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Diagnostic Competence for Dealing with Students’ Errors: Fostering Diagnostic Competence in Error Situations

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Diagnostic Competence of Mathematics Teachers

Part of the book series: Mathematics Teacher Education ((MTEN,volume 11))

Abstract

The project reported in this chapter aimed at assessing and fostering future teachers’ diagnostic competence in teaching and learning situations in which students’ errors occurred. Based on a model of diagnostic processes in error situations a university course and a pre- and post-test were developed. Probabilistic models (such as Item-Response-Theory and Latent-Class-Analysis) were used to assess the future teachers’ diagnostic competence in erroneous teaching and learning situations based on their answers to the test items. The results show that the university course had an influence on the way future teachers hypothesize about the causes of the students’ errors and partly also on their preferred way of dealing with errors. Additionally the importance of practical experience when fostering diagnostic competence in error situations became apparent.

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References

  • Abs, H. J. (2007). Überlegungen zur Modellierung diagnostischer Kompetenz bei Lehrerinnen und Lehrern. In M. Lüders (Ed.), Forschung zur Lehrerbildung (pp. 63–84). Münster, Germany: Waxmann.

    Google Scholar 

  • Ashlock, R. B. (2010). Error patterns in computation: Using error patterns to help each student learn (10th ed.). Boston, MA: Allyn & Bacon.

    Google Scholar 

  • Ball, D., Hill, H. C., & Bass, H. (2005). Knowing mathematics for teaching. American Educator, 29(1), 14–17, 20–22, 43–46.

    Google Scholar 

  • Ball, D., Thames, M. H., & Phelps, G. (2008). Content knowledge for teaching: What makes it special? Journal of Teacher Education, 59(5), 389–407.

    Article  Google Scholar 

  • Bell, A. (1993). Principles for the design of teaching. Educational Studies in Mathematics, 24, 5–34.

    Article  Google Scholar 

  • Borasi, R. (1996). Reconceiving mathematics instruction: A focus on errors. Norwood, OH: Ablex Pub.

    Google Scholar 

  • Brown, J. S., & Burton, R. R. (1978). Diagnostic models for procedural bugs in basic mathematical skills. Cognitive Science, 2(2), 155–192.

    Article  Google Scholar 

  • Clark, C. M., & Peterson, P. L. (1986). Teachers’ thought processes. In M. C. Wittrock (Ed.), Handbook of research on teaching (pp. 255–296). New York, NY: Macmillan.

    Google Scholar 

  • Cooney, T. J. (1988). Teachers’ decision making. In D. Pimm (Ed.), Mathematics, teachers and children (pp. 273–286). London, UK: Hodder und Stoughton in association with the Open University.

    Google Scholar 

  • Cooper, S. (2009). Preservice teachers’ analysis of children’s work to make instructional decisions. School Science and Mathematics, 109(6), 355–362.

    Article  Google Scholar 

  • Cox, L. (1975). Diagnosing and remediating systematic errors in addition and subtraction computations. The Arithmetic Teacher, 22(2), 151–157.

    Google Scholar 

  • Doyle, W. (2006). Ecological approaches to classroom management. In C. S. Weinstein, C. M. Evertson, & J. E. Brophy (Eds.), Handbook of classroom management (pp. 97–125). Mahwah, NJ: Lawrence Erlbaum.

    Google Scholar 

  • Heinze, A. (2004). Zum Umgang mit Fehlern im Unterrichtsgespräch der Sekundarstufe I. Journal für Mathematik-Didaktik, 25(3/4), 221–244.

    Article  Google Scholar 

  • Heinrichs, H. (2015). Diagnostische Kompetenz von Mathematik-Lehramtsstudierenden. Wiesbaden: Springer Spektrum.

    Google Scholar 

  • Hußmann, S., Leuders, T., & Prediger, S. (2007). Schülerleistungen verstehen –Diagnose im Alltag. PM: Praxis der Mathematik in der Schule, 49(15), 1–9.

    Google Scholar 

  • Jäger, R. S. (2010). Diagnostische Kompetenz und Urteilsbildung als Element von Lehrprofessionalität. In O. Zlatkin-Troitschanskaia, K. Beck, D. Sembill, R. Nickolaus & R. Mulder (Eds.), Lehrerprofessionalität (S. 105–116). Landau, Germany: Verl. Empirische Pädagogik.

    Google Scholar 

  • Klug, J., Bruder, S., Kelava, A., Spiel, C., & Schmitz, B. (2013). Diagnostic competence of teachers: A process model that accounts for diagnosing learning behavior tested by means of a case scenario. Teaching and Teacher Education, 30, 38–46.

    Article  Google Scholar 

  • Mayring, P. (2010). Qualitative Inhaltsanalyse: Grundlagen und Techniken (11th ed.). Weinheim, Germany: Beltz, Beltz Pädagogik.

    Google Scholar 

  • Peterson, P. L., & Clark, C. M. (1978). Teachers’ reports of their cognitive processes during teaching. American Educational Research Journal, 15(4), 555–565.

