The competency-based approach conceives mathematics as a necessary tool for dealing with daily-life tasks. Many studies have focused on examining the low math competency people show when solving problems in real-life contexts, but rarely characterize the type of mathematics needed in these contexts and how people use this mathematics. The current study was designed to analyze the mathematics utilized by 312 customers when purchasing carpentry products in a store specialized in home projects. Aspects of the Anthropological Theory of the Didactic, especially the extended praxeological model, were employed to undertake the analysis. While the approach is primarily qualitative, quantitative aspects were also considered to elucidate the nature of the identified mathematics tasks, the techniques that customers employed to solve them, and the difficulties associated with the use of these techniques. The study reveals that having solid mathematical knowledge is insufficient when it comes to solving everyday tasks, because related contextual knowledge is also required. The nature of the tasks identified in this study and the didactic way in which the clerk guided the customers through the projects suggested that there are no only complex relationships between school mathematics and outside-school mathematics, but there exist also different didactics specific to the contexts. For elaborating the home carpentry projects, the customers needed to handle a set of carpentry knowledge and techniques as well as carpentry-related mathematics that are not necessarily taught at school.
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Akkerman, S. F., & Bakker, A. (2012). Crossing boundaries between school and work during apprenticeships. Vocations and learning, 5(2), 153–173. https://doi.org/10.1007/s12186-011-9073-6
Bakker, A. (2014). Characterising and developing vocational mathematical knowledge. Educational Studies in Mathematics, 86(2), 151–156. https://doi.org/10.1007/s10649-014-9560-4
Bryman, A. (2015). Social research methods. New York: Oxford University Press.
Castela, C., & Romo, A. (2011). Des mathématiques à l’automatique: étude des effets de transposition sur la transformée de Laplace dans la formation des ingénieurs [From mathematics to automatization: A study of transpositive effects on the Laplace transform in the training of engineers]. Recherches en Didactique des Mathématiques, 31(1), 79–130.
Chaachoua, H., Bessot, A., Romo, A., & Castela, C. (2019). Developments and functionalities in the praxeological model. In M. Bosch, Y. Chevallard, F. García, & J. Monaghan (Eds.), Working with anthropological theory of the didactic in mathematics education (pp. 41–59). New York: Routledge. https://doi.org/10.4324/9780429198168-4
Chevallard, Y. (1999). L’analyse des pratiques enseignantes en théorie anthropologique du didactique [The analysis of teaching practice in the anthropological theory of the didactic]. Recherches en Didactique des Mathématiques, 19, 221–266.
Chevallard, Y. (2019). Introducing the anthropological theory of the didactic: An attempt at a principled approach. Hiroshima Journal of Mathematics Education, 12, 71–114.
Covián, O., & Romo, A. (2014). Las matemáticas en la construcción: La vivienda maya, el levantamiento y trazo topográfico [The extended praxeological model: A tool to analyze mathematics in practice – the case of mayan house, survey and topographical drawing]. Bolema: Boletim de Educação Matemática., 28(48), 128–148. https://doi.org/10.1590/1980-4415v28n48a07
Creswell, J. W. (2014). Research design: Quantitative, qualitative and mixed methods approaches (4th ed.). Thousand Oaks: Sage Publications.
Diego-Mantecón, J., Blanco, T., Ortiz-Laso, Z., & Lavicza, Z. (2021). STEAM projects with KIKS format for developing key competences. [Proyectos STEAM con formato KIKS para el desarrollo de competencias clave]. Comunicar, 66, 33–43. https://doi.org/10.3916/C66-2021-03
Diego-Mantecón, J. M., Arcera, O., Blanco, T. F., & Lavicza, Z. (2019). An engineering technology problem-solving approach for modifying student mathematics-related beliefs: Building a robot to solve a Rubik’s cube. International Journal for Technology in Mathematics Education, 26(2), 55–64. https://doi.org/10.1564/tme_v26.2.02
Diego-Mantecón, J. M., Blanco, T. F., Búa, J. B., & González, P. (2019). Is the relationship between art and mathematics addressed thoroughly in Spanish secondary school textbooks? Journal of Mathematics and the Arts, 13(1-2), 25–47. https://doi.org/10.1080/17513472.2018.1552068
European Union Council (Ed.) (2018). Council recommendation of 22 May 2018 on key competences for lifelong learning. https://bit.ly/3epV571
Evans, J., Wedege, T., & Yasukawa, K. (2012). Critical perspectives on adults’ mathematics education. In M. A. K. Clements, A. Bishop, C. Keitel-Kreidt, J. Kilpatrick, & F. K. S. Leung (Eds.), Third international handbook of mathematics education (pp. 203–242). New York: Springer. https://doi.org/10.1007/978-1-4614-4684-2_7
FitzSimons, G. E., & Boistrup, L. B. (2017). In the workplace mathematics does not announce itself: Towards overcoming the hiatus between mathematics education and work. Educational Studies in Mathematics, 95(3), 329–349. https://doi.org/10.1007/s10649-017-9752-9
García, F. J., Gascón, J., Ruíz-Higueras, L. & Bosch, M. (2006). Mathematical modelling as a tool for the connection of school mathematics. ZDM-Mathematics Education, 38(3), 226–246. https://doi.org/10.1007/bf02652807
Grando, N. I. (1988). A matematica na agricultura e na escuela [Mathematics in agriculture and in school]. [Unpublished master’s thesis]. Universidade Federal de Pernambuco.
