pply their wider knowledge to related problems which a purely instrumental knowledge would be inadequate for. At GCSE level and below, there is little advantage to the pupil in gaining a relational understanding rather than an instrumental one in terms of exam results, and so a teacher should be aware of these two approaches and make sure that the way they teach allows for both instrumental learning and relational understanding. In practice this usually manifests itself as solving a series of example problems by a given sequence of steps, but also explaining the reasoning behind each at each stage.

This argument is further supported by Hiebert’s (1999) findings demonstrates that once students have memorised and practiced procedures that they do not understand, they tend to have less motivation to understand the meaning or the reasoning behind them, which I can resonate from my own experience of teaching and learning mathematics . At one of the lessons I observed during the first school placement, the session was revising on dividing fractions, where learners recited a predetermined rule, keep flip change (KFC) method for dividing fractions. When I probed them why they multiplied the reciprocal of second fraction to the first fraction, they responded, “It’s what we were taught” This made me reminisce my own learning of mathematics . I did not question my teacher at the time why it was the case and how it worked, but ‘accepted’ that it was a method to divide fractions without ploughing deeper how it worked. When I followed up with the teacher later, they responded “The learners had worked on this on another session, but when they need to recall for exam or generally as means for quick calculation, it is the easiest go-to method to calculate the answer” and while the teacher who taught them could have approached a questioning style that checks their understanding or act as a guide to support and stimulate them, it seems apparent time constraints of the classroom learning and the Curriculum demands means that there is not always the opportunity for learners to “actively explore, discuss, debat