Skip to main content
Erschienen in: Technology, Knowledge and Learning 1/2010

01.04.2010

Mapping Pedagogical Opportunities Provided by Mathematics Analysis Software

verfasst von: Robyn Pierce, Kaye Stacey

Erschienen in: Technology, Knowledge and Learning | Ausgabe 1/2010

Einloggen

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config
loading …

Abstract

This paper proposes a taxonomy of the pedagogical opportunities that are offered by mathematics analysis software such as computer algebra systems, graphics calculators, dynamic geometry or statistical packages. Mathematics analysis software is software for purposes such as calculating, drawing graphs and making accurate diagrams. However, its availability in classrooms also provides opportunities for positive changes to teaching and learning. Very many examples are documented in the professional and research literature, and in this paper we organize them into 10 types. These are displayed in the form of a ‘pedagogical map’, which further classifies them according to whether the opportunity arises from new opportunities for the mathematical tasks used, change to interpersonal aspects of the classroom or change to the point of view on mathematics as a subject. The map can be used in teacher professional development to draw attention to possibilities for lessons or as a catalyst for professional discussion. For research on teaching, it can be used to map current practice, or to track professional growth. The intention of the map is to summarise the potential benefits of teaching with technology in a form that may be useful for both teachers and researchers.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Literatur
Zurück zum Zitat Aldon, G. (Ed.). (2009). La function de l’ensegne. Mathématiques dynamiques. (pp. 46–68). Paris, France: Hachette Livre. Aldon, G. (Ed.). (2009). La function de l’ensegne. Mathématiques dynamiques. (pp. 46–68). Paris, France: Hachette Livre.
Zurück zum Zitat Artigue, M. (2001). Learning mathematics in a CAS environment: The genesis of a reflection about instrumentation and the dialectics between technical and conceptual work. Paper presented at CAME 2001 Symposium. Communicating Mathematics Through Computer Algebra Systems. Utrecht, The Netherlands. Retrieved 13th March 2008 from: http://Itsn.mathstore.ac.uk/came/events/freudenthal. Artigue, M. (2001). Learning mathematics in a CAS environment: The genesis of a reflection about instrumentation and the dialectics between technical and conceptual work. Paper presented at CAME 2001 Symposium. Communicating Mathematics Through Computer Algebra Systems. Utrecht, The Netherlands. Retrieved 13th March 2008 from: http://​Itsn.​mathstore.​ac.​uk/​came/​events/​freudenthal.
Zurück zum Zitat Artigue, M. (2005). The integration of symbolic calculators into secondary education: Some lessons from didactical engineering. In D. Guin, K. Ruthven, & L. Trouche (Eds.), The didactical challenge of symbolic calculators: Turning a computational device into a mathematical instrument (pp. 231–294). Dordrecht, The Netherlands: Kluwer.CrossRef Artigue, M. (2005). The integration of symbolic calculators into secondary education: Some lessons from didactical engineering. In D. Guin, K. Ruthven, & L. Trouche (Eds.), The didactical challenge of symbolic calculators: Turning a computational device into a mathematical instrument (pp. 231–294). Dordrecht, The Netherlands: Kluwer.CrossRef
