How to intervene in mathematics errors? A study with future primary school teachers.
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Abstract
Initial teacher training should include pedagogical knowledge for interpreting students' mathematical thinking. This study analyses how 45 student teachers interpret and respond to a student's error in calculating areas with decimals. Low-level interventions predominate, focused on re-explanation and practice, with little attention to conceptual understanding. A disconnect also emerges between the diagnosis of the error and the support offered. The study underscores the need for training sequences that utilize error analysis to develop pedagogical content knowledge.
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This work is licensed under a Creative Common License (CC BY 3.0 ES)
References
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. https://doi.org/10.1177/0022487108324554
Borasi, R. (1996). Reconceiving mathematics instruction: A focus on errors. Ablex.
Chapin, S. H., O'Connor, C., & Anderson, N. C. (2009). Classroom discussions: Using math talk to help students learn, grades K-6 (2nd ed.). Math Solutions.
Empson, S. B., & Jacobs, V. R. (2008). Learning to listen to children's mathematics. In D. Tirosh & T. Wood (Eds.), Tools and processes in mathematics teacher education (pp. 257-281). Sense Publishers.
Even, R., & Tirosh, D. (2002). Teacher knowledge and understanding of students’ mathematical learning. En L. D. English (Ed.), Handbook of international research in mathematics education (pp. 219–240). Lawrence Erlbaum Associates.
Godino, J. D., Batanero, C., y Font, V. (2004). Didáctica de las matemáticas para maestros. Proyecto Edumat-Maestros, Universidad de Granada.
Grossman, P., Compton, C., Igra, D., Ronfeldt, M., Shahan, E., & Williamson, P. (2009). Teaching practice: A cross-professional perspective. Teachers College Record, 111(9), 2055-2100.
Hernández Suárez, V. M., Ríos Villar, M. C., y Carrión Pérez, J. C. (2002). La formación inicial en matemáticas de los profesores de educación primaria y secundaria. En L. C. Contreras y L. J. Blanco (Eds.), Formación del profesorado e investigación en educación matemática IV (pp. 159-169). Universidad de Extremadura.
Hu, Z., Li, H., Liu, Y., & Su, X. (2024). The impact of teacher facilitation on students' mathematics learning in a problem-based learning environment: A metacognitive strategy perspective. Humanities and Social Sciences Communications, 11(1), 1-15. https://doi.org/10.1057/s41599-024-03520-0
Jacobs, V. R., Lamb, L. L. C., & Philipp, R. A. (2010). Professional noticing of children's mathematical thinking. Journal for Research in Mathematics Education, 41(2), 169-202. https://doi.org/10.5951/jresematheduc.41.2.0169
Llinares, S. (2013). Professional noticing: A component of the mathematics teacher's professional practice. Sisyphus—Journal of Education, 1(3), 76-93.
Martínez Sánchez-Arévalo, B, González-García, R. y Fernández-Cézar, R. (2024). Competencia matemática y plan de mejora: evidencias desde el diagnóstico. Matemáticas, Educación y Sociedad, 7(2), 25-48
Mason, J. (2002). Researching your own practice: The discipline of noticing. RoutledgeFalmer.
Maz-Machado, A. (2018). Investigando en el aula de matemáticas con los maestros en formación. En Rodríguez, A. y otros (Eds.): Livro de Atas do EIEM 2018, Encontro em Investigação em Educação Matemática (pp. 27-37). EIEM.
Morris, A. K., Hiebert, J., & Spitzer, S. M. (2009). Mathematical knowledge for teaching in planning and evaluating instruction: What can preservice teachers learn? Journal for Research in Mathematics Education, 40(5), 491-529. https://doi.org/10.5951/jresematheduc.40.5.0491
Philipp, R. A. (2007). Mathematics teachers’ beliefs and affect. En F. K. Lester Jr. (Ed.), Second handbook of research on mathematics teaching and learning (pp. 257–315). Information Age Publishing.
