Freire (1999) says that the act of teaching requires one to “create possibilities for the construction and production of knowledge rather than to be engaged simply in a game of transferring knowledge” (p. 49). This statement represents one of the most important ideas for an educator; instead of lecturing and acting solely as an interpreter of knowledge, the teacher should facilitate activities and discussions which allow students to construct their own knowledge. Especially in the mathematics classroom, students learn best when they are encouraged to develop their own understanding of the content and create meaning for themselves. One major issue that often arises is students’ inability to appropriately communicate their (mis)understanding (see this page for a more in-depth explanation of the role of communication in my teaching).
In his discussion of the philosophy of mathematics education, however, Ernest (1985) explains that this constructivist approach “objectivises the mathematical activities of computation and proof-construction without reference to the roles or aims of people” (p. 608). This being said, understanding is best developed when what is being taught is relevant to the learner.
Peck (2018) confronts the myth of Plato-formalism in the mathematics classroom through the question of whether mathematics was invented or discovered. To help students understand the applicability of – and necessity for – mathematics in their daily lives, he concludes that mathematics must be embraced “as a human activity, engaging students in mathematical experiences that are active, cultural, historical, critical, and social” (Peck, 2018, p. 9). In this way, teachers must change the way their students see the content they are teaching. If this change is achieved, then students will take what they learnt (in all subjects) and become a better person as a result. Peters (1966) explains the concept that great education is, in fact, transformative: “It would be a logical contradiction to say that a man had been educated but that he had in no way changed for the better” (as cited in Barrow & Woods, 2006, p. 26). In short, Peters (1966, as cited in Barrow & Woods, 2006) idealizes the notion that education is a worthwhile act and aims to improve the lives of all involved. However, this can only be achieved if students take an active role in their education. There is a connection, then, between this notion of the transformative powers of education and the students’ active role which teachers must embrace: “Overwhelmingly, the evidence suggests that students who experience active learning learn more mathematics and develop more positive mathematical identities, as compared to students who experience more passive forms of instruction such as lectures.” (Peck, 2018, p. 7). As a teacher, then, one should always aim to help students construct their own knowledge of the content – which should be applicable to the students – to allow them the opportunity to experience a holistic development, all while helping them take an active role in the process.
References:
Barrow, R., & Woods, R. (2006). The concept of education. In An Introduction to Philosophy of Education (pp. 26-37). Routledge.
Ernest, P. (1985). The philosophy of mathematics and mathematics education. International Journal of Mathematical Education in Science and Technology, 603-612.
Freire, P. (1999). Teaching is Not Just Transferring Knowledge. In Pedagogy of Freedom: Ethics, Democracy, and Civic Courage (pp. 49-84).
Peck, F. A. (2018). Rejecting Platonism: Recovering Humanity in Mathematics Education. Education Sciences. doi:10.3390/educsci8020043
Kevin Paquette 