icme-12 presentation

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

cbokhove@gmail.comwww.fi.uu.nl/~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