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Assessing Pre-Service Secondary School Teachers’ Mathematical Knowledge for Teaching Algebra. Sharon Senk Joan Ferrini-Mundy Michigan State University January 12, 2006. BACKGROUND Mathematical Knowledge for Teaching. Mathematical Education of Teachers RAND Mathematics Study Panel Shulman

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Assessing pre service secondary school teachers mathematical knowledge for teaching algebra

Assessing Pre-Service Secondary School Teachers’ Mathematical Knowledge for Teaching Algebra

Sharon Senk

Joan Ferrini-Mundy

Michigan State University

January 12, 2006


Background mathematical knowledge for teaching
BACKGROUND Mathematical Knowledge for Teaching AlgebraMathematical Knowledge for Teaching

  • Mathematical Education of Teachers

  • RAND Mathematics Study Panel

  • Shulman

  • Ma

  • Ball & Bass

  • Many other scholars


Knowing mathematics for teaching algbra kat project nsf rec no 0337595
KNOWING MATHEMATICS FOR TEACHING ALGBRA (KAT) PROJECT Mathematical Knowledge for Teaching Algebra(NSF REC No. 0337595)

  • Joan Ferrini-Mundy, PI

  • Robert Floden

  • Raven McCrory

  • Mark Reckase

  • Sharon Senk

  • Karen Allen & Xuhui Li


Goals of kat project
GOALS OF KAT PROJECT Mathematical Knowledge for Teaching Algebra

  • Instrument Design (2004 - 2005)

    Develop theoretical constructs, items, test forms

  • Framework Validation (2006)

    Do data support theoretical framework?

  • Status Study (2006-2007)

    How does knowledge for teaching algebra vary among pre-service and in-service teachers across the U.S.?


Item development august 2004 october 2005
Item Development Mathematical Knowledge for Teaching AlgebraAugust 2004 - October 2005

  • Constructs defined

  • Item writing workshops with mathematicians, math educators, secondary teachers

  • Additional Items written by KAT faculty & GAs

  • Items reviewed by mathematicians

  • Items edited by KAT staff


Mathematical knowledge for teaching algebra simplified for assessment design
Mathematical Knowledge for Teaching Algebra Mathematical Knowledge for Teaching Algebra(simplified for assessment design)

  • Knowledge of school algebra

    algebra in middle and high school

  • Advanced mathematical knowledge

    related college math, e.g. calculus, abstract algebra

  • Teaching knowledge

    knowledge of typical errors, canonical uses of school math, curriculum trajectories, etc.


Pilot testing
Pilot Testing Mathematical Knowledge for Teaching Algebra

  • Volunteers were recruited to administer forms of the item sets to target samples.

    • Students in mathematics teacher preparation

    • Practicing teachers

    • Interns/those in professional development

  • Wanted variety in teaching experience and type of mathematics course work


Number of participants in pilot studies november 2004 december 2005
Number of Participants in Pilot Studies Mathematical Knowledge for Teaching AlgebraNovember 2004 - December 2005


Kat pilot sites

Calvin College (MI) Mathematical Knowledge for Teaching Algebra

Cal. State Univ. - Fullerton

George Mason University

Grand Valley State Univ.

Kennesaw State University

Michigan State University

Oregon State University

St. Xavier University

San Diego State University

Syracuse University

Texas State University - San Marcos

University of Arizona

UC Berkeley

University of Delaware

UNC Greensboro

Univ. of South Florida

Valparaiso University

Western Michigan Univ.

In-service teachers in CA,DE,IL, MI, OH

KAT Pilot Sites


Analysis of items
Analysis of Items Mathematical Knowledge for Teaching Algebra

  • Items were analyzed to check a number of features.

    • Difficulty: proportion correct/mean performance

    • Spread of scores

  • Items that were outside target difficulty range, showed little spread of scores, or showed negative discrimination were revised or eliminated.

  • As of December 2005 we have about 100 items of which about 50 meet our criteria.


Sample item identify an exponential function school knowledge
Sample Item: Identify an Exponential Function Mathematical Knowledge for Teaching Algebra(School Knowledge)

Which of the following situations can be modeled using an exponential function?

i. The height h of a ball t seconds after it is thrown into the air.

ii. The population P of a community after t years with an increase of n people annually.

iii. The value V of a car after t years if it depreciates d% per year.

A. i only

B. ii only

C. iii only

D. i and ii only

E. ii and iii only


Results identify exponential function
Results: Identify Exponential Function Mathematical Knowledge for Teaching Algebra


Sample item number systems advanced knowledge
Sample Item: Number Systems Mathematical Knowledge for Teaching Algebra(Advanced Knowledge)

For which of the following sets S is the following statement true?

For all a and b in S, if ab = 0, then either a = 0 or b = 0.

i. the set of real numbers

i. the set of complex numbers

iii. the set of integers mod 6

iv. the set of integers mod 5

v. the set of 2x2 matrices with real number entries

A. i only D. i, ii, iii and iv only

B. i and ii only E. i, ii, iii, iv, and v

C. i, ii and iv only


Results properties of number systems advanced knowledge
Results: Properties of Number Systems Mathematical Knowledge for Teaching Algebra(Advanced Knowledge)


Sample item identifying student s error in solving a linear equation teaching knowledge
Sample Item: Identifying Student’s Error in Solving a Linear Equation(Teaching Knowledge)

A student solved the equation

3(n - 7) = 4 - n

and obtained the solution n = 2.75.

What might the student have done wrong?



Next steps
NEXT STEPS Linear Equation

Validation Study (March - August, 2006)

Need at least 1600 participants

in-service secondary teachers

pre-service secondary teachers

math majors (juniors & seniors)

math graduate students


Contacts for kat project information

Contacts for KAT Project Information Linear Equation

Xuhui Li, Project Manager,[email protected]

Joan Ferrini-Mundy, PI, [email protected]

Sharon Senk, Co-PI,[email protected]


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