Steinhardt*School*of*Culture,*Education,*and*Human*Development*
Department*of*Teaching*and*Learning*
!
MTHED'GE'2008:!Research!Investigations!in!Mathematics!Education
SYLLABUS!–!Spring,!2014!
Monday,!4:55'6:35,!East!302!
!
Professor:!Orit*Zaslavsky!
Office:!408*East*Bldg.,*239*Greene*St.*
Phone:!347J685J0646*
Email:*[email protected]*
Office!Hours:!By*appointment!
Welcome'to'the'class!!'
'
Course!Description*
This*course*will*provide*opportunities*to*become*familiar*with*research*in*mathematics*education.*It*
will* focus* primarily,* but* not* solely,* on* the* links* between* research* and* practice* in* mathematics*
education.* We* will* examine* recent* research* in* mathematics* education* teaching* and* learning* and*
discuss*implications*for*practice.*We*will*also*examine*and*discuss*the*ways*in*which*research*can*be*
responsive*to*questions*of*practice*in*mathematics*education.*The*course*will*primarily*be*run*as*a*
seminar,* and* will* include* critical* discussions* based* on* readings* of* individual* research* studies* and*
collections* of* research* publications* that* address* a* number* of* significant* topics* of* concern* to* the*
community*of*mathematics*education.**
Objectives!
The* goal* of* the* course* is* to* help* students* become* acquainted* with* the* work* of* the* community* of*
research*in*mathematics*education,*and*to*become*effective*consumers*of*research.*The*main*goals*
are*to*have*students:*
• Become*familiar*with*significant*research*publications*in*the*field*of*Mathematics*Education*
• Become*aware*of*possible*goals*and*types*of*research*
• Develop*the*ability*to*analyze*and*critique*some*research*studies,*with*respect*to*their*
conceptual*foundation,*methodology,*and*findings*
• Develop*ideas*of*how*to*use*research*for*teaching*
*
Recommended!Texts*
1. National* Council* of* Teachers* of* Mathematics.* (2000).* Principles' and' Standards' for' School'
Mathematics.*Author:*Reston,*VA.*
2. Kilpatrick,*J.,*Martin,*G.*&*Schifter,*D.**(Eds)*(2003).*Research'Companion'to'the'Principles'and'
Standards'for'School'Mathematics.*NCTM:*Reston,*VA.*ISBN:*978J0J87353J537J3*
3. Sowder,* J.* &* Schappell,* B.* (Eds)* (2002).* Lessons' Learned' from' Research.* NCTM:* Reston,* VA.*
ISBN:*978J0J87353J526J7*
4. Carpenter,*T.*P.,*Dossey,*J.*A.,*&*Koehler,*J.*L.*(Eds)*(2004).*Classics'in'Mathematics'Education'
Research.*NCTM:*Reston,*VA.*ISBN:*978J0J87353J565J6*
5. Articles* from* research* journals* in* Mathematics* Education* (e.g.,* Educational' Studies' in'
Mathematics'Education'(ESM),*Journal'for'Research'in'Mathematics'Education'(JRME),*Journal'
of'Mathematical'Behavior'(JMB),*For'the'Learning'of'Mathematics'(FLM)).***
2
!
Course!Requirements!
!
