Enriching math teaching guides from a competency-based perspective

Albert Vilalta Riera; Jordi Deulofeu Piquet; Laura Morera Úbeda

doi:10.29333/ejmste/14761

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Albert Vilalta Riera ¹ ^* , Jordi Deulofeu Piquet ¹ , Laura Morera Úbeda ²

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¹ Universitat Autònoma de Barcelona, Barcelona, SPAIN² Innovamat Education, Barcelona, SPAIN^* Corresponding Author

Abstract

This study introduces a novel framework designed to enrich mathematics teaching guides from a competency-based perspective. First, we narrow down the concept of a teaching guide in mathematics education, grounded in the documentational approach to didactics. This definition offers an updated perspective on the structure and function of math teaching guides in educational settings. Second, we provide a comprehensive definition of ‘richness’ in math activities, encompassing content, processes, cognitive demand, and classroom management. Lastly, we introduce an analytical tool developed for assessing and enhancing the richness of math teaching guides. This tool, formed through theoretical analysis and empirical testing, assists educators and curriculum developers in creating more balanced and integrative teaching guides. The results suggest that the tool holds potential for broader applications in curriculum design and teacher education. The findings contribute to the broader understanding of how teaching guides can effectively capture and communicate the richness of activities, thereby serving as a valuable tool for improving mathematical education resources.

Keywords

mathematics education
teaching guides
competency-based education
curriculum enrichment
instructional design
documentational approach to didactics

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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, Volume 20, Issue 7, July 2024, Article No: em2477

