Fan and Pick – Kagan Structures

Who did I try it with? Year 10 middle set

What topic was it used for? Mutually exclusive events.

How does it work? Each group has a prepared set of question cards. Person 1 fans the card for person 2 to pick a card at random. Person 2 then reads the question for Person 3 to answer (remember to give thinking time!). Person 3 answers and Person 4 has to decide if it was correct. Roles then rotate.

And did it work? Students seemed to be engaged. I could probably have set more difficult questions. Everyone was participating and it showed that all had understood the concept.

What did it add to the learning? It was able to replace a potentially boring question set. It did involve everyone and didn’t allow for any major disengagement.

Next steps? I’d like to get a class to write questions as a plenary that would then be used as the starter for the next lesson in this way.


Mathematician’s Lament – Paul Lockhart

So – I put out the call to see if there were any voices of inspiration from #mathchat for my assignment and sure enough, I was rewarded. David Wees (@davidwees) pointed me in the direction of this paper and it was more than a little unsettling.

Paul Lockhart is lamenting the state of Mathematics education world-wide which, it would seem, has no redeemable characteristics at all. It’s variably compared to painting by numbers and music without an instrument, presenting what we know as school-based mathematics as “an empty husk”.

Reading the article, I could see what he means and agreed in many places but felt it was a little over egged. I’ve explored the area of the triangle as he states it, we think about puzzles and strategies in my classroom – I try to make students appreciate the process as much as the final result. I know that isn’t the whole story, but neither I think is Lockhart’s presentation. And I’m not alone.

The new GCSE curriculum has an increased focus on “functional mathematics”. The fear of some of the maths departments I’ve been in touch with about this is palpable – just how much are the students going to be expected to do on their own? We are trying to allow our students to look at a problem and apply some of the strategies they have developed. We don’t really have a very clear concept of how this will look on a potential exam paper nor do there seem to be a lot of resources available.

Is this preparing them for the real world? I don’t know. Lockhart argues that when we make things ‘relevant’ we have a danger of making them ‘irrelevant’. For example, do kids really care about compound interest? Rather, we should be asking engaging questions and exploring mathematics for it’s own sake. I think ‘functional mathematics’ has helped me do this more in the high-stakes classes but I think I’d have done most of it anyway.

Maybe I’m being blindly naive but I think there are chinks of this shining through. In the UK there has been major curriculum reform in Maths every two or so years for the past 10. In the midst of all of that, I have been part of groups of teachers who have been passionate about engaging and enthusing their students – in teaching for understanding rather than utility – in deep and meaningful learning.

I’m going to read Lockhart again and think about it more. I think for my question – Are we teaching the right stuff? – it adds a really interesting flavour and distinctive voice. It challenges the issue to be more “Are we even teaching Mathematics?” I’m going to be taking part in a conversation on this article this next Thursday with people I’ve never met in Canada and elsewhere. Exciting!

Subject content – why do we teach what we teach?

For my current MA module – Contemporary Issues in Mathematics – I have to do this:

Assessment: A written report which provides a critical reflection of the chosen issues or concern, discussing the impact and suggesting ways to overcome areas of professional concern. (4000 words).

On the last taught day, I became quite interested in why our curriculum subject content is the way it is.  I couldn’t find much work previously done on this.  I found the work of Geoffrey Howson – he has compared the curricula as they stood in the early 90s of a wide range of European countries.  My problem is I can’t decide what issue I’d like to focus on.

I have a thought to analyse what we teach (subject content) and explore the impact of this on student engagement.  Does the subject content affect engagement?  Are we adequately preparing students for future lives and careers?  For example, should there be more on probability and risk? I can compare this with other countries and come to some kind of conclusion.  Hard to think about gaining data on ‘engagement’ – maybe post-16 take up?  [I’m considering this as a separate issue than how it is taught – I know this is a difficult separation to make but I need to think about manageable questions for this – I only have 2 months!]

I’m also concerned with curriculum reform in and of itself … how often it happens – how effective it is – how much impact it has in the typical mathematics classroom – whether it is done for the ‘right’ reasons or for gaining political capital – whether it is done with research involved or without it – who is involved in the process and are these the right groups.