Halász, G., & Michel, A. (2011). Key competences in Europe: Interpretation, policy formulation and implementation. European Journal of Education, 46(3), 289–306. https://doi.org/10.1111/j.1465-3435.2011.01491.x
Jablonka, E., & Gellert, U. (2007). Mathematisation - demathematisation. In U. Gellert & E. Jablonka (Eds.), Mathematisation and demathematisation: Social, philosophical and educational ramifications (pp. 1–18). Rotterdam: Sense.
Lave, J. (1988). Cognition in practice: Mind, mathematics and culture in everyday life. Cambridge: Cambridge University Press. https://doi.org/10.1017/cbo9780511609268
Lave, J., & Gomes, A. (2019). Learning and everyday life: Access, participation, and changing practice. Cambridge: Cambridge University Press. https://doi.org/10.1017/9781108616416
Lave, J., Murtaugh, M., & de la Rocha, O. (1984). The dialectic of arithmetic in grocery shopping. In B. Rogoff & J. Lave (Eds.), Everyday cognition: Its development in social context (pp. 67–94). Cambridge: Harvard University Press.
Mestre, J. (2002). Transfer of learning: Issues and research agenda. Report of a workshop held at the National Science Foundation. University of Massachusetts-Amherts.
Millroy, W. (1992). An ethnographic study of the mathematical ideas of a group of carpenters. Journal for Research in Mathematics Education, 5, 1–210. https://doi.org/10.2307/749904
Murtaugh, M. (1985). The practice of arithmetic by American grocery shoppers. Anthropology and Education Quarterly, 6(3), 186–192. https://doi.org/10.1525/aeq.1985.16.3.05x1484b
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
Noss, R., Bakker, A., Hoyles, C., & Kent, P. (2007). Situating graphs as workplace knowledge. Educational Studies in Mathematics, 65(3), 367–384. https://doi.org/10.1007/s10649-006-9058-9
Noss, R., Hoyles, C., & Pozzi, S. (2000). Working knowledge: Mathematics in use. In A. Bessot & J. Ridgway (Eds.), Education for Mathematics in the Workplace (pp. 17–35). London: Kluwer. https://doi.org/10.1007/0-306-47226-0_3
Nunes, T., Carraher, D., & Schliemann, A. (1993). Street mathematics and school mathematics. Cambridge: University Press.
OECD (Organization for Economic Cooperation and Development). (2013). OECD skills outlook 2013: First results from the survey of adult skills (PIAAC). Paris: OECD Publishing.
OECD. (2014). PISA 2012 results: What students know and can do – student performance in mathematics, reading and science (Volume I, Revised edition, February 2014). Paris: OECD Publishing.
OECD. (2016). PISA 2015 results (volume I): Excellence and equity in education. Paris: OECD Publishing. https://doi.org/10.1787/9789264266490-9-en
Peters, J., Hochmuth, R., & Schreiber, S. (2017). Applying an extended praxeological ATD-model for analyzing different mathematical discourses in higher engineering courses. In R. Göller, R. Biehler, R. Hochmuth, & H. G. Rück (Eds.), Didactics of mathematics in higher education as a scientific discipline – conference proceedings (pp. 172–178). Kassel: Universitätsbibliothek Kassel.
Schliemann, A. D. (1984). Mathematics among carpenters and apprentices. In P. Damerow, B. F. Nebres, & B. Werry (Eds.), Mathematics for all (pp. 92–95). New York: Academic Press.
Solares, D., Solares, A., & Padilla, E. (2016). La enseñanza de las matemáticas más allá de los salones de clase. Análisis de actividades laborales urbanas y rurales. [Mathematics teaching beyond classrooms. Analysis of urban and rural activities]. Educación Matemática, 28(1), 69–98. https://doi.org/10.24844/em2801.03
Swanson, D., & Williams, J. (2014). Making abstract mathematics concrete in and out of school. Educational Studies in Mathematics, 86(2), 193–209. https://doi.org/10.1007/s10649-014-9536-4
Vázquez, R., Romo-Vázquez, A., Romo-Vázquez, R., & Trigueros, M. (2016). La separación ciega de fuentes: Un puente entre el álgebra lineal y el análisis de señales. [Blind source separation: A bridge between linear algebra and signal analysis]. Educación Matemática, 28(2), 31–57. https://doi.org/10.24844/em2802.02
Wijaya, A., van den Heuvel-Panhuizen, M., & Doorman, M. (2015). Opportunity-to-learn context-based tasks provided by mathematics textbooks. Educational Studies in Mathematics, 89(1), 41–65. https://doi.org/10.1007/s10649-015-9595-1
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Diego-Mantecón, J.M., Haro, E., Blanco, T.F. et al. The chimera of the competency-based approach to teaching mathematics: a study of carpentry purchases for home projects. Educ Stud Math 107, 339–357 (2021). https://doi.org/10.1007/s10649-021-10032-5
- Mathematical competency
- Everyday tasks
- Mathematical knowledge
- Contextual knowledge
- School mathematics
- Anthropological theory of didactic