Importance Of Problem Solving

The value of problem solving as discussed in the article highlights mainly the practical importance of George Polya’s four phases of problem solving. Polya has provided one heuristic for solving problems through understanding the problem, devising a plan, carrying out the plan and looking back on the solution. This cycle of problem solving has an impact on the sustainability of developing students as thinkers – spending time to think rather than working on the problem and being successful in solving it (Hensberry and Jacobbe 2012).

The true essence of problem solving is largely perceived not to have any clear solution method (NCTM 2000; Van de Walle 2003) as students are thrown into situations of confusion and uncertainty (Lambdin 2003).

769-770). There is discourse on learners having to move back and forth between Polya’s four phases for true problem solving to take place. Such metacognition will minimise the often jumpstart to quickly picking one strategy and spending effort on it which often results into a wild goose chase since failure is almost guaranteed as the strategy is usually incorrect and cumbersome (Schoenfeld 1987). Therefore, diary writing is thought to strengthen Mathematics understanding as learners’ thinking is structured to go through the much neglected Polya’s first, second and fourth phases of understanding the problem, devising a plan and looking back on the solution (Jacobbe 2008; Schoenfeld 1987). These phases are essential to bring about successful problem

Sadly, my colleagues have often failed to fully execute the four phases well. For students who are weaker learners in Mathematics, the teachers have proclaimed “there is no time to finish the syllabus and they are so weak, how to revise on word problems when they already have difficulty with multiple-choice and short-answer questions”. This group of teachers has misunderstood problem solving as word problems, they have as much anxiety about problem solving as the struggling learners under their charge. I have my share of teaching mixed-ability and low-ability classes before challenging myself to teach “the top class in Mathematics”. I have never seen the need to finish the syllabus and complete revision as hindrances to teaching proper problem solving. For the struggling learners, there is even a greater need to breakdown questions to help them to understand the requirements of these questions, thinking through the solution before articulating it on paper. What I may be lacking in is the final phase of checking the solution. As I think back now, I realise that I have started to close the gap on this with my constant pausing and asking students to check their solutions upon completion. I have also started to use the formative assessment technique of hinge point questions actively to encourage them to pause through their steps and approaches. This technique helps students to check on their