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The Diagnostic Skills of Mathematics Teachers

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Cognitive Activation in the Mathematics Classroom and Professional Competence of Teachers

Part of the book series: Mathematics Teacher Education ((MTEN,volume 8))

Abstract

Teachers apply their diagnostic skills when grading students’ work as well as when preparing lessons and monitoring students’ understanding during the learning process. Previous research on teachers’ diagnostic skills has focused on teachers at elementary level. Drawing on a large German sample of mathematics teachers at secondary level, this chapter empirically addresses three key questions on teachers’ diagnostic skills (depending on the research question, the number of teachers with valid data varied between n=155 and n=331). The results showed that (a) the accuracy of teachers’ judgments of their classes’ achievement level, distribution of achievement, and motivation is relatively low, (b) diagnostic skills do not represent a one-dimensional but a multidimensional construct, and (c) teachers’ diagnostic skills (in terms of tasks-related judgment error and diagnostic sensitivity) have a positive influence on their students’ achievement gains in mathematics. Training and fostering teachers’ diagnostic skills seems thus to be highly relevant for the valid assignment of grades and for student progress.

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Notes

  1. 1.

    The class mean score on the effort scale (see Ramm et al. 2006) of the national PISA student questionnaire was used as a class-specific indicator of motivation in mathematics. A sample item from this scale is “In mathematics I make a real effort to understand everything.”

  2. 2.

    Different judgment tendencies may thus result in the same judgment error scores. A teacher who overestimates the achievement level of her class by one point will have the same judgment error score as a teacher who underestimates the performance level of her class by one point.

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Author information

Authors and Affiliations

  1. Evaluation and Quality Management in Education, Free University of Berlin and Berlin-Brandenburg Institute for School Quality, Otto-von-Simson-Str. 15, D-14195, Berlin, Germany

    Martin Brunner (Chair)

  2. Early Childhood Education, Free University of Berlin, Habelschwerdter Allee 45, D-14195, Berlin, Germany

    Yvonne Anders (Chair) & Axinja Hachfeld (Chair)

  3. Faculty of Mathematics, Education of Mathematics, University of Regensburg, Universitätsstraße 31, 93053, Regensburg, Germany

    Stefan Krauss

Authors
  1. Martin Brunner
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  2. Yvonne Anders
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  3. Axinja Hachfeld
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  4. Stefan Krauss
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Corresponding author

Correspondence to Martin Brunner .

Editor information

Editors and Affiliations

  1. , Institute of Psychology, University of Frankfurt am Main, Postfach 125, Frankfurt am Main, 60054, Germany

    Mareike Kunter

  2. , Center for Educational Research, Max Planck Institute for Human Developme, Lentzeallee 94, Berlin, 14195, Germany

    Jürgen Baumert

  3. Mathematik/Informatik, Universität Kassel, Kassel, 34109, Germany

    Werner Blum

  4. Christian Albrecht University, Kiel, Lentzeallee 94, Berlin, 14195, Germany

    Ute Klusmann

  5. , Faculty of Mathematics Education of Math, University of Regensburg, Universitätsstr. 31, Regensburg, 93053, Germany

    Stefan Krauss

  6. , Institute of Mathematics, Carl von Ossietzky University of Oldenbu, Oldenburg, 26111, Germany

    Michael Neubrand

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Brunner, M., Anders, Y., Hachfeld, A., Krauss, S. (2013). The Diagnostic Skills of Mathematics Teachers. In: Kunter, M., Baumert, J., Blum, W., Klusmann, U., Krauss, S., Neubrand, M. (eds) Cognitive Activation in the Mathematics Classroom and Professional Competence of Teachers. Mathematics Teacher Education, vol 8. Springer, Boston, MA. https://doi.org/10.1007/978-1-4614-5149-5_11

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