Collaborative learning in mathematics

The answer to this clue from 4 pics 1 word is dull.

The answer to this clue from 4 pics 1 word is “dull”.

 

Mathematics suffers an unfortunate public relationship problem. Dame Mary Marsh DBE, the chair of the NAICE Committee of Inquiry on Adult Numeracy Learning introduces the 2011 report¹ like this:

“We have a numeracy problem in this country – we are a nation quite happy to admit to ‘being bad at maths’, we see people almost wearing it as a badge of honour, in way they would never admit to saying they couldn’t read or write.”

Rachel Riley, the current co-host of countdown echo’s this:

“For some reason we think it’s OK to say we’re bad at maths. People are generally embarrassed to admit they can’t read or write, but think it’s fine to say, ‘I’m rubbish at maths’. We need to end that culture. Maths is important in everything you do, whatever job you have and in everyday life.”

This isn’t something that is just said by the uneducated. Alan Stevens, from the Institute of Mathematics and its Applications says:

“Even engineers sometimes say they’re no good at maths. This makes it seem even more acceptable and projects the wrong image, the image that maths is indeed an ivory tower which is dull and boring and of no interest or use to intelligent people. That’s the wrong image.”²

As maths teachers this is perception of our subject that many of our students hold and that affects the their attitude to learning. Earlier this year I blogged about how I had asked each of my classes what they expected from me. The answers are combined into this Wordle:

Wordle

The two biggest requests from students were that I should make their lessons fun and that I should provide them with enough help and support. Enter collaborative learning…

Collaborative Learning

In order to introduce more collaborative learning into my lessons the first thing that I had to change was my classroom environment. Previously I’d taught with the desks in my classroom either in rows or in a horseshoe shape. I’ve now rearranged them into groups of four – far more conducive to collaboration.

Craig Barton, author of MrBartonMaths.com writes³:

“Group work in mathematics is a tricky one. At times students can see it as a “sit-off” and chaos without any real learning can ensue.”

However, he goes on to say:

“Students can often learn more from each other, and in different ways, than they do from the teacher, and may also embrace the freedom they have been given to produce some incredibly creative, high-quality work.”

In order to introduce collaborative learning, the second thing I’ve had to do has been to teach the students how to work successfully in groups. Initially I did this in discussion based work by making it clear that at the end of the task in question that every, and any, person in the group should be able to give me an answer the question or explain the method. Introducing roles to group members can be useful if groups are finding it difficult to gel, or if you have some students who have a tendency to take over, or to sit back. Some use Kagan structures in order to provide balance to group activities. One of the key things for me has been the realisation that until group work is established as a regular routine, group tasks will need to be simplified.

“If students retain a discipline- or task-achievement focus then this can cause additional stress and anxiety as the students are having to master these new metacognitive aspects along with the pressure of completing the task to a high standard – a significant overload.”4

Ofsted provide backing for collaborative learning in their 2008 mathematics report: 5

In the best lessons, ‘pupils were expected to work productively in pairs or groups, discussing their learning, trying out new skills and exploring concepts.

Impact

As yet, evidence for impact of this in lessons is simply anecdotal. Students have said that they enjoy working collaboratively and pupil motivation does seem to have improved. I am intending to use it to improve pupil’s written communication. Two weeks ago I tweeted the following picture, with the tweet:

“Maths is about communication. How do you encourage your students to use words in their answers?”

communication

Ian Dickerson replied back to me:

Relay. 3 minutes before passing the question on to the next person to continue. Have to communicate to succeed.

I don’t think I will ever go back to teaching in rows – I am now completely sold on the benefits of group work and working collaboratively. Why don’t you try it in your classroom and blog about how you’ve found it?

This post has been written as part of the #blogsync project under the topic of “A Teaching and Learning strategy intended to elicit the highest levels of student motivation in my subject”. To read more posts on this topic, or to sign up for next month’s #blogsync, visit the #blogsync website.

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1 NIACE 2011 Final Report

2 BBC News – How to solve the British Maths Problem

3 TES Resource Collection – MrBartonMaths

4 Collaborative learning and anxiety

5 Mathematics: Understanding the score

 

Bring a teacher to Twitter

This week is Bring a Teacher to Twitter week – a week to show non-tweeting teachers how fantastic Twitter is as a professional development opportunity.

So what is Twitter? Twitter allows you to publish 140 character long “tweets”, in essence micro blog posts that are shared with whoever chooses to follow you. You are free to choose whether your tweets are available for anyone to follow, or published privately – only available to the people you wish to see them. Paul Gillan explains here more about Twitter.

I created my @MrMathsTeacher twitter account on the 16th of November 2011 (WhenDidYouJoinTwitter.com) and started following people who tweet about maths teaching and education. Very quickly I realised how fantastic twitter is to learn more about teaching, to find new resources and to have your thinking challenged. As the NEA say:

Twitter won’t change your life, but it might make your job more fun and a little easier

 My top 5 reasons for using Twitter

  1. Teaching is about sharing – not reinventing the wheel. Nine times out of ten if you’re thinking about making a resource, the chances are that someone somewhere has made something very similar already – something that you can borrow or adapt and so save you time. The internet is full of websites containing resources – the only trouble being the variation in quality between them. Over the last week I’ve been made aware of some great websites containing brilliant resources – all because someone has found them, tested them, and then tweeted about how successful they have been in their classroom.
  2. As you develop your PLN you will be able to use it as a source of information. I’m in the process of making a display designed to inspire pupils about maths (blog post to follow!). As part of this I tweeted this question:

This was retweeted by 23 people and answered by many more. A related tweet even prompted a 5 minute discussion on Chris Evan’s breakfast show on Radio 2! I now have masses of quotes and ideas to use to create a fantastic display.

