The chimera of the competency-based approach to teaching mathematics: a study of carpentry purchases for home projects

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.