CADGME 2010 Design and test of a digital module for algebraic skills Christian Bokhove – Fisme c.bokhove@fi.uu.nl

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

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

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)

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)

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.

3. Experiment Enkhuizen Jan-Mar 2010, Enkhuizen Digital Mathematical Environment (DME) www.fi.uu.nl/dwo/voho Two 6vwo 17/18 yr olds

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.

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

Digital mathematical environment

Example of student work

Authoring this question DESCRIPTIVE CUSTOM CORRECTIVE FEEDBACK HINTS BUG-RELATED

In action EXPLANATORY: MOVIE CLIPS

Another student example

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

Analyzing log data C4.5 Decision trees

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?

Future? http://www.fi.uu.nl/~christianb/downloads/poc_equation.htm

If time permits… http://www.fi.uu.nl/dwo/voho Task 1.7