MESHGuides

Before we start thinking about misconceptions* in the teaching and learning of fractions let us think about the difference between an error and a misconception

an error is an inaccuracy, but a misconception is the result of misunderstanding

Owens (1980) examined the relationship between a pupil’s concept of area and their ability to learn fraction concepts finding a positive connection and he found a positive relationship between success on area tasks and success in fractions tasks based on geometric regions. The teaching for transfer from area tasks aids a pupil’s ability to learn fraction concepts. In contrast the findings from a study by Novillis-Larson (1980, p. 423) demonstrated that pupils working “with tasks involving the location of fractions on number lines” gained an imprecise and inflexible notion of fraction.

It is well documented in the research literature that fractions are among the most complex mathematical abstract concepts (Gabriel et al., 2013) that children encounter and equally as important it is widely acknowledged that fractions are difficult to teach. It has also been claimed that learning fractions is probably one of the most serious obstacles to the mathematical maturation of children and that many of the ‘trouble spots’ in early school mathematics are related to rational-number ideas.

Ainley, J., Bills, L. and Wilson, K., (2004). Constructing Meanings and Utilities within Algebraic Tasks. International Group for the Psychology of Mathematics Education.

Battista, M.T. and Borrow, C.V.A., (1998). Using spreadsheets to promote algebraic thinking. Teaching Children Mathematics, 4(8), pp.470-478.

Bicer, A., Capraro, R.M. and Capraro, M.M., (2014). Pre-service Teachers' Linear and Quadratic Inequalities Understandings. International Journal for Mathematics Teaching & Learning.

Egodawatte, G., (2011). Secondary school students’ misconceptions in algebra. University of Toronto, Toronto.

https://www.ncetm.org.uk/media/dj5o223w/ncetm_ks3_representations_algebra_tilespdf.pdf

https://www.ncetm.org.uk/podcasts/using-algebra-tiles-at-ks3/

Maths is Fun https://www.mathsisfun.com/algebra/introduction.html

Median Software https://donsteward.blogspot.com/

Dave Hewitt Grid Algebra.