West Berkshire CAME Programme
Some case studies
CASE STUDY 1 – FIRTREEPRIMARY SCHOOL
CLASS TEACHER – LIZ HOLLOWAY
As part of our involvement in the first wave of the Primary Leadership Programme, the school’s leadership team identified children’s speaking and listening as a core focus. As part of this, in November 2003, I was offered access to some lessons taught by Sue Clarkson who had had training in a ‘new’ type of maths teaching which developed pupils’ abilities in group discussion techniques and explaining their thinking. Two sessions into CAME maths and I was raving to all who would listen! My year 6 class, with a wide range of abilities, were soon asking for the date of the next ‘thinking maths’ session or rather “Mrs. Clarkson’s maths”.
It would be inappropriate to single out a particular lesson to report on and so, I have recorded some of the thinking which has been startling. The second lesson the class experienced was ‘Digit detective’ and the children were enquiring into 8+ڤ=2? One girl, with relatively low achievement in maths, had realised that a single digit would not give her the required answer. After staring for a time at the class number line, she asked, “Could it be 14?” With a little prompting and some questioning, she managed to convince the other group members and subsequently, the class, that it had to be right because the box could hold 2 digits as well as one and that a ten and some units were required so that a single digit could become 20+. A light had turned on!
Another class member, a young man with a streetwise attitude and lots of bravado who liked maths, initially refused to take part in these sessions. He ‘hated’ them! Why? He was quite able to think clearly and draw conclusions with the best but the question “But why?” caused him to withdraw and refuse to explain his thinking. However, by the time the class visited the maths coordinators’ conference in June 2004, he was desperate to take part and to explain his thinking. Gradually he had accepted that by sharing thinking and ideas they could learn from each other, all ideas were important and questions from teachers did not mean that his idea was “wrong”.
Another “light on” moment happened when a child of very low ability realised during the bridging part of a lesson that the relationship between the number of teams in a Sports League and the matches they play was, in her words “take one”. I felt this was worth pursuing with her; the class had already been introduced to the notion of “n matches” to stand for any number. With prompting she could clarify her thinking to explain that “take one” was necessary because a team could not play themselves; she was supported in explaining this to the rest of the class, which led the more able group to express it as
“n times (n-1)”. They were very impressed with their algebraic ability and she was delighted with her part in it. This confirmed for me that CAME promotes clear thinking and does not place any artificial “ceiling” on learning.
Further, looking at the areas of rectangles, the more able boys could see that a rectangle with constant area could become longer and thinner. The thinking challenge to them was that a straight line on paper would always have a length and width, however thin. They engaged quite happily with this idea, content with the notion that there was not necessarily any way to find an area.
Designing a desk by measuring the children’s height and span and finding the median demonstrates to the children that averages help designers decide what size to make furniture. The children were able to use this thinking to bridge their ideas to the real world where such ‘averages’ inform design such as the height of doors, safety height limits at Thorpe Park and Legoland and the sliding positions of car seats. Sharing this lesson with another class, led a young man with poor communication skills to comment unprompted that Formula 1 cars had to be built specially for the driver because of balance! Wow!
I described this maths as ‘new’ above but the ideas behind CAME are not new in themselves. They are exciting and accessible to all. The informal jottings encourage those with limited literacy skills to join in and the shared thinking includes all. I love to share these lessons with children because they are a conversation in ideas between everyone – teaching by facilitating!
CASE STUDY 2– BUCKLEBURYPRIMARY SCHOOL
CLASS TEACHER – SERENA WILLIAMS
CLASS CONTEXT
The class working on CAME were a mixed age class of 13 year four children and 17 year 5 children.
The class could be largely considered to be quite an ‘able class’ although one year 5 pupil had a support assistant.
WHY DID YOU DECIDE TO JOIN THE PROJECT?
I decided to take part in the pilot having been introduced to it at the coordinators’ conference in the summer of 2004.
As maths coordinator I was happy to volunteer knowing that if we were fortunate enough to play a part in the pilot scheme it would be me doing the work involved!
MAIN ACTIONS
This class contained a significant number of fairly ego-centric children who were finding it difficult to work collaboratively and I saw CAME as a way of addressing these difficulties.
The ideas have given me a refreshing opportunity to teach from a different angle.
The planning and working methods, in groups, with large sheets of paper and pencils, the discussions etc. have provided refreshment when under such a tight framework of activities to cover.
