1. Using ICT for algebraic expertise
xkcd.com
Christian Bokhove
UoS, School of Education
MaSE meeting
October 18th, 2012

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

4. Rationale
Skills..…

8. But even if students do
something right….

10. Many other things can go wrong…
… insight…

11. Meanwhile…

12. ICT gebruik

13. Can we study the potential of using
ICT to address skills and insight?

14. 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

16. Design of the study
Cyclical 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?

17. Phase 1: software characteristics
Results externally validated instrument.
Eerst formulate what we need, then look for
software.
Selected criteria:
– Storage of student results;
– In-between steps when solving equations;
– Authoring;
– Intuitive user interface;
– 60+ tools tried and evaluated;

18. Phase 2
6 thinking-aloud-sessions
17/18 yr olds
Qualitative analysis
Quality Algebra Feedback
software

19. Student can choose own strategy..

20. Student can choose own strategy..also wrong ones

21. Phases 3 and 4
Digital intervention with:
Randomization
Feedback
Using student work for
classroom discussions
“Crises”

22. www.algebrametinzicht.nl

23. 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

24. Change in appearance

25. Design Principles
• Store student results
• Formative scenarios
• Crises
• Feedback

26. Store student results

27. Design principle: formative scenarios
• Hattie and Timperley
• Timing and fading (Renkl et al)

28. Design principle: crises
John Keats
“Failure is, in a sense, the highway to success”
• Crises of learning (Van Hiele)
• Productive failure (Kapur)
• Impasse (VanLehn)
• Doll, Piaget, VanLehn, ….

29. Before a crisis task

30. Students work towards…
http://msmcculloughsmathclass.blogspot.com/2010/12/quadratic-formula.html

31. But this fails in a crisis task

32. Addressing the crisis
Feedback

33. Design principle: feedback
• Black and William (1998)
• Assessment for learning
• Several feedback types
(Hattie and Timperley: FT, FP, FR, FS)

34. Feedback per step

35. Getting hints and worked solutions
IDEAS feedback (Jeuring et al)

36. Results
Indications that crises work
Feedback on task (FT) and feedback for
self-regulation (FR) work
Improvement in performance

38. Min Max Mdn SD N
symsen -6.00 3.00 -1.00 2.35 318
sepre
pre-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
test
symsen -5.00 3.00 1.00 1.50 292
sepost

39. Min Max Mdn SD N
symsen -6.00 3.00 -1.00 2.35 318
sepre
pre-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
test
symsen -5.00 3.00 1.00 1.50 292
sepost

40. Better performance but do we know
why (predictors)?

41. Multilevel analysis

42. 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

43. Looking forward…

44. 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

45. 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

46. New developments

47. 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