https://doi.org/10.29333/ejmste/14761

Publication date: 01 Jul 2024

Online publication date: 24 Jun 2024

Article Views: 82

Article Downloads: 71

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References

ACARA. (2015). F-10 mathematics curriculum (version 8.4). Australian Curriculum, Assessment and Reporting Authority.
Ahl, L., Gunnarsdóttir, G. H., Koljonen, T., & Pálsdóttir, G. (2015). How teachers interact and use teacher’s guides in mathematics–Cases from Sweden and Iceland. Nordic Studies in Mathematics Education, 20(3-4), 179-197.
Bartell, T., Wager, A., Edwards, A., Battey, D., Mary Foote, M., & Spencer, J. (2017) Toward a framework for research linking equitable teaching with the standards for mathematical practice. Journal for Research in Mathematics Education, 48(1), 7-21. https://doi.org/10.5951/jresematheduc.48.1.0007
Boertien, H., & de Lange, J. (1994). The national option of TIMSS in the Netherlands. University of Twente.
Brown, M. (2009). The teacher-tool relationship: Theorizing the design and use of curriculum materials. In J. T. Remillard, B. A. Herbel-Eisenmann, & G. M. Lloyd (Eds.), Mathematics teachers at work: Connecting curriculum materials and classroom instruction (pp. 17-36). Routledge.
Brügner, G. (1984) Three-triangle-tangram. BIT, 24, 380-382. https://doi.org/10.1007/BF02136037
Burgués, C., & Sarramona, J. (2013). Competències bàsiques de l’àmbit matemàtic per a l’educació primària [Mathematical basic competencies for primary education]. Generalitat de Catalunya [Government of Catalonia].
Christiansen, B., & Walther, G. (1986). Task and activity. In B. Christiansen, A. G. Howson, & M. Otte (Eds.), Perspectives on mathematics education (pp. 243-307). D. Reidel. https://doi.org/10.1007/978-94-009-4504-3_7
de Lange, J. (1999). Framework for classroom assessment in mathematics. Freudenthal Institute & National Center for Improving Student Learning and Achievement in Mathematics and Science.
Deulofeu, J. & Vila, A. (2021). Aprender a pensar matemáticamente en ambientes de resolución de problemas [Learning to think mathematically in problem solving environments]. In GIDIMAT-UA (Eds.), Ideas para la educación matematica: Perspectivas desde el trabajo de Mª Luz Callejo de la Vega, (pp. 41-67). Compobell.
Fan, L., & Zhu, Y. (2007). Representation of problem-solving procedures: A comparative look at China, Singapore, and U.S. mathematics textbooks. Educational Studies in Mathematics, 66, 61-75. https://doi.org/10.1007/s10649-006-9069-6
Flick, U. (2013). The SAGE handbook of qualitative data analysis. SAGE. https://doi.org/10.4135/9781446282243
Gojak, L. (2017). A key to deep understanding: The importance of rich tasks in K-12 mathematics. McGraw Hill Education.
Gueudet, G., & Trouche, L. (2009). Towards new documentation systems for mathematics teachers? Educational Studies in Mathematics, 71(3), 199-218. https://doi.org/10.1007/s10649-008-9159-8
Gueudet, G., Pepin, B., & Trouche, L. (2013). Textbooks’ design and digital resources. In C. Margolinas (Ed.), Task design in mathematics education (pp. 325-333).
Hart, K. J., & Team, C. M. (1981). Children’s understanding of mathematics: 11-16. Antony Rowe Limited.
Hiebert, J., Carpenter, T. P., Fennema, E., Fuson, K. C., Wearne, D., Human, P., Murray, H., & Olivier, A. (1997) Making sense: Teaching and learning mathematics with understanding. Heinemann.
Innovamat Education. (2021). Adventures 4th grade. Teaching guide.
Jones, D. L., & Tarr, J. E. (2007). An examination of the levels of cognitive demand required by probability tasks in middle mathematics textbooks. Statistics Education Research Journal, 6(2), 4-27. https://doi.org/10.52041/serj.v6i2.482
Jukić Matić, L., & Glasnović Gracin, D. (2021). How do teacher guides give support to mathematics teachers? Analysis of a teacher guide and exploration of its use in teachers’ practices. Research in Mathematics Education, 23(1), 1-20. https://doi.org/10.1080/14794802.2019.1710554
Kuiper, W., Bos, K., & Plomp, T. (1997). TIMSS populatie 2, nationaal rapport [TIMSS population 2, national report]. University of Twente.
Leikin, R., & Zazkis, R. (2010). Learning through teaching mathematics. Springer. https://doi.org/10.1007/978-90-481-3990-3
Leont’ev, A. (1975). Dieyatelinocti, soznaine, i lichynosti [Activity, consciousness, and personality]. Politizdat [Politician].
LOMLOE. Boletín Oficial del Estado, 340, de 30 de diciembre de 2020, 122868-122953 [Official State Gazette, 340, December 30, 2020, 122868-122953]. Ley Orgánica 3/2020, de 29 de diciembre, por la que se modifica la Ley Orgánica 2/2006, de 3 de mayo, de Educación [Organic Law 3/2020, of December 29, which modifies Organic Law 2/2006, of May 3, on Education]. https://www.boe.es/boe/dias/2020/12/30/pdfs/BOE-A-2020-17264.pdf
Margolinas, C. (2013). Task design in mathematics education. Oxford University Press.
Mason, J., & Johnston-Wilder, S. (2006). Designing and using mathematical tasks. QED Press.
Math For Love. (2022). Rich tasks. https://mathforlove.com/lessons/rich-tasks/
National Governors Association Center for Best Practices, & Council of Chief State School Officers. (2010). Common core state standards for mathematics. https://learning.ccsso.org/wp-content/uploads/2022/11/ADA-Compliant-Math-Standards.pdf
NCTM. (2000). Principles and standards for school mathematics. National Council of Teachers of Mathematics.
Niss, M., & Højgaard, T. (2019). Mathematical competencies revisited. Educational Studies in Mathematics, 102(1), 9-28. https://doi.org/10.1007/s10649-019-09903-9
OECD. (2017a). PISA for development assessment and analysis framework: Reading, mathematics and science. OECD Publishing.
OECD. (2017b). Social and emotional skills: Well-being, connectedness and success. OECD Publishing.
Pepin, B. (2008). Making connections and seeking understanding: Mathematical tasks in English, French and German textbooks [Paper presentation]. Nuffield Seminar Series on Mathematical Knowledge in Teaching.
Piggott, J. (2007). The nature of mathematical enrichment: A case study of implementation. Educate, 7(2), 30-45.
Piggott, J. (2011). Mathematics enrichment: What is it and who is it for? NRICH–Millennium Mathematics Project. https://nrich.maths.org/5737
Remillard, J. T. (2005). Examining key concepts in research on teachers’ use of mathematics curricula. Review of Educational Research, 75(2), 211-246. https://doi.org/10.3102/00346543075002211
Remillard, J. T. (2012). Modes of engagement: Understanding teachers’ transactions with mathematics curriculum resources. In G. Gueudet, B. Pepin, & L. Trouche (Eds.), From text to ‘lived’ resources: Mathematics curriculum materials and teacher development (pp. 105-122). Springer. https://doi.org/10.1007/978-94-007-1966-8_6
Remillard, J. T. (2013). Beyond the script: Educative features of five mathematics curricula and how teachers use them [Paper presentation]. The AERA Annual Meeting.
Schoenfeld, A. H. (2016). An introduction to the teaching for robust understanding (TRU) framework. https://truframework.org/
Shield, M., & Dole, S. (2012). Assessing the potential of mathematics textbooks to promote deep learning. Educational Studies in Mathematics, 82, 183-199. https://doi.org/10.1007/s10649-012-9415-9
The Curriculum Development Council of Honk Kong. (2017). Mathematics education key learning area curriculum guide (primary 1-secondary 6). https://www.edb.gov.hk/attachment/en/curriculum-development/kla/ma/curr/jsmc2017_e.pdf
Thompson, D. R., Huntley, M. A., & Suurtamm, C. (2018). International perspectives on mathematics curriculum. Research in Mathematics Education.
Trouche, L., Drijvers, P., Gueudet, G., & Sacristan, A. I. (2013). Technology-driven developments and policy implications for mathematics education. In A. J. Bishop, M. A. Clements, C. Keitel, J. Kilpatrick, & F. K. S. Leung (Eds.), Third international handbook of mathematics education (pp. 753-790). Springer. https://doi.org/10.1007/978-1-4614-4684-2_24
Trouche, L., Gueudet, G., & Pepin, B. (2018). Documentational approach to didactics. In S. Lerman (Ed.), Encyclopedia of mathematics education (pp. 1-11). Springer. https://doi.org/10.1007/978-3-319-77487-9_100011-1
Valverde, G. A., Bianchi, L. J., Wolfe, R. G., Schmidt, W. H., & Houang, R. T. (2002). According to the book: Using TIMSS to investigate the translation of policy into practice through the world of textbooks. Kluwer Academic Publishers. https://doi.org/10.1007/978-94-007-0844-0_8
Vilalta, A. (2021). Un proyecto para desarrollar la competencia matemática en el aula de primaria [A project to develop mathematical competence in the primary classroom]. Uno: Revista de Didáctica de las Matemáticas, 92, 73-79.
Vilalta, A., Morera, L., Rojas, F., & Solar, H. (2021). Rich math activities for a primary school class [Workshop]. 14th International Congress on Mathematical Education (ICME 14), Shanghái, China.
Vincent, J., & Stacey, K. (2008). Do mathematics textbooks cultivate shallow teaching? Applying the TIMSS video study criteria to Australian eighth-grade mathematics textbooks. Mathematics Education Research Journal, 20(1), 81-106. https://doi.org/10.1007/BF03217470
Virginia Department of Education (2023). Rich mathematical tasks. https://www.doe.virginia.gov/teaching-learning-assessment/k-12-standards-instruction/mathematics/instructional-resources/rich-mathematical-task
Zhu, Y., & Fan, L. (2006). Focus on the presentation of problem types in intended curriculum: A comparison of selected mathematics textbooks from Mainland China and the United States. International Journal of Science and Mathematics Education, 4(4), 609-626. https://doi.org/10.1007/s10763-006-9036-9

