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

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

### Contacts for KAT Project Information Linear Equation

Sharon Senk

Joan Ferrini-Mundy

Michigan State University

January 12, 2006

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 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 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 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 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 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 Mathematical Knowledge for Teaching AlgebraNovember 2004 - December 2005

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 SitesAnalysis 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 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 Mathematical Knowledge for Teaching Algebra

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 Mathematical Knowledge for Teaching Algebra(Advanced 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 Linear Equation

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

Xuhui Li, Project Manager,[email protected]

Joan Ferrini-Mundy, PI, [email protected]

Sharon Senk, Co-PI,[email protected]

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