Zurück zum Zitat Ball, L., & Pierce, R. (2004). CAS: Trainer wheels for algebra using the TI89. In B. Tadich, S. Tobias, C. Brew, B. Beatty, & P. Sullivan (Eds.), Towards excellence in mathematics. Proceedings of the 40th Annual Conference of the MAV, (pp. 13–21). Melbourne: Mathematical Association of Victoria. Ball, L., & Pierce, R. (2004). CAS: Trainer wheels for algebra using the TI89. In B. Tadich, S. Tobias, C. Brew, B. Beatty, & P. Sullivan (Eds.), Towards excellence in mathematics. Proceedings of the 40th Annual Conference of the MAV, (pp. 13–21). Melbourne: Mathematical Association of Victoria.
Zurück zum Zitat Ball, L., & Stacey, K. (2003). What should students record when solving problems with CAS? Reasons, information, the plan and some answers. In J. T. Fey, A. Cuoco, C. Kieran, L. Mullin, & R. M. Zbiek (Eds.), Computer algebra systems in secondary school mathematics education (pp. 289–303). Reston, VA: The National Council of Teachers of Mathematics. Ball, L., & Stacey, K. (2003). What should students record when solving problems with CAS? Reasons, information, the plan and some answers. In J. T. Fey, A. Cuoco, C. Kieran, L. Mullin, & R. M. Zbiek (Eds.), Computer algebra systems in secondary school mathematics education (pp. 289–303). Reston, VA: The National Council of Teachers of Mathematics.
Zurück zum Zitat Ball, L., & Stacey, K. (2007). Using technology in high-stakes assessment: How teachers balance by-hand and automated techniques. In C.-S. Lim et al. Proceedings of EARCOME4 2007 4th East Asia Regional Conference on Mathematics Education, (pp. 90–97) Penang, Malaysia: Universiti Sains Malaysia. Ball, L., & Stacey, K. (2007). Using technology in high-stakes assessment: How teachers balance by-hand and automated techniques. In C.-S. Lim et al. Proceedings of EARCOME4 2007 4th East Asia Regional Conference on Mathematics Education, (pp. 90–97) Penang, Malaysia: Universiti Sains Malaysia.
Zurück zum Zitat Black, T. (1999). Simulations on spreadsheets for complex concepts: Teaching statistical power as an example. International Journal of Mathematics Education in Science and Technology, 30(4), 473–481.CrossRef Black, T. (1999). Simulations on spreadsheets for complex concepts: Teaching statistical power as an example. International Journal of Mathematics Education in Science and Technology, 30(4), 473–481.CrossRef
Zurück zum Zitat Brousseau, G. (1997). Theory of didactical situations in mathematics : didactique des mathématiques, 1970–1990 (Edited and translated by N. Balacheff, M. Cooper, R. Sutherland, V. Warfield). Dordrecht: Kluwer. Brousseau, G. (1997). Theory of didactical situations in mathematics : didactique des mathématiques, 19701990 (Edited and translated by N. Balacheff, M. Cooper, R. Sutherland, V. Warfield). Dordrecht: Kluwer.
Zurück zum Zitat Brown, J. (2005). Affordances of a technology-rich teaching and learning environment. In P. Clarkson, A. Downton, D. Gronn, M. Horne, A. McDonough, R. Pierce, & A. Roche (Eds.), Building connections: Theory, research, and practice, Proceedings of the 28th Annual Conference of the Mathematics Education Research Group of Australasia (Vol. 1), (pp. 177–184). Sydney: MERGA. Brown, J. (2005). Affordances of a technology-rich teaching and learning environment. In P. Clarkson, A. Downton, D. Gronn, M. Horne, A. McDonough, R. Pierce, & A. Roche (Eds.), Building connections: Theory, research, and practice, Proceedings of the 28th Annual Conference of the Mathematics Education Research Group of Australasia (Vol. 1), (pp. 177–184). Sydney: MERGA.
Zurück zum Zitat Etlinger, L. (1974). The electronic calculator: A new trend in school mathematics. Educational Technology, XIV(12), 43–45. Etlinger, L. (1974). The electronic calculator: A new trend in school mathematics. Educational Technology, XIV(12), 43–45.
