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

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

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

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  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. 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

  8. Number of Participants in Pilot Studies November 2004 - December 2005

  9. 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 KAT Pilot Sites

  10. 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.

  11. 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

  12. Results: Identify Exponential Function

  13. 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

  14. Results: Properties of Number Systems(Advanced Knowledge)

  15. 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?

  16. Results: Identify Student’s Error

  17. 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

  18. 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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