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This presentation of our Norwegian MKT (mathematical knowledge for teaching) project was held by Arne Jakobsen.

This presentation of our Norwegian MKT (mathematical knowledge for teaching) project was held by Arne Jakobsen.

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  • 1. Lessons learned from adapting U.S. developed MKT measures for use in NorwayPresentation at the University of Huelva, SpainMay 27th, 2011
    Arne Jakobsen
    Department of Education
    University of Stavanger, Norway
  • 2. Disposition
    History and background (Norway)
    Students (TIMSS, PISA,…)
    Teachers’ knowledge is important for students achievement
    Government decide to invest in Professional development
    Professional development programs to meet teachers’ needs
    Mathematical knowledge for teaching (MKT)
    Our project research question: What are the possibilities and challenges of using the MKT measures in Norway?
    • The project so far
    Translation of items
    Pilot: 142 (150) teachers measured and 7 focus group interviews
  • 3. MKT
    • Classroom studies in the U.S.
    • 4. Workofteaching
    • 5. Tasks ofteaching
    • 6. Areas of MKT
    • 7. MKT items
    • 8. MQI - back to theclassroom
  • 9. Tasks ofteachingwithitems.
    Giving and evaluating explanations
    Explaining a common procedure
    Explain a concept or idea
    Evaluating student explanations for evidence of understanding
    Characterizing the quality of an explanation
    Interpreting and evaluating non-standard methods/ideas and multiple solutions
    Evaluating a particular non-standard method
    Evaluating multiple possible solutions for a particular problem
    Choosing examples and problems
    Choosing examples to introduce a concept
    Choosing examples that use or illustrate a particular idea
    Choosing examples that lend themselves to particular strategies
    Changing the context/numbers of a problem without changing the mathematical content
    Designing a mathematically similar problem
    Designing a simpler version of a problem
    Designing a sequence of problems to teach an idea
  • 10. Tasks withitems (cont.)
    Choosing and using representations
    Representing a particular idea in multiple ways
    Interpreting a particular representation in multiple ways
    Choosing a diagram/story/model to represent and idea/concept/expression
    Selecting a representation to match an instructional purpose
    Analyzing student errors
    Identifying errors of the same type
    Evaluating difficulty
    Choosing and using definitions
    (+ more.) 
  • 11. MKT - the «egg»
    Ball, D. L., Thames, M. H., & Phelps, G. (2008, p. 403).
  • 12. Example item
  • 13. Translation and adaptionofmeasures
    • Delaney's studies (Irland)
    • 14. Documentationofchanges
    • 15. Aspectsofequivalence
  • Aspectsofequivalence
  • 16. Translation and adaption
  • 17. Translation and adaptation
    MKT, releaseditems
    Mosvold, R., Fauskanger, J., Jakobsen, A., & Melhus, K. (2009). 
  • 18. The multiple-choice format
    How can Norwegian teachers’ reflections about the MKT items contribute to our understanding of challenges related to the multiple-choice format?
  • 19. Item ResponceTheory (IRT)
    How can information about items psychometric properties give new insight when adapting U.S. developed MKT measure for use in Norway?
    An item performance is described by an item characteristic function (with different difficulty and slopes).
    Monotonically increasing function – as the MKT increase the probability of correct answer increase.
    Slope and difficulty is of importance.
  • 20. Item performance
  • 21. From IRT analyses of data
  • 22. IRT findings
    We found that items can be divided into three groups:
    Items that do not seem to function in Norway
    Items that function well, but have relatively high difference in item characteristics in Norway compared to the U.S., and
    Items that seem to function well and that have item characteristics close to what is reported in the U.S.
    Quantitative + qualitative analyses!
  • 23. From IRT analyses ofthe data
    • Snippets from theresults
    • 24. Quantitative + qualitative analyses
    • 25. Aspectsofequivalence
  • Teachers’ MKT
    Focus group interviews:
    We expected that teachers with strong MKT in one content area would be strong in other content areas relevant for their level of teaching.
    The teachers argued that some of the content areas were not relevant and more difficult compared to others
    - our motivation to study correlations
  • 26. Correlation between NCOP and GEOMETRY is 0.701 (p-value < 0.0005).
  • 27. Correlations (Pearson, p-value<0.005)
    Teachers’ MKT scores in differentcontent areas arecorrelated
    All correlationsaresignificant – weakestcorrelationbetween PFA and NCOP
  • 28. Conclusion
    We find that teachers’ MKT scores in the three content areas are correlated
    Teachers with high MKT in one content area have high MKT in other content areas and vice versa
    Despite comments from teachers that not finding PFA items relevant for their teaching, their PFA MKT is related to MKT in the other content areas
  • 29. Final comments
    • Psychometrically items seems to function well in Norway
    • 30. Want to establish link between Norwegian teachers’ MKT and student achievements (UiO-TIMSS 2011)
    • 31. Discussing items as part of professional development to learn more about teachers MKT?
    • 32. Framework and othertheories?
    • 33. Possibilities and limitations?