With 33 years of experience in Remedial Education, Karyn Coetzer challenges us to consider the importance of developing Mathematical concepts through problem solving.
Research has shown that learning in Mathematics occurs when learners grapple with problems for which they have no routine methods.
It is important to distinguish between learning how to solve problems and learning through problem solving.
Instead of teaching mathematical skills and then applying them, we need to start with problems and allow the learner to actualize existing knowledge and intuitions to solve the problems and establish concepts.
The traditional transmission of knowledge by teachers has resulted in the learners having to retain these methodologies and memory comes into play and confusion results. It is a marked paradigm shift for adults to stop believing themselves to be the sources of all knowledge which they must pass on with prescribed methods and presentation.
When children begin to see patterns, relationships, regularities and irregularities within, and between, numbers and operations, they are forming concepts. This internal knowledge is constructed by each individual for themselves. Learners will be at different levels of conceptual development and should not be forced to function at levels of abstraction which they have not yet reached, but will reach over time with a carefully structured problem solving approach.
The logico-maths knowledge needs to be constructed where the learner’s thinking space is not invaded by more advanced ideas. The integrity of their thinking is preserved – if someone doesn’t start demonstrating methods to them.
At School – The Three Pillars of the approach in the Elementary Grades (simplified for the purpose of this article) are:
- Well planned number concept activities, building patterns and relationships
- Well planned problems
- Effective discussion
This approach is critical in the Foundation Phase and must not be neglected.
At home – a great deal of experience can be gained if the learners are involved in lots of practical and fun activities.
- Discussing the cost of items bought and change received while at the shops.
- Making children aware of mass and capacity when baking and cooking; measuring liquid and weighing dry ingredients.
- Telling the time, measuring time taken for various activities
- Measuring distances in the car.
- Keeping a visible record of your child’s height.
- Using mathematical language and posing simple problems to your child at home will increase their familiarity with these terms. eg. bigger than/smaller than/less than/greater than/difference/total
If children are given the opportunity to engage in a practical way with real life experiences, they will begin to have an understanding of mathematical concepts.
Maths is real…Maths is a part of everyday life…It is a vital life skill!!
An enquiring environment in the home and classroom is essential.