Presentation MaSE 18-102012
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Using ICT for algebraic expertise
Christian BokhoveUoS, School of Education
MaSE meetingOctober 18th, 2012
xkcd.com
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• Christian Bokhove
• From 1998-2012 teacher maths, computer science, head of ICT secondary school NL
• National projects maths+ict at FreudenthalInstituut, Utrecht University
• PhD, december 2011www.dudocprogramma.nl
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Skills..…
Rationale
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But even if students do something right….
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Many other things can go wrong…
… insight…
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Meanwhile…
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ICT gebruik
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Can we study the potential of usingICT to address skills and insight?
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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- Instrumentation- Task, technology, theory
(Chevallard, 1991)- Teacher, student- TPACK
Algebraic expertise- Basic skills- Symbol Sense
(Arcavi, 1994)- Transition sec.ed. To higher ed.Christian Bokhove
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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?
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Phase 1: software characteristics
Results 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;
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Phase 2
Qualitative analysis
AlgebraQualitysoftware
Feedback
6 thinking-aloud-sessions17/18 yr olds
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Student can choose own strategy..also wrong ones
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Phases 3 and 4
Digital intervention with:RandomizationFeedbackUsing student work forclassroom discussions“Crises”
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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
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Change in appearance
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Design Principles
• Store student results
• Formative scenarios
• Crises
• Feedback
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Store student results
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Design principle: formative scenarios
• Hattie and Timperley
• Timing and fading (Renkl et al)
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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, ….
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Before a crisis task
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Students work towards…
http://msmcculloughsmathclass.blogspot.com/2010/12/quadratic-formula.html
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But this fails in a crisis task
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Addressing the crisis
Feedback
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Design principle: feedback• Black and William (1998)
• Assessment for learning
• Several feedback types (Hattie and Timperley: FT, FP, FR, FS)
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Feedback per step
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Getting hints and worked solutions
IDEAS feedback (Jeuring et al)
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Results
Indications that crises work
Feedback on task (FT) and feedback forself-regulation (FR) work
Improvement in performance
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Min Max Mdn SD N
symsensepre -6.00 3.00 -1.00 2.35 318
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-test 10.00 100.00 82.00 15.46 292
symsensepost -5.00 3.00 1.00 1.50 292
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Min Max Mdn SD N
symsensepre -6.00 3.00 -1.00 2.35 318
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-test 10.00 100.00 82.00 15.46 292
symsensepost -5.00 3.00 1.00 1.50 292
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Better performance but do we knowwhy (predictors)?
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Multilevel analysis
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Predictors
• Pre-knowledge
• Relatively more time spent on parts 5 and 6
• Attitude towardsmaths
No predictors
• Gender
• ICT knowledge
• More time spent on whole module
• More time spent at home or at school
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Looking forward…
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Quantitative AND Qualitative
• Complementary
• Qualitative
– Insight processes
– Why does it work?
– What can work?
• Quantitative
– Effectiveness
– Does it work?
- Grounded theory- Case study- 1 to 1 sessions- Smallscale- Atlas-TI
- Multilevel analysis- Learning analytics- Datamining techniques
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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
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New developments
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Questions
• In what way are digital tools best integrated intoclassroom 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