Summary Literature Review
This assignment will analyse the common misconceptions pupils have when working with fractions. This essay will look at what some the misconceptions are and how we can try to help pupils overcome them.
Common misconception associated with fractions.
Fractions is a great area of mathematics to explore misconceptions as
‘Many errors occur when children work with fractions because of the lack of understanding of the concept of the unit involved.’
Frobisher et al (1999).
Thus this assignment will only to look at a few misconceptions that occur at the beginning of studying fractions. We will look at what the common errors are when pupils are studying ...view middle of the document...
There are a various reasons why pupils have this misconception one of which is that pupils find it hard to visualise the fraction to compare them or they do not realise they have to make sure the diagrams are comparable (Small, 2010). One way Small (2010) suggest to overcome this misconception is the use of ‘Fraction Tower’ so pupils become familiar with the size of fractions and give pupils diagrams of fractions of similar size so pupils can compare them.
Understanding the denominator
Frobisher et al (1999) discusses that pupils do not understand what the denominator is representing and that they would think that a shape that is split into 3 parts and one of those parts shaded would mean that ½ of the shape is not shaded. The reason pupils treat fractions like this is due to the fact that they look at a shape like the one described above and will treat it like a ‘ratio of the shaded to the unshaded parts’ (Frobisher et al, 1999). Evans Newton Incorporated (2009) suggests giving the pupils definitions of the terms denominator, numerator and fraction so the pupils have a reference points and give them a good range of questions where the pupils have to shade shapes and identify what amount of the shape is shaded.
Understanding the size of a fraction
Another area of confusion is one where pupils think that ‘the larger fraction is one with the larger numerator’ (An, 2004). The reason for this error can be related to other misconceptions mentioned earlier however it also shows pupils lack of understanding of having a ‘common denominator’ will assist them in finding out what the size of the fraction is compared to other fractions (An,2004). Blinko et al (2003) suggests using a ‘fraction...