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Perception of student errors under time limitation: are teachers faster than mathematicians or students?

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Abstract

The ability to offer constructive feedback to students concerning their errors is an indispensable requirement for mathematics teachers, for the purpose of providing cognitively challenging learning opportunities. However, if they are to react adequately, teachers need to identify student errors immediately. The fast perception of student errors can therefore be described as an indispensable part of mathematics teachers’ professional competence. Data on this facet of teacher competence were gathered as part of a national follow-up-study of the IEA’s international TEDS-M (Teacher Education and Development Study in Mathematics) that used a time-limited test to measure teachers’ perception of student errors. This paper aims to provide evidence for the validity of the test interpretation of fast student-error perception as an indicator of professional competence by drawing on contrast groups already used in other studies. Overall, the study could support the validity of the test interpretation because the chosen contrast groups were found to perform either better than the tested teachers—as is the case for the contrast group of mathematicians—or more poorly, as is the case for the group of students. Furthermore, the present study shows that the competence facet of fast student error perception is closer to the domain of teachers’ mathematical content knowledge than it is to the domain of teachers’ mathematics pedagogical content knowledge.

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References

  • Allmendinger, H., Lengnink, K., Vohns, A., & Wickel, G. (2013). Mathematik verständlich unterrichten: Perspektiven für Unterricht und Lehrerbildung. Wiesbaden: Springer.

    Book  Google Scholar 

  • Altmann, A. F., & Nückles, M. (2017). Empirische Studien zu Qualitätsindikatoren für den diagnostischen Prozess. In A. Südkamp & A.-K. Praetorius (Eds.), Diagnostische Kompetenz von Lehrkräften. Theoretische und methodische Weiterentwicklungen (pp. 142–149). Münster: Waxmann.

    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 

  • Bandalos, D. L., & Finney, S. J. (2009). Item parceling issues in structural equation modeling. In G. A. Marcoulides & R. E. Schumacker (Eds.), New developments and techniques in structural equation modeling (pp. 269–296). Mahwah: Erlbaum.

    Google Scholar 

  • Binder, K., Krauss, S., Hilbert, S., Brunner, M., Anders, Y., & Kunter, M. (2018). Diagnostic Skills of mathematics teachers in the COACTIV study. In T. Leuders & K. Philipp K., & J. Leuders (Eds.), Diagnostic competence of mathematics teachers (pp. 33–53). Mathematics Teacher Education. Cham: Springer.

    Chapter  Google Scholar 

  • Blömeke, S., Busse, A., Kaiser, G., König, J., & Suhl, U. (2016). The relation between content-specific and general teacher knowledge and skills. Teaching and Teacher Education, 56(May), 35–46.

    Article  Google Scholar 

  • Blömeke, S., Gustafsson, J.-E., & Shavelson, R. J. (2015). Beyond dichotomies: Competence viewed as a Continuum. Zeitschrift für Psychologie, 223(1), 3–13.

    Article  Google Scholar 

  • Blömeke, S., Kaiser, G., & Lehmann, R. (2010). (Eds.). TEDS-M 2008—Professionelle Kompetenz und Lerngelegenheiten angehender Mathematik-Lehrkräfte für die Sekundarstufe I im internationalen Vergleich. Münster: Waxmann.

    Google Scholar 

  • Blömeke, S., König, J., Busse, A., Suhl, U., Benthien, J., Döhrmann, M., & Kaiser, G. (2014). Von der Lehrerausbildung in den Beruf—Fachbezogenes Wissen als Voraussetzung für Wahrnehmung, Interpretation und Handeln im Unterricht. Zeitschrift für Erziehungswissenschaft, 17(3), 509–542.

    Article  Google Scholar 

  • Bortz, J., & Döring, N. (2006). Forschungsmethoden und Evaluation: Für Human- und Sozialwissenschaftler (4. edn.). Heidelberg: Springer.

    Book  Google Scholar 

  • Brühwiler, C. (2017). Diagnostische und didaktische Kompetenz als Kern adaptiver Lehrkompetenz. In: A. Südkamp, & A.-K. Praetorius (Eds.), Diagnostische Kompetenz von Lehrkräften. Theoretische und methodische Weiterentwicklungen (pp. 123–134). Münster: Waxmann.

