*Lovie Harris The video I selected was Persistence in Problem Solving This video related to micro-credential with ways to allow students to explain how they came up with an answer to a math problem.*

Yet intelligence is essentially the ability to solve problems: everyday problems, personal problems ... Modern definitions of intelligence (Gardner, 1985) talk about practical intelligence which enables 'the individual to resolve genuine problems or difficulties that he or she encounters' (p.60) and also encourages the individual to find or create problems 'thereby laying the groundwork for the acquisition of new knowledge' (p.85).

As was pointed out earlier, standard mathematics, with the emphasis on the acquisition of knowledge, does not necessarily cater for these needs.

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

'If education fails to contribute to the development of the intelligence, it is obviously incomplete.

Training in problem-solving techniques equips people more readily with the ability to adapt to such situations.

A further reason why a problem-solving approach is valuable is as an aesthetic form. 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, 1989). National Council of Teachers of Mathematics (NCTM) (1989). 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.18). Curriculum and Evaluation Standards for School Mathematics, Reston, Virginia: NCTM. 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, 1989), rather than just as the means to an end of finding the correct answer. Cockcroft (1982) 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.73) because it is the means by which mathematics can be applied to a variety of unfamiliar situations. 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. 8 would be two groups of 4 or 4 groups of 2) My concerns would be monitoring during group activity to make sure everyone in the group is participating and not just relying on one person to do the work.It is great how these students are working, but is it realistic to have the students solve the same problem three different ways?

## Comments Teaching Problem Solving In Math

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