curriculum__jeremy_kilpatrick_and_john_dossey.ppt

7/25/2019 Curriculum__Jeremy_Kilpatrick_and_John_Dossey.ppt

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The MathematicsThe MathematicsCurriculum K12Curriculum K12


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Curriculum

Not just a syllabus or textbook Includes

Aims

Content Methods

Assessment procedures

Depends on ones position

Plan

Experience

A linear path throuh a multi!dimensional domain


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What is a curriculum?

A plan o" action directin the content and deli#eryo" a proram o" mathematics learnin "or aspeci"ied roup o" students

$his plan consists o" an articulated set o"

statements that pro#ide% eneral oals "or the plan

a structure o" content domains and coniti#e processesto be de#eloped

a philosophy concernin the eneral conditions o"learnin expected

a listin o" eneral standards and speci"ic outcomes o"learnin related to le#els o" schoolin ermane to the

population "or &hich the curriculum is intended


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The Importance of Mission

'A discussion o" mathematical education( and o" &ays

and means o" enhancin its #alue( must bemust be

approached first of allapproached first of allon the basis ofon the basis ofa precise and

comprehensi#e"ormulation o" thevalid aims andvalid aims andpurposespurposeso" such education) *nly on such basis can

&e approach intelliently the problems relatin to the

selection and orani+ation o" material( the methods o"

teachin and the point o" #ie& &hich should o#erninstruction), -The Reorganization of Mathematics in

Secondary Education,./012


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Source of Goals

3ociety45ork"orce

Discipline

Psycholoy

Mathematics

Education

Assessments


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Most Curricula do not answerWho?, What?, Where?, Wh?

3ituatin a curriculum

NC$M and PI3A discuss%Personal Life, Workplace(

Culturaland Societal( and Scientific and Technological)

College oard Standards for College Success!

Mathematics and Statistics!'Collee 6oard presents

these standards 7as a uide to8pro"ide all students &ith

the riorous education that &ill prepare them "or

success in collee( opportunity in the &orkplace( and

e""ecti#e participation in ci#ic li"e),


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!ecommendation 1

5hat is the purpose o" the curriculum9

5ho is it to ser#e9

5hat are the intended outcomes in%

6road brush strokes -o#er#ie&2

:nit le#el content and processes -teachers and

materials2

3peci"ic concepts( principles( and skills-specialist and resource uide le#el2


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"re#ious "eriods of Curricular!eform

Early ./;;s Commissions

)))) late ?;s 'Ne& math,

/;s 3tandards

Early 0;;;s 6ased on

assessments


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Toda $ !ecent "ast

NC


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3tructurin a curriculum

o& are the 'le#els, laid out9

o& is the 'content, di#ided9

o& are the 'processes, described and

inter&o#en9 o& is kno&lede itsel" related to intended

learnin -and to en#isioned pedaoy29

Problems% Connection


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"ro#idin% Structure

Content

DomainsCognitiveProcesses


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Content &omains

Number B operations

Alebra B "unctions

eometry B trans"ormations

Measurement

Data analysis

Chance

Be careful to%

A#oid strayin too "ar "rom a concise listbecause that rapidly leads to a lack o" "ocus

Make sure there are ample areas to connect


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E.g., algebra is algebra?

Mararet endal and aye 3tacey in The #uture of the

Teaching and Learning of &lge'ra! The ()th *CM*

Study-3tacey et al)( 0;;F2% 'Dont take your countrys

curriculum and approach to teachin alebra "or

ranted and dont assume all other educationaljurisdictions operate in a similar &ayGthey

conspicuously do not),

3trikin di""erences in

5ho takes alebra 5hether interated or layered across years

Emphasis put on enerality and pattern

Attention to symbolism( "ormalism( and abstraction

5hether approached throuh "unctions and multiple representations

Hole played by technoloy


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Interconnected Content&omains $ Co%niti#e "rocesses

Content&omains

Concepts

!elationships

"rocedure

'acts


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!ecommendation 2

eep the lists o" content and processes

"ocused and concise

Do not stray reatly "rom current models

&ithout stron justi"icationGit just makes

&ork "or teachers and costs moneyGlittle real

chane

Make sure statements o" oals( standards( and

outcomes ha#e clarity and re"lect a rane o"

coniti#e processes


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( "hilosoph )f "eda%o%

Reasoning and Sense Making

$eachin should #alue and emphasi+e re"lecti#e reasonin-sense makin2 on the part o" the student in order to promoteconstruction o" ne& mathematical concepts based on pre#iouslylearned concepts and ne& ideas)

$eachin should help students see the need "or justi"yin their

&ork and help students to de#elop justi"ication strateies) Problem Solving and Mathematical Modeling

$eachin should enae students in sol#in open!endedproblems( in roups and indi#idually( to illustrate the need "or

mathematics and demonstrate the connectedness o"mathematical ideas)

$eachin &ith a problem!sol#in approach should encouraestudents to in#estiate mathematical models as a #ehicle "oranaly+in problems( makin sense o" related content and

structures( and "indin problem solutions)


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( "hilosoph )f "eda%o% *cont+

Multiple Perspectives

$eachin should de#elop students capabilities to look atmathematical situations and outcomes "rom multipleperspecti#es( compare and critiue methods( and re"lect on the#alue o" each)

$eachin mathematics should encourae students to employ

appropriate tools and techniues such as computin( raphin(and other analytical methods)

Mathematical Autonomy

$eachin mathematics should support student de#elopmentand o&nership o" mathematical ideas)

$eachin mathematics should strenthen students capability toillustrate and communicate their mathematical ideas( imbuineach student &ith the belie" that they ha#e the "oundations andrelated capabilities reuired to succeed in mathematics)


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"eda%o%ical 'ramewor-

5hile the instructional implementation is a

partially separate matter( a broad statement o"

the boundaries and shape o" the proram

should be included)

'5hat you learn re"lects ho& you learned it),

3uch a "rame&ork also re"lects the

approaches and conditions "or achie#in

'depth o" understandin),


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Coherence

Abo#e allGa curriculum must ha#e coherence)

5here coherencecan be measured as the ratio o"

the number o" outcomes that link to other outcomes

&hen compared to the total number o" potential

outcome pairs)

In addition( coherencerelates to the o#erallconsistency o" expected depth o" understandin and

coniti#e le#el consistency)


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!ecommendation ./ (TT0& tothe Challen%es

Attend to the related teachin models

:nderstand di""iculty o" makin 'real chane,

3tri#e "or balance% content and processes

et buy!in o" schools( teachers( parents

6e responsi#e to challenes o" di#ersity >&LL C&+

- *T and*T *S #-R &LL. i#e it time to ro& and prosper

Pro#ide "or systematic re#ision

curriculum__jeremy_kilpatrick_and_john_dossey.ppt

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