Date post: | 05-Jul-2015 |
Category: |
Education |
Upload: | christian-bokhove |
View: | 224 times |
Download: | 0 times |
Using ICT for algebraic expertise
Christian BokhoveUoS, School of Education
MaSE meetingOctober 18th, 2012
xkcd.com
• 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
Skills..…
Rationale
But even if students do something right….
Many other things can go wrong…
… insight…
Meanwhile…
ICT gebruik
Can we study the potential of usingICT to address skills and insight?
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
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?
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;
Phase 2
Qualitative analysis
AlgebraQualitysoftware
Feedback
6 thinking-aloud-sessions17/18 yr olds
Student can choose own strategy..also wrong ones
Phases 3 and 4
Digital intervention with:RandomizationFeedbackUsing student work forclassroom discussions“Crises”
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
Change in appearance
Design Principles
• Store student results
• Formative scenarios
• Crises
• Feedback
Store student results
Design principle: formative scenarios
• Hattie and Timperley
• Timing and fading (Renkl et al)
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, ….
Before a crisis task
Students work towards…
http://msmcculloughsmathclass.blogspot.com/2010/12/quadratic-formula.html
But this fails in a crisis task
Addressing the crisis
Feedback
Design principle: feedback• Black and William (1998)
• Assessment for learning
• Several feedback types (Hattie and Timperley: FT, FP, FR, FS)
Feedback per step
Getting hints and worked solutions
IDEAS feedback (Jeuring et al)
Results
Indications that crises work
Feedback on task (FT) and feedback forself-regulation (FR) work
Improvement in performance
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
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
Better performance but do we knowwhy (predictors)?
Multilevel analysis
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
Looking forward…
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
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
New developments
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