Theory of didactical suitability: An enlarged view of the quality of mathematics instruction

Juan D. Godino; Carmen Batanero; María Burgos

doi:10.29333/ejmste/13187

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Juan D. Godino ¹ ^* , Carmen Batanero ¹ , María Burgos ¹

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¹ Universidad de Granada, Granada, SPAIN^* Corresponding Author

Abstract

Characterizing and measuring the quality of instruction is a matter of growing interest in mathematics education. Based on the notion of didactic suitability and the theoretical assumptions of the onto-semiotic approach, we develop an instrument to systematically analyze the different facets involved in a mathematics instruction process. We also explore the concordances and complementarities with instruments for measuring the quality of instruction. Thus, quantitative quality measurement efforts are complemented by another qualitative approach, focusing on the initiative and responsibility of teachers when they have to make decisions about their teaching practices. This reflective activity must be supported by specific instruments that reveal the complexity of the processes and the difficulty of achieving a balance between sometimes conflicting didactic principles.

Keywords

mathematics education
didactic suitability
instructional quality
onto-semiotic approach

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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Article Type: Research Article

EURASIA J Math Sci Tech Ed, 2023, Volume 19, Issue 6, Article No: em2270

https://doi.org/10.29333/ejmste/13187

Publication date: 01 Jun 2023

Online publication date: 12 Apr 2023

Article Views: 2363

Article Downloads: 1146

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References

Andrew, L. (2007). Comparison of teacher educators’ instructional methods with the constructivist ideal. The Teacher Educator, 42(3), 157-184. https://doi.org/10.1080/08878730709555401
Bartolini, M. G., & Martignone, F. (2020). Manipulatives in mathematics education. In S. Lerman (Ed.) Encyclopedia of mathematics education. Springer. https://doi.org/10.1007/978-3-030-15789-0_93
Batanero, C., & Díaz, C. (2007). Meaning and understanding of mathematics. The case of probability. In J. P. Van Bendegen, & K. François (Eds.), Philosophical dimensions in mathematics education (pp. 107-128). Springer. https://doi.org/10.1007/978-0-387-71575-9_6
Beltrán-Pellicer, P., & Godino, J. D. (2020). An onto-semiotic approach to the analysis of the affective domain in mathematics education. Cambridge Journal of Education, 50(1), 1-20. https://doi.org/10.1080/0305764X.2019.1623175
Beltrán-Pellicer, P., Giacomone, B., & Burgos, M. (2018). Los vídeos educativos en línea desde las didácticas específicas: El caso de las matemáticas [Online educational videos from specific didactics: The case of mathematics]. Cultura y Educación, 30(4), 633-662. https://doi.org/10.1080/11356405.2018.1524651
Berlin, R., & Cohen, J. (2018). Understanding instructional quality through a relational lens. ZDM, 50, 367-379. https://doi.org/10.1007/s11858-018-0940-6
Biesta, G. J. J. (2010). Why ‘what works’ still won’t work: from evidence-based education to value-based education. Studies in Philosophy and Education, 29, 491-503. https://doi.org/10.1007/s11217-010-9191-x
Bostic, J., Lesseig, K., Sherman, M., & Boston, M. (2021). Classroom observation and mathematics education research. Journal of Mathematics Teacher Education, 24, 5-31. https://doi.org/10.1007/s10857-019-09445-0
Boston, M. D. (2012). Assessing instructional quality in mathematics. Elementary School Journal, 113, 76-104. https://doi.org/10.1086/666387
Breda, A., Font, V., & Pino-Fan, L. (2018). Criterios valorativos y normativos en la didáctica de las matemáticas: El caso del constructo idoneidad didáctica [Evaluative and normative criteria in the didactics of mathematics: The case of the didactic suitability construct]. Bolema: Boletim de Educação Matemática, 32(60), 255-278. https://doi.org/10.1590/1980-4415v32n60a13
Breda, A., Pino-Fan, L., & Font, V. (2017). Meta didactic-mathematical knowledge of teachers: Criteria for the reflection and assessment on teaching practice. EURASIA Journal of Mathematics Science and Technology Education, 13(6), 1893-1918. https://doi.org/10.12973/eurasia.2017.01207a
Brousseau, B. (1997). Theory of didactical situations in mathematics. Kluwer Academic Publishing.
Burgos, M., & Godino, J. D. (2020). Modelo ontosemiótico de referencia de la proporcionalidad. Implicaciones para la planificación curricular en primaria y secundaria [Reference onto-semiotic model of proportionality. Implications for curriculum planning in primary and secondary]. AIEM, 18, 1-20. https://doi.org/10.35763/aiem.v0i18.255
