Mathematics has been taught ever since ancient civilizations existed yet research in mathematics education only started to be considered at the beginning of the 19th century according to Jeremy Kilpatrick (2014). Since then the different ways in which students and teachers interact has been studied, with increasingly special emphasis on the student. Many theories now exist on how people learn mathematics and one such theory is the relational-instrumental framework defined by Richard R. Skemp (1976) which has been used to further analyse learning methods. Specifically, relational understanding in this framework is seen as true understanding or mathematical understanding. Although relational and instrumental understanding in mathematics can be seen as two contrasting ideas, it is most beneficial to consider them together. The relationship between these two understandings can be used to inform educational theories in mathematics and allow for further analysis and growth in the field.
Relational understanding in mathematics is one of two forms of understanding. Skemp defines it as ‘knowing both what to do and why’. This kind of understanding allows for students to take various paths to reach an answer, and more emphasis is placed on the process of understanding rather than reaching the answer. It can also be called ‘conceptual understanding’, a term coined by James Hiebert (1986). Hiebert discusses knowledge of concepts that isn’t tied to a particular type of problem and that