The role of and connection between systematization and representation when young children work on a combinatorial task

The study investigates how six-year-olds solve a combinatorial mathematics task: How many ways can three different stuffed toys be arranged next to each other? The researchers study whether there is a correlation between the children’s spontaneous systematisation and the organisation of the task and the way in which they solve it. The three research questions are: 1) Are there correlations between the systematisation of children’s representations and how they solve the combinatorial task? 2) Are there correlations between the representations the children use and how they solve the combinatorial task? 3) Are there correlations between the systematisation and the representation the children use?

The results indicate that there are some correlations between the ways in which the children systematise and document the task, and that both systematisation and documentation have an impact on the solutions they arrive at. The four children who came up with the correct answer used iconic representations of the stuffed toys. Two of these children systematised the teddy bears using a trial-and-error method (in which the children had to check each of their new permutations with all their previous ones to find out whether each permutation was new or not), while the other two used an odometer approach (where one element is kept constant while the others vary systematically). Although only four of the 114 children reached the correct number of combinations when working individually on the task, all the children were involved in the group discussion and found the task difficult but fun to work with. The researchers believe this result supports a type of didactics based on shared reflections of experiences after working on tasks, rather than a teaching approach where the children learn in advance about systematisation and representation.

The study is part of a larger project that focused on mathematical problem solving in kindergarten, in which ten Swedish pre-school classes with a total of 123 children participated. The results of this study are based on analysis of one of the mathematics tasks in the project. In the task, the children were shown three stuffed toys and asked how many different ways (permutations) they could be arranged next to each other. The children were given paper and crayons, but were given no instructions on how to solve the task. Approximately 12-14 children solved the task at the same time. Firstly, the children worked individually, before being placed together in pairs to solve the task. Finally, the task and any solutions were discussed within the whole group. After the group discussion, the children individually evaluated how difficult they found the task to be and how they liked it.

Palmér, H. & van Bommel, J. (2018). «The role of and connection between systematization and representation when young children work on a combinatorial task”. European Early Childhood Education Research Journal, 26(4):562-573.