urther studies in

mathematics

develop the ability to reect critically upon their own work and the work o others.

In MYP mathematics, the objectives relect the act that students should be able to know and use

mathematics in a variety o contexts (including authentic real-lie situations), perorm investigations

and communicate mathematics clearly.

A Knowing and understanding

Knowledge

Connecting IB to the Core: Mathematics Relationship Studies to Inform Curriculum Alignment

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