I feel they are two distinct questions … the second one seems more meaty but not sure how much work has been done on it.

Does anyone have any thoughts or research that might be useful for this?

Kagan Structures thus far!

So, I’ve been working with Kagan’s vision of collaborative learning over the past school year.  I’ve gone a bit hot and cold with these.  I want to gather the structures I’ve used so far, who I’ve done them with and some reflections on them.

1) Mix-pair-share

By far, this is my favourite structure so far.  I really enjoy it and have done it with Year 7, 8 and 12s.  Also tried them with my year 10s.

There are two different ways I have tried these.  The first, I generate the questions or the questions and the answers.  The student then works on their own question to understand or generate the answer.  Then the mix-pair-share.

The other is as a plenary whereon students generate the question and the answer.  This needs to modelled with and example question on the board and thinking about what the key elements we might include are.

This didn’t work with my Year 10s.  They weren’t really on board – didn’t want to move around – think this would be different if I’d tried to do this at the start of the year rather than near the middle.

2) Roundtable

I’ve used this with most of my classes and modelled it with some teachers.  The version I’ve been using is more accurately called Simultaneous Roundtable.

This works well with multi-step procedural problems or with situations where you can ask several questions about the same situation.  The first makes me worry I’m drilling students to think and answer in a particular way.  I like the second.  I like that students have to sign off that the previous person was right and then add to the thinking.  Really helps with the individual accountability of PIES.

3) Inside-Outside Circle

I did this with a class of year 12s and can’t imagine the chaos if I had done this with a larger class.  It was good but a bit chaotic.

In terms of structures, I’m not sure how many others I have used.  Again – I’m on holiday so might have forgotten some.  I’m going to aim to post about a new structure once a week.

All the projects in the world … the blog restart!

So, I’m on holiday and there is one half-term left until the Summer holidays.  I’m in Norfolk with my wife and some friends, with some nice spare time to reflect and think about the past year.

I started this blog thinking I’d update it more but I don’t think I had a real plan for it.  At the moment, I feel like I have lots of different things going on professionally that this might be a good space to explore and think about those.  I don’t really feel many people are going to read what I’ve got to say but I think it would be helpful for me to put some stuff up here and see what is going on in my head.

Here are the things I’m thinking about at the moment.

1) Collaborative Learning – I’ve been working on this off and on over the past year and had a lot of fun with it.  I wrote an assignment on it for my MA and reflected on it quite a bit.  I’ve noticed that I’ve ignored it recently though.  We just had a really short half-term and I think that might be part of it but I have plans to use it extensively for the final 7 weeks.  I want to aim to use a new structure every week – so that is going to be aim number one to reflect on back here.

2) Subject content – For my MA, I’m supposed to be looking at a Contemporary Issue in Mathematics.  I got initially quite interested in why we study what we do – why are angle rules in the maths curriculum?  Who decided and were they right?  I’m going to be writing and researching this, so I’ll try to post something after each research session to help me with my thinking.

3) Use of Web 2.0 Tools.  Okay – this is something I’ve been thinking about recently and would like to use this space to think and explore it more.  There are three obvious outlets for this.

a) Twitter – I’m thinking about how to use this more.  I’m quite enjoying the #mathchat hashtag to get in touch and hear about other educators.  Thinking about whether I can join in on the conversations and whether they’d be useful.

b) Wiki – I’m thinking about using a wiki for my new Year 10s in September.  I don’t know what set I’ll have next year but I think it might be useful.  The maths curriculum is really large and this might be a good way to help gather the information over the course of the two-year course.  A way to collect links, videos, information, etc for the students.

c) Blog – This feels like it might be a repeat of the wiki thing – I feel for this it is more about what I put up and how students comment, whereas wikis tend to be more user generated.


I want to use this blog to help with the reflections on each of those.  Now, the fact I can’t do this from school is a minor issue but maybe not insurmountable.  We’ll see.

There is another plan set around gathering useful resources but I think I might do that slightly differently.  Rather than cataloguing everything that I have – which is loads – I want to have a ‘new’ catalogue that I only add to and comment on when it is useful and it has worked.  I want to help myself move away from ‘sage on the stage’ and worksheet – and so the structures thing will help with that.