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EFFECTS OF A DIGITAL INTERVENTION ON THE DEVELOPMENT OF ALGEBRAIC EXPERTISE
Christian BokhoveFIsme, Utrecht University
July 14th, ICME-12
xkcd.com
Rationale
Algebraic skills Year 12 students Netherlandsoftendisappointing
But even when rewriting skills are OK…
…many things can go wrong
So conceptual understanding and pattern recognition are important!
Use of ICT
So can’t we use ICT for acquiring, practicing and
assessing algebraic expertise?
Research questions:What is the effect of an intervention on the development of algebraic expertise, including both procedural skills and symbol sense? Which factors predict the resulting algebraic performance?
Conceptual framework, elements of:
• Symbol sense – basic skills (e.g. Arcavi)
• Formative – summative assessment (e.g. Black & Wiliam)
• Feedback
Research set-up
Rnd Focus Target N
Pre What software, what characteristics?
Experts
1 Could it work? 1-to-1s, qualitative
N=5
2 In what way can it work?
2 classes in 1 school
N=31
3 Does it work? 9 schools, quantitative
N=324
Research set-up
Rnd Focus Target N
Pre What software, what characteristics?
Experts
1 Could it work? 1-to-1s, qualitative
N=5
2 In what way can it work?
2 classes in 1 school
N=31
3 Does it work? 9 schools, quantitative
N=324
Third round design
• 324 students in 9 schools (N=324)
• Year 12, nature and health stream
• Digital module: 6 hours, 6 parts
• Teachers were free in how to deploy the module, but were asked afterwards
• Data collection
– Scores pen-and-paper pre- and posttests
– Scores and logfiles
–Questionnaires
Some features of the digital module1
1Made with the authoring environment of
the Digital Mathematical Environment,
Peter Boon
www.algebrametinzicht.nl
Equations: in-between steps, multiple strategies allowed
Store student results, and use these as a teacher to study misconceptions and for starting classroom discussions
students
Feedback
Feedback: worked examples and hints
IDEAS feedback, webservice with Jeuring
et al
Other features of the digital tool
• Intentional “crises” tasks: hard-to-solve tasks to force students to rethink strategies
• Formative scenarios: at first feedback at every step, but gradually fading it away towards the end of the module
• Instructional screencasts
• Randomization
Posttest (M=78.71, SE=15.175) is significantly higher than the pretest score (M=51.55, SE=21.094), t(285)=-22.589, p<.001, r=.801.
Symbol sense score on the posttest (M=1.462, SE=1.504) is significantly higher than the pretest score (M=-1.493, SE=2.339), t(285)=-20.602, p<.001, r=.773.
Effect
Significant predictors higher posttest score
• Previous knowledge
• Time spent in self-test and summative-test modes
• General attitude towards mathematics
Non-significant predictors higher posttest score
• Gender
• Attitude towards ICT
• Total time spent on module
• More time spent at home or at school
Predictors
New developments
Christian BokhoveTwitter: cb1601ej
[email protected]/~christianb
www.algebrametinzicht.nl(also for pdf of thesis)
감사합니다Thank you
Crises“Failure is, in a sense, the highway to success” Keats
• Van Hiele: crisis of learning• Productive failure (Kapur)• Impasse (VanLehn et al)• Perturbation (Doll)• Disequilibrium (Piaget)
Extra: example of crisis task
Many students work towards…
http://msmcculloughsmathclass.blogspot.com/2010/12/quadratic-formula.html
Crisis-task
xkcd.com
Overcoming a crisis
Feedback
Youtube clips
Formative scenarios