Burgos, M., Beltrán-Pellicer, P., & Godino, J. D. (2020). The issue of didactical suitability in mathematics educational videos: Experience of analysis with prospective primary school teachers. Revista Española de Pedagogía, 78(275), 27-49. https://doi.org/10.22550/REP78-1-2020-07
Castillo, M. J., & Burgos, M. (2022a). Developing reflective competence in prospective mathematics teachers by analyzing textbooks lessons. EURASIA Journal of Mathematics, Science and Technology Education, 18(6), em2121. https://doi.org/10.29333/ejmste/12092
Castillo, M. J., & Burgos, M. (2022b). Reflexiones de futuros maestros sobre la idoneidad didáctica y modo de uso de una lección de libro de texto [Reflections of future teachers on the didactic suitability and mode of use of a textbook lesson]. Bolema: Boletim de Educação Matemática, 36, 555-579. https://doi.org/10.1590/1980-4415v36n72a25
Charalambous, C. Y., & Praetorius, A. K. (2018). Studying instructional quality in mathematics through different lenses: In search of common ground. ZDM, 50, 355-366. https://doi.org/10.1007/s11858-018-0914-8
Duval, R. (1995). Sémiosis et pensée: Registres sémiotiques et apprentissages intellectuels [Semiosis and thought: Semiotic registers and intellectual learning]. Peter Lang.
Duval, R. (2006). A cognitive analysis of problems of comprehension in a learning of mathematics. Educational Studies in Mathematics, 61(1-2), 103-131. https://doi.org/10.1007/s10649-006-0400-z
Ernest, P. (1998). Social constructivism as a philosophy of mathematics. SUNY.
Font, V., Godino, J. D., & Gallardo, J. (2013). The emergence of objects from mathematical practices. Educational Studies in Mathematics, 82, 97-124. https://doi.org/10.1007/s10649-012-9411-0
Franke, M. L., Kazemi, E., & Battey, D. (2007). Mathematics teaching and classroom practice. In F. K. Lester (ed.), Second handbook of research on mathematics teaching and learning (pp. 225-256). NCTM & IAP.
Freudenthal, H. (1983). Didactical phenomenology of mathematical structures. Reidel.
Freudenthal, H. (1991). Revisiting mathematics education. Springer Science & Business Media.
Garcés, W., Font, V., & Morales-Maure, L. (2021). Criteria that guide the professor’s practice to explain mathematics at basic sciences courses in engineering degrees in Perú: A case study. Acta Scientiae, 23(3), 1-33. https://doi.org/10.17648/acta.scientiae.6389
Giacomone, B., Godino, J. D., & Beltrán-Pellicer, P. (2018). Desarrollo de la competencia de análisis de la idoneidad didáctica en futuros profesores de matemáticas [Development of the didactic suitability analysis competence in future mathematics teachers]. Educação e Pesquisa, 44, e172011.
https://doi.org/10.1590/s1678-4634201844172011
Godino, J. D. (2013). Indicadores de la idoneidad didáctica de procesos de enseñanza y aprendizaje de las matemáticas [Indicators of the didactic suitability of mathematics teaching and learning processes]. Cuadernos de Investigación y Formación en Educación Matemática, 11, 111-132.
Godino, J. D. (2014). Síntesis del enfoque ontosemiótico del conocimiento y la instrucción matemáticos: motivación, supuestos y herramientas teóricas [Synthesis of the ontosemiotic approach to mathematical knowledge and instruction: motivation, assumptions and theoretical tools]. http://enfoqueontosemitico.ugr.es/documentos/sintesis_EOS_2abril2016.pdf
Godino, J. D. Batanero, C., & Font, V. (2007). The onto-semiotic approach to research in mathematics education. ZDM, 39(1-2), 127-135. https://doi.org/10.1007/s11858-006-0004-1
Godino, J. D., & Batanero, C. (1994). Significado institucional y personal de los objetos matemáticos [Institutional and personal meaning of mathematical objects]. Recherches en Didactique des Mathématiques, 14(3), 325-355.
Godino, J. D., Batanero, C., & Font, V. (2019). The onto-semiotic approach: Implications for the prescriptive character of didactics. For the Learning of Mathematics, 39(1), 37-42.
Godino, J. D., Batanero, C., Burgos, M., & Gea, M. M. (2021). Una perspectiva ontosemiótica de los problemas y métodos de investigación en educación matemática. [An ontosemiotic perspective of research problems and methods in mathematics education]. Revemop, 3, e202107. https://doi.org/10.33532/revemop.e202107
Godino, J. D., Burgos, M., & Gea, M. (2021). Analyzing theories of meaning in mathematics education from the onto-semiotic approach. International Journal of Mathematical Education in Science and Technology, 53(10), 2609-2636. https://doi.org/10.1080/0020739X.2021.1896042