  1. Regular webchats take place on Twitter using hashtags to identify themselves. They are basically hour or half hour long CPD sessions on a given topic. Ian Addison explains more about #ukedchat in his blog article. I usually read and take part in #mathchat and sometimes #sltchat. Most webchats are archived on the internet to enable you to look back at them.
  2. Sometimes, despite the number of years of teaching experience you have, you can struggle with teaching a particular topic. You might lack ideas for making a dull topic interesting, or find it difficult to convey a concept to a group of pupils. Twitter is great for collaborative planning – particularly in conjunction with tools such as Dropbox or Google Documents. One great example of this is #UMFac – the Ultimate Maths Faculty, set up by Dave Gale – where maths teachers from across Twitter have contributed their ideas on teaching particular topics.
  3. Twitter allows you to keep up with the newest things in education and allows you to find out what is happening and seek advise and assistance. When the English results dropped in the Summer I saw teachers using Twitter to find out if it was just their school or whether others had been affected. I’ve seen teachers asking for advice on the latest technology they’ve been given to use in their classrooms; teachers seeking support on exam board changes and syllabus changes.

 Read more:

Getting started on Twitter

Registering an account on Twitter is very straightforward. Once registered though, you might find yourself asking where is all this wonderful CPD everyone has told me about? Who do I follow? How can I get started?

Hundreds of people have written about this so rather than me repeating what has already been said, have a look at some of these:

I will give two pieces of advise though:

  1. Make sure you fill in your profile information – people rarely follow accounts where there is no information about the person tweeting.
  2. Keep your tweets professional. I see my Twitter account and blog as being part of me as a teacher, and something that I would reference on a job application. Even if you don’t think you would do that, you want to be memorable for the right reasons to future colleagues or employers who might choose to follow you.

Using pupil voice

At the start of the year I changed my usual practice and did something completely different with each class in their first lesson. As a school we had launched a whole new pastoral system including a new behaviour policy, and consequently had spent a good deal of time letting pupils know exactly what our expectations of them were.

ActivExpression – a future blog post.

In my first lesson rather than spending too much time going over my expectations of the pupils, I put a question up on the interactive whiteboard and gave pupils two minutes to discuss it in pairs. The question was: “What do you expect of me?” Once the two minutes were up I used the ActivExpression learner response devices to collect in the responses and then displayed them on the interactive whiteboard so we could discuss them as a class. It was then very easy to steer the conversation round to what I required from the pupils in order to meet their expectations.

The first class I did this with was with my top set year 7. I was really impressed with the maturity of the responses given – lots of pupils wanting me to really push them and challenge them. Some of the responses gave little insights into the small insecurities the pupils had in moving up into secondary school – comments such as “don’t get angry if we get something wrong”. It has taken a few weeks to completely address that fear so the pupils have understood that it is okay to be wrong , it is okay to make mistakes; and that it is actually part of the process of learning.

 

Although doing this did lead really well into a discussion about what I required from the pupils in order to be able to meet their expectations, that wasn’t the reason for doing this. At the end of this half term I want to return back to this with the pupils and get them to assess how well I have met their expectations. I planning on doing that by summarising their comments into no more than ten statements, and then using likert scales (1-5) on the ActivExpressions in order to collect the results.

I’ll post an update at half term to let you know how I got on!

Expanding brackets

Last week after teaching an algebra topic to a low ability year 8 class I tweeted:

Used coloured counters in cups to introduce expanding brackets: 3(2b+5g). Worked really well! #mathchat

The tweet seemed to provoke a reasonable amount of interest – it received a few retweets, several replies, and a few direct messages. All of the direct messages were along the lines of: sounds interesting – I’d like to hear more about that.

So here goes.

Aside from mini whiteboards (a post for another day), I think cups and counters are possible some of the most useful pieces of equipment for teaching mathematical concepts – particularly for algebra.

At its simplest level, algebra is usually introduced in terms of items in a cafe or shop – 2c standing for 2 cups of tea, or 2b standing for 2 buns. As well as being simplistic, this introduces a conceptual error right from the start; mathematically 2c represents c + c. One cannot add a cup of tea to another cup of tea – one can, however, add the price of a cup of tea, to the price of a cup of tea.

Tal Greengard expands on this – his blog is worth a read.

I’ve now moved on to introducing algebra using cups. Cheap plastic cups – easily written on using a whiteboard marker. Instead of a standing for apple, instead a represents the cup with a written on it. I then use counters inside the cup to show what value a represents.

So how do you expand brackets?

Last week I used the cup to represent the bracket. My example was 3(2b + 5g). I had 3 cups, each containing 2 black counters and 5 green counters. Previously when teaching brackets without visual aids, pupils have struggled to understand why we’re multiplying the contents of the bracket by the number on the outside. Doing it this way only took three practical demonstrations, backed up with the maths on the board, before the pupils were confident with what they were doing and ready to move on to practising on mini whiteboards.

 

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