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
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 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

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 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
B. i and ii only
C. i, ii and iv only
D. i, ii, iii and iv only
E. i, ii, iii, iv, and v
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