The co-emergence of machine techniques, paper-and-pencil techniques, and theoretical reflection: A study of cas use in secondary school algebra

International Journal of Computers for Mathematical Learning

Volumn 11, Issue 2, 2006, Pages 205-263

  Kieran, Carolyn ^a   Drijvers, Paul ^b  

^a UNIVERSITÉ DU QUÉBEC À MONTRÉAL   (Canada)

^b UTRECHT UNIVERSITY   (Netherlands)

Author keywords

Algebra; CAS; Computer algebra; Instrumentation; Technique in algebra; Technology; Theoretical thinking in algebra

Indexed keywords

COMPUTER AIDED INSTRUCTION; COMPUTER PROGRAMMING LANGUAGES; LEARNING SYSTEMS; TEACHING; TECHNOLOGICAL FORECASTING;

COMPUTER ALGEBRA; INSTRUMENTATION; PAPER-AND-PENCIL TECHNIQUES; TECHNIQUE IN ALGEBRA;

ALGEBRA;

EID: 33749315160     PISSN: 13823892     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10758-006-0006-7     Document Type: Article

References (40)

1. Arcavi, A. (1994). Symbol sense: Informal sense-making in formal mathematics. For the Learning of Mathematics 14(3): 24-35.
2. Artigue, M. (1997). Le Logiciel 'Derive' comme révélateur de phénomènes didactiques liés à l'utilisation d'environnements informatiques pour l'apprentissage. Educational Studies in Mathematics 33: 133-169.
3. Artigue, M. (2002). Learning mathematics in a CAS environment: The genesis of a reflection about instrumentation and the dialectics between technical and conceptual work. International Journal of Computers for Mathematical Learning 7: 245-274.
4. Bartolini Bussi, M.G. and Mariotti, M.A. (1999). Semiotic mediation: From history to the mathematics classroom. For the Learning of Mathematics 19(2): 27-35.
5. Boon, P. and Drijvers, P. (2005). Chaining operations to get insight in expressions and functions. In M. Bosch (Ed), Proceedings CERME4 Conference, February 2005. Retrieved on December 20, 2005 from http://www.cerme4.crm.es/.
6. Cerulli, M. and Mariotti, M.A. (2002). L'Algebrista: un micromonde pour l'enseignement et l'apprentissage de l'algèbre. Sciences et techniques éducatives 9(1-2): 149-170.
7. Chevallard, Y. (1999). L'analyse des pratiques enseignantes en théorie anthropologique du didactique. Recherches en Didactique des Mathématiques 19: 221-266.
8. Drijvers, P. (2002). Learning mathematics in a computer algebra environment: Obstacles are opportunities. Zentralblatt für Didaktik der Mathematik 34(5): 221-228.
9. Drijvers, P. (2003). Learning algebra in a computer algebra environment, Design research on the understanding of the concept of parameter, Doctoral Dissertation, Freudenthal Institute, Utrecht University, the Netherlands. Also available through http://www.fi.uu.nl/~pauld/dissertation.
10. Drijvers, P. and Trouche, L. (in press). From artifacts to instruments, a theoretical framework behind the orchestra metaphor. In M.K. Heid and G.W. Blume (Eds), Research on Technology and the Teaching and Learning of Mathematics: Syntheses, Cases, and Perspectives. Greenwich, CT: Information Age Publishing.
11. Falcade, R. (2003). Instruments de médiation sémiotique dans Cabri pour la notion de fonction. Paper Presented at the ITEM Conference, June 2003, Reims, France.
12. Guin, D., Ruthven, K. and Trouche, L., (Eds). (2004). The Didactical Challenge of Symbolic Calculators: Turning a Computational Device into a Mathematical Instrument. Dordrecht, the Netherlands: Kluwer Academic Publishers.
13. Haspekian, M. (2005). An "Instrumental Approach" to study the integration of a computer tool into mathematics teaching: The case of spreadsheets. International Journal of Computers for Mathematical Learning 10: 109-141.
14. Healy, L. and Hoyles, C. (2000). A study of proof conceptions in algebra. Journal for Research in Mathematics Education 31: 396-428.
15. Heid, M.K. (1996). A technology-intensive functional approach to the emergence of mathematical thinking. In N. Bednarz, C. Kieran and L. Lee (Eds), Approaches to Algebra: Perspectives for Research and Teaching (pp. 239-256). Dordrecht, the Netherlands: Kluwer.
16. Hoyles, C. (2001). From describing to designing mathematical activity: The next step in developing a social approach to research in mathematics education?. Educational Studies in Mathematics 46: 273-286.
17. Hoyles, C. and Noss, R. (2003). What can digital technologies take from and bring to research in mathematics education? In A.J. Bishop, M.A. Clements, C. Keitel, J. Kilpatrick and F. Leung (Eds), Second International Handbook of Mathematics Education (Vol. 1, pp. 323-349). Dordrecht, the Netherlands: Kluwer Academic.
18. Kieran, C. (1996). The changing face of school algebra. In C. Alsina, J. Alvarez, B. Hodgson, C. Laborde and A. Pérez (Eds), 8th International Congress on Mathematical Education: Selected Lectures (pp. 271-290). Sevilla, Spain: S.A.E.M. Thales.
