PROBLEM POSING, PROBLEM SOLVING AND PEDAGOGY

Assumption (epistemologically) -  mathematics as result of human problem posing and solving
                                                    -  mathematics as a mental construction (creation, invention or
                                                       discovery)  

In term of learning, social constructivism identifies all learners of mathematics as creators of mathematics involving problem posing and solving.

Therefore as a consequences of problem posing and solving pedagogy :

1. School maths for all should be centrally concerned with mathematical problem posing and solving
    (reduce content- oriented mathematics curriculum)

2. Inquiry, investigation, problem posing or formulation should occupy a central place in the school
    maths curriculum and precedes problem solving

3. The pedagogy (teaching, learning and assessment) should be process and inquiry(or investigation)
    focused (vs product)

4. learner-centered view of investigation as a learner directed activities (new questions posed, new
    situations are generated and explored- promotes active learning)

5.  Increase learner autonomy and self- regulation ( develop reflective and meta-cognitive skills)


Mathematical problem posing (formulation, investigation etc) is divergent (creative thinking and higher order thinking) as the process of mathematical problem solving (critical thinking and higher order thinking - eg by using Polya method)) is convergent.