Zurück zum Zitat Galbraith, P., Stillman, G., Brown, J., & Edwards, I. (2007). Facilitating middle secondary modelling competencies. In C. Haines, P. Galbraith, W. Blum, & S. Khan (Eds.), Mathematical modelling (ICTMA12): Education, engineering and economics (pp. 130–140). Chichester, UK: Horwood Press. Galbraith, P., Stillman, G., Brown, J., & Edwards, I. (2007). Facilitating middle secondary modelling competencies. In C. Haines, P. Galbraith, W. Blum, & S. Khan (Eds.), Mathematical modelling (ICTMA12): Education, engineering and economics (pp. 130–140). Chichester, UK: Horwood Press.
Zurück zum Zitat Garner, S. (2004). The CAS classroom. Australian Senior Mathematics Journal, 18(2), 28–42. Garner, S. (2004). The CAS classroom. Australian Senior Mathematics Journal, 18(2), 28–42.
Zurück zum Zitat Garry, T. (2003). Computing, conjecturing and confirming with a CAS Tool. In J. T. Fey, A. Cuoco, C. Kieran, L. Mullin, & R. M. Zbiek (Eds.), Computer algebra systems in secondary school mathematics education (pp. 289–303). Reston, VA: The National Council of Teachers of Mathematics. Garry, T. (2003). Computing, conjecturing and confirming with a CAS Tool. In J. T. Fey, A. Cuoco, C. Kieran, L. Mullin, & R. M. Zbiek (Eds.), Computer algebra systems in secondary school mathematics education (pp. 289–303). Reston, VA: The National Council of Teachers of Mathematics.
Zurück zum Zitat Gibson, J. J. (1977). The theory of affordances. In R. Shaw & J. Bransford (Eds.), Perceiving, acting and knowing: Towards an ecological psychology (pp. 67–82). Hillsdale, NJ: Erlbaum. Gibson, J. J. (1977). The theory of affordances. In R. Shaw & J. Bransford (Eds.), Perceiving, acting and knowing: Towards an ecological psychology (pp. 67–82). Hillsdale, NJ: Erlbaum.
Zurück zum Zitat González-López, M. J. (2001). Using dynamic geometry software to simulate physical motion. International Journal of Computers for Mathematical Learning, 6(2), 127–142.CrossRef González-López, M. J. (2001). Using dynamic geometry software to simulate physical motion. International Journal of Computers for Mathematical Learning, 6(2), 127–142.CrossRef
Zurück zum Zitat Heid, M. K. (1988). Resequencing skills and concepts in applied calculus using the computer as a tool. Journal for Research in Mathematics Education, 19(1), 3–25.CrossRef Heid, M. K. (1988). Resequencing skills and concepts in applied calculus using the computer as a tool. Journal for Research in Mathematics Education, 19(1), 3–25.CrossRef
Zurück zum Zitat Heid, M. K., & Blume, G. W. (2008a). Research on technology and the teaching and learning of mathematics: Vol. 1: Research syntheses. Charlotte, NC: Information Age Publishing. Heid, M. K., & Blume, G. W. (2008a). Research on technology and the teaching and learning of mathematics: Vol. 1: Research syntheses. Charlotte, NC: Information Age Publishing.
Zurück zum Zitat Heid, M. K., & Blume, G. W. (2008b). Research on technology and the teaching and learning of mathematics: Vol. 2: Cases and perspectives. Charlotte, NC: Information Age Publishing. Heid, M. K., & Blume, G. W. (2008b). Research on technology and the teaching and learning of mathematics: Vol. 2: Cases and perspectives. Charlotte, NC: Information Age Publishing.
Zurück zum Zitat Heugl, H. (1997). Experimental and active learning with DERIVE. Zentralblatt für Didaktik der Mathematik, 29(5), 142–148.CrossRef Heugl, H. (1997). Experimental and active learning with DERIVE. Zentralblatt für Didaktik der Mathematik, 29(5), 142–148.CrossRef
Zurück zum Zitat Kendal, M., & Stacey, K. (2001). The impact of teacher privileging on learning differentiation with technology. International Journal of Computers for Mathematical Learning, 6(2), 143–165.CrossRef Kendal, M., & Stacey, K. (2001). The impact of teacher privileging on learning differentiation with technology. International Journal of Computers for Mathematical Learning, 6(2), 143–165.CrossRef