1.** Full!Participation.*(24%)*
The*quality*of*this*class*depends*on*your*attendance,*preparation*for*scheduled*discussions,*and*
engagement*in*and*contributions*to*class*discussion.*Good*contributions*to*classroom*discussion*
do*more*than*simply*push*the*conversation*along.*Positive,*substantive*contributions*make*your*
thinking* available* to* the* class,* raise* new* questions,* and* challenge* the* group* and* yourself.* We*
really*encourage*you*to*speak*up,*question*what*you*do*not*understand,*and*make*proposals*in*
class.*You*cannot*go*wrong*by*engaging*
*
2.** Weekly!Assignments*that*include*readings,*short*summaries,*and*responses*to*specific*questions*
(up*to*4*points*per*assignment).*(32%)**
*
3.** Mid'term! Paper:* Submit* an* annotated* bibliography* paper* based* on* at* least* five* empirical*
research* studies* on* a* topic* of* interest* to* the* student* (detailed* instructions* will* be* provided*
regarding*the*structure*and*content*of*the*paper);*The*students*will*be*required*to*prepare*and*
conduct*a*presentation*of*the*topic,*and*lead*a*discussion*around*it.*(20%)*
* Dates:**
• Submit*the*selected*topic*and*list*of*publications*that*will*form*the*basis*for*the*paper,*by*
2/24/2014.*
• Get*approval*by*3/3/2014.*
• Submit*the*paper*by*3/24/2014.*
• Be*prepared*to*present*and*lead*a*discussion*on*3/31/2014.*
*
4.* Final!Project:*According*to*student’s*choice*(24%).**
Possible*types*of*projects:**
• Produce*a*paper*that*is*based*on*your*replicating*an*empirical*study*that*you’ve*read,*with*
middle*or*secondary*school*student(s),*and*comparing*your*findings*with*the*findings*
reported*in*the*paper.**
• Produce*a*paper*based*on*a*miniJstudy*(action*research)*that*you*will*have*conducted*with*
your*students.*
• Produce*a*paper*on*how*you*can*use*research*to*assist*you*in*some*capacity*of*your*job*(or*
future*job)*in*teaching.*The*paper*should*connect*the*results*of*research*to*a*plan*of*action.**
For*each*type*of*project*you*will*receive*a*detailed*description*of*what*is*required*and*how*it*will*
be*assessed.*
Dates:**
• Submit*and*get*approval*of*a*plan*for*your*project*by*4/7/2014.*
• Submit*a*draft*of*your*project*by*4/21/2014.*
• Be*prepared*to*present*and*share*your*initial*work*on*your*project*by*5/5/2014*(you*will*then*
get*feedback*from*your*classmates*that*may*help*you*proceed).*
• Submit*the*final*project*by*5/18/2014.*
!
!
Research!Investigations!in!Mathematics!Education!!
MTHED'GE'2008,!Spring!2014!
! October!2010!
3
Attendance!Policy!
Full*participation*is*required.**
Unexcused!absences!are!not!allowed!in!this!course.**
Absences*will*be*excused*at*the*discretion*of*the*instructor.*Please*contact*the*instructor*as*soon*as*
you*anticipate*missing*class.**
Three*or*more*absences*will*result*in*no*credit*for*the*course*
!
Grading!Policy!
Participation:*The*instructor*will*take*attendance*and*keep*notes*on*your*participation*in*class.*For*
each*class*you*will*receive*0J2*points*for*active*participation.*For*your*final*grade,*only*the*12*classes*
for*which*you*received*the*highest*scores*will*count.*Each*unexcused*absence*will*result*in*decrease*
of*2*points*in*the*final*grade.*Unexcused*tardiness*(15*minutes*or*more)*or*early*departures*count*as*
unexcused*absences.*For*an*excused*absence,*the*calculation*of*points*for*participation*will*be*done*
proportionally*so*that*the*student*is*not*penalized.*
*
Your*written*work*and*oral*presentations*will*be*graded*holistically.**
Weekly* Assignments:* Each* assignment* will* receive* 0J4* points.* For* full* credit,* you* need* to*
demonstrate* that* you* have* read* all* the* assigned* readings* carefully,* and* answer* the* assigned*
questions*thoughtfully.*The*summaries*should*be*concise,*and*should*focus*on*the*main*ideas*in*the*
readings.*
MidJTerm*Paper:*You*will*receive*detailed*guidelines*for*the*preparation*of*this*paper,*as*well*as*an*
explanation*how*it*will*be*graded.*
Final*Project:*You*will*receive*detailed*guidelines*for*your*final*project*that*will*include*explanation*
how*it*will*be*graded.*
!
Course!Overview**J*Tentative∗*
(The*collection*of*articles*listed*below*form*a*resource*for*the*topics*that*will*be*discussed*in*class.*
Not*all*are*required*readings.*For*some*topics*different*students*will*get*different*articles*to*read.)*
*
Week*
Topic*
Introduction!
Students’!and!Teachers’!conception!of!a!mathematical!definition!
Based*on:**
Week*1*
1/27/2014*
Zaslavsky, O. & Shir, K. (2005). Students’ conceptions of a mathematical definition.
Journal for Research in Mathematics Education (JRME), 36(4), 317-346.
van*Dormolen,*J.*&*Zaslavsky,*O.*(2003).*The*many*facets*of*a*definition:*The*case*of*
periodicity.'Journal'of'Mathematical'Behavior,'22(1),*91J106.*
Shir,*K.*&*Zaslavsky,*O.*(2001).*What*constitutes*a*(good)*definition?*The*case*of*a*
square.*In*M.*van*den*HeuvelJPanhuizen*(Ed.),*Proceedings'of'the'25th'''Conference'of'
the'International'Group'for'the'Psychology'of'Mathematics'Education,'v.4,*161J168.*
∗
There*may*be*slight*changes*in*the*topics*and*the*time*allocated*to*them;
Research!Investigations!in!Mathematics!Education!!