How to cite this article

APA

Vilalta Riera, A., Deulofeu Piquet, J., & Morera Úbeda, L. (2024). Enriching math teaching guides from a competency-based perspective. Eurasia Journal of Mathematics, Science and Technology Education, 20(7), em2477. https://doi.org/10.29333/ejmste/14761

Vancouver

Vilalta Riera A, Deulofeu Piquet J, Morera Úbeda L. Enriching math teaching guides from a competency-based perspective. EURASIA J Math Sci Tech Ed. 2024;20(7):em2477. https://doi.org/10.29333/ejmste/14761

AMA

Vilalta Riera A, Deulofeu Piquet J, Morera Úbeda L. Enriching math teaching guides from a competency-based perspective. EURASIA J Math Sci Tech Ed. 2024;20(7), em2477. https://doi.org/10.29333/ejmste/14761

Chicago

Vilalta Riera, Albert, Jordi Deulofeu Piquet, and Laura Morera Úbeda. "Enriching math teaching guides from a competency-based perspective". Eurasia Journal of Mathematics, Science and Technology Education 2024 20 no. 7 (2024): em2477. https://doi.org/10.29333/ejmste/14761

Harvard

Vilalta Riera, A., Deulofeu Piquet, J., and Morera Úbeda, L. (2024). Enriching math teaching guides from a competency-based perspective. Eurasia Journal of Mathematics, Science and Technology Education, 20(7), em2477. https://doi.org/10.29333/ejmste/14761

MLA

Vilalta Riera, Albert et al. "Enriching math teaching guides from a competency-based perspective". Eurasia Journal of Mathematics, Science and Technology Education, vol. 20, no. 7, 2024, em2477. https://doi.org/10.29333/ejmste/14761