Using the students to teach little bits and pieces is something I use fairly regularly in my lessons. It is usually as simple as sitting students in pairs, such that one understands, and another does not quite get it yet, and then the magic happens automatically. Sometimes, I also use those who finish an exercise particularly quickly as an extra pair of hands to help others. This proves particularly useful in topics such as fractions, where some students can do it very quickly, but others still need a lot of support. This provides those struggling with extra support, and those who get it, really have to understand the material to teach it.
In one of my A-Level groups, I have a fairly mixed bag, with some of the students having done Additional Maths alongside the IGCSE we offer, and some having come from other schools for the Sixth Form, with the GCSE. The whole group are very capable mathematicians, but there are large chunks of the C1 and C2 course that those who did Additional Maths have already covered.
In particular, an early problem arose when doing differentiation, since this is on the IGCSE syllabus, so all the students from our school had already done it, but those new to the school had no idea. The major downside to this was that those who had already done it, thought they knew it, and wanted to skim through it. However, as has become apparent recently, they did not get a proper understanding of the First Principles (which is not on the IGCSE), as they felt they knew it, and did not necessarily give it their full attention.
I have been trying different approaches to get round the difference in knowledge, and recently I tried something a bit different.
In C2 there are 3 topics that those who did Additional Maths have already covered: Integration; Binomial Theorem; Factor and Remainder Theorem. In one lesson last half term, I told them that they were going to teach these topics to the rest of the class, and asked them to choose which they would like. The numbers split in a very nice way, and it was decided. In the last couple of weeks before the half term, the group who were doing Integration taught their bit.
This experience was very eye-opening for me, as well as the students. Firstly, they prepared powerpoints and printed notes for each mini-section of Integration. They went well beyond what I was expecting (I had said an introductory lesson), teaching the whole topic over 3 lessons.
As well as the obvious benefits for the group teaching (they cemented their understanding etc), the other students really engaged with everything that was being said. In fact, if I was to deliver the exact same lesson, I don't think I would have the same level of engagement as they gave their own peers. It also gave me an opportunity to watch the class as they were learning, and I very quickly picked out those who were struggling with the concept. This enabled me to intervene with individuals as necessary.
It also made me realise that I have been going slower than they can manage, as the material covered in three lessons was very pacy and succint. I now know that they can take a much faster pace than I have been giving them, and will be using this after the half term.
They have their mocks straight after the half term, but after that, the other two groups will be doing their topics (which are shorter, so will only be two lessons worth). It has been a very insightful and useful exercise for me, and also to get those who have done the topics before to think about them in a bit more depth (they need to be prepared to answer questions as well). Definitely something I will use again if in the same situation.
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I am a maths teacher looking to share good ideas for use in the classroom, with a current interest in integrating educational research into my practice.