Case studies of teacher development on a mathematical


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Case studies of teacher development on a mathematical

  1. 1. Case studies of teacher development on a Mathematical Literacy ACE course<br />
  2. 2. Background<br />ACE ML course focused on <br /><ul><li>the ‘re-skilling’ of in-service teachers as ML teachers
  3. 3. development of ML curriculum understanding and teaching practice
  4. 4. 2007-2008
  5. 5. nineteen teachers
  6. 6. four modules
  7. 7. mathematical content presented within real-life contexts
  8. 8. aimed to build teachers’ understanding of the connection between mathematical content and real-life contexts</li></li></ul><li>Research questions<br />Question 1 <br />How does the ACE Mathematical Literacy teacher teach Mathematical Literacy in the classroom, and how does this change over time? <br /><ul><li> Focus on the relationship between mathematics and context</li></ul>Question 2<br />What are the types of questions and the cognitive level of questions teachers develop for assessment tasks, and how does this change over time?<br />
  9. 9. Theoretical framework<br /><ul><li>Wenger’s (1998) social theory of learning
  10. 10. 2 Communities of practice
  11. 11. Meaning, practice, community and identity
  12. 12. Elements of learning are ‘deeply interconnected and mutually defining’ (Wenger, 1998)
  13. 13. Meaning - ACE teachers’ understanding and experience of the new ML curriculum as meaningful
  14. 14. Practice - lesson planning, assessment tasks and ML lesson presentation</li></li></ul><li>Literature review<br /><ul><li>Nature and purpose of mathematical literacy
  15. 15. Contextual frames - Steen (2001), Skovsmose (1992)
  16. 16. Mathematical frame - Pugalee (1999)
  17. 17. ML curriculum documents - a hybrid of the contextual and mathematical orientations
  18. 18. Curriculum documents convey mixed messages on how to teach ML (Venkatakrishnan and Graven, 2006, p20)</li></li></ul><li>Literature review<br /><ul><li>Spectrum of ML teaching practices (Graven and Venkat, 2007)
  19. 19. Assessment in ML needs to reflect interplay between content and context (DoE, 2008, p7)
  20. 20. Reasoning and reflection questions imply higher-order cognitive skills (DoE, 2008, p27-28)
  21. 21. Moral literacy (Tuana, 2007, p2)
  22. 22. Ethics sensitivity
  23. 23. Ethical reasoning skills
  24. 24. Moral imagination</li></li></ul><li>Methodology<br /><ul><li>Trajectory data for all ACE Mathematical Literacy teachers collected over 16 months
  25. 25. Data for 2 case studies selected at late stage of data collection
  26. 26. Central data-collection tool based on contextual data on the rate of smoking amongst adults in different countries
  27. 27. First session - informally plan a lesson using data
  28. 28. 9 months later - design a lesson, worksheet, lesson presentation
  29. 29. Nine data collection instruments
  30. 30. Written ACE assessment tasks
  31. 31. Informal written tasks collected for research purposes
  32. 32. Interviews
  33. 33. Videos of classroom practice</li></li></ul><li>Key findings refer to:<br />Classification of ML questions<br />Cognitive level of ML questions<br />Adaptation of the spectrum of ML teaching agendas (Graven and Venkat, 2007)<br />
  34. 34. Key findings<br />1. Classification of ML questions<br /><ul><li>Contextual questions
  35. 35. Contextual questions where the mathematics is in service of the context
  36. 36. Dialectical questions
  37. 37. Mathematical questions where the context is in service of the mathematics
  38. 38. Mathematical questions</li></li></ul><li>Key findings<br />2. Cognitive level of ML questions<br /><ul><li>Questions set at ‘n relatively low cognitive level
  39. 39. Low-level reflective questions
  40. 40. Require contextual reflection based on personal opinion or experience
  41. 41. No mathematical reasoning or calculations are required to answer these questions</li></li></ul><li>Key findings<br />3. Adaptation of the spectrum of ML teaching agendas<br /><ul><li>Context-driven agenda (without mathematical connections)
  42. 42. focuses on the engagement and investigation of context without engaging with the mathematics
  43. 43. includes contextual questions </li></li></ul><li>Key findings<br /><ul><li>Adaptation of Mainly content-driven agenda
  44. 44. To learn the context and then to use the context to do the mathematics
  45. 45. Context and contents largely dealt with separately
  46. 46. Spectrum of agendas expanded to include reference to ethical and moral values discussion
  47. 47. Development of moral literacy</li></li></ul><li>Conclusion<br /><ul><li>Need for ML teacher training
  48. 48. Teachers need to make a coherent connection between contexts and mathematics required for solving real-life problems
  49. 49. Training with respect to:
  50. 50. Curriculum implementation
  51. 51. Lesson planning
  52. 52. Lesson presentation
  53. 53. Assessment</li></li></ul><li>Rate of Smoking amongst adults<br />Tobacco is the cause of death of 560 people every hour, or 13400 people every day or 4,9 million people each year. The World Health Organisation says that tobacco is the only product that will cause the death of one in every two people who use it. <br /> (Vermeulen et al, 2005, p50)<br />