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Problem-solving enhances teaching of mathematics

 

Problem-solving plays an important role in the learning of mathematics by children, and should form an integral part of the entire mathematics curriculum.

Teachers should view problem-solving as a teaching strategy that should be integrated across the board into the implementation of the curriculum, but not in isolation from concepts and procedures. However, incorporating problem-solving meaningfully into mathematics instruction continues to be a major challenge to many mathematics teachers.

Generally, problem-solving refers to the process of assigning tasks that can potentially provide intellectual challenges to enhance children’s mathematical development. Such tasks promote children’s conceptual understanding and challenge them to reason and communicate mathematically.

Intellectual challenges  

Story or word problems should not generally be construed as problem-solving because many of such problems do not offer intellectual challenges that children need. 

For example, when children are asked to find the perimeter of a square, given the length of a side, they could add these numbers and get the right answer without understanding the concept of “perimeter.” 

On the other hand, some non-story problems such as those found while playing mathematical games could offer children the much needed intellectual challenges.

For children to become successful problem solvers, teachers should always assign them tasks which are intriguing and contain a level of challenge that requires intense reasoning and speculation. Such tasks should direct children to investigate important ideas towards their learning goals.

Children could enhance their problem-solving abilities if teachers assigned them tasks that have important and useful mathematics embedded in them. For such tasks, teachers could ask children, for example, to calculate the number of square metres of tiles needed to tile a floor, and estimate the cost.

Different solution strategies 

Children could approach this problem in multiple ways by using different solution strategies. These multiple ways allow children to explore procedures and test conjectures.

Children could also enhance their problem-solving abilities if teachers frequently assigned them tasks that require high-level thinking.

High-level thinking tasks do not readily provide on the spot answers, they need much time for children to process and thoroughly understand the best approach to adopt to solve a problem. But this could be feasible if children are able to use various solution strategies and defend different decisions or positions they make or take. 

Apart from high-level thinking tasks, children could enhance their problem- solving abilities if teachers assign them tasks that create an opportunity for teachers to assess what children learn and the difficulty they experience.

Feedback and interaction

Such feedback and interaction ultimately builds a level of confidence in children and enables them to explore “unchartered” territories when the need arises. By unchartered territories, I mean the very topics in mathematics whose concepts and methodologies seem difficult for most children to comprehend, yet teachers sometimes select questions from these topics for children to solve.  By this trajectory, children build their strength from the concepts and procedures teachers demonstrate during class discussions. 

Children draw on the experiences from these discussions and interactions to extend their thinking to include upper-level cognitive thoughts. For such thoughts and ideas to be operative, these problems should connect to other important mathematical ideas and facts.

It should be emphasised, however, that children do not become successful problem solvers overnight. Such skills develop slowly among children and require long-term sustained attention to make problem-solving an integral part of the curriculum. Teachers in this regard could develop the problem-solving culture in the classroom to make problem-solving a regular and consistent part of teachers’ classroom practice. 

The writer is a lecturer, Department of Mathematics Education, University of Education, Winneba. 

Email: [email protected]

 

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