Radatz, H. (1979). Error analysis in mathematics education. Journal for Research in Mathematics Education, 10(3), 163–172. https://doi.org/10.2307/748804
Rico, L., Gómez, P., y Cañadas, M. C. (2011). Formación inicial en educación matemática de los maestros de Primaria en España, 1991-2010. Revista de Educación, 363, 1-16. https://doi.org/10.4438/1988-592X-RE-2011-362-152
Russo, J., & Hopkins, S. (2026). Designing and implementing a teacher professional learning program to support teachers' exercise of professional judgment to interpret and respond to student mathematical thinking. Mathematics Education Research Journal, 38(1), 1-25. https://doi.org/10.1007/s13394-024-00499-0
Santagata, R., & Guarino, J. (2011). Using video to teach future teachers to learn from teaching. ZDM–Mathematics Education, 43(1), 133-145. https://doi.org/10.1007/s11858-010-0292-3
Schoenfeld, A. H. (2010). How we think: A theory of goal-oriented decision making and its educational applications. Routledge.
Sherin, M. G., & van Es, E. A. (2009). Effects of video club participation on teachers' professional vision. Journal of Teacher Education, 60(1), 20-37. https://doi.org/10.1177/0022487108328155
Sherin, M. G., Jacobs, V. R., & Philipp, R. A. (Eds.). (2011). Mathematics teacher noticing: Seeing through teachers' eyes. Routledge.
Shulman, L. S. (1986). Those who understand: Knowledge growth in teaching. Educational Researcher, 15(2), 4–14. https://doi.org/10.3102/0013189X015002004
Shulman, L. S. (1987). Knowledge and teaching: Foundations of the new reform. Harvard Educational Review, 57(1), 1–22. https://doi.org/10.17763/haer.57.1.j463w79r56455411
Son, J. W., & Crespo, S. (2009). Prospective teachers' reasoning and response to a student's non-traditional strategy when dividing fractions. Journal of Mathematics Teacher Education, 12(4), 235-261. https://doi.org/10.1007/s10857-009-9112-5
Stockero, S. L., & Van Zoest, L. R. (2013). Characterizing pivotal teaching moments in beginning mathematics teachers' practice. Journal of Mathematics Teacher Education, 16(2), 125-147. https://doi.org/10.1007/s10857-012-9222-3
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. https://doi.org/10.1177/0022487108324554
Borasi, R. (1996). Reconceiving mathematics instruction: A focus on errors. Ablex.
Chapin, S. H., O'Connor, C., & Anderson, N. C. (2009). Classroom discussions: Using math talk to help students learn, grades K-6 (2nd ed.). Math Solutions.
Empson, S. B., & Jacobs, V. R. (2008). Learning to listen to children's mathematics. In D. Tirosh & T. Wood (Eds.), Tools and processes in mathematics teacher education (pp. 257-281). Sense Publishers.
Even, R., & Tirosh, D. (2002). Teacher knowledge and understanding of students’ mathematical learning. En L. D. English (Ed.), Handbook of international research in mathematics education (pp. 219–240). Lawrence Erlbaum Associates.
Godino, J. D., Batanero, C., y Font, V. (2004). Didáctica de las matemáticas para maestros. Proyecto Edumat-Maestros, Universidad de Granada.
Grossman, P., Compton, C., Igra, D., Ronfeldt, M., Shahan, E., & Williamson, P. (2009). Teaching practice: A cross-professional perspective. Teachers College Record, 111(9), 2055-2100.
Hernández Suárez, V. M., Ríos Villar, M. C., y Carrión Pérez, J. C. (2002). La formación inicial en matemáticas de los profesores de educación primaria y secundaria. En L. C. Contreras y L. J. Blanco (Eds.), Formación del profesorado e investigación en educación matemática IV (pp. 159-169). Universidad de Extremadura.
