Transitioning Knowledge Levels Through Problem Solving Methods

Abstract

Problem solving is one of the most important goals of mathematics teaching. Several researches, such as the one attached to this dissertation, demonstrate that the problems of mathematics and their resolution are ultimately a problem for the majority of students. The very low performance for pupils in our 15-year-old country in the PISA international competition, coupled with references to problem solving research, demonstrates the weakness of our country’s education system to bridge the gap between school reality and everyday problems or original problems. In contrast to the unpleasant results of the mathematical problem solving research, several theories in the science of mathematics teaching describe problem solving methods, such as Polya’s method of questioning, which help the student develop the thinking skills he/she has, his/her metacognostic abilities, and above all he/she can raise a level of knowledge in relation to what he/she is before dealing with problem solving. Key findings of the research are that there is no absolute link between pupils’ skills in solving original problems and answers to the problems of school reality. However, the questionnaire method we applied in the second phase of the survey has shown to deliver. The students found the value of the method in solving a problem by correcting errors or shortcomings and eventually answering correctly. Methods and research on them, however, present the way to acquiring mathematical knowledge through problems. For safer conclusions, we expect as a learning community the results of research in cognitive science and neuroscience around problem solving. The last two areas of educational research, cognitive science and neuro-education, are expected to provide answers for the transition of knowledge from one level to another.