Educational Studies in Mathematics

, Volume 29, Issue 1, pp 1–20 | Cite as

Subject-matter knowledge and knowledge about students as sources of teacher presentations of the subject-matter

  • Ruhama Even
  • Dina Tirosh

Abstract

Pedagogical content knowledge is made up of several components. In this paper we concentrate on one of these: teachers' planned presentations of the subject-matter. We deal with two main sources of this component of pedagogical content knowledge: knowledge about the subject-matter and knowledge about students. Illustrations are given in two mathematical domains: functions and undefined mathematical operations. The paper concludes with a discussion of the nature of teachers' knowledge and the interconnections between the three constructs: subject-matter knowledge, knowledge about students, and knowledge about ways of presenting the subject-matter.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Ball, D.L.: 1988,Knowledge and reasoning in mathematical pedagogy: Examining what prospective teachers bring with them to teacher education, unpublished doctoral dissertation, Michigan State University, East Lansing, MI.Google Scholar
  2. Ball, D.L.: 1990, ‘Examining the subject-matter knowledge of prospective mathematics teachers’,Journal for Research in Mathematics Education 21(2), 132–143.Google Scholar
  3. Ball, D.L.: 1991, ‘Research on teaching mathematics: Making subject matter knowledge part of the equation’, in J. Brophy (ed.),Advances in research on teaching, Vol. 2, JAI Press Inc., Greenwich, CT, pp. 1–48.Google Scholar
  4. Begle, E.G.: 1979,Critical Variables in Mathematics Education, Mathematics Association of America and the National Council of Teachers of Mathematics, WA.Google Scholar
  5. Brophy, J. and Good, T.: 1986, ‘Teacher behavior and student achievement’, in M.C. Wittrock (ed.),Handbook of Research on Teaching (3rd ed.), Macmillan, NY, pp. 328–375.Google Scholar
  6. Even, R.: 1989, ‘Prospective secondary teachers' knowledge and understanding about mathematical functions (Doctoral dissertation, Michigan State University, 1989)’,Dissertation Abstracts International 50, 642A.Google Scholar
  7. Even, R.: 1990, ‘Subject matter knowledge for teaching and the case of functions’,Educational Studies in Mathematics 21, 521–544.Google Scholar
  8. Even, R.: 1993, ‘Subject-matter knowledge and pedagogical content knowledge: prospective secondary teachers and the function concept’,Journal for Research in Mathematics Education 24(2), 94–116.Google Scholar
  9. Even, R. and Markovits, Z.: 1993, ‘Teachers' pedagogical content knowledge of functions: characterization and applications’,Journal of Structural Learning 12(1), 35–51.Google Scholar
  10. Freudenthal, H.: 1983,Didactical Phenomenology of Mathematical Structures, Dordrecht: D. Reidel Publishing Company.Google Scholar
  11. Gage, N.: 1978,The Scientific Basis of the Art of Teaching, Teachers College Press, Columbia University, NY.Google Scholar
  12. Hershkowitz, R., Bruckheimer, M. and Vinner, S.: 1987, ‘Activities for teachers based on cognitive research’, in M.M. Lindquist and A.P. Shulte (eds.),Learning and Teaching Geometry, K-12, 1987 Yearbook, National Council of Teachers of Mathematics, Reston, VA, pp. 222–235.Google Scholar
  13. Hiebert, J. (Ed.): 1986,Conceptual and Procedural Knowledge: The Case of Mathematics, Lawrence Erlbaum Associates, Inc., NJ.Google Scholar
  14. Kieran, C.: 1992, ‘The learning and teaching of school algebra’, in D.A. Grouws (ed.),Handbook of Research in the Teaching and Learning of Mathematics, Macmillan, NY, pp. 390–419.Google Scholar
  15. Leinhardt, G.: 1988, ‘Expertise in instructional lessons: An example from fractions’, in D.A. Grouws, T.J. Cooney, and D. Jones (eds.),Effective Mathematics Teaching, National Council of Teachers of Mathematics, Reston, VA, pp. 47–66.Google Scholar
  16. Leinhardt, G., Putnam, R.T., Stein, M.K., and Baxter, J.: 1991, ‘Where subject knowledge matters’, in J.E. Brophy (ed.),Advances in Research on Teaching, Vol. 2, JAI Press, Greenwich, CT, pp. 87–113.Google Scholar
  17. Leinhardt, G. and Smith, D.A.: 1985, ‘Expertise in mathematics instruction: Subject matter knowledge’,Journal of Educational Psychology 77, 247–271.Google Scholar
  18. Maher, C.A. and Davis, R.B.: 1990, ‘Teachers' learning: Building representations of children's meanings’, in R.B. Davis, C.A. Maher, and N. Noddings (eds.),Constructivist Views on the Teaching and Learning of Mathematics (Journal for Research in Mathematics Education: Monograph Number 4, pp. 7–18), National Council of Teachers of Mathematics, Reston, VA.Google Scholar
  19. Nesher, P.: 1986, ‘Are mathematical understanding and algorithmic performance related?,For the Learning of Mathematics 6(3), 2–9.Google Scholar
  20. Peterson, P.L., Fennema, E., and Carpenter, T.P.: 1991, ‘Teachers' knowledge of students' mathematics problem solving knowledge’, in J.E. Brophy (ed.),Advances in Research on Teaching: Vol. 2. Teachers' Subject Matter Knowledge, JAI Press, Greenwich, CT, pp. 87–113.Google Scholar
  21. Schoenfeld, A., Smith, J., and Arcavi, A.: 1993, ‘Learning — The microgenetic analysis of one student's evolving understanding of a complex subject-matter domain’, in R. Glaser (ed.),Advances in Instructional Psychology (Vol. 4), Erlbaum, Hillsdale, NJ, pp. 55–175.Google Scholar
  22. Shulman, L.S.: 1986, ‘Those who understand: Knowledge growth in teaching’,Educational Researcher 15(2), 4–14.Google Scholar
  23. Skemp, R.R.: 1976, ‘Relational understanding and instrumental understanding’,Mathematics Teaching 77.Google Scholar
  24. Strauss, S. and Shilony, T.: (in press), ‘Teachers' models of children's minds and learning’, in I. Hirschfeld and S.A. Gelman (eds.),Mapping in Mind: Domain Specificity in Cognition and Culture, Cambridge University Press, Cambridge.Google Scholar
  25. Tamir, P.: 1987,Subject Matter and Related Pedagogical Knowledge in Teacher Education. Paper presented at the annual meeting of the American Association for Educational Research, Washington, DC.Google Scholar
  26. Tirosh, D.: 1993, ‘Teachers' understanding of undefined mathematical expressions’,Substratum: Temas Fundamentales en Psicologia Education 1, 61–86.Google Scholar
  27. Tirosh, D. and Graeber, A.: 1990, ‘Inconsistencies in preservice teachers' beliefs about multiplication and division’,Focus on Learning Problems in Mathematics 12, 65–74.Google Scholar
  28. Wilson, S.M., Shulman, L.S., and Richert, A.: 1987, ‘“150 ways of knowing”: Representations of knowledge in teaching’, in J. Calderhead (ed.),Exploring Teacher Thinking, Holt, Rinehart, and Winston, Sussex, pp. 104–124.Google Scholar

Copyright information

© Kluwer Academic Publishers 1995

Authors and Affiliations

  • Ruhama Even
    • 1
  • Dina Tirosh
    • 2
  1. 1.Department of Science TeachingWeizmann Institute of ScienceRehovotIsrael
  2. 2.School of EducationTel Aviv UniversityTel AvivIsrael

Personalised recommendations