Sharing successful methods verbally has been a great learning curve for the children together with listening to what others have to offer and then trying out others’ methods too.
I also decided to purchase an additional file of CAME materials as a valuable resource, for the year 6 teacher, who I felt would be positive towards this new approach.
IMPACT OF ACTIONS IN CLASSROOM
After this pilot project I feel the class co-operate more with each other and are now more prepared to listen to the methods others have used.
They appear less anxious when committing their thoughts and ideas to paper and will attempt activities using methods they are familiar with. Their discussions have more focus and in other subjects or regular maths lessons they are happy to share their results even if the final answer is not accurate. They love the challenges offered through CAME.
IMPACT IN OTHER AREAS OF THE CURRICULUM
Through the year I have used these ideas in other aspects of the curriculum, in RE for example, because team work now has a higher chance of success. The CAME approach supports development of group cooperation, which does not come easily to all children.
CHALLENGES
Initially I felt that I could not follow the advice to form similar ability groups, due to their difficulties in co-operating, so a compromise was required, allowing them to have some choice of partners. This in turn led to them being more flexible and working with others in time.
Pairs worked best, leading then to working in groups of four.
NEXT STEPS
I would like to continue using this material with my next class in September but also introduce the KS1 material in school. It will be interesting to see what impact an earlier exposure to collaborative working will have by the time pupils move to KS2.
FINALLY…..
Suddenly there is that element of fun back in the lessons without the stress of completing or covering elements from strict guidelines.
It is what teaching is all about, working and learning alongside the children. Learning can be such fun when you use CAME, both for the children and for the teacher.
CASE STUDY 3 –ST. MARY’S CHURCH OF ENGLAND JUNIOR SCHOOL (now ThatchamParkPrimary School)
CLASS TEACHER – RACHEL MALEY
The project was run with just one of the year six classes to start with and will feed into both year six and five classes next year. The year six class involved in the pilot consisted of 25 mixed ability pupils, some of whom were very able.
WHY DID YOU DECIDE TO JOIN THE PROJECT?
One of the main thrusts of our school development plan is to encourage good speaking and listening skills. The maths co-ordinator saw the demonstration lesson at a conference and felt that CAME would help to foster these skills through focused maths activities. It was also used as part of our involvement in the Primary Leadership Programme.
MAIN ACTIONS
My initial focus was to try out a few of the lessons and gauge the responses of the children. Initially I was apprehensive but that all changed after my first lesson. The activities are clearly laid out with step by step phases which made them easy to follow. The children were also very focused on the task and all the discussion centred around the maths problems not what was on TV last night! I was amazed at how on task the children were.
I then started to use the lessons more regularly – about two every half term. After each lesson I found myself becoming more confident in teaching this way and the children really looked forward to their thinking maths lessons.
Towards the end of this year I have started to show other members of staff how CAME maths works so that next year all year 5 and 6 teachers will be teaching these lessons twice a half term.
IMPACT OF ACTIONS IN CLASSROOM
The main impact of CAME has been the improvement in the pupils’ ability to problem solve. By letting the children work in pairs and small groups it gives children the confidence to discuss possible solutions and try out new ideas. They feel secure working in this setting and when asked about what helped them learn in CAME lessons they gave answers like;
“Working as a team and talking as a team.”
“Listening to others ideas and opinions”
“Being able to talk about it.”
I have found the children are much more motivated for problem solving as the context for each lesson is very engaging and easy to set into a real life context. It is something that the children can visualise and relate to.
IMPACT IN OTHER AREAS OF THE CURRICULUM
The CAME maths project links effectively to the speaking and listening materials. The skills that CAME lessons enhance are also required in all other curriculum areas. The need to listen to others, discuss ideas and opinions and making decisions as a group. They really develop the ethos of being part of a team and these are life skills that they children will be able to apply to many other situations.
The CAME maths lessons also allow you as the teacher to take a step back and let the children think for themselves. It requires them to develop independence and stops them becoming over- reliant on the teacher, a quality clearly needed for successful transfer to secondary school.
CHALLENGES
One of the main challenges has been how best to organise my class to get the best from these lessons. Should it be mixed ability or working within ability groups? I have found the best approach has been to use groups of near ability. I found that in mixed ability groups the more able would dominate and the less able would soon lose interest. By using near ability grouping you get some good ideas generated and everyone can be involved as they are working at a similar level.
