Edgar Dale, the American educationalist, said that we learn a great deal more when we teach something than when we read about it. From experience, this certainly seems true. Where did most of my mathematical understanding come from? From the experience of teaching it. Prior to teaching mathematics, I only knew how to ‘do it’. Most math teachers would agree.

So how do we apply this information to the classroom?

So how do we apply this information to the classroom?

Enable organic, natural peer teaching between students.

If you are a teacher who understands what it is to be a facilitator of learning and is comfortable with a controlled level of working noise, then you will know that peer teaching between students is something will occur spontaneously if you allow it to happen.

A great number of articles written on peer teaching can be found on the net. Some differentiate between peer teaching, peer tutoring, and peer instruction. Many advocate a structured approach - designating the peer teachers, assigning seating positions and using detailed instructions for the peer teachers. In this article I won’t be making any comment for or against a structured approach nor will I be differentiating between the terms peer teaching, peer tutoring, and peer instruction.

I have written several articles which reference the value of a well–scaffolded, student–centred, conceptually-based approach to teaching mathematics. Such an approach is more aligned to fostering spontaneous peer teaching than a traditional approach premised on a teacher-directed procedural approach. Obviously, as with any pedagogy, spontaneous peer teaching works best with students who are mostly engaged and onside with your attempts to enable learning to occur.

A great number of articles written on peer teaching can be found on the net. Some differentiate between peer teaching, peer tutoring, and peer instruction. Many advocate a structured approach - designating the peer teachers, assigning seating positions and using detailed instructions for the peer teachers. In this article I won’t be making any comment for or against a structured approach nor will I be differentiating between the terms peer teaching, peer tutoring, and peer instruction.

I have written several articles which reference the value of a well–scaffolded, student–centred, conceptually-based approach to teaching mathematics. Such an approach is more aligned to fostering spontaneous peer teaching than a traditional approach premised on a teacher-directed procedural approach. Obviously, as with any pedagogy, spontaneous peer teaching works best with students who are mostly engaged and onside with your attempts to enable learning to occur.

Allow me to paint a picture. You are a maths teacher, well established and respected by your students. You are focused on maximising engagement amongst your students. In part, you engineer this by using a well–structured, student–centred approach. Your classroom is characterised by a general 'buzz of learning' in the air. Students are more interested in learning together than in disrupting the lesson. You may or may not have a seating plan but regardless, students are relatively free to work with whoever they choose because their choices are mostly sound. Those couple of students who do not work well together are restricted from doing so. You may have established such a restriction by announcing (with smile on face) ...

*“Class, here’s the seating plan … Pete and Joey, you can’t sit within 3 desks of each other. That’s it!” *

Students know about acceptable levels of working noise and you have structures in place to keep the noise level conducive to learning. In such a class most students will naturally sit next to, or between, students who they work well with and you understand that by allowing this to occur you help build trust between you and your students.

A classroom which closely – or loosely – fits the above description will contain students who naturally gravitate towards helping each other, an action which I am loosely calling organic, natural peer teaching. If students in an engaged learning environment are motivated towards this sort of peer teaching, why not encourage it?

Students know about acceptable levels of working noise and you have structures in place to keep the noise level conducive to learning. In such a class most students will naturally sit next to, or between, students who they work well with and you understand that by allowing this to occur you help build trust between you and your students.

A classroom which closely – or loosely – fits the above description will contain students who naturally gravitate towards helping each other, an action which I am loosely calling organic, natural peer teaching. If students in an engaged learning environment are motivated towards this sort of peer teaching, why not encourage it?

- Make organic, natural peer teaching a part of your plan.
- Talk to the class about it - explain what you are looking for, establish the boundaries of what is acceptable and what’s not. In this way you are drawing on something the students want to do anyway and making it part of your classroom culture. You are simply steering their natural desire to maximise the positive outcomes of peer teaching.
- Praise students when demonstrating exemplary peer teaching/peer learning behaviour.

Often there are students in class who require focussed, individual instruction which is beyond the scope of organic, natural peer teaching. For example, a student, three lessons into a new unit, is completely 'lost' and has very little understanding of work. If you are unable to devote the one–on–one time in class for this student then utilising a trusted student who you know can explain the mathematics can be your saviour.

I vividly recall one such situation. We were three-quarters the way through a Yr 9 Trigonometry unit and the students were lining up at the classroom door for their next lesson. I was practising my ‘convivial teacher demeanour’, chatting to students as they lined up. Then I spotted Caleb. Caleb, a good–natured student and a hard worker, had been absent for the entire unit. I had, I must admit, amongst the busyness of everything, temporarily forgotten he’d been absent! (Yes, poor form, I know!) “Caleb”, I said, “you’re back! Right … well … umm … you’ve missed the entire Trig unit … and it’s different sort of work to anything you’ve covered before!” I was a long way short of panicking but nevertheless wondering how on Earth I was going to deal with this situation when Daniel, a friend of Caleb's who also happened to be one of the brightest students in the class, piped up saying “I’ll teach him!” My facial expression turned, in an instant, from “What to do ... what to do ... " to “Of course, YES, why didn’t I think of that!!” And in one lesson Frederick taught Caleb all the work we had covered to date. I was somewhat astonished. Admittedly Daniel was an exceptional peer teacher, but the story illustrates what is possible with peer teaching – and what can be achieved one–to–one.

End note: Caleb worked hard during the remaining lessons of the unit and performed similarly to his usual assessment scores relative to the other students.

End note: Caleb worked hard during the remaining lessons of the unit and performed similarly to his usual assessment scores relative to the other students.

"I don’t want my (bright) son/daughter spending time in class teaching other, needier students”

If you choose to draw on the talents of one or two talented students for specific peer teaching tasks you will need to be mindful of a couple of things. Firstly, ensure they are not missing out on consolidation and extension work. Secondly, it would be wise to reassure the parents of the talented student that he/she is benefitting from the experience. My view, clearly aligned with Mr. Dale's, is that the best way to consolidate understanding is to explain it to someone. Therefore, as long as any one student is only used for targeted peer teaching occasionally then it will be the peer teacher who benefits as much – if not more - than the peer student.

The issue of some organic, natural peer teaching being incorrect is a valid one. But so is the issue of students misinterpreting math instruction from the teacher. Therefore, strategies employed to check for understanding in the latter need to be applied to the former. It is possible that the issue of incorrect peer teaching is not as great as some people suspect. After all, we are not handing over the teaching role to students. You are, after all, running a well scaffolded, student-centred, engaged classroom in which you, the teacher, are facilitating the learning between students as well as using a lot of direct instruction.

- Make a point of checking in on some of the specific peer teaching occurring between students.
- Run the usual, quick, ‘checking for understanding’ quizzes with students.
- Occasionally ask a trusted student to sit in on a peer teaching session after giving 'the sitter' some appropriate instructions.

One of the advantages of fostering organic, natural peer teaching is that it helps build engagement in the classroom. Why? Because you are harnessing the natural instinct of students to collaborate and help each other and in so doing you help to build an engaged learning environment. The only downside is that sometimes it can be challenging to pull students away from their engaged “buzz” when you need to deliver their next instruction – a small price to pay!

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The article, Peer teaching in Teams of 3 contains a video explaining a highly engaging, well structured peer-teaching-in-teams-of-3 competition.

Do you use peer teaching? If yes, is it of a form similar to the above, or more structured? If no, are you tempted? I'd love you to share your thoughts. (Your email address will not be required)

Do you use peer teaching? If yes, is it of a form similar to the above, or more structured? If no, are you tempted? I'd love you to share your thoughts. (Your email address will not be required)

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