Zurück zum Zitat Kieran, C. (2007). Learning and teaching of algebra at the middle school through college levels: Building meaning for symbols and their manipulation. In F. Lester (Ed.), Second handbook of research on mathematics teaching and learning (pp. 707–762). Charlotte, NC: Information Age Publishing. Kieran, C. (2007). Learning and teaching of algebra at the middle school through college levels: Building meaning for symbols and their manipulation. In F. Lester (Ed.), Second handbook of research on mathematics teaching and learning (pp. 707–762). Charlotte, NC: Information Age Publishing.
Zurück zum Zitat Kieran, C. & Damboise, C. (2007). “How can we describe the relation between the factored form and the expanded form of these trinomials?-We don’t even know if our paper and pencil factorizations are right”: The case for computer algebra systems (CAS) with weaker algebra students. In J. H. Woo, H. C. Lew, K. S. Park, & D. Y. Seo, (Eds.), Proceedings of the 31st Conference of the International Group for the Psychology of Mathematics Education (Vol. 3, pp. 105–112). Seoul: PME. Kieran, C. & Damboise, C. (2007). “How can we describe the relation between the factored form and the expanded form of these trinomials?-We don’t even know if our paper and pencil factorizations are right”: The case for computer algebra systems (CAS) with weaker algebra students. In J. H. Woo, H. C. Lew, K. S. Park, & D. Y. Seo, (Eds.), Proceedings of the 31st Conference of the International Group for the Psychology of Mathematics Education (Vol. 3, pp. 105–112). Seoul: PME.
Zurück zum Zitat Kieran, C., & Yerushalmy, M. (2004). Computer algebra systems and algebra: Curriculum, assessment, teaching, and learning. In K. Stacey, H. Chick, & M. Kendal (Eds.), The future of the teaching and learning of algebra: The 12th ICMI study (pp. 99–154). Norwood, MA: Kluwer. Kieran, C., & Yerushalmy, M. (2004). Computer algebra systems and algebra: Curriculum, assessment, teaching, and learning. In K. Stacey, H. Chick, & M. Kendal (Eds.), The future of the teaching and learning of algebra: The 12th ICMI study (pp. 99–154). Norwood, MA: Kluwer.
Zurück zum Zitat Laborde, C. (2000). Dynamic geometry environments as a source of rich learning contexts for the complex activity of proving. Educational Studies in Mathematics, 44(1/2), 151–161.CrossRef Laborde, C. (2000). Dynamic geometry environments as a source of rich learning contexts for the complex activity of proving. Educational Studies in Mathematics, 44(1/2), 151–161.CrossRef
Zurück zum Zitat Lagrange, J.-B. (2003). Learning techniques and concepts using CAS: A practical and theoretical reflection. In J. T. Fey, A. Cuoco, C. Kieran, L. McMullin, & R. M. Zbiek (Eds.), Computer algebra systems in secondary school mathematics education (pp. 269–283). Reston, VA: NCTM. Lagrange, J.-B. (2003). Learning techniques and concepts using CAS: A practical and theoretical reflection. In J. T. Fey, A. Cuoco, C. Kieran, L. McMullin, & R. M. Zbiek (Eds.), Computer algebra systems in secondary school mathematics education (pp. 269–283). Reston, VA: NCTM.
Zurück zum Zitat Lagrange, J.-B., Artigue, M., Laborde, C., & Trouche, L. (2003). Technology and mathematics education: A multidimensional study of the evolution of research and innovation. In A. J. Bishop, M. A. Clements, C. Keitel, J. Kilpatrick, & F. K. S. Leung (Eds.), Second international handbook of mathematics education (pp. 237–270). Dordecht, Netherlands: Kluwer. Lagrange, J.-B., Artigue, M., Laborde, C., & Trouche, L. (2003). Technology and mathematics education: A multidimensional study of the evolution of research and innovation. In A. J. Bishop, M. A. Clements, C. Keitel, J. Kilpatrick, & F. K. S. Leung (Eds.), Second international handbook of mathematics education (pp. 237–270). Dordecht, Netherlands: Kluwer.
