Mathematical representations can aid children’s understanding of mathematical concepts but depending on the type of representation, children can have difficulties interpreting them correctly. So, not all representations are applicable in the same manner.
A current study, by researchers of the University of Durham (UK) and the University of the Witwatersrand (South Africa), uses eyetracking to examine different mathematical representations on the example of multiplication. The multiplication can be visualized e.g. in groups (left figure), in a matrix (middle figure) or in a linear array of numbers (‘number line’) (right figure).
In the study, different representations were shown to primary pupils. An eyetracker captured the way children viewed and interpreted these pictures. The captured data was analysed quantitatively and qualitatively.
For both, the data capturing and the data analysis, the software MangoldVision was used. This software is characterized by easy handling, enormous capabilities, and wide range of analysis options.
The results show, that the representation in form of the ‘number line’ was less successful than the other representations. The success of children to think multiplicative with the ‘groups’ and the ‘matrix’ representations, was related to their general mathematics attainment levels.
These finding have an impact on how teachers use the different representations, knowing now the disadvantages of particular representations.
The detailed study is available here >>>