Connecting learning to what students are thinking

In planning for learning, effective teachers put students’ current knowledge and interests at the centre of their instructional decision making. Instead of trying to fix weaknesses and fill gaps, they build on existing proficiencies, adjusting their instruction to meet students’ learning needs. Because they view thinking as “understanding in progress”, they are able to use their students’ thinking as a resource for further learning. Such teachers are responsive both to their students and to the discipline of mathematics.

Effective teachers take student competencies as starting points for their planning and their moment-by-moment decision making. Existing competencies, including language, reading and listening skills, ability to cope with complexity, and mathematical reasoning, become resources to build upon. Experientially real tasks are also valuable for advancing understanding. When students can envisage the situations or events in which a problem is embedded, they can use their own experiences and knowledge as a basis for developing context-related strategies that they can later refine into generalized strategies. For example, young children trying to work out how to share three pies among four family members will typically use informal methods that pre-empt formal division procedures. Because they focus on the thinking that goes on when their students are engaged in tasks, effective teachers are able to pose new questions or design new tasks that will challenge and extend thinking. Consider this problem: It takes a dragonfly about 2 seconds to fly 18 metres. How long should it take it to fly 110 metres? Knowing that a student has solved this problem using additive thinking, a teacher might adapt the task so that it is more likely to invite multiplicative reasoning: How long should it take the dragonfly to fly 1100 metres? or How long should it take a dragonfly to fly 110 metres if it flies about 9

metres in 1 second?

Effective teachers plan mathematics learning experiences that enable students to build on their existing proficiencies, interests, and experiences.