Use of ICT for acquiring, practicing and assessing algebraic expertise

Christian Bokhovec.bokhove@fi.uu.nlwww.fi.uu.nl/~christianbSupervisors: Paul Drijvers and Jan van MaanenDudoc 18-jan-2011

Refresh

- ICT and algebraic expertise- Assessment and feedback

- In what way can the use of ICT support acquiring, practicing and assessing relevant mathematical skills?

Algebraic expertise

• Arcavi• Kop & Drijvers• Pierce & Stacey• (Structure sense,

e.g. Hoch & Dreyfus)

Extension of Gestalt

• Gestalt• Visual salience

Bokhove, C., & Drijvers, P. (2010b). Symbol sense behavior in digital activities. For the Learning of Mathematics, 30(3), 43-49.

Gestalt view: pattern salience, local salience and strategic decision

Design research

(Tessmer)

1st cycle

2nd cycle

3rd cycle

Prelim cycle: criteria for toolsFirst choose a toolEvaluation instrument, externally validated, first formulate

want we want, then see what there is. A selection:– Stores both answers & solutions students;– Steps & freedom to choose own strategy;– Authoring tool for own questions;– Intuitive interface incl. equation editor

(‘use to learn’ vs. ‘learn to use’)– 60+ tools evaluated;

Bokhove, C., & Drijvers, P. (2010). Digital tools for algebra education: criteria and evaluation. International Journal of Computers for Mathematical Learning, 15(1), 45-62. (link)

1st cycle: 1-to-1s

Qual. analysis (video, camtasia, atlas TI)

Symbol SenseQuality of tool Feedback

6 multihour think-aloud1-to-1 sessions with

17/18 year oldsI want to know what’s going

on in their minds

2nd cycle

Jan-Mar 2010, EnkhuizenDigital Mathematical Environment (DME)

www.fi.uu.nl/dwo/voho Two 6vwo 17/18 yr olds

Design choices

Follow from 1-to-1 sessions prototype•4 activities in 4 categories•Randomization (note “strange values”)•Feedback (many types, Hattie & Timperley)•Crises•Formative scenarios: first a lot of feedback then gradually less

Bokhove, C. (2010). Implementing feedback in a digital tool for symbol sense.. International Journal for Technology in Mathematics Education. 17(3)

Crises“Failure is, in a sense, the

highway to success, inasmuch as every discovery of what is

false leads us to seek earnestly after what is true, and every fresh experience

points out some form of error which we shall afterwards

carefully avoid.” Keats.

• Van Hiele: crisis of learning• Productive failure (Kapur)• Impasse (VanLehn et al)• Perturbation (Doll)• Disequilibrium (Piaget)

Formative scenarios

Results

Tentative conclusions

• Indication that crisis: attempts & errors ↓ scores ↑

• Formative scenarios • Higher score pre-test less gain

3rd cycle

• Oct-dec 2010• 9 schools,

around 330 students

• “Algebra met Inzicht” (AmI)

• www.algebrametinzicht.nl

Data collection & analysis

• Scores per module in DME• Pre- and posttest scores• Pre and post questionnaires

Students: attitude, evaluationTeachers: evaluation

• General characteristics• Log files

Excel

Still to come

– Data analysis for 3rd cycle (stat. methods already known from 2nd cycle, e.g. Multilevel MLwin) > feb finished

– (To be) submitted:• ORD2011• PME35• ICTMT10

– One more article to submit to C&E– Dissertation (about half done) > 31/8/11

Future?

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

Discussion

– Questions?– Almost every time discussion understandibly

ends with the cut Skills vs. Understanding– Causality– Methodology: what about distance learning?

Can we ‘control’ an uncontrolled (e.g. home) situation?

Selected references

Bokhove, C., & Drijvers, P. (2010). Digital tools for algebra education: criteria and evaluation. International Journal of Computers for Mathematical Learning, 15(1), 45-62. (link)

Bokhove, C., & Drijvers, P. (2010). Symbol sense behavior in digital activities. For the Learning of Mathematics, 30(3), 43-49.

Kilpatrick, J., Swafford, J. & Findell, B. (2001). The Strands of Mathematical Proficiency. In J. Kilpatrick, J. Swafford & B. Findell (Eds.), Adding It Up: Helping Children Learn Mathematics (pp 115-155). Washington: National Research Council.

Sfard, A. (1991). On The Dual Nature Of Mathematical Conceptions: Reflections on Processes and Objects as Different Sides of the Same Coin. Educational Studies in Mathematics 22, 1-36.

Tall, D. (2008). The Transition to Formal Thinking in Mathematics. Mathematics Education Research Journal, 20(2), 5-24.