    Article  Google Scholar 

  • Praetorius, A.-K., Lipowsky, F., & Karst, K. (2012). Diagnostische Kompetenz von Lehrkräften: Aktueller Forschungsstand, unterrichtspraktische Umsetzbarkeit und Bedeutung für den Unterricht. In R. Lazarides (Ed.), Differenzierung im mathematisch-naturwissenschaftlichen Unterricht (pp. 115–146). Bad Heilbrunn, Germany: Klinkhardt.

    Google Scholar 

  • Putnam, R. T. (1987). Structuring and adjusting content for students: A study of live and simulated tutoring of addition. American Educational Research Journal, 24(1), 13–48.

    Article  Google Scholar 

  • Radatz, H. (1980). Fehleranalysen im Mathematikunterricht. Braunschweig, Germany: F. Vieweg.

    Book  Google Scholar 

  • Reisman, F. K. (1982). A guide to the diagnostic of teaching of arithmetic (3rd ed.). Columbus, OH: C. E. Merrill.

    Google Scholar 

  • Rheinberg, F. (1978). Gefahren Pädagogischer Diagnostik. In K. J. Klauer (Ed.), Handbuch der pädagogischen Diagnostik (pp. 27–38). Düsseldorf, Germany: Schwann.

    Google Scholar 

  • Schoenfeld, A. H. (2011). Toward professional development for teachers grounded in a theory of decision making. ZDM Mathematics Education, 43(4), 457–469.

    Article  Google Scholar 

  • Schoy-Lutz, M. (2005). Fehlerkultur im Mathematikunterricht: Theoretische Grundlegung und evaluierte unterrichtspraktische Erprobung anhand der Unterrichtseinheit “Einführung in die Satzgruppe des Pythagoras”. Hildesheim, Germany: Franzbecker.

    Google Scholar 

  • Schrader, F.-W. (1989). Diagnostische Kompetenzen von Lehrern und ihre Bedeutung für die Gestaltung und Effektivität des Unterrichts. Frankfurt, Germany: Lang.

    Google Scholar 

  • Schrader, F.-W. (2006). Diagnostische Kompetenz von Eltern und Lehrern. In D. H. Rost (Ed.), Handwörterbuch Pädagogische Psychologie (pp. 68–71). Weinheim, Germany: Beltz.

    Google Scholar 

  • Schrader, F.-W. (2011). Lehrer als Diagnostiker. In E. Terhart (Hrsg.), Handbuch der Forschung zum Lehrerberuf (S. 683–698). Münster, Germany: Waxmann.

    Google Scholar 

  • Schumacher, R. (2008). Der produktive Umgang mit Fehlern: Fehler als Lerngelegenheit und Orientierungshilfe. In R. Caspary (Ed.), Nur wer Fehler macht, kommt weiter (pp. 49–72). Freiburg im Breisgau, Germany: Herder.

    Google Scholar 

  • Seifried, J., & Wuttke, E. (2010). "Professionelle Fehlerkompetenz" – Operationalisierung einer vernachlässigten Kompetenzfacette von (angehenden) Lehrkräften. Wirtschaftspsychologie, 12(4), 17–28.

    Google Scholar 

  • Shavelson, R. J., & Stern, P. (1981). Research on teachers’ pedagogical thoughts, judgements, decisions and behavior. Review of Educational Research, 51(4), 455–498.

    Article  Google Scholar 

  • Shulman, L. (1986). Those who understand: Knowledge growth in teaching. Educational Researcher, 15(2), 4–14.

    Article  Google Scholar 

  • Smith, J. P., diSessa, A. A., & Roschelle, J. (1993). Misconceptions reconceived: A constructivist analysis of knowledge in transition. The Journal of the Learning Sciences, 3(2), 115–163.

    Article  Google Scholar 

  • Son, J.-W., & Sinclair, N. (2010). How preservice teachers interpret and respond to student geometric errors. School Science and Mathematics, 110(1), 31–46.

    Article  Google Scholar 

  • Swan, M. (2001). Dealing with misconceptions in mathematics. In P. Gates (Ed.), Issues in mathematics teaching. London, UK: Routledge Falmer.

    Google Scholar 

  • Tsamir, P. (2005). Enhancing prospective teachers’ knowledge of learners’ intuitive conceptions: The case of same A–same B. Journal of Mathematics Teacher Education, 8(6), 469–497.

    Article  Google Scholar 

  • Türling, J. M., Seifried, J., & Wuttke, E. (2012). Teachers’ knowledge about domain specific student errors. In J. Seifried & E. Wuttke (Eds.), Learning from errors at school and at work (Vol. 1, pp. 95–110). Opladen, Germany: Budrich.

    Google Scholar 

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Heinrichs, H., Kaiser, G. (2018). Diagnostic Competence for Dealing with Students’ Errors: Fostering Diagnostic Competence in Error Situations. In: Leuders, T., Philipp, K., Leuders, J. (eds) Diagnostic Competence of Mathematics Teachers. Mathematics Teacher Education, vol 11. Springer, Cham. https://doi.org/10.1007/978-3-319-66327-2_4

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  • DOI: https://doi.org/10.1007/978-3-319-66327-2_4

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-66325-8

  • Online ISBN: 978-3-319-66327-2

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