# Mathagogy, one question lessons and making cones

Monday 27 May 2013

### Mathagogy

This is a blog antry to support my video enty to the mathagogy project from @pepsmccrea. The project is a fabulous idea and I can hardly wait to see some of the video entries! Anyway, I have made my video about what I have called 'One Question Lessons' for the sake of argument. By that I mean the sorts of lessons where the formal input of the teacher is limited to the expression of a single, concrete task that should occupy students for the rest of the lesson. The video is below along with some links to support the idea and the sorts of activities that I think exemplify what I am getting at. Each of the links goes on to talk about where I see the value in this particular type of mathematical task. The mathagogy project quite rightly requires that videos try to keep under two minutes, but presumambly if you are here then you want to know more about the idea, so the video below is the extended version running to just over five minutes. (Actually, it was the first take when I first learned how difficult it was going to be to squeeze what I wanted to say in to 2 minutes!)

So, the advantage of multimedia should be that I dont now write down everything I just said in the video! I will just try and pick out the key parts!

#### Elements of the one questions lesson

- Task has to be very easily explained and understood. Lets be clear that I am talking about the end goal and not the journey/task itself.
- The task has to draw people in and make theùm want to have go. As such it has to appear possible and achievable by all students and and appeal to them.
- There must be opportunities for students to make conjectures, challenge misconceptions and get feedback on their efforst straight away.
- There must also be opportunitites to discover some fairly profound mathematics.

#### Making Cones

Here are a couple of links to more detaimls about the cones activity described in the video.

Making Cones activity Making Cones teacher notes

#### More One Question lessons

Given the description of one question lessons, the following are some examples of similar types of activity!

Dr Who - this is one of my all time favourites. the task is simple, make the animation shown in the video below! Watch carefully and pay attention to the details.

The task can be approached from a number of angles in the teaching of a number of topics and more detail and options are given here. Dr Who

I have spent a long time thinking about similar activities and done a couple of workshops on the idea of what I have called Animated Questions which you can read more about by following the link.

This is another lovely geometry one where students are given 8 sectors of the circle and simply asked to say - with justifications - which is the biggest. Nothing more! So much can spin off that one question

Another very visual and algebraic task where students are asked to recreate different different images all based on trig functions.

#### Task design

Some of you may have noticed the obvious product placement in my video. It is 'Designing and using mathematical tasks by John Mason and Sue Johnston Wilder. This is a book that has been hugley influential on my career. I have been lucky enough to work a bit with both John Mason and his wife Anne Watson who both made me think deeply about task design. I recommend all their work, but particularly this book! Much of it is behind my thoughts on The Mathematical Experience.

#### The Mathagogy project

I just wanted to end by saying what a wonderful idea I think this project is and how keen I am to watch and hear what so many other maths teachers around the world have to say. I also hope that those teachers will help me develop these ideas in this blog post further! Thanks.

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