Mental Representations of Fractions and Decimals: Differences, Commonalities and Implications for Understanding

The purpose of this thesis is to seek evidence of commonalities in the mental representations of fractions and decimals between zero and one. The focus is on the mental representations of non-familiar fractions and decimals in adults. In addition, individual differences in the extent of common fraction and decimal mental representations are explored and their links to mathematical understanding of numbers between zero and one.

For whole numbers, number comparison tasks have found evidence of an ordered, magnitude mental representation known as the mental number line through which the magnitude of a whole number is automatically processed. This evidence consists of phenomena such as the distance effect and SNARC effect. Here, indications of a similar magnitude representation common to both fractions and decimals are sought through a task in which a fraction is compared with a decimal.

Substantial evidence of a distance effect is presented but not a SNARC effect, indicating that fractions and decimals can have mental representations containing or accessing a common magnitude but that this magnitude is not automatically processed.

In addition, two emergent phenomena are reported. The first is an effect of location which is contrasted with the size effect in whole numbers and a previously reported anchor-point effect. The second is a larger-stimulus effect which is an indication of differences in the mental representations of fractions and decimals. These effects are explored in two additional, simple magnitude and location tasks.

Furthermore, success but not speed within the comparison task is linked to strength of the distance effect for individuals. Therefore the number comparison task is repeated in series with a test designed to uncover common misconceptions of fractions and decimals. Patterns with the individual differences in responses to the test and comparison task are explored.

By making links between the features and commonalities of individuals’ mental representations of fractions and decimals and quality of their understanding, this research hopes to be of value to mathematical educators.