Secondary school teachers' perceptions of diagrams in mathematics

Abstract

The study of diagrams and diagrammatic representations has received growing interest from diverse disciplines. Diagrams remain a central feature of science, technology, engineering and mathematics (STEM) learning areas, in schools and beyond. The revised secondary school mathematics curriculum of Singapore places emphasis on Big Ideas in Mathematics with the aim to develop greater awareness of the nature of mathematics and bring coherence across topics and content strands. Specifically, diagrams as a Big Idea are defined as succinct visual representations of real-world or mathematical objects that serve to effectively communicate properties and facilitate problem-solving. External representations, such as diagrams, often appear in teachers’ repertoire of pedagogical tools to support students’ conceptual learning and problem solving activities. To support the use of diagrams as Big Ideas, it is pertinent to explore their perceptions of diagrams and how they influence their instructional practices. This will allow for appropriate developments in support of enhancing their pedagogies for mathematics.<br><br>This study examined secondary school teachers’ perceptions of diagrams in mathematics. Specifically, it focused on two aspects. The first was teachers’ perceptions on the utility value of diagrams and how they incorporated them in their instructional practice to communicate and make connections between mathematical ideas. The second was teachers’ perceptions about their students’ use of diagrams in mathematics. An open ended survey was administered to 20 secondary school teachers each of whom has at least three years of mathematics teaching experience.<br><br>The findings show that teachers perceived diagrams as a tool for communication of mathematical ideas during instruction. They use diagrams to make representations, link concepts within and between topics and as a problem-solving tool. Amongst some of the challenges which teachers perceived in their students’ encounter with diagrams include the lack of diagram-specific skills, cognitive demand of constructing diagrams, and less than proficient visuospatial abilities to decode and extract pertinent information.<br><br>The possible reasons for these findings are discussed with the support of existing literature, inform potential teacher learning programmes and serve as a springboard for future research.