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 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
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