Mathematical Problem Solving Theory

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Several studies have been focused on the research of heuristic processes.

These studies found that task specific heuristic instruction was more effective than general heuristic instruction.

One should be able to change methodology if it is not effective for a mathematical problem.

Brainstorming techniques are quite useful in mathematical problem solving.

After gaining knowledge, suitable approaches to problem solving must be selected, along with techniques which can help solve the problem fast and save time.

Different techniques have not the same effectiveness and one must find the most effective.However, using an algorithm is still not problem solving.The process of creating an algorithm is problem solving.There are various techniques for solving mathematical problems and their application vary from one mathematical problem to the other.The key to successfully solving mathematical problems is flexibility and creativity.Garofola and Lester suggest in their article, Metacognition, cognitive monitoring, and mathematical performance,that problem solving is a series of processes of which students are unaware.Students with a good knowledge base are more able to use heuristics in solving geometry problems.Problem solving can be taught by teaching children to create their algorithms. These are types of information that help students find a solution to a math problem.Heuristics are similar to strategies, techniques, and rules-of-thumb.A deep understanding of binary number systems, counting techniques, linear programming techniques and matrix algebra are also crucial for solving mathematical problems.Important techniques are also probability laws, calculus ideas such as differentiation, integrals and different equation solving techniques, complex numbers, probability distributions and solid geometrical concepts and ideas.

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