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Mathematical Knowledge for Teaching Algebra: Validating an Assessment of Teacher Knowledge

Mathematical Knowledge for Teaching Algebra: Validating an Assessment of Teacher Knowledge. Robert E. Floden Raven McCrory Michigan State University January , 2007. KNOWING MATHEMATICS FOR TEACHING ALGBRA (KAT) PROJECT (NSF REC No. 0337595). Joan Ferrini-Mundy, Initial PI

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Mathematical Knowledge for Teaching Algebra: Validating an Assessment of Teacher Knowledge

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  1. Mathematical Knowledge for Teaching Algebra: Validating an Assessment of Teacher Knowledge Robert E. Floden Raven McCrory Michigan State University January , 2007

  2. KNOWING MATHEMATICS FOR TEACHING ALGBRA (KAT) PROJECT(NSF REC No. 0337595) • Joan Ferrini-Mundy, Initial PI • Robert Floden, Current PI • Raven McCrory • Mark Reckase • Sharon Senk • Karen Allen & Xuhui Li

  3. GOALS OF KAT PROJECT • Instrument Design (2004 - 2005) Develop theoretical constructs, items, test forms • Assessment Validation (2006 - 2008) Do the forms measure distinct constructs? What differences in knowledge affect teacher responses? • Sensitivity to Instruction (2007 - 2008) How do teacher preparation experiences affect responses?

  4. 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

  5. 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.

  6. 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

  7. Pilot Test Results: Identify Exponential Function

  8. 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

  9. Pilot Test Results: Properties of Number Systems(Advanced Knowledge)

  10. 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?

  11. Pilot Test Results: Identify Student’s Error

  12. Validation Study Design • Recruit sample with varying combinations of constructs • Combination of factor analysis and cluster analysis to identify empirical sub-scales • Analysis of clustered items to interpret clusters • Interviews with test-takers to understand reasoning behind correct and incorrect responses

  13. Number of Participants in Validation Studies

  14. Next Steps • Complete interpretation of clusters • Examine results for special samples (e.g., very high math knowledge) • Interview study of new sample of teachers • Measure change in assessment results in selected teacher preparation programs

  15. Questions for the Future • Will our assessment reveal differences in the effects among approaches to mathematics teacher education (pre-service or inservice)? • Will programs vary in their relative impact on the three components?: • Knowledge of school algebra • Advanced mathematical knowledge • Teaching knowledge • Will differences in assessment results predict differences in teaching effectiveness?

  16. Discussion • What information from our project would be useful to you in designing courses for teachers? • How can we best make our results useful to teacher educators? • What do you hope our project can tell you?

  17. Contacts for KAT Project Information Xuhui Li, Project Manager,lixuh@msu.edu Robert E. Floden, PI, floden@msu.edu Raven McCrory, Co-PI,mccrory@msu.edu

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