Analysis of students’ mathematical errors as a means to promote future primary school teachers’ diagnostic competence


The conceptualization of teachers’ professional competencies has evolved in the last decades. The specification of the types of knowledge that teachers require, the inclusion of affective and motivational aspects and the acknowledgments of the processes that connect these dispositions to the behavior of teachers in the classroom are considered especially important. In particular, teachers’ diagnostic competence has been regarded as crucial for successful teaching because it allows teachers to understand students’ thinking and make a corresponding plan to promote learning. Errors have been recognized as a valuable source of information about students’ thinking and therefore, teachers’ diagnostic competence in error situation is the focus of this study. This article shares the design of a university course and the theoretical basis aimed at developing pre-service primary school teachers’ diagnostic competence in error situations within their initial teacher education programs. Its implementation in Chilean universities suggests a valuable opportunity for future teachers to learn and discuss about mathematics and its teaching and learning.  


La descarga de datos todavía no está disponible.


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

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

Baroody, A. J. & Hume, J. (1991). Meaningful Mathematics Instruction: The case of fractions. Remedial and Special Education, 12 (3), 54-68.

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

Brodie, K. (2014). Learning about learner errors in professional learning communities. Educational Studies in Mathematics, 85(2), 221-239.

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

Döhrmann, M., Kaiser, G., & Blömeke, S. (2014). The conceptualisation of mathematics competencies in the international teacher education study TEDS-M. In International perspectives on teacher knowledge, beliefs and opportunities to learn (pp. 431-456). Springer, Dordrecht.

Gerster, H.-D. (1982). Schülerfehler bei schriftlichen Rechenverfahren – Diagnose und Therapie. Freiburg: Herder.

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, Switzerland: Springer.

Helmke, A., & Schrader, F.-W. (1987) Interactional effects of instructional quality and teacher judgement accuracy on achievement. Teaching and Teacher Education, 3, 91-98.

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

Hoth, J., Döhrmann, M., Kaiser, G., Busse, A., König, J., & Blömeke, S. (2016). Diagnostic competence of primary school mathematics teachers during classroom situations. ZDM Mathematics Education, 48(1-2), 41-53.

Jacobs, V. R., & Philipp, R. A. (2004). Mathematical Thinking: Helping Prospective and Practicing Teachers Focus. Teaching Children Mathematics, 11(4), 194-201.

Kaiser, G., Blömeke, S., Koenig, J., Busse, A., Doehrmann, M., & Hoth, J. (2017). Professional competencies of (prospective) mathematics teachers—cognitive versus situated approaches. Educational Studies in Mathematics, 94(2), 161-182.

Kaiser, G., Busse, A., Hoth, J., König, J., & Blömeke, S. (2015). About the complexities of video-based assessments: theoretical and methodological approaches to overcoming shortcomings of research on teachers’ competence. International Journal of Science and Mathematics Education, 13, 369-387.

Koeppen, K., Hartig, J., Klieme, E., & Leutner, D. (2008). Current issues in competence modeling and assessment. Zeitschrift für Psychologie/Journal of Psychology, 216(2), 61-73.

König, J., Blömeke, S., Paine, L., Schmidt, W. H. & Hsieh, F.-J. (2011). General Pedagogical Knowledge of Future Middle School Teachers: On the Complex Ecology of Teacher Education in the United States, Germany, and Taiwan. Journal of Teacher Education, 62(2), 188-201.

Larrain, M. (2016). Comprensión del razonamiento matemático de los estudiantes: una práctica pedagógica inclusiva. UNIÓN: Revista Iberoamericana de Educación Matemática. 45: 152-161.

Lucchini, G., Cuadrado, B. & Tapia, L. (2006). Errar no es siempre un error. Santiago, Chile: Fundación Educacional Arauco (Fundar). Retrieved from

McGuire, P. (2013). Using online error analysis items to support preservice teachers' pedagogical content knowledge in mathematics. Contemporary Issues in Technology and Teacher Education, 13(3), 207-218.

Mineduc (2012). Matemática. Programa de Estudio para tercer Año Básico. Santiago, Chile: MIneduc.

Padberg, F., & Benz, C. (2011). Didaktik der Arithmetik. Für Lehrerausbildung und Lehrerfortbildung (4th ed.). Heidelberg: Spektrum.

Padberg, F. (2002): Didaktik der Bruchrechnung. Heidelberg: Spektrum.

Prediger, S. (2010). How to develop mathematics-for-teaching and for understanding: the case of meanings of the equal sign. Journal of Mathematics Teacher Education, 13(1), 73-93.

Radatz, H. (1979). Error analysis in mathematics education. Journal for Research in Mathematics Education, 10(3), 163-172.

Rico, L. (1995). Errores y dificultades en el aprendizaje de las matemáticas. In J. Kilpatrick, P. Gómez, L. Rico (Eds.), Educación matemática: errores y dificultades de los estudiantes. Resolución de problemas. Evaluación. Historia: Primer Simposio Internacional de Educación Matemática. (pp. 69-108). Grupo Editorial Iberoamericana.

Schoenfeld, A.H. (2011). How we think: a theory of goal-oriented decision making and its educational applications. New York: Routledge.

Selter, C., & Spiegel, H. (1997). Wie Kinder rechnen. Leipzig: Klett.

Sherin, M.G., Jacobs, V.R., & Philipp, R.A. (Eds.) (2011). Mathematics Teacher Noticing. Seeing Through Teachers’ Eyes. New York: Routledge.

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

Tatto, M.T., Schwille, J., Senk, S., Ingvarson, L., Peck, R., & Rowley, G. (2008). Teacher Education and Development Study in Mathematics (TEDS-M): policy, practice, and readiness to teach primary and secondary mathematics. Conceptual framework. East Lansing: Michigan State University.

Van de Walle, J. A., Lovin, L. A. H., Karp, K. S., & Bay-Williams, J. M. (2014). Teaching Student-centered Mathematics: Developmentally Appropriate Instruction for Grades 3-5 (Vol. 2). Pearson Higher Ed.

Weinert, F. E. (2001). Concept of competence: a conceptual clarification. In D. Rychen, & L. Salganik (Eds.), Defining and selecting key competencies (pp. 45-65). Seattle, WA: Hogrefe and Huber.