Month: February 2011

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?

I am reading Inclusive Mathematics 11-18 by Mike Ollerton* and Anne Watson (my two biggest maths education idols?). I’m only on page 7 and my ideas are being challenged and shaped. There are a lot of fthings they say that I believe in principle but find hard to apply in the classroom.

Maths (as a school subject) should be something to do, they argue. I agree completely. Often maths is viewed as a body of knowledge that others have created that we need to learn (and memorise). In this way maths skills can be seen like a checklist to master. Some of my lessons have this theme: the aim of the lesson is to master the skill of finding one amount as a percentage of another. But Ollerton and Watson contend that thinking mathematically and doing mathematics are what maths is all about. Memorising (“learning”) techniques is somewhat useful–because of future maths study or work-related skills or everyday numeracy. But the goal of thinking and doing mathematics, I believe,  is to have a more mathematical mind, to be more logical, and to be a beautiful thinker.

In this way studying maths at school could be similar to studying art or music. Students take music, art, or drama in order to appreciate these realms of life. They broaden their minds through artisitic expression. All students are painters or actors who have something to learn in school performing arts classes because they are developing their creative talents. Only a small proportion of the students go further with art or music–and the same is true of maths (though perhaps the percentage is higher?). But the arts and maths are still valuable to those students since their minds and creativity are improved.

So how can I teach maths to be more like an arts subject? I can do this by focusing on maths as a process to be explored rather than memorised. I can also give problems which allow students to investigate and apply their mathematical ideas. Ollerton and Watson say that students “sometimes learn more when plunged into a complex mathematical situation”–so I can avoid giving five simple examples then asking for skill practice. I can develop activities that make students think about why things work.

Would you say you teach maths like a list of skills to be mastered? Or do you focus on “doing” mathematics?

*Ollerton seems to have no website. Take me on as your apprentice, Mike, and I will create your website in return!