17 September 2010 We were sitting in a circle, about 6 of us, under the shade of a tree, discussing our past experiences learning mathematics. It came out that most of us had been taught by rote. We laughed at the fact that when someone was asked say a multiplication question like 6 x 7 =... they would need to go through the times tables ... 1 x 6 = 6, 2 x 6 = 12, 3 x 6 = 18 ... 6 x 7 = 42 ... to get their answer. However, most people found ways to 'get by' because failure to answer correctly was usually met with corporal punishment. I don't think this is historically too different from Australia. Such history has left its imprints on the present. Mathematics is generally feared by teachers and students alike. This has implications for both teaching and learning. From my own personal experience, when I feel threatened in a teaching role, I almost automatically find myself reverting to more didactic, teacher controlled methods of instruction, even though this goes against my ideas of how learning occurs. Furthermore, the way teachers themselves were taught can effect the way they teach when they enter the profession. Personally, some of my early experiences of problem solving have most likely led to my love of maths and a desire to teach it with problem solving as a centrepiece. For students, it means that they are also likely taught largely through rote methods, receive incorrect instruction, or simply skip areas that are not confidently understood by the teacher. Students may be able to find ways to 'get answers' but the more complicated it gets, the more they fall victims to a lack of real mathematical understanding and useful problem solving strategies. I haven't met many students who can really demonstrate flexibility with the number system, or problem solving thinking in general. They seem destined to repeat the pattern laid down by the previous generation - a generation where some don't understand maths and the language of numbers, don't see the point of it, and can't use it to improve the quality of their life. Mathematics is usually the subject that most students fail in the core examinations. To what extent does the climate of fear and the lack of alternative teaching methods contribute to this? How do we shift people from these habitual ways of behaving towards mathematics?

From my own personal experience, when I feel threatened in a teaching role, I almost automatically find myself reverting to more didactic, teacher controlled methods of instruction, even though this goes against my ideas of how learning occurs.

Generally, my maths radar is taking readings 24/7, but in an environment where most children are living in some degree of poverty, school is quite detached from everyday experience and even the language of instruction is foreign, it is understandable that other issues generally take precedence. Meanwhile, it's not effective for me to try and push my own agenda; really I'm only passing through. It's more effective to engage with people who are active here and work together on issues in which we share concern.

But that's a very interesting lesson about participation and shared commitment that I might save for another email...

12 October 2010

Also, remember how I was talking about using the Menu to give teachers choice, and doing research 'with and for' teachers? Well, I was thinking of ways that we could allow teachers the freedom to focus on what they think is necessary, still provide enough structure to encourage learning, but also model a more constructivist approach through the professional development. What I came up with, and I think fits these criteria, is Lesson Study.

In an investigation, when the kids get used to them, the teacher takes on more of a facilitator role and helps the students pursue their own learning.

We are going to group about 4/5 schools together, then group teachers by grade level, and over the course of three sessions they will collectively construct, deliver, review and modify, redeliver and reflect on the same lesson. I think this sends the implicit message that matches the implicit message about moving from seeing education as the 'transfer of knowledge' to the 'social construction of knowledge'. And because we teachers are always only passing through (except for perhaps for Steiner education) I think it's important for the learners to be able to take ownership of what they learn. I've been thinking about this ownership issue and levels of participation in relation to investigations, or tasks for that matter, and it's really the same kind of thing. In an investigation, when the kids get used to them, the teacher takes on more of a facilitator role and helps the students pursue their own learning. At the other end of the spectrum, you can at least inform students of what they are learning about and why - but we don't even think to do that much of the time!

You can find more of Aaron's writing in news items from Eritrea: February 2009 and March 2009.
He has also written more extensively on Eritrea and, before he left, on Menu Maths in his 3/4/5 composite class.