Tags:Mathematical proving, overcoming threshold concepts and reasons for the troublesomeness of proving
Abstract:
In 2015 the curriculum of the last three years of school secondary mathematics for students who prepare themselves for studying mathematics at a university, changed. In this new curriculum the three main parts are algebra, calculus and analytic geometry. Mathematical proving doesn’t get much attention. In 2018 the first students who were taught according to the new curriculum, entered the Dutch universities. Naturally, these students find mathematical proving new and hardtop get used to it. So, we decided to get a deeper insight in this phenomenon through a research about mathematical proving using the threshold concepts framework (TCF) (Meyer & Land, 2003, 2005). An example in mathematics, mentioned by many authors, is the concept ‘limit of a function’. This was also a result of our own research (Zwaneveld & Sterk, 2019), The first question we addressed is: can mathematical proving (proving for short) be conceived as a threshold concept? It will be not surprising that our answer is yes. In our contribution we shall present our arguments. There are several reasons for this question. Proving is not a mathematical object like an equation or a linear space. Neither is it a procedure like solving a linear equation, which is more a skill. Proving is a much more complex activity. We analyzed what proving really is about, more specifically, how it is treated in mathematics, mathematical didactical theories, and how we can connect it with TCF. We asked the students, at the end of their first year, as an obligatory reflection assignment, to fill in a questionnaire, comparable to the one used in our earlier mathematical threshold concepts research (Zwaneveld & Sterk, 2019). In this questionnaire the focus is on proving, e.g. why is it troublesome. Further, we asked how the students overcame their problems with proving.