A comparative analysis of problem-solving procedures of a South Korean and a South African grade six mathematics textbook.

Abstract

Mathematical tasks play a critical role in the teaching and learning of mathematics. Textbooks have been valued as an important tool in the teaching-learning process of Mathematics. This study aimed to analyse how problem-solving procedures are represented in selected mathematics textbooks in South Korea and South Africa using a composite framework. In the past few decades, international comparative studies have transformed the way mathematics education is perceived and has provided insight for improving student learning in many ways. In this study, 6th Grade South Korean and South African mathematics textbooks were compared with textbook analysis frameworks and Polya’s 4-stage model being used to analyse data. The comparison involved textbook design features, and the criteria for their quality (visual design, nature of approach, cognitive demand, content, learning, teaching, structure, organisation, linguistics characteristics and internal organisation). The focus included the basic structure, curriculum weighting, colour-coding or use of colour, topic representation, introduction and conclusion of topics and non- textual representations. This study revealed similarities, such as the use of visuals, models, acting it out, guess and check and identify the pattern. The heuristics were present in both textbooks; however, the key difference being the South Korean textbook had been designed according to Polya’s 4 stagemodel, with several heuristics being integrated in the design process, which created a strong foundation in developing critical thinking skills. The more salient features of the South African textbook are key words, mathematic ideas and ‘did you know?’ information boxes which aid second language students in understanding mathematical concepts. This may account for the differences in the Trends in International Mathematics and Science Study (TIMSS) results of the two countries, with South Korea scoring 1st while South African had been placed 47th. The implementation of a model in the design process (e.g. Polya’s 4 stagemodel and heuristics) by curriculum developers and textbook authors will result in the improvement of the quality of mathematical results as problem-based learning improves academic performance. The enhancement of students’ attitude towards problem-solving and progress in mathematics results by including differentiated learning materials in the mathematics textbook. This will cater for their varying levels of ability and the development of critical thinking and cognitive domains of knowledge.