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A thinking skills approach to learning maths (CAME)

The Cognitive Acceleration in Mathematics Education (CAME) project aims to improve math skills in students aged 11-14. Research shows higher achievement levels and transferable skills in science and English. Lessons focus on collaborative learning and teacher mediation to prompt critical thinking. Key stages involve concrete preparation, collaborative tasks, and whole-class discussions. Findings suggest that pupils benefit more from mixed-ability classes. Teachers can support student dialogue and decision-making while leaders can explore flexible delivery methods and coaching partnerships. Learn more from the CAME project study by Shayer and Adhami (2007).

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A thinking skills approach to learning maths (CAME)

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  1. A thinking skills approach to learning maths (CAME)

  2. Schools implementing cognitive skills in maths saw: over half participating classes achieve larger than expected maths achievement from year 7 to year 8 significantly higher GCSE pass rates in maths than in control schools (0.8 of a GCSE grade higher)

  3. The impact of setting on pupil outcomes • pupils in low ability sets gained little from CAME lessons despite being taught by experienced CAME teachers • A CAME school with mixed ability classes reported gains for pupils of all abilities • Researchers believed the reason was that higher-ability pupils provide a range of insights that help lower-attaining pupils extend their thinking

  4. Evidence of thinking skills developed in maths transferring to other subjects • CAME pupils achieved value-added gains of 0.30 of a grade in science and 0.32 of a grade in English • this may be evidence for transfer of thinking skills from maths to other subjects

  5. The Cognitive acceleration in mathematics education (CAME) project • The CAME project: • is based on research and theory about pupils’ thinking • aims to boost mathematical thinking of pupils aged 11 to 14 years and raise their attainment in standard tests

  6. The key ideas behind CAME are that: • through collaboration children who are further on in their understanding of a problem can help move other pupils forward too (from Vygotsky) • the teacher’s role is to prompt pupils thinking with questions (mediation) • all adolescents have the potential to achieve in mathematics

  7. The key stages of a CAME lesson • CAME mathematics lessons follow a structure of: • concrete preparation • collaborative learning • whole-class discussion

  8. Concrete preparation • In the opening phase the teacher: - introduces the task to the whole group - asks pupils to explain to each other what they think the task is about

  9. Collaborative learning pupils work in pairs or small groups on tasks which challenge pupils’ existing ideas pupils make notes from discussion for feedback later The teacher moves around the class observing interaction and prompting with questions when discussion falters

  10. Whole-class discussion The session closes with a whole class discussion in which the teacher: asks groups to report their ideas encourages pupils to reflect on their reasoning using probing questions draw pupils’ attention to key ideas and vocabulary encourages others to ask questions

  11. The tasks pupils tackle in a CAME session In the ‘twigs and leaves’ task pupils describe the pattern relating to the numbers of leaves on some twigs The teacher then asks pupils to express the pattern in a word equation eg: The total number of leaves = number of twigs times 3 plus 2 leaves at the trunk pupils then replace the words by letter symbols, in this case: L = (3 x t) + 2

  12. Who were the children in the study? • The intervention involved 78 classes of 11-12 year olds in 12 project schools • Project pupils received 30 CAME lessons (called Thinking Mathematics) over two years

  13. How was the information gathered? Findings are based on: tests of mathematics understanding at the start of Year 7 and end of Year 8 GCSE results in mathematics, English and science three years later

  14. How might teachers use this evidence? • Group discussion was a key element in developing pupils’ thinking skills, and the teacher played an active role in ensuring this happened effectively • In what ways could you support your pupils to listen to each other’s ideas more effectively, and reach a decision together? Could you weave in opportunities to model effective dialogue for them?

  15. How might leaders use this evidence? • The CAME approach used a quite specific pattern of delivery – preparation, collaborative task, whole class discussion • How flexible, open to new approaches are teachers in your school? If you were to introduce a new approach like CAME which department or team of teachers is best placed to develop the practice? What scope is there for coaching partnerships to extend the practice?

  16. Find out more • Study reference: Shayer, M and Adhami, M (2007) Fostering cognitive development through the context of mathematics: Results of the CAME projectin Educational Studies in Mathematics (2007) Vol. 64, pp. 265-291 • You might like to read a summary of the work of Vygotsky available here: http://www.curee.co.uk/node/4883

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