Teachers' Point of View in Teaching Mathematical Problem-Solving

András Ambrus,Dániel Katona

doi:10.15291/magistra.1489

Abstract

There is still a deep gap between the theories of the didactics of mathematics and mathematics teaching practice worldwide. In our article, we analyse our trial to reach practicing mathematics teachers and summarize their opinion about some basic issues of teaching mathematics problem-solving from the point of view of cognitive load theory, what is a quite new topic in mathematics didactics society. We asked on the one hand, teachers from a small town in Hungary, and on the other hand, expert teachers and four young teachers from elite schools in the capital. The four young teachers have also started their PhD studies in mathematics education, besides school teaching. The opinions of the two groups of teachers reflect different attitudes towards teaching problem-solving, but in both cases relevant and important perspectives of the Hungarian school reality. The base of our study was a talk and an article of the first author, related to the role of human memory in learning and teaching mathematical problem-solving. We have been interested in how classroom teachers can take into consideration some results of the cognitive load theory, e.g. the split-attention effect and schema automation in their teaching practice, as well as in their attitudes to the use of worked examples and distributed practice. We analyse the results mostly from the perspective of desirable developments in in-service teacher training in Hungary.

Highlights

INTRODUCTIONThere has always been a great difficulty in reaching the practicing teachers, and incorporating their opinions in connection with particular issues into research studies in the field of mathematics didactics
THE HUNGARIAN CONTEXT REGARDING THE MATHEMATICS TEACHERSThere has always been a great difficulty in reaching the practicing teachers, and incorporating their opinions in connection with particular issues into research studies in the field of mathematics didactics
4300 practicing mathematics teachers completed the questionnaire, which is slightly more than one fifth of the number of all practicing mathematics teachers in the country

Summary

INTRODUCTION

There has always been a great difficulty in reaching the practicing teachers, and incorporating their opinions in connection with particular issues into research studies in the field of mathematics didactics. (Clark et al, 2012) Based on (Clark, 2012) we claim for the importance of incorporating guided discussions, and the use of worked examples into the problem solving process, which seem to be present for instance in the Pósa method too, for instance as recurring phases between periods of individual thinking and discovery, making those relevant information available to students which they could not find themselves during their discovery. If the schema corresponding to the problem to be solved is not available in the student’s LTM, the student must search for, or construct a relevant solution process with a highly loading use of the working memory. If the students already have the relevant schemas, the use of worked examples may be redundant and disturbing, that is called the expertise reversal effect (Kalyuga, 2007)

METHODOLOGY

DISCUSSION