Godino, J. D., Burgos, M., & Wilhelmi, M. R. (2020). Papel de las situaciones adidácticas en el aprendizaje matemático. Una mirada crítica desde el enfoque ontosemiótico [Role of didactic situations in mathematical learning. A critical look from the ontosemiotic approach]. Enseñanza de las Ciencias, 38(1), 147-164. https://doi.org/10.5565/rev/ensciencias.2906
Gómez-Chacón, I. M. (2000). Affective influences in the knowledge of mathematics. Educational Studies in Mathematics, 43, 149-168. https://doi.org/10.1023/A:1017518812079
Hanna, G., & de Villiers, M. (Eds.) (2012). Proof and proving in mathematics education. Springer. https://doi.org/10.1007/978-94-007-2129-6
Hill, H. C., Blunk, M. L., Charalambous, C. Y., Lewis, J. M., Phelps, G. C., Sleep, L., & Ball, D. L. (2008). Mathematical knowledge for teaching and the mathematical quality of instruction: An exploratory study. Cognition and Instruction, 26(4), 430-511. https://doi.org/10.1080/07370000802177235
Hjelmslev, L. (1943). Prolegomena to a theory of language. The University of Wisconsin Press.
Karsenty, R., & Arcavi, A. (2017). Mathematics, lenses and videotapes: A framework and a language for developing reflective practices of teaching. Journal of Mathematics Teacher Education, 20, 433-455. https://doi.org/10.1007/s10857-017-9379-x
Learning Mathematics for Teaching Project. (2011). Measuring the mathematical quality of instruction. Journal of Mathematics Teacher Education, 14(1), 25-47. https://doi.org/10.1007/s10857-010-9140-1
Matsumura, L. C., Garnier, H., Slater, S. C., & Boston, M. (2008). Toward measuring instructional interactions ‘at scale’. Educational Assessment, 13(4), 267-300. https://doi.org/10.1080/10627190802602541
McLeod, D. B. (1992). Research on affect in mathematics education: A reconceptualization. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 575-598). Macmillan.
McNeil, N. M., & Jarvin, L. (2007). When theory don’t add up: disentangling the manipulatives debate. Theory into Practice, 46(4), 309-316. https://doi.org/10.1080/00405840701593899
NCTM. (2000). Principles and standards for school mathematics. National Council of Teachers of Mathematics.
Peirce, C. S. (1958). Collected papers of Charles Sanders Peirce. Harvard University Press.
Praetorius, A. K., & Charalambous, C. Y. (2018). Classroom observation frameworks for studying instructional quality: looking back and looking forward. ZDM, 50, 535-553. https://doi.org/10.1007/s11858-018-0946-0
Schoenfeld, A. (2018). Video analyses for research and professional development: the teaching for robust understanding (TRU) framework. ZDM, 50, 491-506. https://doi.org/10.1007/s11858-017-0908-y
Schoenfeld, A. H. (2013). Classroom observations in theory and practice. ZDM, 45, 607-621. https://doi.org/10.1007/s11858-012-0483-1
Skovsmose, O. (2012). An invitation to critical mathematics education. Springer Science & Business Media. https://doi.org/10.1007/978-94-6091-442-3
Thompson, C. J., & Davis, S. B. (2014). Classroom observation data and instruction in primary mathematics education: Improving design and rigor. Mathematics Education Research Journal, 26(2), 301-323. https://doi.org/10.1007/s13394-013-0099-y
Tzur, R. (2001). Becoming a mathematics teacher-educator: Conceptualizing the terrain through self-reflective analysis. Journal of Mathematics Teacher Education, 4, 259-283. https://doi.org/10.1023/A:1013314009952
Uttal, D. H., Scudder, K. V., & Deloache, J. S. (1997). Manipulatives as symbols: A new perspective on the use of concrete objects to teach mathematics. Journal of Applied Developmental Psychology, 18, 37-54.https://doi.org/10.1016/S0193-3973(97)90013-7
Van den Heuvel-Panhuizen, M., & Wijers, M. (2005). Mathematics standards and curricula in the Netherlands. ZDM, 37(4), 287-306. https://doi.org/10.1007/BF02655816
Vygotsky, L. S. (1934). El desarrollo de los procesos psicológicos superiors [The development of higher psychological processes]. Crítica-Grijalbo.
Walkowiak, T. A., Berry, R. Q., Meyer, J. P., Rimm-Kaufman, S. E., & Ottmar, E. R. (2014). Introducing an observational measure of standards-based mathematics teaching practices: Evidence of validity and score reliability. Educational Studies in Mathematics, 85(1), 109128. https://doi.org/10.1007/s10649-013-9499-x
Wilhelmi, M. R., Godino, J. D., & Lacasta, E. (2007). Configuraciones epistémicas asociadas a la noción de igualdad de números reales [Epistemic configurations associated with the notion of equality of real numbers]. Recherches en Didactique des Mathematiques, 27(1), 77-120.
Wittgenstein, L. (1953). Philosophical investigations. The MacMillan Company.

