Catagory of representations

The cognitive analysis of each response to each open-ended problem focused on four critical cognitive aspects:
1.solution strategies
2.mathematical errors
3. mathematical justifications
4. solution representations

In particular, solution representations were evaluated in terms of the ways in which students represented their solutions. Six categories wereinitially used to classify the representations:
1. verbal
2.pictorial
3.arithmetic symbolic
4.algebraic symbolic
5.tabular
6.physical manipulative