Within mathematics if a student gives an incorrect answer to a question or problem, it will be one of two things. The answer can either be a mistake; (Almeida, 2010)

“The pupil understands an algorithm but there is a computational error due to carelessness. A mistake is normally a one-off phenomenon.”

Or a misconception;

“The pupil has misleading idea or misapplies concepts or algorithms. A misconception is frequently observed.”

A misconception can be a natural stage of conceptual development. I.e. the idea “multiplication gives bigger numbers” is a valid generalisation when applied to natural numbers; however the idea fails when it is applied to the rational numbers. (Swan, 2001, p. 154)

“Although I do not believe it is possible to prevent misconceptions arising, a skilled classroom teacher will plan ahead when giving explanations so that he or she does not actively encourage pupils to believe that learning mathematics is about following an extensive set of unrelated, arbitrary rules. Indeed, it is wor4thwhile offering ‘rules’ to pupils and asking them to discuss their domain of validity.” (Swan, 2001, p. 154)

One of the main misconceptions made by secondary school mathematics teachers is by assuming that the year 7 pupils have no prior knowledge of mathematics and so must be taught from basics. However this is not the case as year 7 pupils have been building their mathematics knowledge since the age of 4, so by the time students are in year 7 at secondary school they have been practising mathematics for the past 7 years.

It is vital that mathematics teachers consider the misconceptions that may arise within the lessons. Children construct meanings internally by accommodating new concepts within their existing mental frameworks. Therefore unless there is intervention, there is likelihood that the pupil’s conception may deviate from the intended one. Pupils are also known to misapply...