Zurück zum Zitat Oldknow, A. (1996). Micromaths: Tea cups, T Cubed, discharge and the elimination of drips. Teaching Mathematics and its Applications, 15(4), 179–185.CrossRef Oldknow, A. (1996). Micromaths: Tea cups, T Cubed, discharge and the elimination of drips. Teaching Mathematics and its Applications, 15(4), 179–185.CrossRef
Zurück zum Zitat Pea, R. D. (1985). Beyond amplification: Using the computer to reorganise mental functioning. Educational Psychologist, 20(4), 167–182.CrossRef Pea, R. D. (1985). Beyond amplification: Using the computer to reorganise mental functioning. Educational Psychologist, 20(4), 167–182.CrossRef
Zurück zum Zitat Pierce, R., & Stacey, K. (2001a). Reflections on the changing pedagogical use of computer algebra systems: Assistance for doing or learning mathematics. Journal of Computers in Mathematics and Science Teaching, 20(1), 141–163. Pierce, R., & Stacey, K. (2001a). Reflections on the changing pedagogical use of computer algebra systems: Assistance for doing or learning mathematics. Journal of Computers in Mathematics and Science Teaching, 20(1), 141–163.
Zurück zum Zitat Pierce, R., & Stacey, K. (2001b). Observations on students’ responses to learning in a CAS environment. Mathematical Education Research Journal, 3(1), 28–46. Pierce, R., & Stacey, K. (2001b). Observations on students’ responses to learning in a CAS environment. Mathematical Education Research Journal, 3(1), 28–46.
Zurück zum Zitat Pierce, R., & Stacey, K. (2004a). A framework for monitoring progress and planning teaching towards effective use of computer algebra systems. International Journal of Computers for Mathematical Learning, 9(1), 59–93.CrossRef Pierce, R., & Stacey, K. (2004a). A framework for monitoring progress and planning teaching towards effective use of computer algebra systems. International Journal of Computers for Mathematical Learning, 9(1), 59–93.CrossRef
Zurück zum Zitat Pierce, R., & Stacey, K. (2004b). Monitoring progress in algebra in a CAS active context: Symbol Sense, algebraic insight and algebraic expectation. International Journal for Technology in Mathematics Education, 11(1), 3–11. Pierce, R., & Stacey, K. (2004b). Monitoring progress in algebra in a CAS active context: Symbol Sense, algebraic insight and algebraic expectation. International Journal for Technology in Mathematics Education, 11(1), 3–11.
Zurück zum Zitat Pierce, R., & Stacey, K. (2006). Enhancing the image of mathematics by association with simple pleasures from real world contexts. Zentralblatt für Didaktik der Mathematik, 38(2), 214–225.CrossRef Pierce, R., & Stacey, K. (2006). Enhancing the image of mathematics by association with simple pleasures from real world contexts. Zentralblatt für Didaktik der Mathematik, 38(2), 214–225.CrossRef
Zurück zum Zitat Pierce, R., & Stacey, K. (2008). Using pedagogical maps to show the opportunities afforded by CAS for improving the teaching of mathematics. Australian Senior Mathematics Journal, 22(1), 6–12. Pierce, R., & Stacey, K. (2008). Using pedagogical maps to show the opportunities afforded by CAS for improving the teaching of mathematics. Australian Senior Mathematics Journal, 22(1), 6–12.
Zurück zum Zitat Thomas, M. O. J., & Holton, D. (2003). Technology as a tool for teaching undergraduate mathematics. In A. J. Bishop, M. A. Clements, C. Keitel, J. Kilpatrick, & F. K. S. Leung (Eds.), Second international handbook of mathematics education (pp. 351–394). Dordrecht, Netherlands: Kluwer. Thomas, M. O. J., & Holton, D. (2003). Technology as a tool for teaching undergraduate mathematics. In A. J. Bishop, M. A. Clements, C. Keitel, J. Kilpatrick, & F. K. S. Leung (Eds.), Second international handbook of mathematics education (pp. 351–394). Dordrecht, Netherlands: Kluwer.