How to cite this article

APA

Godino, J. D., Batanero, C., & Burgos, M. (2023). Theory of didactical suitability: An enlarged view of the quality of mathematics instruction. Eurasia Journal of Mathematics, Science and Technology Education, 19(6), em2270. https://doi.org/10.29333/ejmste/13187

Vancouver

Godino JD, Batanero C, Burgos M. Theory of didactical suitability: An enlarged view of the quality of mathematics instruction. EURASIA J Math Sci Tech Ed. 2023;19(6):em2270. https://doi.org/10.29333/ejmste/13187

AMA

Godino JD, Batanero C, Burgos M. Theory of didactical suitability: An enlarged view of the quality of mathematics instruction. EURASIA J Math Sci Tech Ed. 2023;19(6), em2270. https://doi.org/10.29333/ejmste/13187

Chicago

Godino, Juan D., Carmen Batanero, and María Burgos. "Theory of didactical suitability: An enlarged view of the quality of mathematics instruction". Eurasia Journal of Mathematics, Science and Technology Education 2023 19 no. 6 (2023): em2270. https://doi.org/10.29333/ejmste/13187

Harvard

Godino, J. D., Batanero, C., and Burgos, M. (2023). Theory of didactical suitability: An enlarged view of the quality of mathematics instruction. Eurasia Journal of Mathematics, Science and Technology Education, 19(6), em2270. https://doi.org/10.29333/ejmste/13187

MLA

Godino, Juan D. et al. "Theory of didactical suitability: An enlarged view of the quality of mathematics instruction". Eurasia Journal of Mathematics, Science and Technology Education, vol. 19, no. 6, 2023, em2270. https://doi.org/10.29333/ejmste/13187