To know or not to know, that is not the question

Abstract

In teaching, expressions such as: "we have worked on equations", "we have already seen equations", "there is an exam on equations", "after equations comes..." are used. The mathematical content is then perceived as a term unit. The logic of the evolution of mathematics is transferred to learning, according to which knowledge is linear, in a process of gradual accumulation, without setbacks or revision by the learner of the meaning attributed to the objects involved. However, someone knows a mathematical content "in a certain way", which allows him/her to "perform certain tasks" and to progress in the learning of other contents "with a certain depth". The Ontosemiotic Approach to mathematical knowledge and instruction (EOS) provides theoretical and methodological tools for the analysis of the meaning attributed by a subject or an institution to mathematical objects. It also allows the assessment of mathematical study processes in a contextualized manner, identifying suitable and evolving aspects of these processes. This paper analyzes the performance of future teachers in a task of calculating dates in the calendar.