Presentation Mathmaster 031210
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This document discusses using ICT (information and communication technology) to help students acquire, practice, and assess algebraic expertise. It describes a design research project that involved evaluating digital math tools, conducting think-aloud sessions with students, developing prototype activities, and testing those activities with 350 students across 11 schools. The goal was to help students develop symbol sense and algebraic thinking skills through formative feedback in a digital environment. Data was collected and analyzed to understand how tools and activities impacted students' scores, attitudes, and behaviors.
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Presentation Mathmaster 031210
- 1. Use of ICT for acquiring, practicing and assessing algebraic expertise Christian Bokhove [email_address] www.fi.uu.nl/~christianb
- 2. Context Christian Bokhove 12 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
- 3. Problem statement Transition secondary higher education 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. Overview 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) ICT tool use - Instrumentation - Task, technology, theory (Chevallard, 1991) Algebraic expertise - Basic skills - Symbol Sense: gestalt, pattern salience, local salience, circularity (Arcavi, 1994)
- 6. Sfard "First there must be a process performed on the already familiar objects, then the idea of turning this process into a more compact, self-contained whole should emerge, and finally an ability to view this new entity as a permanent object in its own right must be acquired.“ (Sfard, 1992) "interiorization", "condensation", and "reification"
- 8. Algebraic expertise Arcavi Kop & Drijvers Pierce & Stacey (Structure sense, e.g. Hoch & Dreyfus)
- 9. Extension of Gestalt Gestalt Visual salience Bokhove, C., & Drijvers, P. (2010). Symbol sense behavior in digital activities. In press. For the Learning of Mathematics . Gestalt view: pattern salience, local salience and strategic decision
- 11. Prelim: 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 )
- 12. 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
- 13. 2nd cycle Jan-Mar 2010, Enkhuizen Digital Mathematical Environment (DME) www.fi.uu.nl/dwo/voho Two 6vwo 17/18 yr olds
- 14. Design choices Follow from 1-to-1 sessions prototype 4 activities in 4 categories Randomization (note “strange values”) Crises Feedback (many types, Hattie & Timperley) Formative scenario’s: 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)
- 15. 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)
- 16. Digital mathematical environment http://www.fi.uu.nl/dwo/voho , developer: Peter Boon
- 17. Authoring tasks CUSTOM CORRECTIVE FEEDBACK DESCRIPTIVE BUG-RELATED HINTS
- 19. In action
- 21. 3rd cycle Oct/nov 2010 11 schools, around 350 students “ Algebra met Inzicht” (AmI) www.algebrametinzicht.nl
- 22. Data collection & analysis Scores per module in DME Pre- and posttest scores Attitude scales General characteristics Log files Log notes Audio, video clips Excel
- 24. Analyzing log data C4.5 Decision trees
- 26. Discussion Questions? Almost every time discussion understandibly ends with the cut Skills vs. Understanding Is one is more dominant? Does symbol sense exist apart from skills and/or vice versa Methodology: what about distance learning?
- 27. 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.