The use of variation theory in a problem-based task design study

Abstract

The aim of this pilot study is to test the usefulness of variation theory as a theoretical framework in guiding the researcher to design the main study of developing students’ deep learning in mathematics. Both Marton’s variation theory of learning and Gu’s theory of teaching with variation were used in the design-based pilot study. Two teachers and 106 Grade four students from an elementary school in a large north-west city in Ethiopia participated in the pilot study. The pilot study data included transcripts of audio-recording of preparatory meetings (the first author with the two teachers) and students’ interview, video-recording of lesson observation, and pre and post-tests. The pilot study topic was of learning concepts of area and perimeter of rectangles. We find that the theoretical framework of variation helped us to address the systematic use of patterns of variation and invariance in the problem-based task design and to analyze the three patterns of variation in the problem-based tasks implementation in the classroom learning.