19. Kieran, C. (2004). The core of algebra: Reflections on its main activities. In K. Stacey, H. Chick and M. Kendal (Eds), The Future of the Teaching and Learning of Algebra: The 12th ICMI Study (pp. 21-33). Dordrecht, the Netherlands: Kluwer Academic.
20. Kieran, C. (2006). Research on the learning and teaching of algebra: A broadening of sources of meaning. In A. Gutiérrez and P. Boero (Eds), Handbook of Research on the Psychology of Mathematics Education (pp. 11-49). Rotterdam, the Netherlands: Sense Publishers.
21. Kieran, C. and Saldanha, L. (in press). Designing tasks for the co-development of conceptual and technical knowledge in CAS activity: An example from factoring. In K. Heid and G. Blume (Eds), Research on Technology and the Teaching and Learning of Mathematics: Syntheses, Cases, and Perspectives. Greenwich, CT: Information Age Publishing.
22. Kieran, C. and Yerushalmy, M. (2004). Research on the role of technological environments in algebra learning and teaching. In K. Stacey, H. Chick and M. Kendal (Eds), The Future of the Teaching and Learning of Algebra: The 12th ICMI Study (pp. 95-152). Dordrecht, the Netherlands: Kluwer Academic.
23. Lagrange, J.-b. (2000). L'intégration d'instruments informatiques dans l'enseignement: une approche par les techniques. Educational Studies in Mathematics 43:1-30.
24. Lagrange, J.-b. (2002). Étudier les mathématiques avec les calculatrices symboliques. Quelle place pour les techniques?. In D. Guin and L. Trouche (Eds), Calculatrices Symboliques. Transformer un outil en un instrument du travail mathématique: un problème didactique (pp. 151-185). France: La Pensée Sauvage, Grenoble.
25. Lagrange, J.-b. (2003). Learning techniques and concepts using CAS: A practical and theoretical reflection. In J.T. Fey (Ed.), Computer Algebra Systems in Secondary School Mathematics Education (pp. 269-283). Reston, VA: National Council of Teachers of Mathematics.
26. Lagrange, J.-b. (2005). Curriculum, classroom practices, and tool design in the learning of functions through technology-aided experimental approaches. International Journal of Computers for Mathematical Learning 10: 143-189.
27. Lerman, S. (1998). A moment in the zoom of a lens: Toward a discursive psychology of mathematics teaching and learning. In A. Olivier and K. Newstead (Eds), Proceedings of the 22nd International Conference for the Psychology of Mathematics Education (Vol. 1, pp. 66-81). Stellenbosch, South Africa: PME Program Committee.
28. Mariotti, M.A. (2006). Proof and proving in mathematics education. In A. Gutiérrez and P. Boero (Eds), Handbook of Research on the Psychology of Mathematics Education (pp. 173-204). Rotterdam, the Netherlands: Sense Publishers.
29. Monaghan, J. (2005). Computer algebra, instrumentation and the anthropological approach. Paper Presented at the 4th CAME Conference, October 2005. Retrieved on December 20, 2005 from http://www.lonklab.ac.uk/came/events/ CAME4/index.html.
30. n-1. International DERIVE Journal 3: 51-61.
31. Nicaud, J.-F., Bouhineau, D. and Chaachoua, H. (2004). Mixing microworld and CAS features in building computer systems that help students learn algebra. International Journal of Computers for Mathematical Learning 9: 169-211.
32. Noss, R. and Hoyles, C. (1996). Windows on Mathematical Meanings: Learning Cultures and Computers. Dordrecht, the Netherlands: Kluwer Academic.
33. Rabardel, P. (2002). People and Technology - A Cognitive Approach to Contemporary Instruments. Retrieved on December 20, 2005 from http://www.ergoserv.psy.univ-paris8.fr/.
34. Rabardel, P. and Samurçay, R. (2001). From Artifact to Instrument Mediated Learning. New Challenges to Research on Learning 22. Helsinki, Finland: University of Helsinki.
35. Radford, L. (2000). Signs and meanings in students' emergent algebraic thinking: A semiotic analysis. Educational Studies in Mathematics 42: 237-268.
36. Trouche, L. (2000). La parabole du gaucher et de la casserole à bec verseur: étude des processus d'apprentissage dans un environnement de calculatrices symboliques. Educational Studies in Mathematics 41: 239-264.
37. Trouche, L. (2004a). Environnements informatisés et mathématiques: quels usages pour quels apprentissages?. Educational Studies in Mathematics 55: 181-197.
38. Trouche, L. (2004b). Managing complexity of human/machine interactions in computerized learning environments: Guiding students' command process through instrumental orchestrations. International Journal of Computers for Mathematical Learning 9: 281-307.
39. Vérillon, P. and Rabardel, P. (1995). Cognition and artifacts: A contribution to the study of thought in relation to instrumented activity. European Journal of Psychology of Education 10: 77-103.
40. Vygotsky, L.S. (1930). La méthode instrumentale en psychologie. In B. Schneuwly and J.P. Bronckart (Eds), Vygotsky aujourd'hui (pp. 39-47). Neufchâtel: Delachaux et Niestlé.