MTHED'GE'2008,!Spring!2014!
! October!2010!
4
Week*
Topic*
Understanding!and!Meaning!in!Mathematics!
Week*2*
2/3/2014*
Brownell,*W.A.*(1947).*The*place*of*meaning*in*teaching*arithmetic.*Elementary'School'
Journal,*47,*256J265.*[Attached*is*a*reprint*that*appears*in:*Carpenter,*T.*P.,*Dossey,*J.*
A.,*&*Koehler,*J.*L.*(Eds.)*(2004).*Classics'in'Mathematics'Education'Research.*NCTM:*
Reston.*
Skemp,*R.*(1976).*Relational*Understanding*and*Instrumental*Understanding.*
Mathematics'Teaching,'77,'20–26.*
Nesher,*P.*(1986).*Are*Mathematical*Understanding*and*Algorithmic*Performance*
Related?*For'the'Learning'of'Mathematics,'6(3),*2J9.*
Intuition!!
Week*3*
2/10/2014*
Fischbein,*E.*(1982).*Intuition*and*Proof.*For'the'Learning'of'Mathematics,'3(2),*9J18,*
24.*
Fischbein,*E.*&*Baltsan,*M.*(1997).*The*evolution*with*age*of*probabilistic,*intuitively*
based*misconceptions.*Journal'for'Research'in'Mathematics'Education,'28(1),*96J105.*
Fischbein,*E.*&*Schnarch,*D.*(1998/9).*The*mathematical*concept*of*set*and*the*
'collection'*model.*Educational'Studies'in'Mathematics,'37(1),*1J22.*
Fischbein,*E.,*Tirosh,*D.,*&*Hess,*P.*(1979).*The**Intuition*of*Infinity.*Educational'Studies'
in'Mathematics,'10(1),*3J40.*
Fischbein,*E.,*Tirosh,*D.,*&*Melamed,*U.*(1981).*Is*It*Possible*to*Measure*the*Intuitive*
Acceptance*of*a*Mathematical*Statement?*Educational'Studies'in'Mathematics,'12(4),*
491J512.*
Concept!Image!and!Concept!Definition!
Week*4*
2/24/2014*
Vinner,*S.,*&*Dreyfus,*T.*(1989).*Images*and*definitions*for*the*concept*of*function.*
Journal'for'Research'in'Mathematics'Education,'20(4),*356J366.*
Tall,*D.,*&*Vinner,*S.*(1981).*Concept*image*and*concept*definition*in*mathematics,*with*
special*reference*to*limits*and*continuity.*Educational'Studies'in'Mathematics,*12(2),*
151J169.*
Bingolbali,*E.,*&*Monaghan,*J.*(2008).*Concept*Image*revisited.*Educational'Studies'in'
Mathematics,'68(1),*19J35.*
Semadeni,*Z.*(2008).*Deep*intuition*as*a*level*in*the*development*of*the*Concept*Image.*
Educational'Studies'in'Mathematics,'68(1),*1J17.*
Research!Investigations!in!Mathematics!Education!!
MTHED'GE'2008,!Spring!2014!
! October!2010!
5
Week*
Topic*
The!notion!of!function!and!related!concepts!!
Week*5*
3/3/2014*
Knuth,*E.*J.*(2000).*Student*Understanding*of*the*Cartesian*Connection:*An*Exploratory*
Study.*Journal'for'Research'in'Mathematics'Education,*31(4),*500J507.*
Lloyd,*G.*M.*&*Wilson,*M.*(1998).*Supporting*Innovation:*The*Impact*of*a*Teacher’s*
Conceptions*of*Functions*on*His*Implementation*of*a*Reform*Curriculum.**Journal'for'
Research'in'Mathematics'Education,*29(3),*248J274.*
O’Callaghan,*B.*R.*(2002).*Students’*conceptual*knowledge*of*functions.*In*J.*Sowder*&*
B.*Schappell*(Eds.),*Lessons'Learned'from'Research*(pp.*207J208).*NCTM:*Reston,*VA.*
Zaslavsky,*O.,*Sela*H.,*&*Leron,*U.*(2002).*Being*sloppy*about*slope:*The*effect*of*
changing*the*scale.*Educational'Studies'in'Mathematics,'49(1),*119J140.*
Mathematical!Tasks!(Cognitive!Demanding)!and!Problem!Solving!
Week*6*
3/10/2014*
Henningsen,*M.*&*Stein,*M.*K.*(1997).*Mathematical*tasks*and*student*cognition:*
ClassroomJbased*factors*that*support*and*inhibit*highJlevel*mathematical*thinking*and*
reasoning.*Journal'for'Research'in'Mathematics'Education,'28(5),*524J549.*
Stein,*M.*K.,*Grover,*B.*W.,*&*Henningsen,*M.*(1996).*Building*student*capacity*for*
mathematical*thinking*and*reasoning:*An*analysis*of*mathematical*tasks*used*in*reform*
cl.assrooms.*American'Educational'Research'Journal,'33(2),*455J488.**
Smith,*M.*S.,*&*Stein,*M.*K.*(1998).*Selecting*and*creating*mathematical*tasks:*From*
research*to*practice.*Mathematics'Teaching'in'the'Middle'School,'3,*344J350.**
Stein,*M.*K.,*&*Smith,*M.*S.*(1998).*Mathematical*tasks*as*a*framework*for*reflection.*
Mathematics'Teaching'in'the'Middle'School,'3,*268J275.**
Boston,*M.*D.,*&*Smith,*M.*P.*(2009).*Transforming*secondary*mathematics*teaching:*
Increasing*the*Cognitive*Demands*of*instructional*tasks*used*in*teachers’*classrooms.*
Journal'for'Research'in'Mathematics'Education,'40(2),*119J156.*
Levenson,*E.*(2013).*Tasks*that*may*occasion*mathematical*creativity:*Teachers’*choice.*
Journal'of'Mathematics'Teacher'Education,'16,*269J291.*
Jones,*D.*L.*&*Tarr,*J.*E.*(2007).*An*examination*of*the*levels*of*cognitive*demand*
required*by*probability*tasks*in*middle*grade*mathematics*textbooks.*Statistics'
Education'Research'Journal,'6(2),*4J27.*
Jackson,*K.,*Shahan,*E.,*Gibbons,*L.,*&*Cobb,*P.*(2012).*Setting*up*complex*tasks.*
Mathematics.*Teaching'in'the'Middle'School,'18,*24J29.*
Jackson,*K.,*Garrison,*A.,*Wilson,*J.,*Gibbons,*L.,*&*Shahan,*E.*(2013).*Exploring*
relationships*between*setting*up*complex*tasks*and*opportunities*to*learn*in*
concluding*wholeJclass*discussions*in*middleJgrades*mathematics*instruction.*Journal'
for'Research'in'Mathematics'Education,'44(4),**646J682.*
DiMatteo,*R.*W.*&*Lester,*F.*K.*(2010).*The*role*of*problem*solving*in*the*secondary*
school*mathematics*classroom.*In*J.*Lobato*(Ed.),*Teaching*and*Learning*Mathematics:*
Translating*Research*for*secondary*school*teachers,*pp.*7J12.*Reston,*VA:*NCTM.*
Research!Investigations!in!Mathematics!Education!!
MTHED'GE'2008,!Spring!2014!
! October!2010!
6
Week*
Topic*
Socio!Mathematical!Norms!in!the!Classroom!
Yackel,*E.,*&*Cobb,*P.*(1996).*Sociomathematical*norms,*argumentation,*and*autonomy*
in*mathematics.*Journal'for'Research'in'Mathematics'Education,'27,*458J477.*
Week*7*
3/24/2014*
McClain,*K.*&*Cobb,*P.*(2001).**The*development*of*sociomathematical*norms*in*one*
firstJgrade*classroom.**Journal'for'Research'in'Mathematics'Education,'32,*234J266.*
Lampert,*M.*(1990).*When*the*problem*is*not*the*questions*and*the*solution*is*not*the*
answer:*Mathematics*knowing*and*teaching.*A,erican'Educational'Research'Journal,'
27(1),*29J64.!
Week*8*
3/31/2014*
Week*9*
4/7/2014*
Presentation!of!papers!
Presentation!of!papers*
Week*10*
Work!on!Projects!!
4/14/2014*
*
*Group!work!in!the!Mathematics!Classroom!
