ICME-12 presentation

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EFFECTS OF A DIGITAL INTERVENTION ON THE DEVELOPMENT OF ALGEBRAIC EXPERTISE Christian Bokhove FIsme, Utrecht University July 14th, ICME-12 xkcd.com

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EFFECTS OF A DIGITAL INTERVENTION ON THE DEVELOPMENT OF ALGEBRAIC EXPERTISE

Transcript of ICME-12 presentation

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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

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Rationale

Algebraic skills Year 12 students Netherlandsoftendisappointing

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But even when rewriting skills are OK…

…many things can go wrong

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So conceptual understanding and pattern recognition are important!

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Use of ICT

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So can’t we use ICT for acquiring, practicing and

assessing algebraic expertise?

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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

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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

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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

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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

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Some features of the digital module1

1Made with the authoring environment of

the Digital Mathematical Environment,

Peter Boon

www.algebrametinzicht.nl

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Equations: in-between steps, multiple strategies allowed

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Store student results, and use these as a teacher to study misconceptions and for starting classroom discussions

students

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Feedback

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Feedback: worked examples and hints

IDEAS feedback, webservice with Jeuring

et al

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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

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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

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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

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New developments

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Christian BokhoveTwitter: cb1601ej

[email protected]/~christianb

www.algebrametinzicht.nl(also for pdf of thesis)

감사합니다Thank you

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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)

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Extra: example of crisis task

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Many students work towards…

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http://msmcculloughsmathclass.blogspot.com/2010/12/quadratic-formula.html

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Crisis-task

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xkcd.com

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Overcoming a crisis

Feedback

Youtube clips

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Formative scenarios

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