Problem Solving in Mathematics

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WHY PROBLEM SOLVING?

• Problem solving is the most basic of mathematical skills- the reason for studying mathematics • Problem solving is an integral part of the larger area of critical thinking, which is universally accepted goal for all education • Problem solving shows an interaction between mathematical ideas • In the classroom can lessen the gap between real world problem and the classroom worlds and thus set more positive mood in the classroom.

WHAT IS PROBLEM?
The normal process for solving a problem will initially involve defining the problem we want to solve. We need to decide what we want achieve and write it down. Often people keep the problem in their head as a vague idea and can so often get lost in what they are trying to solve that no solution seems to fit. Merely writing down the problem forces us to think about what we are actually trying to solve and how much we want to achieve. The first part of the process not only involves writing down the problem to solve, but also checking that we are answering the right problem. It is a check-step to ensure that we do not answer a side issue or only solve the part of the problem that is most easy to solve. People often use the most immediate solution to the first problem definition that they find without spending time checking the problem is the right one to answer.

• A problem is a task for the person confronting it
• Wants or need to find a solution
• Has no readily available procedure for finding a solution and • Must make an attempt to find a solution.

Charles & Lester (1982)

TYPES OF PROBLEMS

• ROUTINE PROBLEM
• NON- ROUTINE PROBLEM

ROUTINE PROBLEM
From the curricular point of view, routine problem solving involves using at least one of the four arithmetic operations and/or ratio to solve problems that are practical in nature. Routine problem solving concerns to a large degree the kind of problem solving that serves a socially useful function that has immediate and future payoff. Children typically do routine problem solving as early as age 5 or 6. They combine and separate things such as toys in the course of their normal activities. Adults are regularly called upon to do simple and complex routine problem solving. The research evidence suggests that good routine problem solvers have a repertoire of automatic symbol-based and context-based responses to problem situations. They do not rely on manipulating concrete materials, nor on using strategies such as 'guess and check' or ‘think backwards’. Rather, they rely on representing what is going on in a problem by selecting from a limited set of mathematical templates or model.

• Routine problem are those that merely involved an arithmetic operation with the characteristics • Presents a question to be answered
• Gives the facts or numbers to use
• Can be solved by direct application of previously learned algorithms and the basic task is to identify the operation appropriate for solving the problem.

NON - ROUTINE PROBLEM
Non-routine problem solving serves a different purpose than routine problem solving. While routine problem solving concerns solving problems that are useful for daily living (in the present or in the future), non-routine problem solving concerns that only indirectly. Non-routine problem solving is mostly concerned with developing students’ mathematical reasoning power and fostering the understanding that mathematics is a creative endeavour. Non-routine problem solving can be seen as evoking an ‘I tried this and I tried that, and eureka, I finally figured it out.’ reaction. That involves a search for heuristics (strategies seeking to discover). There is no convenient model or solution path that is readily available to apply to solving a problem. That is in sharp contrast to routine problem solving where there are readily...
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