Assessing%20Pre-Service%20Secondary%20School%20Teachers

1
Assessing Pre-Service Secondary School Teachers
Mathematical Knowledge for Teaching Algebra

• Sharon Senk
• Joan Ferrini-Mundy
• Michigan State University
• January 12, 2006

2
BACKGROUNDMathematical Knowledge for Teaching

• Mathematical Education of Teachers
• RAND Mathematics Study Panel
• Shulman
• Ma
• Ball Bass
• Many other scholars

3
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

4
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.?

5
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

6
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.

7
(No Transcript)
8
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

9
Number of Participants in Pilot Studies November
2004 - December 2005
Pre-service teachers 387
In-service teachers 423
Total 810
10
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

11
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.

12
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

13
Results Identify Exponential Function
Number of cases Difficulty
Pre-service teachers 138 0.297
In-service teachers 287 0.324
Total 431 0.313
14
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 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

15
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
16
Sample Item Identifying Students 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?

17
Results Identify Students Error
Number of cases Difficulty
Pre-service teachers 97 0.760
In-service teachers 14 0.946
Total 115 0.787
18
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

19
Contacts for KAT Project Information

• Xuhui Li, Project Manager,lixuh_at_msu.edu
• Joan Ferrini-Mundy, PI, jferrini_at_msu.edu
• Sharon Senk, Co-PI,senk_at_msu.edu