1. CADGME 2010 Design and test of a digital module for algebraic skills
Christian Bokhove – Fisme

2. Context Christian Bokhove 11 yr Teacher maths/ict secondary school
St. Michaël College, Zaandam, the Netherlands, tradition math/ict projects
Phd research. ( aimed at math curriculum.
Freudenthal Institute of Science and Mathematics Education, Utrecht University, the Netherlands
Supervisors: Paul Drijvers and Jan van Maanen
Educational research

3. Problem statement Transition secondary  higher education Use of ICT
Lack of Algebraic expertise
Entry exams
Use of ICT
“Use to learn” vs. “Learn to use”
Position statement NCTM (2008): ICT can be a valuable asset

4. Conceptual framework
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)
Algebraic expertise - Basic skills - Symbol Sense: gestalt, pattern
salience, local salience, circularity (Arcavi, 1994)
ICT tool use - Instrumentation - Task, technology, theory (Chevallard, 1991)

5. 1. Criteria for tools
Evaluation instrument, externally validated, first formulate want we want, then see what there is
A selection:
Assesses both basic skills and symbol sense;
Provides an open environment and feedback to facilitate formative assessment;
Stores both answers and the solution process of the student;
Steps;
Freedom to choose own strategy;
Authoring tool for own questions;
Intuitive interface incl. equation editor (‘use to learn’ vs. ‘learn to use’)
Close to paper-and-pencil notation;
60+ tools evaluated;
Bokhove, C., & Drijvers, P. (2010). Digital tools for algebra education: criteria and evaluation. International Journal of Computers for Mathematical Learning.  (link)

6. 2. Case studies / 1-to-1s
6 multihour think-aloud 1-to-1 sessions with 17/18 year olds I want to know what’s going on in their minds
Qual. analysis (video, camtasia, atlas TI)
Quality of tool (no focus)
Symbol Sense
Feedback
Bokhove, C., & Drijvers, P. (2010). Symbol sense behavior in digital activities. In press. For the Learning of Mathematics.

7. 3. Experiment Enkhuizen Jan-Mar 2010, Enkhuizen
Digital Mathematical Environment (DME)
Two 6vwo 17/18 yr olds

8. Design choices Follows from 1-to-1 sessions prototype
4 activities in 4 categories
Randomization (note “strange values”)
Crises
Feedback (many types)
Formative scenario’s: first a lot of feedback then gradually less
Bokhove, C. (2010). Implementing feedback in a digital tool for symbol sense. In press. International Journal for Technology in Mathematics Education.

9. Depending on the Internet connection:
Live DME
Pictures and clips
The case of
Solve

10. Digital mathematical environment

11. Example of student work

12. Authoring this question
DESCRIPTIVE
CUSTOM CORRECTIVE FEEDBACK
HINTS
BUG-RELATED

13. In action
EXPLANATORY: MOVIE CLIPS

14. Another student example

15. Data collection & analysis
Scores per module in DME
Pre- and posttest scores
Attitude scales
General characteristics
Log files
Notes
Audio, video clips
Excel

17. Analyzing log data
C4.5
Decision trees

18. 4. To be continued
Upscaling: next cycle with around 200+ students in about 15 schools in autumn 2010
Focus on feedback
Scaffolding (crises, from a lot of feedback to less)
Revision of tool
Further data analysis, contact with CS dept. Of the UU
European collaboration?

19. Future?

20. If time permits…
Task 1.7