Another challenge related to the use of my Learning Support Assistant (LSA). I found that placing her with the less able was the most useful, but I have encouraged her to ask questions rather than give answers. I have been lucky as my LSA is extremely good at questioning and has provided sufficient challenge and support for this group.
My initial apprehension about lack of pupil motivation proved to be unfounded. The lessons are so engaging that many of the children do not want the lesson to finish and often take problems home to continue working!
Assessment is also a challenge as there is little formal recording of work. However, I found that I had a very good understanding of what the children had understood by getting each group to report back their findings and through listening to group discussions during the course of the lessons. The children have also become very good at self evaluation and are able to share what they found difficult or easy and what helped them to solve the problem They are becoming much better at being able to verbalise their thought processes.
NEXT STEPS
- To ensure that CAME is used in all the year 6 and 5 classes next year and supporting the teachers in this.
- Discuss the use of Let’s Think for KS1 and lower KS2
- Review my use of transition materials, which focus on more abstract, algebraic ideas. The effectiveness of CAME in developing these has implications for adapting and extending such materials.
FINALLY…
Pupils
“It is fun to discuss things you are stuck on.”
“I like sharing ideas with my friends, but they really made me think!”
“I was not confident in maths before, now I can ask my friends for help.”
Class Teacher
“I have been amazed at how focussed and motivated the pupils have been about solving some quite challenging maths problems.”
LSA
“It is good to watch the pupils working together to solve the problem. In order to solve the problem they must share information, otherwise they cannot move forward.”
CASE STUDY 4 -SPURCROFTPRIMARY SCHOOL
CLASS TEACHER – ANNA HOLMGREN
CLASS CONTEXT
I taught the CAME lessons to a mixed ability class of Year 5/6 children. There were 28 children in the class and their ability ranged from level 2 to level5. There was an even split between the number of boys and girls.
WHY DID YOU DECIDE TO JOIN THE PROJECT?
The main reasons why our school decided to pilot the CAME project was firstly because we wanted to enhance the children’s problem solving skills, in particular their ability to systematically solve a problem. Secondly, we wanted to develop the children’s speaking and listening skills in mathematics and improve their ability to explain their mathematical thinking and justify their answers. This aim was linked to our school SDP.
MAIN ACTIONS
I taught the CAME lessons every other week to the Year 5 and 6 children using two of the week’s lessons to cover them. I did this to ensure that the children had enough time to explore the mathematical concepts, explain their thinking and justify their opinions. In the first two terms the order of the lessons was agreed by all of the schools involved in the Pilot. In the final term the lessons were chosen to fit into the maths focus for the week. Before beginning the lessons, I made sure that I was familiar with the main aims and expectations. It was also important to know what different Piagetian levels the children could achieve within the lesson.
I adapted the lessons to meet the needs of my class, using a support assistant where appropriate. In certain lessons the children had practical apparatus to help them to understand the ideas. It was also sometimes necessary to move the more able children’s learning forward at a quicker pace as they had grasped the concepts. Consequently these children moved swiftly though the first three episodes of the lesson to episodes 4 and 5. I did not always use the worksheets from the folder as they would not have enhanced the children’s learning. If I did use them, I made sure that they were enlarged to A3 so that they were able to work in pairs. In some of the CAME lessons, for example the Bean bag lesson, I tried to make it more practical so that the children could explore their theories. During the spring term other colleagues in Year 5 and 6 began to use the CAME materials.
IMPACT OF ACTIONS IN CLASSROOM
The overall benefits of the lessons relate to the children becoming more competent and articulate when explaining their thinking. Children who would previously not put up their hand to answer questions were willing to explain their answers to their groups and, eventually to the class. The children’s realisation of the need to think carefully about their answers was highlighted when the Numeracy Consultant asked a child in my class a question; instead of giving an immediate answer which they would have done in the past the child said “ I am not sure at the moment; I need to think about it then I will give you an answer.” I think that other benefits of the scheme include the fact that it enhances the children’s problem solving abilities. This is because they have the time to explore their ideas. The lessons are also interesting and relate mathematical concepts to real life situations. They help children to welcome challenge and accept uncertainty. The discussions that have taken place during and after the lessons have been in-depth. The children really enjoyed the CAME lessons as these quotes show: