Skip to main content
SpringerLink
Log in

How Might Computer Algebra Systems Change the Role of Algebra in the School Curriculum?

  • Chapter
  • First Online:
Third International Handbook of Mathematics Education

Part of the book series: Springer International Handbooks of Education ((SIHE,volume 27))

Abstract

Computer Algebra Systems (CAS) are software systems with the capability of symbolic manipulation linked with graphical, numerical, and tabular utilities, and increasingly include interactive symbolic links to spreadsheets and dynamical geometry programs. School classrooms that incorporate CAS allow for new explorations of mathematical invariants, active linking of dynamic representations, engagement with real data, and simulations of real and mathematical relationships. Changes can occur not only in the tasks but also in the modes of interaction among teachers and students, shifting the source of mathematical authority toward the students themselves, and students’ and teachers’ attention toward more global mathematical perspectives. With CAS a welcome partner in school algebra, different concepts can be emphasized, concepts that are taught can be done so more deeply and in ways clearly connected to technical skills, investigations of procedures can be extended, new attention can be placed on structure, and thinking and reasoning can be inspired. CAS can also create the opportunity to extend some algebraic procedures and introduce and assist exploration of new structures. A result is the enrichment of multiple views of algebra and changing classroom dynamics. Suggestions are offered for future research centred on the use of CAS in school algebra.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 709.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 899.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 899.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Notes

  1. 1.

    Cassyopée is the spelling used in the referenced paper.

References

  • Alonso, F., Garcia, A., Garcia, F., Hoya, S., Rodriguez, G., & de la Valla, A. (2001). Some unexpected results using computer algebra systems. International Journal of Computer Algebra in Mathematics Education, 8, 239–252.

    Google Scholar 

  • Arcavi, A. (1994). Symbol sense: Informal sense-making in formal mathematics. For the Learning of Mathematics, 14(3), 24–35.

    Google Scholar 

  • 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. doi:10.1023/A:1022103903080.

    Article  Google Scholar 

  • Arzarello, F., & Robutti, O. (2010). Multimodality in multi-representational environments. ZDM–International Journal of Mathematics Education, 42, 715–731. doi:10.1007/s11858-010-0288-z.

    Article  Google Scholar 

  • Balacheff, N. (1994). La transposition informatique. Note sur un nouveau problème pour la didactique. In M. Artigue, R. Gras, C. Laborde, & P. Tavignot (Eds.), Vingt ans de didactique des mathématiques en France: Hommage à Guy Brousseau et à Gérard Vergnaud(pp. 364–370). Grenoble, France: La Pensée Sauvage.

    Google Scholar 

  • Ball, D. L., Hill, H. C., & Bass, H. (2005). Knowing mathematics for teaching: Who knows mathematics well enough to teach third grade, and how can we decide? American Educator, 29(1), 14–17, 20–22, 43–46.

    Google Scholar 

  • Ball, L., & Stacey, K. (2004). A new practice evolving in learning mathematics: Differences in students’ written records with CAS. 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, Melbourne (Vol. 1, pp. 177–184). Sydney, Australia: Mathematics Education Research Group of Australasia.

    Google Scholar 

  • Ball, L., & Stacey, K. (2005). Students’ views on using CAS in senior mathematics. Building connections: Theory, research, and practice.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, Melbourne (Vol. 1, pp. 121–128). Sydney, Australia: Mathematics Education Research Group of Australasia.

    Google Scholar 

  • Ball, L., & Stacey, K. (2006). Coming to appreciate the pedagogical uses of CAS. In J. Novotná, H. Moraová, M. Krátká, & N. Stehlíková (Eds.), Proceedings of the 30th Conference of the International Group for the Psychology of Mathematics Education(Vol. 2, pp. 105–112). Prague, Czech Republic: International Group for the Psychology of Mathematics Education.

    Google Scholar 

  • Bednarz, N., & Janvier, B. (1996). Emergence and development of algebra as a problem-solving tool: Continuities and discontinuities with arithmetic. In N. Bednarz, C. Kieran, & L. Lee (Eds.), Approaches to algebra: Perspectives for research and teaching(pp. 115–136). Boston, MA: Kluwer.

    Google Scholar 

  • Boers van Oosterum, M. A. M. (1990). Understanding of variables and their uses acquired by students in their traditional and computer-intensive algebra(PhD dissertation). University of Maryland, College Park, MD.

    Google Scholar 

  • Böhm, J. (2007, June). Why is happening with CAS in classrooms? Example Austria. CAME 2007 Symposium: Connecting and Extending the Roles of Computer Algebra in Mathematics Education, Pécs, Hungary. Retrieved from http://www.lkl.ac.uk/research/came/events/CAME5/CAME5-Theme2-Boehm.pdf.

  • Buchberger, B. (1989). Should students learn integration rules? SIGSAM Bulletin, 24(1), 10–17.

    Article  Google Scholar 

  • Cedillo, T., & Kieran, C. (2003). Initiating students into algebra with symbol-manipulating calculators. In J. Fey, A. Cuoco, C. Kieran, L. McMullin, & R. M. Zbiek (Eds.), Computer algebra systems in secondary school mathematics education(pp. 219–239). Reston, VA: National Council of Teachers of Mathematics.

    Google Scholar 

  • Chazan, D., & Yerushalmy, M. (2003). On appreciating the cognitive complexity of school algebra: Research on algebra learning and directions of curricular change. In J. Kilpatrick, D. Schifter, & G. Martin (Eds.), A research companion to the Principles and Standards for School Mathematics(pp. 123–135). Reston, VA: National Council of Teachers of Mathematics.

    Google Scholar 

  • Clark-Wilson, A. (2010). Emergent pedagogies and the changing role of the teacher in the TI-Nspire Navigator-networked mathematics classroom. ZDM–International Journal of Mathematics Education, 42, 747–761. doi:10.1007/s11858-010-0279-0.

    Article  Google Scholar 

  • Cuoco, A. (2002). Thoughts on reading Artigue’s “Learning mathematics in a CAS environment”. International Journal of Computers for Mathematical Learning, 7, 245–274. doi:10.1023/A:1022112104897.

    Article  Google Scholar 

  • Dana-Picard, T. (2007). Motivating constraints of a pedagogy-embedded computer algebra system. International Journal of Science and Mathematics Education, 5, 217–235. doi:10.1007/s10763-006-9052-9.

    Article  Google Scholar 

  • Dick, T. P. (1992). Symbolic-graphical calculators: Teaching tools for mathematics. School Science and Mathematics, 92, 1–5. doi:10.1111/j.1949-8594.1992.tb12128.x.

    Article  Google Scholar 

  • Drijvers, P., & Weigand, H.-G. (2010). The role of handheld technology in the mathematics classroom. ZDM–International Journal of Mathematics Education, 42, 665–666. doi:10.1007/s11858-010-0285-2.

    Article  Google Scholar 

  • Duncan, A. G. (2010). Teachers’ views on dynamically linked multiple representations, pedagogical practices and students’ understanding of mathematics using TI-Nspire in Scottish secondary schools. ZDM–International Journal of Mathematics Education, 42, 763–774. doi:10.1007/s11858-010-0273-6.

    Article  Google Scholar 

  • Duval, R. (2006). A cognitive analysis of problems of comprehension in a learning of mathematics. Educational Studies in Mathematics, 61, 103–131. doi:10.1007/s10649-006-0400-z.

    Article  Google Scholar 

  • Edwards, M. T. (2001). The electronic“other”: A study of calculator-based symbolic manipulation utilities with secondary school mathematics students(PhD dissertation). The Ohio State University, Columbus, OH.

    Google Scholar 

  • Evans, M., Norton, P., & Leigh-Lancaster, D. (2005). Mathematical methods Computer Algebra System: 2004 pilot examinations and links to a broader research agenda. 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. 329–336). Melbourne, Australia: Mathematics Education Research Group of Australasia.

    Google Scholar 

  • Fey, J. T., Heid, M. K., Good, R. A., Sheets, C., Blume, G., & Zbiek, R. M. (1995). Concepts in algebra: A technological approach. Dedham, MA: Janson Publications, Inc.

    Google Scholar 

  • Fitzallen, N. (2005). Integrating ICT into professional practice: A case study of four mathematics teachers. 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. 353–360). Melbourne, Australia: Mathematics Education Research Group of Australasia.

    Google Scholar 

  • Forgasz, H. J. (2006a). Factors that encourage and inhibit computer use for secondary mathematics teaching. Journal of Computers in Mathematics and Science Teaching, 25(1), 77–93. doi:10.1007/s10857-006-9014-8.

    Google Scholar 

  • Forgasz, H. J. (2006b). Teachers, equity, and computers for secondary mathematics learning. Journal of Mathematics Teacher Education, 9, 437–469. doi:10.1007/s10857-006-9014-8.

    Article  Google Scholar 

  • Geiger, V., Faragher, R., Redmond, T., & Lowe, J. (2008). CAS-enabled devices as provocative agents in the process of mathematical modeling. In M. Goos, R. Brown, & K. Makar (Eds.), Navigating currents and charting directions(Proceedings of the 30th Annual Conference of the Mathematics Education Research Group of Australasia, Vol. 1, pp. 219–226). Brisbane, Australia: Mathematics Education Research Group of Australasia.

    Google Scholar 

  • Godfrey, D., & Thomas, M. O. J. (2008). Student perspectives on equation: The transition from school to university. Mathematics Education Research Journal, 20(2), 71–92. doi:10.1007/BF03217478.

    Article  Google Scholar 

  • Goos, M. (2005). A sociocultural analysis of the development of pre-service and beginning teachers’ pedagogical identities as users of technology. Journal of Mathematics Teacher Education, 8, 35–59. doi:10.1007/s10857-005-0457-0.

    Article  Google Scholar 

  • Goos, M., & Bennison, A. (2005). The role of online discussion in building a community of practice for beginning teachers of secondary mathematics. 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. 385–392). Melbourne, Australia: Mathematics Education Research Group of Australasia.

    Google Scholar 

  • Gray, E. M., & Tall, D. O. (1994). Duality, ambiguity and flexibility: A proceptual view of simple arithmetic. Journal for Research in Mathematics Education, 26, 115–141. doi:10.2307/749505.

    Google Scholar 

  • Guin, D., & Trouche, L. (1999). The complex process of converting tools into mathematical instruments: The case of calculators. International Journal of Computers for Mathematical Learning, 3, 195–227.

    Article  Google Scholar 

  • Guin, D., Ruthven, K., & Trouche, L. (2005). The didactical challenge of symbolic calculators: Turning a computational device into a mathematical instrument. New York, NY: Springer.

    Book  Google Scholar 

  • Harel, G. (2008). DNR perspectives on mathematics curriculum and instruction, Part I: Focus on proving. ZDM–International Journal of Mathematics Education, 40, 487–500. doi:10.1007/s11858-008-0104-1.

    Article  Google Scholar 

  • Hasenbank, J. F., & Hodgson, T. (2007, February). A framework for developing algebraic understanding & procedural skill: An initial assessment. Paper presented at the tenth conference on Research in Undergraduate Mathematics Education, Special Interest Group of Mathematical Association of America (SIG-MAA), San Diego, CA.

    Google Scholar 

  • Hegedus, S., & Kaput, J. (2007). Lessons from SimCalc: What research says(Research Note 6). Dallas, TX: Texas Instruments.

    Google Scholar 

  • Heid, M. K. (1984). An exploratory study to examine the effects of resequencing concepts and skills in an applied calculus curriculum through the use of a microcomputer(PhD dissertation). University of Maryland, College Park, MD.

    Google Scholar 

  • Heid, M. K. (1988). Resequencing skills and concepts in applied calculus using the computer as a tool. Journal for Research in Mathematics Education, 19, 3–25. doi:10.2307/749108.

    Article  Google Scholar 

  • Heid, M. K. (1992). Final report: Computer-intensive curriculum for secondary school algebra. Final report NSF project number MDR 8751499. University Park: The Pennsylvania State University, Department of Curriculum and Instruction.

    Google Scholar 

  • Heid, M. K. (1996). A technology-intensive functional approach to the emergence of algebraic thinking. In N. Bednarz, C. Kieran, & L. Lee (Eds.), Approaches to algebra: Perspectives for research and teaching(pp. 239–256). Boston, MA: Kluwer Academic Publishers.

    Google Scholar 

  • Heid, M. K. (1997). The technological revolution and the reform of school mathematics. American Journal of Education, 106, 5–61. doi:10.1086/444175.

    Article  Google Scholar 

  • Heid, M. K., & Blume, G. W. (2008). Algebra and function development. In M. K. Heid & G. W. Blume (Eds.), Research on technology and the teaching and learning of mathematics(Research syntheses, Vol. 1, pp. 55–108). Charlotte, NC: Information Age Publishers.

    Google Scholar 

  • Heid, M. K., Sheets, C., Matras, M. A., & Menasian, J. (1988, April). Classroom and computer lab interaction in a computer-intensive algebra curriculum. Paper presented at the annual meeting of the American Educational Research Association, New Orleans.

    Google Scholar 

  • Hill, H., & Ball, D. L. (2004). Learning mathematics for teaching: Results from California’s mathematics professional development institutes. Journal for Research in Mathematics Education, 35, 330–351. doi:10.2307/30034819.

    Article  Google Scholar 

  • Hillel, J., Kieran, C., & Gurtner, J. (1989). Solving structured geometric tasks on the computer: The role of feedback in generating strategies. Educational Studies in Mathematics, 20, 1–39. doi:10.1007/BF00356039.

    Article  Google Scholar 

  • Hoehn, L. (1989, December). Solutions of xn+yn=zn+1. Mathematics Magazine, 342. doi:10.2307/2689491

    Google Scholar 

  • Hollar, J. C., & Norwood, K. (1999). The effects of a graphing-approach intermediate algebra curriculum on students’ understanding of function. Journal for Research in Mathematics Education, 30, 220–226. doi:10.2307/749612.

    Article  Google Scholar 

  • Holton, D., Thomas, M. O. J., & Harradine, A. (2009). The excircle problem: A case study in how mathematics develops. In B. Davis & S. Lerman (Eds.), Mathematical action & structures of noticing: Studies inspired by John Mason(pp. 31–48). Rotterdam, The Netherlands: Sense.

    Google Scholar 

  • Hong, Y. Y., & Thomas, M. O. J. (2006). Factors influencing teacher integration of graphic calculators in teaching. In Proceedings of the 11th Asian Technology Conference in Mathematics(pp. 234–243). Hong Kong: Asian Technology Conference in Mathematics.

    Google Scholar 

  • Hoyles, C., & Noss, R. (2009). The technological mediation of mathematics and its learning. Human development, 52, 129–147. doi:10.1159/000202730.

    Article  Google Scholar 

  • Judson, P. T. (1990). Elementary business calculus with computer algebra. Journal of Mathematical Behavior, 9, 153–157.

    Google Scholar 

  • Kendal, M., & Stacey, K. (1999). Varieties of teacher privileging for teaching calculus with computer algebra systems. The International Journal of Computer Algebra in Mathematics Education, 6, 233–247.

    Google Scholar 

  • Kendal, M., & Stacey, K. (2001). The impact of teacher privileging on learning differentiation with technology. International Journal of Computers for Mathematical Learning, 6, 143–165. doi:10.1023/A:1017986520658.

    Article  Google Scholar 

  • Kidron, I. (2010). Constructing knowledge about the notion of limit in the definition of the horizontal asymptote. International Journal of Science and Mathematics Education[published online]. Retrieved from http://www.springerlink.com/content/b4757j83v8826527.

  • Kieran, C. (2007). Learning and teaching algebra at the middle school through college levels. In F. K. Lester Jr. (Ed.), Second handbook of research on mathematics teaching and learning(pp. 707–762). Charlotte, NC: Information Age Publishing.

    Google Scholar 

  • Kieran, C., & Drijvers, P. (2006). 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, 11, 205–263. doi:10.1007/s10758-006-0006-7.

    Article  Google Scholar 

  • Kieran, C., & Saldanha, L. (2008). Designing tasks for the co-development of conceptual and technical knowledge in CAS activity: An example from factoring. In G. W. Blume & M. K. Heid (Eds.), Research on technology and the teaching and learning of mathematics(Cases and perspectives, Vol. 2, pp. 393–414). Charlotte, NC: Information Age Publishing.

    Google Scholar 

  • Laborde, C. (2002). The process of introducing new tasks using dynamic geometry into the teaching of mathematics. In B. Barton, K. C. Irwin, M. Pfannkuch, & M. O. J. Thomas (Eds.), Mathematics education in the South Pacific(Proceedings of the 25th annual conference of the Mathematics Education Research Group of Australasia, pp. 15–33). Auckland, NZ: Mathematics Education Research Group of Australasia.

    Google Scholar 

  • Lagrange, J.-B. (1999). Complex calculators in the classroom: Theoretical and practical reflections on teaching pre-calculus. International Journal of Computers for Mathematical Learning, 4, 51–81. doi:10.1023/A:1009858714113.

    Article  Google Scholar 

  • Lagrange, J.-B. (2002). Étudier les mathématiques avec les calculatrices symboliques. Quelle place pour les techniques? In D. Guin & L. Trouche (Eds.), Calculatrices Symboliques. Transformer un outil en un instrument du travail mathématique: Un problème didactique(pp. 151–185). Grenoble, France: La Pensée Sauvage.

    Google Scholar 

  • 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: National Council of Teachers of Mathematics.

    Google Scholar 

  • Lagrange, J.-B., Artigue, M., Laborde, C., & Trouche, L. (2003). Technology and math education: A multidimensional overview of recent research and innovation. In A. J. Bishop, M. A. Clements, C. Keitel, J. Kilpatrick, & F. Leung (Eds.), Second international handbook of mathematics education(Part 1, pp. 237–270). Dordrecht, The Netherlands: Kluwer.

    Chapter  Google Scholar 

  • Lagrange, J.-B., & Chiappini, J. P. (2007). Integrating the learning of algebra with technology at the European level: Two examples in the ReMath Project. In Proceedings of Conference of European Society of Research in Mathematics Education(CERME 5) (pp. 903–912). Larnaca, Cyprus: European Society of Research in Mathematics Education.

    Google Scholar 

  • Lagrange, J.-B., & Gelis, J.-M. (2008). The Casyopee project: A computer algebra systems environment for students’ better access to algebra. International Journal of Continuing Engineering Education and Life-Long Learning, 18(5/6), 575–584. doi:10.1504/IJCEELL.2008.022164.

    Article  Google Scholar 

  • Lee, L. (1996). An initiation into algebraic culture through generalization activities. In N. Bednarz, C. Kieran, & L. Lee (Eds.), Approaches to algebra: Perspectives for research and teaching(pp. 87–106). Boston, MA: Kluwer.

    Google Scholar 

  • Mason, J. (1995). Less may be more on a screen. In L. Burton & B. Jaworski (Eds.), Technology in mathematics teaching: A bridge between teaching and learning(pp. 119–134). London, UK: Chartwell-Bratt.

    Google Scholar 

  • Mason, J. (1996). Expressing generality and roots of algebra. In N. Bednarz, C. Kieran, & L. Lee (Eds.), Approaches to algebra: Perspectives for research and teaching(pp. 65–86). Boston, MA: Kluwer.

    Google Scholar 

  • Mason, J., Graham, A., & Johnston-Wilder, S. (2005). Developing thinking in algebra. London, UK: Paul Chapman Publishing and The Open University.

    Google Scholar 

  • Matras, M. A. (1988). The effects of curricula on students’ ability to analyze and solve problems in algebra(PhD dissertation). University of Maryland, College Park, MD.

    Google Scholar 

  • Mayes, R. (1995). The application of a computer algebra system as a tool in college algebra. School Science and Mathematics, 95, 61–68. doi:10.1111/j.1949-8594.1995.tb15729.x.

    Article  Google Scholar 

  • Mayes, R. (2001). CAS applied in a functional perspective college algebra curriculum. Computers in the Schools, 17(1&2), 57–75. doi:10.1300/J025v17n01_06.

    Article  Google Scholar 

  • McMullin, L. (2003). Activity 8. In J. Fey, A. Cuoco, C. Kieran, L. McMullin, & R. M. Zbiek (Eds.), Computer algebra systems in secondary school mathematics education(p. 268). Reston, VA: The National Council of Teachers of Mathematics.

    Google Scholar 

  • Monaghan, J. (2004). Teachers’ activities in technology-based mathematics lessons. International Journal of Computers for Mathematical Learning, 9, 327–357. doi:10.1007/s10758-004-3467-6.

    Article  Google Scholar 

  • Nemirovsky, R. (1996). Mathematical narratives, modeling, and algebra. In N. Bednarz, C. Kieran, & L. Lee (Eds.), Approaches to algebra: Perspectives for research and teaching(pp. 197–220). Boston, MA: Kluwer.

    Google Scholar 

  • Norton, P., Leigh-Lancaster, D., Jones, P., & Evans, M. (2007). Mathematical methods and mathematical methods computer algebra systems (CAS) 2006—Concurrent implementation with a common technology free examination. In J. Watson & K. Beswick (Eds.), Mathematics: Essential research, essential practice(Proceedings of the 30th Annual Conference of the Mathematics Education Research Group of Australasia, Vol. 2, pp. 543–550). Hobart, Australia: Mathematics Education Research Group of Australasia.

    Google Scholar 

  • O’Callaghan, B. R. (1998). Computer-intensive algebra and students’ conceptual knowledge of functions. Journal for Research in Mathematics Education, 29, 21–40. doi:10.2307/749716.

    Article  Google Scholar 

  • Oates, G. (2004). Measuring the degree of technology use in tertiary mathematics courses. In W.-C. Yang, S.-C. Chu, T. de Alwis, & K.-C. Ang (Eds.), Proceedings of the 9th Asian Technology Conference in Mathematics(pp. 282–291). Blacksburg, VA: Asian Technology Conference in Mathematics.

    Google Scholar 

  • Oates, G. (2009). Relative values of curriculum topics in undergraduate mathematics in an integrated technology environment. In R. Hunter, B. Bicknell, & T. Burgess (Eds.), Proceedings of the 32nd Annual Conference of the Mathematics Education Research Group of Australasia(Vol. 2, pp. 419–427). Palmerston North, New Zealand: Mathematics Education Research Group of Australasia.

    Google Scholar 

  • Palmiter, J. (1991). Effects of computer-algebra systems on concept and skill acquisition in calculus. Journal for Research in Mathematics Education, 22, 151–156. doi:10.2307/749591.

    Article  Google Scholar 

  • Paterson, J., Thomas, M. O. J., & Taylor, S. (2011). Reaching decisions via internal dialogue: Its role in a lecturer professional development model. In B. Ubuz (Ed.), Proceedings of the 35th Conference of the International Group for the Psychology of Mathematics Education(Vol. 3, pp. 353–360). Ankara, Turkey: International Group for the Psychology of Mathematics Education.

    Google Scholar 

  • Pierce, R. (2005). Using CAS to enrich the teaching and learning of mathematics. In S.-C. Chu, H.-C. Lew, & W.-C. Yang (Eds.), Enriching technology and enhancing mathematics for all. Proceedings of the 10th Asian Conference on Technology in Mathematics(pp. 47–58). Blacksburg VA: Asian Technology Conference in Mathematics.

    Google Scholar 

  • Pierce, R., & Ball, L. (2009). Perceptions that may affect teachers’ intention to use technology in secondary mathematics classes. Educational Studies in Mathematics, 71, 299–317. doi:10.1007/s10649-008-9177-6.

    Article  Google Scholar 

  • Pierce, R., Herbert, S., & Giri, J. (2004). CAS: Student engagement requires unambiguous advantages. In I. Putt, R. Faragher, & M. I. McLean (Eds.), Mathematics education for the third millennium: Towards 2010(Proceedings of the 27th Annual Conference of the Mathematics Education Group of Australasia, pp. 462–469). Townsville, Australia: Mathematics Education Research Group of Australasia.

    Google Scholar 

  • Pierce, R., & Stacey, K. (2010). Mapping pedagogical opportunities provided by mathematics analysis software. International Journal of Computers for Mathematical Learning, 15, 1–20. doi:10.1007/s10758-010-9158-6.

    Article  Google Scholar 

  • Pierce, R., Stacey, K., & Wander, R. (2010). Examining the didactic contract when handheld technology is permitted in the mathematics classroom. ZDM–International Journal of Mathematics Education, 42, 683–695. doi:10.1007/s11858-010-0271-8.

    Article  Google Scholar 

  • Rabardel, P. (1995). Les hommes et les technologies, approche cognitive des instruments contemporains. Paris, France: Armand Colin.

    Google Scholar 

  • Rojano, T. (1996). Developing algebraic aspects of problem solving within a spreadsheet environment. In N. Bednarz, C. Kieran, & L. Lee (Eds.), Approaches to algebra: Perspectives for research and teaching(pp. 137–146). Boston, MA: Kluwer.

    Google Scholar 

  • Roschelle, J., Vahey, P., Tatar, D., Kaput, J., & Hegedus, S. J. (2003). Five key considerations for networking in a handheld-based mathematics classroom. In N. A. Pateman, B. J. Dougherty, & J. T. Zilliox (Eds.), Proceedings of the 2003 Joint Meeting of PME and PMENA(Vol. 4, pp. 71–78). Honolulu, Hawaii: University of Hawaii.

    Google Scholar 

  • Ruthven, K. (1990). The influence of graphic calculator use on translation from graphic to symbolic forms. Educational Studies in Mathematics, 21(5), 431–450. doi:10.1007/BF00398862.

    Article  Google Scholar 

  • Schoenfeld, A. H. (2008). On modeling teachers’ in-the-moment decision-making. In A. H. Schoenfeld (Ed.), A study of teaching: Multiple lenses, multiple views(Journal for Research in Mathematics Education Monograph No. 14, pp. 45–96). Reston, VA: National Council of Teachers of Mathematics.

    Google Scholar 

  • Schoenfeld, A. H. (2011). How we think. A theory of goal-oriented decision making and its educational applications. New York, NY: Routledge.

    Google Scholar 

  • Sheets, C. (1993). Effects of computer learning and problem-solving tools on the development of secondary school students’ understanding of mathematical functions(PhD dissertation). University of Maryland, College Park, MD.

    Google Scholar 

  • Shulman, L. (1986). Those who understand: Knowledge growth in teaching. Educational Researcher, 15(2), 4–14. doi:10.3102/0013189X015002004.

    Google Scholar 

  • Stewart, S. (2005). Concerns relating to the use of CAS at university level. In P. Clarkson, A. Downton, D. Gronn, M. Horne, A. McDonough, R. Pierce, & A. Roche (Eds.), Building connections: Research, theory and practice(Proceedings of the 28th Annual Conference of the Mathematics Education Research Group of Australasia, Vol. 2, pp. 704–711). Melbourne, Australia: MERGA.

    Google Scholar 

  • Stewart, S., & Thomas, M. O. J. (2005). University student perceptions of CAS use in mathematics learning. In H. L. Chick & J. L. Vincent (Eds.), Proceedings of the 29th Conference for the International Group for the Psychology of Mathematics Education(Vol. 4, pp. 233–240). Melbourne, Australia: The University of Melbourne.

    Google Scholar 

  • Stewart, S., Thomas, M. O. J., & Hannah, J. (2005). Towards student instrumentation of computer-based algebra systems in university courses. International Journal of Mathematical Education in Science and Technology, 36, 741–750. doi:10.1080/00207390500271651.

    Article  Google Scholar 

  • Tall, D. O., Thomas, M. O. J., Davis, G., Gray, E., & Simpson, A. (2000). What is the object of the encapsulation of a process? Journal of Mathematical Behavior, 18, 223–241.

    Article  Google Scholar 

  • Thomas, M. O. J. (2006). Teachers using computers in the mathematics classroom: A longitudinal study. In J. Novotná, H. Moraová, M. Krátká, & N. Stehlíková (Eds.), Proceedings of the 30th Conference of the International Group for the Psychology of Mathematics Education(Vol. 5, pp. 265–272). Prague, Czech Republic: Charles University.

    Google Scholar 

  • Thomas, M. O. J. (2008a). Developing versatility in mathematical thinking. Mediterranean Journal for Research in Mathematics Education, 7(2), 67–87.

    Google Scholar 

  • Thomas, M. O. J. (2008b). Conceptual representations and versatile mathematical thinking. In Proceedings of ICME-10(CD version of proceedings, pp. 1–18). Copenhagen, Denmark, Paper available from http://www.icme10.dk/proceedings/pages/regular_pdf/RL_Mike_Thomas.pdf.

  • Thomas, M. O. J. (2009). Hand-held technology in the mathematics classroom: Developing pedagogical technology knowledge. In J. Averill, D. Smith, & R. Harvey (Eds.), Teaching secondary school students mathematics and statistics: Evidence-based practice(Vol. 2, pp. 147–160). Wellington, New Zealand: NZCER.

    Google Scholar 

  • Thomas, M. O. J., & Chinnappan, M. (2008). Teaching and learning with technology: Realising the potential. In H. Forgasz, A. Barkatsas, A. Bishop, B. Clarke, S. Keast, W.-T. Seah, P. Sullivan, & S. Willis (Eds.), Research in mathematics education in Australasia 2004-2007(pp. 167–194). Sydney, Australia: Sense Publishers.

    Google Scholar 

  • Thomas, M. O. J., & Hong, Y. Y. (2004). Integrating CAS calculators into mathematics learning: Issues of partnership. In M. J. Høines & A. B. Fuglestad (Eds.), Proceedings of the 28th Annual Conference of the International Group for the Psychology of Mathematics Education(Vol. 4, pp. 297–304). Bergen, Norway: Bergen University College.

    Google Scholar 

  • Thomas, M. O. J., & Hong, Y. Y. (2005a). Teacher factors in integration of graphic calculators into mathematics learning. In H. L. Chick & J. L. Vincent (Eds.), Proceedings of the 29th Annual Conference of the International Group for the Psychology of Mathematics Education(Vol. 4, pp. 257–264). Melbourne, Australia: The University of Melbourne.

    Google Scholar 

  • Thomas, M. O. J., & Hong, Y. Y. (2005b). Learning mathematics with CAS calculators: Integration and partnership issues. The Journal of Educational Research in Mathematics, 15(2), 215–232.

    Google Scholar 

  • Thomas, M. O. J., Hong, Y. Y., Bosley, J., & delos Santos, A. (2008). Use of calculators in the mathematics classroom. The Electronic Journal of Mathematics and Technology (eJMT)[On-line Serial] 2(2). Retrieved from https://php.radford.edu/∼ejmt/ContentIndex.phpand http://www.radford.edu/ejmt.

  • 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 teaching and learning of algebra: The 12th ICMI study(pp. 155–186). Norwood, MA: Kluwer.

    Google Scholar 

  • Thomas, P. G., & Rickhuss, M. G. (1992). An experiment in the use of computer algebra in the classroom. Education & Computing, 8, 255–263. doi:10.1016/0167-9287(92)92793-Y.