Week*11*
4/21/2014*
Linchevski,*L.*&*Kutscher,*B.*(1998).*Tell*me*with*whom*you’re*learning,*and*I’ll*tell*you*
how*much*you’ve*learned:*MixedJability*versus*sameJability*grouping*in*mathematics.*
Journal'for'Research'in'Mathematics'Education,'29(5),*533J554.*
Allen,*K.*C.*(2012).*Keys*to*successful*group*work:*Culture,*structure,*nurture.*
Mathematics'Teacher,'106(4),*308J312.'
Webel,*C.*(2013).*Classroom*collaboration:*Moving*beyond*helping.*Mathematics'
Teacher,'106(6),*464J466.*
Beliefs!in!Mathematics!
Week*12*
4/28/2014*
Nicholls,*J.,*Cobb,*P.,*Wood,*T.,*Yackel,*E.,*&*Patashnick,*M.*(1990).*Goals*and*beliefs*in*
mathematics:*Individual*differences*and*consequences*of*a*constructivist*curriculum.*
Journal'for'Research'in'Mathematics'Education,'21,*109J122*
Schoenfeld,*A.*H.*(1989).*Explorations*of*students’*mathematical*beliefs*and*behavior.*
Journal'for'Research'in'Mathematics'Education,'20(4),*338J355.*
Week*13*
5/5/2014*
Week*14*
5/12/2014*
Presentation!of!projects*
Presentation!of!projects*
*
Research!Investigations!in!Mathematics!Education!!
MTHED'GE'2008,!Spring!2014!
! October!2010!
7
Accomodation!for!NYU!Students!with!Disabilities*
Any*student*attending*NYU*who*needs*an*accommodation*due*to*a*chronic,*psychological,*visual,*mobility,*
and/or*learning*disability,*or*is*Deaf*or*Hard*of*Hearing*should*register*with*the*Moses*Center*for*Students*
with*Disabilities*at*212*998J5980,*240*Greene*Street.*See*www.nyu.edu/csd. *
*
Academic!Integrity*
The*relationship*between*students*and*faculty*is*the*keystone*of*the*educational*experience*in*The*
Steinhardt*School*of*Culture,*Education,*and*Human*Development*at*New*York*University.*This*relationship*
takes*an*honor*code*for*granted.*Mutual*trust,*respect*and*responsibility*are*foundational*requirements.*Thus,*
how*you*learn*is*as*important*as*what*you*learn.*A*university*education*aims*not*only*to*produce*high*quality*
scholars,*but*to*also*cultivate*honorable*citizens.**
*
Academic'integrity*is*the*guiding*principle*for*all*that*you*do;*from*taking*exams,*making*oral*presentations*to*
writing*term*papers.*It*requires*that*you*recognize*and*acknowledge*information*derived*from*others,*and*
take*credit*only*for*ideas*and*work*that*are*yours.*
*
You*violate*the*principle*of*academic*integrity*when*you:*
• Cheat*on*an*exam;**
• Submit*the*same*work*for*two*or*more*different*courses*without*prior*permission*from*your*professors;**
• Receive*help*on*a*takeJhome*examination*that*calls*for*independent*work;**
• Plagiarize.**
*
Plagiarism,*one*of*the*gravest*forms*of*academic*dishonesty*in*university*life,*whether*intended*or*not,*is*
academic*fraud.*In*a*community*of*scholars,*whose*members*are*teaching,*learning*and*discovering*
knowledge,*plagiarism*cannot*be*tolerated.*Plagiarism*is*failure*to*properly*assign*authorship*to*a*paper,*a*
document,*an*oral*presentation,*a*musical*score*and/or*other*materials,*which*are*not*your*original*work.**
*
You*plagiarize*when,*without*proper*attribution,*you*do*any*of*the*following:*
• Copy*verbatim*from*a*book,*an*article*or*other*media;**
• Download*documents*from*the*Internet;**
• Purchase*documents;**
• Report*from*other's*oral*work;**
• Paraphrase*or*restate*someone*else's*facts,*analysis*and/or*conclusions;**
• Copy*directly*from*a*classmate*or*allow*a*classmate*to*copy*from*you.**
*
For*more*on*academic*integrity*see*http://steinhardt.nyu.edu/policies/academic_integrity.*
Research!Investigations!in!Mathematics!Education!!
MTHED'GE'2008,!Spring!2014!
! October!2010!