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

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

4. Workofteaching

5. Tasks ofteaching

6. Areas of MKT

7. MKT items

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

14. Documentationofchanges

16. Translation and adaption

17. Translation and adaptation MKT, releaseditems Mosvold, R., Fauskanger, J., Jakobsen, A., & Melhus, K. (2009).

18. The multiple-choice format Focusgroupinterviews. 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!

24. Quantitative + qualitative analyses

26. Correlation between NCOP and GEOMETRY is 0.701 (p-value < 0.0005).

27. Correlations (Pearson, p-value<0.005) Correlations 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

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?