As a teacher, I have to provide experiences for young children to be involved in problem solving. They need to have sufficient schema to enable them to build on their prior knowledge, to accomodate and assimilate information in their learning process.
I have discovered van's Hiele theory of geometric thought which is made up of 5 levels:
1) Level 0 -visualization
2) Level 1 - analysis
3) Level 2 - informal deduction
4) Level 3 - deduction
5) Level 4 - rigor
At the same time, it is important that I need to teach at the student's level of thought, encouraging them to move on to the next level and adapting activities accordingly.