The Investigation of the Relationship between Math and Philosophical Problems to Improve Teaching of Problem Solving

Abstract

Teaching math problem solving is one of the most important parts of curricula in schools and universities in most fields of study. There have been numerous studies, which have shown the problems and challenges of this field as well as the advantages of its improvements. Teaching the math problem solving is not merely learning the science of mathematics, but it is learning a set of skills to face different types of problems, which may be encountered for the first time. In addition, numerous studies are showing the role of cognitive and metacognitive processes such as logical reasoning in the improvement of the teaching and learning of mathematics. Many philosophers such as Wittgenstein have considered philosophical research equal to the philosophical problem solving. In the current study, the similarities that, in past and present time, have led people such as Descartes and Pólya to use philosophical problem solving, which is referred to as philosophical research, for math problem solving to improve teaching math problem solving, have been investigated and it has been indicated that how the philosophical problem solving methods lead to development of math problem solving skills. The results of the current study show that the commonality in the use of argumentation, cognitive and metacognitive processes, uncertainty, reasoning, and understanding and use of abstract concepts have led people such as Descartes to try to utilize the philosophical problem solving for math problem solving. Accordingly, the transfer of learning between the philosophical research and math problem solving phenomenon can be used in teaching or in another way, through the combination of the problem solving with the philosophical methods, the teaching of math problem solving can be developed.