Do you remember how you learned maths in school? And do you remember if it was effective? As I teach I test out many different strategies, activities, and ideas. I am looking for methods that help everyone learn maths. Are some methods better than others for everyone?
There are certainly some students who learn well by listening to explanations and copying examples. I know that students can be trained to work this way and I have worked in schools where this got very good results. But is everyone able to learn this way? Can all students be trained to learn this way? Ollerton and Watson think not, in their book Inclusive Mathematics 11-18, which I am reading at the moment. (Yesterday I had read to page 7 and was already learning!)
“It is commonly believed now,” they write, “that all learning involves the learner interacting with the environment through experience and making sense of those experiences personally and through communicating with others.” So my job evolves from example-giver to activity-designer. I need to provide sense-making tasks for students to experience and communicate their ideas.
I struggle sometimes with knowing how to make these activities. I enjoy making different types of activities, but often I just pick an activity I like, somewhat randomly. But the key is to look at the underlying mathematical structure. Maths topics are often about classifying–and so sorting and classifying tasks will expose those ideas. Maths is frequently about justifying, so I need to ask questions that ask students to back up their ideas. I hope that Ollerton and Watson discuss task design in more detail. (I am still only on page 10.)
What thinking drives your task design? How do you decide what activities to give to students?