Why problem solving is important in math

Rather than directing a lesson, the teacher needs to provide time for students to grapple with problems, search for strategies and solutions on their own, and learn to evaluate their own results. To understand how students become problem solvers we need to look at the theories that underpin learning in mathematics.

The concept of co-construction of learning is the basis for the theory. Moreover, we know that each student is on their unique path of development. Children arrive at school with intuitive mathematical understandings. A teacher needs to connect with and build on those understandings through experiences that allow students to explore mathematics and to communicate their ideas in a meaningful dialogue with the teacher and their peers.

Learning takes place within social settings Vygotsky, Students construct understandings through engagement with problems and interaction with others in these activities. Through these social interactions, students feel that they can take risks, try new strategies, and give and receive feedback.

They learn cooperatively as they share a range of points of view or discuss ways of solving a problem. It is through talking about problems and discussing their ideas that children construct knowledge and acquire the language to make sense of experiences. Students acquire their understanding of mathematics and develop problem-solving skills as a result of solving problems, rather than being taught something directly Hiebert The importance of problem-solving in learning mathematics comes from the belief that mathematics is primarily about reasoning, not memorization.

Problem-solving allows students to develop understanding and explain the processes used to arrive at solutions, rather than remembering and applying a set of procedures. It is through problem-solving that students develop a deeper understanding of mathematical concepts, become more engaged, and appreciate the relevance and usefulness of mathematics Wu and Zhang Problem-solving in mathematics supports the development of:.

Problem-solving should underlie all aspects of mathematics teaching in order to give students the experience of the power of mathematics in the world around them.

This method allows students to see problem-solving as a vehicle to construct, evaluate, and refine their theories about mathematics and the theories of others. Students only learn to handle complex problems by being exposed to them.

Students need to have opportunities to work on complex tasks rather than a series of simple tasks devolved from a complex task. See if you can find other answers? Try to tell someone how you found these answers out? Main menu Search. Problem Solving and the New Curriculum. What's the point of doing maths?

I wonder what answers your class would give to this question. In a research project a few years ago I asked children of all ages what they thought maths was all about, and why they learned it at school. It allows students to work at their own pace and make decisions about the way they explore the problem. Because the focus is not limited to a specific answer students at different ability levels can experience both challenges and successes on the same problem. Problem solving better represents the nature of mathematics.

Research mathematicians apply this exact approach in their work on a daily basis. Schoenfeld in Olkin and Schoenfeld, , p. My early problem-solving courses focused on problems amenable to solutions by Polya-type heuristics: draw a diagram, examine special cases or analogies, specialize, generalize, and so on.

Over the years the courses evolved to the point where they focused less on heuristics per se and more on introducing students to fundamental ideas: the importance of mathematical reasoning and proof Schoenfeld also suggested that a good problem should be one which can be extended to lead to mathematical explorations and generalisations.

He described three characteristics of mathematical thinking:. Problem solving is an important component of mathematics education because it is the single vehicle which seems to be able to achieve at school level all three of the values of mathematics listed at the outset of this article: functional, logical and aesthetic.

Let us consider how problem solving is a useful medium for each of these. It has already been pointed out that mathematics is an essential discipline because of its practical role to the individual and society. Through a problem-solving approach, this aspect of mathematics can be developed.

Presenting a problem and developing the skills needed to solve that problem is more motivational than teaching the skills without a context. Such motivation gives problem solving special value as a vehicle for learning new concepts and skills or the reinforcement of skills already acquired Stanic and Kilpatrick, , NCTM, Approaching mathematics through problem solving can create a context which simulates real life and therefore justifies the mathematics rather than treating it as an end in itself.

The National Council of Teachers of Mathematics NCTM, recommended that problem solving be the focus of mathematics teaching because, they say, it encompasses skills and functions which are an important part of everyday life. Furthermore it can help people to adapt to changes and unexpected problems in their careers and other aspects of their lives.

More recently the Council endorsed this recommendation NCTM, with the statement that problem solving should underly all aspects of mathematics teaching in order to give students experience of the power of mathematics in the world around them. They see problem solving as a vehicle for students to construct, evaluate and refine their own theories about mathematics and the theories of others. According to Resnick a problem-solving approach contributes to the practical use of mathematics by helping people to develop the facility to be adaptable when, for instance, technology breaks down.

It can thus also help people to transfer into new work environments at this time when most are likely to be faced with several career changes during a working lifetime NCTM, Resnick expressed the belief that 'school should focus its efforts on preparing people to be good adaptive learners, so that they can perform effectively when situations are unpredictable and task demands change' p.

Cockcroft also advocated problem solving as a means of developing mathematical thinking as a tool for daily living, saying that problem-solving ability lies 'at the heart of mathematics' p. Problem solving is, however, more than a vehicle for teaching and reinforcing mathematical knowledge and helping to meet everyday challenges. It is also a skill which can enhance logical reasoning. Individuals can no longer function optimally in society by just knowing the rules to follow to obtain a correct answer.

They also need to be able to decide through a process of logical deduction what algorithm, if any, a situation requires, and sometimes need to be able to develop their own rules in a situation where an algorithm cannot be directly applied. For these reasons problem solving can be developed as a valuable skill in itself, a way of thinking NCTM, , rather than just as the means to an end of finding the correct answer.

Many writers have emphasised the importance of problem solving as a means of developing the logical thinking aspect of mathematics.