  • Bühner, M. (2011). Einführung in die Test- und Fragebogenkonstruktion. München: Pearson Deutschland.

    Google Scholar 

  • Charalambous, C. Y. (2016). Investigating the knowledge needed for teaching mathematics. Journal of Teacher Education, 67(3), 220–237.

    Article  Google Scholar 

  • Heinrichs, H., & Kaiser, G. (2018). Diagnostic competence for dealing with students’ errors: Fostering diagnostic competence in error situations. In T. Leuders, K. Philipp & J. Leuders (Eds.), Diagnostic competence of mathematics teachers (pp. 79–94). Cham: Springer.

    Chapter  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 

  • Hill, H. C., Ball, D., & Schilling, S. (2008). Unpacking pedagogical content knowledge: Conceptualizing and measuring teachers’ topic-specific knowledge of students. Journal for Research in Mathematics Education, 39(4), 372–400.

    Google Scholar 

  • Hill, H. C., Dean, C., & Goffney, I. M. (2007). Assessing elemental and structural validity: Data from teachers, non-teachers, and mathematicians. Measurement: Interdisciplinary Research & Perspective, 5(2–3), 81–92.

    Google Scholar 

  • Hoth, J., Döhrmann, M., Kaiser, G., Busse, A., König, J., & Blömeke, S. (2016). Diagnostic competence of primary school mathematics teachers during classroom situations. ZDM, 48(1), 41–53.

    Article  Google Scholar 

  • Kane, M. T. (2001). Current concerns in validity theory. Journal of Educational Measurement, 38(4), 319–342.

    Article  Google Scholar 

  • Krauss, S., Baumert, J., & Blum, W. (2008). Secondary mathematics teachers’ pedagogical content knowledge and content knowledge: Validation of the COACTIV constructs. ZDM—The International Journal on Mathematics Education, 40(5), 873–892.

    Article  Google Scholar 

  • Krauss, S., & Brunner, M. (2011). Schnelles Beurteilen von Schülerantworten: Ein Reaktionszeittest für Mathematiklehrer/innen. Journal für Mathematik-Didaktik, 32(2), 233–251.

    Article  Google Scholar 

  • Krauss, S., Brunner, M., Kunter, M., Baumert, J., Blum, W., Neubrand, M., & Jordan, A. (2008). Pedagogical content knowledge and content knowledge of secondary mathematics teachers. Journal of Educational Psychology, 100(3), 716–725.

    Article  Google Scholar 

  • Leuders, T. (2001). Qualität im Mathematikunterricht in der Sekundarstufe I und II. Berlin: Cornelsen Scriptor.

    Google Scholar 

  • Leuders, T., Philipp, K. & Leuders, J. (2018). Diagnostic competence of mathematics teachers. Cham: Springer.

    Book  Google Scholar 

  • Lindmeier, A. M., Heinze, A., & Reiss, K. (2013). Eine Machbarkeitsstudie zur Operationalisierung aktionsbezogener Kompetenz von Mathematiklehrkräften mit videobasierten Maßen. Journal für Mathematik-Didaktik, 34(1), 99–119.

    Article  Google Scholar 

  • Lissitz, R. W., & Samuelsen, K. (2007). A suggested change in terminology and emphasis regarding validity and education. Educational Researcher, 36(8), 437–448.

    Article  Google Scholar 

  • Madden, D. J. (2007). Ageing and visual attention. Current Directions in Psychological Science, 16, 2, 70–74.

    Article  Google Scholar 

  • Newton, P., & Shaw, S. (2016). Disagreement over the best way to use the word ‘validity’ and options for reaching consensus. Assessment in Education: Principles, Policy & Practice, 23(2), 178–197.

    Article  Google Scholar 

  • Oser, F., Hascher, T., & Spychiger, M. (1999). Lernen aus Fehlern: Zur Psychologie des “negativen” Wissens. In W. Althof (Ed.), Fehlerwelten. Vom Fehlermachen und Lernen aus Fehlern (pp. 11–41). Wiesbaden: VS Verlag für Sozialwissenschaften.

