Affordances and constraints by mathematical tasks, questions, prompts and teacher actions: Insights from a lesson on fraction

Given the complexity of the interaction between the teaching and learning processes in a mathematics lesson, much research attention has been geared towards understanding in situ what mathematics teachers do as they teach and interact with students. The affordances and constraints initiated by the teacher can be a powerful tool to assess the extent to which mathematical concepts are made accessible to students (Watson, 2007). Similarly, the unpredictable constraints generated in a lesson can shed much light in terms of the impediment to learning emanating from teaching actions. This case study reports the mathematical affordances initiated by an experienced teacher as he developed an introductory lesson on fractions in a Grade 7 class. Our moment-by-moment analysis of the lesson trajectories traces the constraints generated by the experienced teacher as he attempted to prompt students to develop the concept of fractions. We address the following research question—an issue more generally raised by Watson (2007): What opportunities to act mathematically are afforded and constrained by tasks, questions, prompts and teacher actions in the teaching of fractions?