Zurück zum Zitat Thomas, M. O. J., Monaghan, J., & Pierce, R. (2004). Computer algebra systems and algebra: Curriculum, assessment, teaching, and learning. In K. Stacey, H. Chick, & M. Kendal (Eds.), The future of the teaching and learning of algebra: The 12th ICMI study (pp. 155–186). Norwood, MA: Kluwer. Thomas, M. O. J., Monaghan, J., & Pierce, R. (2004). Computer algebra systems and algebra: Curriculum, assessment, teaching, and learning. In K. Stacey, H. Chick, & M. Kendal (Eds.), The future of the teaching and learning of algebra: The 12th ICMI study (pp. 155–186). Norwood, MA: Kluwer.
Zurück zum Zitat Vincent, J. (2003). Year 8 students’ reasoning in a Cabri environment. In L. Bragg, C. Campbell, G. Herbert, & J. Mousley (Eds.), Mathematics education researching: Innovation, networking, opportunity. Proceedings of the 26th Annual Conference of the Mathematics Education Research Group of Australasia. (pp. 696–703). Sydney: MERGA. Vincent, J. (2003). Year 8 students’ reasoning in a Cabri environment. In L. Bragg, C. Campbell, G. Herbert, & J. Mousley (Eds.), Mathematics education researching: Innovation, networking, opportunity. Proceedings of the 26th Annual Conference of the Mathematics Education Research Group of Australasia. (pp. 696–703). Sydney: MERGA.
Zurück zum Zitat Wander, R., & Pierce, R. (2009). Marina’s fish shop: A mathematically- and technologically-rich lesson. Australian Mathematics Teacher, 65(2), 6–12. Wander, R., & Pierce, R. (2009). Marina’s fish shop: A mathematically- and technologically-rich lesson. Australian Mathematics Teacher, 65(2), 6–12.
Zurück zum Zitat Wilf, H. S. (1982). The disc with the college education. The American Mathematical Monthly, 89, 4–8.CrossRef Wilf, H. S. (1982). The disc with the college education. The American Mathematical Monthly, 89, 4–8.CrossRef
Zurück zum Zitat Yearwood, J., & Glover, B. (1995). Computer algebra systems in teaching engineering mathematics. Australasian Journal of Engineering Education, 6(1), 87–94. Yearwood, J., & Glover, B. (1995). Computer algebra systems in teaching engineering mathematics. Australasian Journal of Engineering Education, 6(1), 87–94.
Zurück zum Zitat Zbiek, R. M., Heid, M. K., Blume, G. W., & Dick, T. (2007). Research on technology in mathematics education: A perspective of constructs. In F. Lester (Ed.), Second handbook of research on mathematics teaching and learning (pp. 1169–1207). Charlotte, NC: Information Age. Zbiek, R. M., Heid, M. K., Blume, G. W., & Dick, T. (2007). Research on technology in mathematics education: A perspective of constructs. In F. Lester (Ed.), Second handbook of research on mathematics teaching and learning (pp. 1169–1207). Charlotte, NC: Information Age.
Metadaten
Titel
Mapping Pedagogical Opportunities Provided by Mathematics Analysis Software
verfasst von
Robyn Pierce
Kaye Stacey
Publikationsdatum
01.04.2010
Verlag
Springer Netherlands
Erschienen in
Technology, Knowledge and Learning / Ausgabe 1/2010
Print ISSN: 2211-1662
Elektronische ISSN: 2211-1670
DOI
https://doi.org/10.1007/s10758-010-9158-6

Weitere Artikel der Ausgabe 1/2010

Technology, Knowledge and Learning 1/2010 Zur Ausgabe

Computer Math Snapshots - Column Editor: Uri Wilensky* Computational Diversions

When Two Circles Determine a Triangle. Discovering and Proving a Geometrical Condition in a Computer Environment

    Marktübersichten

    Die im Laufe eines Jahres in der „adhäsion“ veröffentlichten Marktübersichten helfen Anwendern verschiedenster Branchen, sich einen gezielten Überblick über Lieferantenangebote zu verschaffen.