Assessing pre service secondary school teachers mathematical knowledge for teaching algebra
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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

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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

BACKGROUNDMathematical 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(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

  • 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 August 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(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

  • 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 November 2004 - December 2005


Kat pilot sites

Calvin College (MI)

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

  • 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(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


Sample item number systems advanced knowledge

Sample Item: Number Systems(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 onlyD. i, ii, iii and iv only

B. i and ii onlyE. i, ii, iii, iv, and v

C. i, ii and iv only


Results properties of number systems advanced knowledge

Results: Properties of Number Systems(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?


Results identify student s error

Results: Identify Student’s Error


Next steps

NEXT STEPS

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

Xuhui Li, Project Manager,[email protected]

Joan Ferrini-Mundy, PI, [email protected]

Sharon Senk, Co-PI,[email protected]


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