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Dudoc 160111 1
Dudoc 160111 1
Dudoc 160111 1
Dudoc 160111 1
Dudoc 160111 1
Dudoc 160111 1
Dudoc 160111 1
Dudoc 160111 1
Dudoc 160111 1
Dudoc 160111 1
Dudoc 160111 1
Dudoc 160111 1
Dudoc 160111 1
Dudoc 160111 1
Dudoc 160111 1
Dudoc 160111 1
Dudoc 160111 1
Dudoc 160111 1
Dudoc 160111 1
Dudoc 160111 1
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Dudoc 160111 1

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  • 1. Use of ICT for acquiring, practicing and assessing algebraic expertise Christian Bokhove [email_address] www.fi.uu.nl/~christianb Supervisors: Paul Drijvers and Jan van Maanen Dudoc 18-jan-2011
  • 2. Refresh
    • ICT and algebraic expertise
    • Assessment and feedback
    • In what way can the use of ICT support acquiring, practicing and assessing relevant mathematical skills?
  • 3. Algebraic expertise
    • Arcavi
    • Kop & Drijvers
    • Pierce & Stacey
    • (Structure sense, e.g. Hoch & Dreyfus)
  • 4. 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  
  • 5. Design research (Tessmer) 1st cycle 2nd cycle 3rd cycle
  • 6. Prelim cycle: criteria for tools
    • First choose a tool
    • Evaluation instrument, externally validated, f irst 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 )
  • 7. 1st cycle: 1-to-1s Qual. analysis (video, camtasia, atlas TI) Symbol Sense Quality of tool Feedback 6 multihour think-aloud 1-to-1 sessions with 17/18 year olds I want to know what’s going on in their minds
  • 8. 2nd cycle
    • Jan-Mar 2010, Enkhuizen
    • Digital Mathematical Environment (DME) www.fi.uu.nl/dwo/voho
    • Two 6vwo 17/18 yr olds
  • 9. 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)
  • 10. 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)
  • 11. Formative scenarios
  • 12. Results
  • 13. Tentative conclusions
    • Indication that crisis: attempts & errors  scores 
    • Formative scenarios
    • Higher score pre-test less gain
  • 14. 3rd cycle
    • Oct-dec 2010
    • 9 schools, around 330 students
    • “ Algebra met Inzicht” (AmI)
    • www.algebrametinzicht.nl
  • 15. Data collection & analysis
    • Scores per module in DME
    • Pre- and posttest scores
    • Pre and post questionnaires Students: attitude, evaluation Teachers: evaluation
    • General characteristics
    • Log files
    Excel
  • 16.  
  • 17. 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
  • 18. Future?
    • http://www.fi.uu.nl/~christianb/downloads/poc_equation.htm
  • 19. 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?
  • 20. 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.

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