Engaging multiple representations in grade eight: exploring mathematics teachers' perspectives and instructional practices in Canada and Nigeria

Abstract

This study was inspired by and utilises representations, one of the mathematical learning processes (NCTM, 2000), which is currently acclaimed as one of the reform-based instructional approaches to teaching and learning algebra. This concurrent mixed methods research project explored elementary in-service teachers’ goals for, beliefs about and knowledge of representations, both in Ontario and Lagos. Data were collected through an online survey completed by 91 middle school in-service teachers concurrently with interviews with ten of them. Findings from the survey indicated that teachers from the Lagos subsample had weaker understandings about representations compared with their counterparts from Ontario. In the interviews, participants described to varying degrees their goals for and use of representations as opportunities for students to show connections, relationships, and reasoning, supporting students’ confidence in problem-solving, and facilitation and opportunities for questioning and discussion. This research suggests that teachers generally, but particularly in Lagos, need a deeper understanding of representations and need to further develop the specialized mathematics content knowledge related to patterning and algebra. Other findings showed that: planning and sequencing instruction, use of contextual learning tasks, opportunities for students to generate their own representations, linking students’ prior knowledge to new situations, and translation among multiple representations were reported as critical to teachers’ use of representations. Recommendations are made to create more awareness among teachers, of the value, use and knowledge about representations. These findings would be relevant to school boards, teacher educators, researchers, and professional development providers wishing to improve teachers’ use of representations, via enhanced beliefs, and knowledge.