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..

Student can choose own strategy..also wrong ones

Phases 3 and 4

Digital intervention with:RandomizationFeedbackUsing student work forclassroom discussions“Crises”

www.algebrametinzicht.nl

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