Hu, Z., Li, H., Liu, Y., & Su, X. (2024). The impact of teacher facilitation on students' mathematics learning in a problem-based learning environment: A metacognitive strategy perspective. Humanities and Social Sciences Communications, 11(1), 1-15. https://doi.org/10.1057/s41599-024-03520-0
Jacobs, V. R., Lamb, L. L. C., & Philipp, R. A. (2010). Professional noticing of children's mathematical thinking. Journal for Research in Mathematics Education, 41(2), 169-202. https://doi.org/10.5951/jresematheduc.41.2.0169
Llinares, S. (2013). Professional noticing: A component of the mathematics teacher's professional practice. Sisyphus—Journal of Education, 1(3), 76-93.
Martínez Sánchez-Arévalo, B, González-García, R. y Fernández-Cézar, R. (2024). Competencia matemática y plan de mejora: evidencias desde el diagnóstico. Matemáticas, Educación y Sociedad, 7(2), 25-48
Mason, J. (2002). Researching your own practice: The discipline of noticing. RoutledgeFalmer.
Maz-Machado, A. (2018). Investigando en el aula de matemáticas con los maestros en formación. En Rodríguez, A. y otros (Eds.): Livro de Atas do EIEM 2018, Encontro em Investigação em Educação Matemática (pp. 27-37). EIEM.
Morris, A. K., Hiebert, J., & Spitzer, S. M. (2009). Mathematical knowledge for teaching in planning and evaluating instruction: What can preservice teachers learn? Journal for Research in Mathematics Education, 40(5), 491-529. https://doi.org/10.5951/jresematheduc.40.5.0491
Philipp, R. A. (2007). Mathematics teachers’ beliefs and affect. En F. K. Lester Jr. (Ed.), Second handbook of research on mathematics teaching and learning (pp. 257–315). Information Age Publishing.
Radatz, H. (1979). Error analysis in mathematics education. Journal for Research in Mathematics Education, 10(3), 163–172. https://doi.org/10.2307/748804
Rico, L., Gómez, P., y Cañadas, M. C. (2011). Formación inicial en educación matemática de los maestros de Primaria en España, 1991-2010. Revista de Educación, 363, 1-16. https://doi.org/10.4438/1988-592X-RE-2011-362-152
Russo, J., & Hopkins, S. (2026). Designing and implementing a teacher professional learning program to support teachers' exercise of professional judgment to interpret and respond to student mathematical thinking. Mathematics Education Research Journal, 38(1), 1-25. https://doi.org/10.1007/s13394-024-00499-0
Santagata, R., & Guarino, J. (2011). Using video to teach future teachers to learn from teaching. ZDM–Mathematics Education, 43(1), 133-145. https://doi.org/10.1007/s11858-010-0292-3
Schoenfeld, A. H. (2010). How we think: A theory of goal-oriented decision making and its educational applications. Routledge.
Sherin, M. G., & van Es, E. A. (2009). Effects of video club participation on teachers' professional vision. Journal of Teacher Education, 60(1), 20-37. https://doi.org/10.1177/0022487108328155
Sherin, M. G., Jacobs, V. R., & Philipp, R. A. (Eds.). (2011). Mathematics teacher noticing: Seeing through teachers' eyes. Routledge.
Shulman, L. S. (1986). Those who understand: Knowledge growth in teaching. Educational Researcher, 15(2), 4–14. https://doi.org/10.3102/0013189X015002004
Shulman, L. S. (1987). Knowledge and teaching: Foundations of the new reform. Harvard Educational Review, 57(1), 1–22. https://doi.org/10.17763/haer.57.1.j463w79r56455411
Son, J. W., & Crespo, S. (2009). Prospective teachers' reasoning and response to a student's non-traditional strategy when dividing fractions. Journal of Mathematics Teacher Education, 12(4), 235-261. https://doi.org/10.1007/s10857-009-9112-5
Stockero, S. L., & Van Zoest, L. R. (2013). Characterizing pivotal teaching moments in beginning mathematics teachers' practice. Journal of Mathematics Teacher Education, 16(2), 125-147. https://doi.org/10.1007/s10857-012-9222-3