Thinking skills and mathematics can best be described as unchartered territory. A quick search on the internet will soon tell you that there are very few books or resources available.
But with the help of Julie Temperley from the Bedfordshire Schools Improvement Partnership (BSIP) I set up the Thinking Maths Group last year with teachers from the county's schools.
Twenty of us met once every half-term for half a day to look at a different area of thinking skills, but we also focused on areas such as "group work" or "questioning skills". This was a new experience for many. When trying out new ideas there are inevitably obstacles to negotiate and lessons to be learnt. Admitting to other teachers that you had a terrible lesson requires a certain amount of courage, but the group soon reached the point where they would freely talk about their successes and failures.
Sally Taverner, lecturer in mathematics education and director of continuing professional secondary development at the University of Newcastle, had given us a selection of ideas from her soon-to-be-published resource pack Thinking through Mathematics. We then devised new resources, ideas and lesson plans.
The first activity we tried as a group, Mystery, is designed to teach pupils how to select the relevant data to solve a problem. I chose Mystery because it needed little explanation and was appropriate for most ages. Every teacher turned up buzzing about this activity. A teacher who had tried Mystery with Year 4 and one who had tried it with Year 11 were equally amazed. At this point I realised we had something special.
Mystery begins with 18 statements printed on individual slips of paper:
* All of Rebecca's friends are going abroad this year.
* Jack likes all sorts of sports including football, swimming, snooker and especially tennis all of which are available at the Holiday Park.
* Rebecca wants to go back to school in September with a tan.
* Mrs Hunter thinks this could be their last holiday as a family. She thinks Rebecca will want to go on holiday with her friends next year when she starts in the sixth form.
* Mr Hunter would prefer not to fly.
* It will cost about pound;8 a day to put HP into kennels.
* They have saved pound;60 a month for the last year.
* Rita has seen a holiday in a travel agents for 10 days B+B in a hotel in the Canaries for pound;300 each; children under 16 go half price.
* Bob says when they went to the Holiday Park nine years a go, it was about 150 miles away.
* Bob reckons their car does about 30 miles to the gallon.
* Petrol is about 82p a litre.
* The average temperature for the Canaries during August is about 28C.
* Rita has only 15 days holiday left to take until January.
* Bob reckons HP is getting a bit old at the age of nine to be going into kennels.
* Rita says they normally spend about pound;100 a week on food.
* Bob got Jack to go on to the Holiday Park website and found an apartment for two weeks self-catering based on a family of four sharing, for pound;950. This included free access to the swimming pool, but things such as tennis were extra and charged by the hour.
* pound;1 is approximately 1.6 euro.
* Rita's work colleague Ardvind says he took his wife and daughter to the Canaries last year and the food was very reasonably priced. They spent about 30 euro a day on food and about one and a half times that amount on entertainment.
The activity is designed for groups of about four. They share out the 18 comments and then work together to decide whether the Hunter family should go to the Canaries or a holiday park.
Obviously teamwork is important, but the emphasis is on how they reach agreement. Some of the statements can be both in support of and against a destination so discussion is an integral part of the process. Pupils will, for example, deliberate over contrasting statements such as "Rebecca wants to go back to school in September with a tan" and "Mr Hunter would prefer not to fly".
This kind of discussion develops the ability to sort relevant from irrelevant information. They also learn to classify and interpret information, make links between pieces, form hypotheses, check, refine, explain and justify.
They can also take part in question and answer sessions after each presentation. This part of the lesson can easily take 20 minutes.
This type of activity is often seen in humanities subjects. However, we feel it has a great deal to offer maths teachers. All too often pupils are given only the information they need to solve a problem; it is unusual to have to select the correct data before starting.
The group met six times during the year and we developed a whole range of activities to develop these kinds of skills. They are also relevant to all ages and they develop literacy and group work. But most of all they teach students how to make a decision and then justify it.
Resources created by the group can be found at www.schools.bedfordshire.gov.uknumeracyindex.htmlThinking through Mathematics by Sally Taverner will be published next year by Chris Kington PublishingTel: 01223 412260www.chriskingtonpublishing.co.ukNick Martin is a key stage 3 maths consultant in Bedfordshire