Progressive formalizaton

This is an approach to developing learner-entered environments for formal disciplines such as math.

Here the idea is to startt with the informal knowledge that kids bring to school and show tem how to transform these to formal knowledge. Initially students use their own words and picture to describe mathematical situations. Over time, kids are then encouraged to formalize these represntations. Initially, they are allowed to invent their own notationss etc. Gradually, they are encouraged to replace these with conventional, formal notations.

This path is not always one way. Learners may back and forth between these levels.