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Approaches to problem solving in mathematics

Approaches to problem solving in mathematics. Anna Cooper, WCMT Fellow 2016 acooper49.306@lgflmail.org. What is a WCMT F ellowship?. Funding for a project that requires overseas travel, enabling the recipient to bring back fresh ideas and new solutions to today’s issues

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Approaches to problem solving in mathematics

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  1. Approaches to problem solving in mathematics Anna Cooper, WCMT Fellow 2016 acooper49.306@lgflmail.org

  2. What is a WCMT Fellowship? • Funding for a project that requires overseas travel, enabling the recipient to bring back fresh ideas and new solutions to today’s issues • Available to UK citizens of any age, gender, ethnicity or religion, with or without educational qualifications, and in any occupation or none

  3. Purpose of my Fellowship • Ascertain how problem solving is used within the Japanese and Australian mathematics curriculum to further a student’s understanding of key concepts • Identify strategies and resources from Japan and Australia that can be used in the UK to improve teaching and learning

  4. My background • Consultant with Maths No Problem • Former middle years teacher with eleven years’ experience of teaching maths • Former Lead Maths teacher in the London Borough of Southwark • Former Numicon Consultant • Completed NCETM (National Centre for Excellence in the Teaching of Mathematics) professional development lead accreditation • Regularly support colleagues with their subject knowledge through bespoke CPD, model lessons, team teaching and drop-in sessions

  5. My journey • Japan: visited 7 establishments • Elementary, Junior and High Schools • Universities • Research Institute • Australia: visited 11 establishments • Private and State-funded Schools for all ages • Universities • Research Institute

  6. My journey https://transformingteachingblog.wordpress.com/

  7. Key findings UK teaching practice could be improved by considering: • Structured problem solving and rich tasks • Concrete manipulatives • Pupil talk • Independent project-based learning • Flipped classroom

  8. Structured problem solving

  9. Engaging tasks Real life contexts Discussion prompts Problem solving: text books

  10. Concrete manipulatives • Pupils in Japan and Australia are given physical resources to help with problem solving • Ofsted says UK schools don’t use these tools as effectively or as widely as they could

  11. Manipulatives: resource kit • All students prepared • Parental engagement • Consistency with available resources

  12. Manipulatives: the Soroban • Japanese abacus • Displays numbers in base 10 in a way that makes calculating easy

  13. How to use a Soroban

  14. Calculating using a Soroban

  15. From concrete to abstract

  16. Pupil talk • Happens frequently • Scaffolded using talk prompts • Children are not afraid to take a chance • The journey is more important than the answer

  17. Pupil talk: scaffolding • Effective modelling of spoken language • High expectations for participation • Talk prompts for partner work

  18. Project-based learning

  19. A flipped classroom • Students prepare by watching video lessons • Classroom time is exercises, projects or discussions • Every student takes responsibility for their learning

  20. Key findings: impact and proposed next steps • Structure of lessons: begin with a problem and let students grapple with the task rather than giving them direct instruction • Concrete manipulatives: focus on a ‘Concrete Pictorial Abstract’ approach to develop a depth of understanding • Talk prompts: greater student participation in discussion and increased resilience • Staff CPD and drop-in sessions to improve subject knowledge • Next steps: Rich task bank: free up time to plan for misconceptions and to personalise learning

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