A thinking skills approach to learning maths CAME

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A thinking skills approach to learning maths
(CAME)
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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)

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The impact of setting on student outcomes

• Students 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 students of all abilities
• Researchers believed the reason was that
  higher-ability students provide a range of
  insights that helped lower-attaining students
  extend their thinking

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Evidence of thinking skills developed in maths
transferring to other subjects

• CAME students 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

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The Cognitive acceleration in mathematics
education (CAME) project

• The CAME project
• is based on research and theory about students
  thinking
• aims to boost mathematical thinking of students
  aged 11 to 14 years and raise their attainment in
  standard tests

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The key ideas behind CAME are that

• through collaboration children who are further on
  in their understanding of a problem can help move
  other students forward too (from Vygotsky)
• the teachers role is to prompt students
  thinking with questions (mediation)
• all adolescents have the potential to achieve in
  mathematics

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The key stages of a CAME lesson

• CAME mathematics lessons follow a structure of
• concrete preparation
• collaborative learning
• whole-class discussion

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Concrete preparation

• In the opening phase the teacher
• - introduces the task to the whole group
• - asks students to explain to each other what
  they think the task is about

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Collaborative learning

• Students work in pairs or small groups on tasks
  which challenge students existing ideas
• Students make notes from discussion for feedback
  later
• The teacher moves around the class observing
  interaction and prompting with questions when
  discussion falters

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Whole-class discussion

• The session closes with a whole class discussion
  in which the teacher
• asks groups to report their ideas
• encourages students to reflect on their reasoning
  using probing questions
• draws pupils attention to key ideas and
  vocabulary
• encourages others to ask questions

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The tasks students tackle in a CAME session

• In the twigs and leaves task students describe
  the pattern relating to the numbers of leaves on
  some twigs
• The teacher then asks students to express the
  pattern in a word equation e.g
• The total number of leaves number of twigs
  times 3 plus 2 leaves at the trunk
• Students then replace the words by letter
  symbols, in this case
• L (3 x t) 2

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Who were the children in the study?

• The intervention involved 78 classes of 11-12
  year olds in 12 project schools
• Project students received 30 CAME lessons (called
  Thinking Mathematics) over two years

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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

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How might teachers use this evidence?

• Group discussion was a key element in developing
  students thinking skills, and the teacher played
  an active role in ensuring this happened
  effectively
• In what ways could you support your students to
  listen to each others ideas more effectively,
  and reach a decision together? Could you weave in
  opportunities to model effective dialogue for
  them?

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How might leaders use this evidence?

• The CAME approach used a quite specific pattern
  of delivery preparation, collaborative task,
  whole class discussion
• How flexible and 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?

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Find out more

• Study reference Shayer, M and Adhami, M (2007)
  Fostering cognitive development through the
  context of mathematics Results of the CAME
  project in Educational Studies in Mathematics
  (2007) Vol. 64, pp. 265-291
• You might like to read a summary of the work of
  Vygotsky on the GTC website http//www.gtce.org.u
  k/research/romtopics/rom_teachingandlearning/vygot
  sky_dec03/

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