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.

The design in educational environments: learner-centered environments

Environments that pay attention to the knowledge, skills, attitudes, and beliefs that learners bring to the educational setting.

Also called "culturally appropriate", "culturally responsive"...

Also called "diagnostic teaching": a key strategy is to prompt children to explain the reasons for predictions, their answers etc. Create congnitive conflicts and then have discussions about conflicting viewpoints. Test for known misconceptions.

Important to be sensitive to cultural practiced. In Hawaii, a reading program included discussions of learners' personal experiences and gave them opportunities to practice "talk-story"-a native custom of constructing stories jointly. This led to improvements in standardized test scores.

Not all kids come to school with practice in "school talk" - I.e. Impersonal and expository way of talking without relating to personal experiences or stories.

In one case, African American students were shown that many of their forms of everyday communication are examples of high forms of literacy.

In learner centered environments, teachers pay attention to what learners know and can do, and in their interests and passion - what do they want to do.