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Presentation MaSE 18-102012

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Presentation MaSE 18-102012

  1. 1. Using ICT for algebraic expertise xkcd.com Christian Bokhove UoS, School of Education MaSE meeting October 18th, 2012
  2. 2. • Christian Bokhove• From 1998-2012 teacher maths, computer science, head of ICT secondary school NL• National projects maths+ict at Freudenthal Instituut, Utrecht University• PhD, december 2011 www.dudocprogramma.nl
  3. 3. Rationale Skills..…
  4. 4. But even if students do something right….
  5. 5. Many other things can go wrong… … insight…
  6. 6. Meanwhile…
  7. 7. ICT gebruik
  8. 8. Can we study the potential of using ICT to address skills and insight?
  9. 9. In what way can the use of ICT support acquiring,practicing and assessing relevant mathematical skills Assessment - Formative (for) v Summative (of) - Feedback (Black & Wiliam, 1998) ICT tool use Algebraic expertise - Instrumentation - Basic skills - Task, technology, theory - Symbol Sense (Chevallard, 1991) (Arcavi, 1994) - Teacher, student - Transition sec. - TPACK ed. To higher ed. Christian Bokhove
  10. 10. Design of the studyCyclical design:Phase 1: What software with what characteristics?Phase 2: Could it work?Phase 3: In what way could it work?Phase 4: Does it work and why?
  11. 11. Phase 1: software characteristicsResults externally validated instrument.Eerst formulate what we need, then look forsoftware.Selected criteria: – Storage of student results; – In-between steps when solving equations; – Authoring; – Intuitive user interface; – 60+ tools tried and evaluated;
  12. 12. Phase 2 6 thinking-aloud-sessions 17/18 yr olds Qualitative analysis Quality Algebra Feedbacksoftware
  13. 13. Student can choose own strategy..
  14. 14. Student can choose own strategy..also wrong ones
  15. 15. Phases 3 and 4Digital intervention with: Randomization Feedback Using student work for classroom discussions “Crises”
  16. 16. www.algebrametinzicht.nl
  17. 17. Phase 4• 324 students, 9 schools• Module 6 hours in 6 parts• Differences in deployment• Data collection – Scores pre/post for both skills and symbol sense – Digital scores and logfiles – Questionnaires
  18. 18. Change in appearance
  19. 19. Design Principles• Store student results• Formative scenarios• Crises• Feedback
  20. 20. Store student results
  21. 21. Design principle: formative scenarios• Hattie and Timperley• Timing and fading (Renkl et al)
  22. 22. Design principle: crisesJohn Keats“Failure is, in a sense, the highway to success”• Crises of learning (Van Hiele)• Productive failure (Kapur)• Impasse (VanLehn)• Doll, Piaget, VanLehn, ….
  23. 23. Before a crisis task
  24. 24. Students work towards… http://msmcculloughsmathclass.blogspot.com/2010/12/quadratic-formula.html
  25. 25. But this fails in a crisis task
  26. 26. Addressing the crisis Feedback
  27. 27. Design principle: feedback• Black and William (1998)• Assessment for learning• Several feedback types (Hattie and Timperley: FT, FP, FR, FS)
  28. 28. Feedback per step
  29. 29. Getting hints and worked solutions IDEAS feedback (Jeuring et al)
  30. 30. ResultsIndications that crises workFeedback on task (FT) and feedback forself-regulation (FR) workImprovement in performance
  31. 31. Min Max Mdn SD Nsymsen -6.00 3.00 -1.00 2.35 318 seprepre-test 2.00 98.00 51.00 21.37 318 d1-d4 0.00 100.00 97.25 21.08 311 d5 0.00 106.00 48.50 31.89 254 d6 1.00 100.00 68.00 28.44 223 post- 10.00 100.00 82.00 15.46 292 testsymsen -5.00 3.00 1.00 1.50 292 sepost
  32. 32. Min Max Mdn SD Nsymsen -6.00 3.00 -1.00 2.35 318 seprepre-test 2.00 98.00 51.00 21.37 318 d1-d4 0.00 100.00 97.25 21.08 311 d5 0.00 106.00 48.50 31.89 254 d6 1.00 100.00 68.00 28.44 223 post- 10.00 100.00 82.00 15.46 292 testsymsen -5.00 3.00 1.00 1.50 292 sepost
  33. 33. Better performance but do we know why (predictors)?
  34. 34. Multilevel analysis
  35. 35. Predictors No predictors• Pre-knowledge • Gender• Relatively more time • ICT knowledge spent on parts 5 and 6 • More time spent on• Attitude towards whole module maths • More time spent at home or at school
  36. 36. Looking forward…
  37. 37. Quantitative AND Qualitative• Complementary• Qualitative – Insight processes - Grounded theory – Why does it work? - - Case study 1 to 1 sessions – What can work? - Smallscale - Atlas-TI• Quantitative – Effectiveness - Multilevel analysis - Learning analytics – Does it work? - Datamining techniques
  38. 38. Theory AND Practice• www.algebrametinzicht.nl• Practice learns from research – What could work? – How does it work? – Validated intervention• Theory learns from practice – Observe best practices Photo’s classroom experiments
  39. 39. New developments
  40. 40. Questions• In what way are digital tools best integrated into classroom practice?• What characteristics does a digital tool need?• What does this mean for students and teachers?• What are the differences between maths with pen- and-paper and maths with digital tools?• What do recent developments mean for Maths education – Big Data – Tablets: handwriting recognition – Khan academy – Math Wars

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