    Article  Google Scholar 

  • Trouche, L. (2005a). An instrumental approach to mathematics learning in symbolic calculator environments. In D. Guin, K. Ruthven, & L. Trouche (Eds.), The didactical challenge of symbolic calculators(pp. 137–162). New York, NY: Springer.

    Chapter  Google Scholar 

  • Trouche, L. (2005b). Instrumental genesis, individual and social aspects. In D. Guin, K. Ruthven, & L. Trouche (Eds.), The didactical challenge of symbolic calculators(pp. 197–230). New York, NY: Springer.

    Chapter  Google Scholar 

  • Usiskin, Z. (2004). A K-12 mathematics curriculum with CAS: What is it and what would it take to get it? In W. C. Yang, S. C. Chu, T. de Alwis, & K. C. Ang (Eds.), Proceedings of the 9th Asian Technology Conference in Mathematics(pp. 5–16). Blacksburg, VA: Asian Technology Conference in Mathematics.

    Google Scholar 

  • Vérillon, P., & Rabardel, P. (1995). Cognition and artifacts: A contribution to the study of though [sic] in relation to instrumented activity. European Journal of Psychology of Education, 10, 77–101.

    Article  Google Scholar 

  • Yerushalmy, M., & Chazan, D. (2002). Flux in school algebra: Curricular change, graphing, technology, and research on student learning and teacher knowledge. In L. D. English (Ed.), Handbook of international research in mathematics education(pp. 725–755). Mahwah, NJ: Lawrence Erlbaum.

    Google Scholar 

  • Zbiek, R. M., & Heid, M. K. (2001). Dynamic aspects of function representations. In H. Chick, K. Stacey, J. Vincent, & J. Vincent (Eds.), Proceedings of the 12th ICMI on the future of the teaching and learning of algebra(pp. 682–689). Melbourne, Australia: The University of Melbourne.

    Google Scholar 

  • Zbiek, R. M., & Heid, M. K. (2011). Using technology to make sense of symbols and graphs and to reason about general cases. In T. Dick & K. Hollebrands (Eds.), Focus on reasoning and sense making: Technology to support reasoning and sense making(pp. 19–31). Reston, VA: National Council of Teachers of Mathematics.

    Google Scholar 

  • Zbiek, R. M., Heid, M. K., Blume, G. W., & Dick, T. P. (2007). Research on technology in mathematics education: A perspective of constructs. In F. Lester Jr. (Ed.), Second handbook of research on mathematics teaching and learning(pp. 1169–1207). Charlotte, NC: Information Age Publishing.

    Google Scholar 

  • Zbiek, R. M., & Hollebrands, K. (2008). A research-informed view of the process of incorporating mathematics technology into classroom practice by inservice and prospective teachers. In M. K. Heid & G. W. Blume (Eds.), Research on technology and the teaching and learning of mathematics(Research syntheses, Vol. 1, pp. 287–344). Charlotte, NC: Information Age Publishing.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. The Pennsylvania State University, University Park, PA, USA

    M. Kathleen Heid & Rose Mary Zbiek

  2. The University of Auckland, Auckland, New Zealand

    Michael O. J. Thomas

Authors
  1. M. Kathleen Heid
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Michael O. J. Thomas
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Rose Mary Zbiek
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to M. Kathleen Heid .

Editor information

Editors and Affiliations

  1. Illinois State University, n/a, Normal, 61790-4520, Illinois, USA

    M.A. (Ken) Clements

  2. Fac. Education, Centre for Science, Mathematics &, Monash University, Clayton, 3800, Victoria, Australia

    Alan J. Bishop

  3. FB Erziehungswissenschaft und, Psychologie, FU Berlin, Habelschwerdter Allee 45, Berlin, 14195, Germany

    Christine Keitel

  4. Dept. Mathematics Education, University of Georgia, Aderhold Hall 105, Athens, 30602-7124, Georgia, USA

    Jeremy Kilpatrick

  5. Fac. Education, University of Hong Kong, Pokfulam Road, Hong Kong, Hong Kong SAR

    Frederick K.S. Leung

Rights and permissions

Reprints and permissions

Copyright information

© 2012 Springer Science+Business Media New York

About this chapter

Cite this chapter

Heid, M.K., Thomas, M.O.J., Zbiek, R.M. (2012). How Might Computer Algebra Systems Change the Role of Algebra in the School Curriculum?. In: Clements, M., Bishop, A., Keitel, C., Kilpatrick, J., Leung, F. (eds) Third International Handbook of Mathematics Education. Springer International Handbooks of Education, vol 27. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-4684-2_20

Download citation

Publish with us

Policies and ethics

Search

Navigation