    Google Scholar 

  • Padberg, F. (2009). Didaktik der Bruchrechnung. Heidelberg: Springer.

    Book  Google Scholar 

  • Pankow, L., Kaiser, G., Busse, A., König, J., Blömeke, S., Hoth, J., & Döhrmann, M. (2016). Early career teachers’ ability to focus on typical students errors in relation to the complexity of a mathematical topic. ZDM, 48(1–2), 55–67.

    Article  Google Scholar 

  • Radatz, H. (1980a). Fehleranalysen im Mathematikunterricht. Wiesbaden: Vieweg + Teubner Verlag.

    Book  Google Scholar 

  • Radatz, H. (1980b). Students’ errors in the mathematical learning process: A survey. For the Learning of Mathematics, 1, 16–20.

    Google Scholar 

  • Reisman, F. K. (1976). A guide to the diagnostic teaching of arithmetic. Columbus: Merrill.

    Google Scholar 

  • Ritter, S., & Voß, U. (2015). Erfolgreich Starten ins Ingenieurstudium: Grundlagen der Mathematik anwendungsorientiert erklärt. Berlin: Springer Vieweg.

    Book  Google Scholar 

  • Rosseel, Y. (2017). Package “lavaan”: Latent variable analysis. Comprehensive R Archive Network. Retrieved from http://lavaan.org. Accessed 23 Dec 2017.

  • Salthouse, T. A. (1996). The processing-speed theory of adult age differences in cognition. Psychological Review, 103(3), 403–428.

    Article  Google Scholar 

  • Schlag, B. (1993). Elderly drivers in Germany—Fitness and driving behavior. Accident Analysis and Prevention, 25(1), 47–55.

    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: Franzbecker.

    Google Scholar 

  • Schwab, S., & Helm, C. (2015). Überprüfung von Messinvarianz mittels CFA und DIF-Analysen. Empirische Sonderpädagogik, 7(3), 175–193.

    Google Scholar 

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

    Article  Google Scholar 

  • Südkamp, A., & Praetorius, A.-K. (Eds.). (2017). Diagnostische Kompetenz von Lehrkräften: Theoretische und methodische Weiterentwicklungen. Münster: Waxmann.

    Google Scholar 

  • Swan, M. (2004). Making sense of mathematics. In I. Thompson (Ed.), Enhancing primary mathematics teaching and learning (pp. 111–124). Maidenhead: Open University Press.

    Google Scholar 

  • Türling, J. M. (2014). Die professionelle Fehlerkompetenz von (angehenden) Lehrkräften: Eine empirische Untersuchung im Rechnungswesenunterricht. Wiesbaden: Springer.

    Book  Google Scholar 

  • Wahl, D., Weinert, F. E., & Huber, G. L. (1984). Psychologie für die Schulpraxis: Ein handlungsorientiertes Lehrbuch für Lehrer. München: Kösel.

    Google Scholar 

  • Wartha, S. (2007). Längsschnittliche Untersuchungen zur Entwicklung des Bruchzahlbegriffs. Hildesheim: Franzbecker.

    Google Scholar 

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Authors and Affiliations

  1. University of Hamburg, Hamburg, Germany

    Lena Pankow & Gabriele Kaiser

  2. Australian Catholic University, Brisbane, Australia

    Gabriele Kaiser

  3. University of Cologne, Cologne, Germany

    Johannes König

  4. Centre for Educational Measurement at University of Oslo, Oslo, Norway

    Sigrid Blömeke

Authors
  1. Lena Pankow
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  2. Gabriele Kaiser
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  3. Johannes König
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  4. Sigrid Blömeke
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Correspondence to Lena Pankow.

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Pankow, L., Kaiser, G., König, J. et al. Perception of student errors under time limitation: are teachers faster than mathematicians or students?. ZDM Mathematics Education 50, 631–642 (2018). https://doi.org/10.1007/s11858-018-0945-1

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