Assessing Pre-Service Secondary School Teachers’ Mathematical

Knowledge for Teaching Algebra

Sharon SenkJoan Ferrini-Mundy

Michigan State University

January 12, 2006

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)

Joan Ferrini-Mundy, PI Robert Floden Raven McCrory Mark Reckase Sharon Senk Karen Allen & Xuhui Li

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

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)

Knowledge of school algebraalgebra in middle and high school

Advanced mathematical knowledgerelated college math, e.g. calculus, abstract

algebra Teaching knowledge

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

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

Pre-service teachers 387

In-service teachers 423

Total 810

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

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)

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

Number of cases Difficulty

Pre-service teachers

138 0.297

In-service teachers

287 0.324

Total 431 0.313

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 numbersi. the set of complex numbersiii. the set of integers mod 6iv. the set of integers mod 5v. the set of 2x2 matrices with real number entries

A. i only D. i, ii, iii and iv onlyB. i and ii only E. i, ii, iii, iv, and vC. i, ii and iv only

Results: Properties of Number Systems

(Advanced Knowledge)

Number of cases Difficulty

Pre-service teachers

86 0.151

In-service teachers

96 0.177

Total 186 0.161

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

Number of cases Difficulty

Pre-service teachers

97 0.760

In-service teachers

14 0.946

Total 115 0.787

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

Xuhui Li, Project Manager,lixuh@msu.edu

Joan Ferrini-Mundy, PI, jferrini@msu.edu

Sharon Senk, Co-PI,senk@msu.edu