ICME-12 presentation
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The document summarizes research on the effects of a digital intervention on the development of algebraic expertise in students. The intervention involved students using a digital module for 6 hours over 6 parts. Testing of 324 students across 9 schools found that post-test scores were significantly higher than pre-test scores, indicating the module was effective. Additional factors that predicted higher post-test scores included previous knowledge, time spent in self-testing and summative assessment modes, and general attitude towards mathematics. The digital module included features like formative feedback, worked examples, and "crisis tasks" to challenge students' problem-solving strategies.
ICME-12 presentation
- 1. EFFECTS OF A DIGITAL INTERVENTION ON THE DEVELOPMENT OF ALGEBRAIC EXPERTISE xkcd.com Christian Bokhove FIsme, Utrecht University July 14th, ICME-12
- 2. Rationale Algebraic skills Year 12 students Netherlands often disappointing
- 3. But even when rewriting skills are OK… …many things can go wrong
- 4. So conceptual understanding and pattern recognition are important!
- 5. Use of ICT
- 6. So can’t we use ICT for acquiring, practicing and assessing algebraic expertise?
- 7. 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
- 8. Research set-up Rnd Focus Target N Pre What software, what Experts characteristics? 1 Could it work? 1-to-1s, N=5 qualitative 2 In what way can it 2 classes in 1 N=31 work? school 3 Does it work? 9 schools, N=324 quantitative
- 9. Research set-up Rnd Focus Target N Pre What software, what Experts characteristics? 1 Could it work? 1-to-1s, N=5 qualitative 2 In what way can it 2 classes in 1 N=31 work? school 3 Does it work? 9 schools, N=324 quantitative
- 10. 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
- 11. Some features of the digital module1 www.algebrametinzicht.nl 1Made with the authoring environment of the Digital Mathematical Environment,
- 12. Equations: in-between steps, multiple strategies allowed
- 13. Store student results, and use these as a teacher to study misconceptions and for starting classroom discussions students
- 14. Feedback
- 15. Feedback: worked examples and hints IDEAS feedback, webservice with Jeuring
- 16. 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
- 17. Effect 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.
- 18. Predictors Significant Non-significant predictors higher predictors higher posttest score posttest score • Previous knowledge • Gender • Time spent in self- • Attitude towards ICT test and summative- • Total time spent on test modes module • General attitude • More time spent at towards mathematics home or at school
- 19. New developments
- 20. Thank you 감사합니다 Christian Bokhove Twitter: cb1601ej [email protected] www.fi.uu.nl/~christianb www.algebrametinzicht.nl (also for pdf of thesis)
- 21. 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)
- 22. Extra: example of crisis task
- 23. Many students work towards…
- 25. Crisis-task
- 26. xkcd.com
- 27. Overcoming a crisis Feedback Youtube clips