Computer Algebra Systems (CAS): From Where Did They Come, and Where Might They Go?

Transcription

1 Computer Algebra Systems (CAS): From Where Did They Come, and Where Might They Go? Ed Dickey University of South Carolina References and Bibliography Relevant to the presentation at the NCTM Annual Meeting in San Diego on 22 April 2010 Aspetsberger, K. and G. Funk (1984). Experiments with mumath in Austrian High Schools. ACM SIGSAM Bulletin 18-19, 4-1, pp Benson, Steve with Susan Addington, Nina Arshavsky, Al Cuoco, Paul Goldenberg, and Eric Karnowski. Ways to Think About Mathematics: Activities and Investigations for Grade 6.12 Teachers. Thousand Oaks, CA: Corwin Press, Burke, Maurice J. and Elizabeth A. Burroughs (2009) Using CAS to Solve Classical Mathematics Problems. Mathematics Teacher 102, 9, Cuoco. Al et al. CME Project Algebra I, Geometry, Algebra II, Precalculus. Lebanon, IN: Pearson School, 2009 [ Dick, Thomas P. Keeping the Faith: Fidelity in Technological Tools for Mathematics Education. In Research on Technology and the Teaching and Learning of Mathematics: Vol 2. Cases and Perspectives edited by M. Kathleen Heid and Glendon W. Blume, pp Charlotte, NC: IAP, 2008 Dickey, Edwin. mumath-80 Reference Manual and Teacher s Guide. Columbia, SC: University of South Carolina, Drijvers, P. (2003). Learning algebra in a computer algebra environment. Design research on the understanding of the concept of parameter. Dissertation. Utrecht, the Netherlands: CD-bèta press. Also available through Drijvers, P. (2003). Algebra on a screen, on paper and in the mind. In: J. Fey, A. Cuoco, C. Kieran, L. McMullin, & R. M. Zbiek (Eds.): Computer Algebra Systems in - 1 -

2 Secondary School Mathematics Education (pp ). Reston, VA: National Council of Teachers of Mathematics. Drijvers, P. (2002). Learning mathematics in a computer algebra environment: obstacles are opportunities. Zentralblatt für Didaktik der Mathematik, 34(5), Drijvers, P. (2009). Tools and tests: technology in national final mathematics examinations. In Winslow, C. (Ed.), Nordic Research on Mathematics Education, Proceedings from NORMA08 (pp ). Rotterdam: Sense. Drijvers, P. & Gravemeijer, K.P.E. (2004). Computer algebra as an instrument: Examples of algebraic schemes. In: Guin, D., Ruthven, K., & Trouche, L. (Eds.), The didactical challenge of symbolic calculators: turning a computational device into a mathematical instrument (pp ). Dordrecht, the Netherlands: Kluwer Academic Publishers. Drijvers, P., Kieran, C., & Mariotti, M.A. (2010). Integrating technology into mathematics education: theoretical perspectives. In Hoyles, C. & Lagrange, J.-B. (Eds.), Mathematics education and technology - Rethinking the terrain (pp ). New York/Berlin: Springer. Drijvers, Paul and Luc Trouche. From Artifacts to Instrument: A Theoretical Framework Behind the Orchestra Metaphor. In Research on Technology and the Teaching and Learning of Mathematics: Vol 2. Cases and Perspectives edited by M. Kathleen Heid and Glendon W. Blume, pp Charlotte, NC: IAP, 2008 Edwards, M. T. (2002). Symbolic Manipulation in a Technological Age. Mathematics Teacher 95, 9, Edwards, Thomas G. and Asli Özgün-Koca (2009). Creating a Mathematical B Movie: The Effect of b on the Graph of a Quadratic. Mathematics Teacher 103, 3, Fey, James Taylor, Richard Good, Glendon Blume, Rose Marie Zbiek, and M. Kathleen Heid. Concepts in Algebra: A Technological Approach. Dedham, MA: Janson Publications, Fey, James T. et al. (Eds.). Computing and Mathematics: The Impact on Secondary School Curricula. Reston, VA: NCTM, Fey, James and Kathleen Heid. Imperatives and Possibilities for New Curricula in Secondary School Mathematics. In Computers in Mathematics Education, edited by Viggo P. Hansen, pp Reston, VA: NCTM,

3 Fey, James, Al Cuoco, Carolyn Kieran, Lin McMullin, and Rose Mary Zbiek (Eds.). Computer Algebra Systems in Secondary School Mathematics Education. Reston, VA: NCTM, Flynn, Peter. Inserting a Slider. Retrieved March 10, 2010 from Insert-a-Slider.pdf Hanna, John. Function+Polar Trace: TI Nspire file. Retrieved March 10, 2010 from Heid, M. Kathleen (1989). How Symbolic Mathematical Systems Could and Should Affect Precollege Mathematics. Mathematics Teacher 82, 6, Heid, Kathleen (2002). Computer Algebra Systems in Secondary Mathematics Classes: The Time to Act Is Now! Mathematics Teacher 95, 9, Heid, M. Kathleen, Karen Hollebrands, and Linda W. Iseri (2002). Reasoning and Justification with Examples from Technological Environments. Mathematics Teacher 95, 3, Hitt, F., & Kieran, C. (2009). Constructing knowledge via a peer interaction in a CAS environment with tasks designed from a Task-Technique-Theory perspective. International Journal of Computers for Mathematical Learning, 14, (available from Springer On-line) Kieran, C., & Drijvers, P., with Boileau, A., Hitt, F., Tanguay, D., Saldanha, L., & Guzmán, J. (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, Kieran, C., & Paul Drijvers with Boileau, A., Hitt, F., Tanguay, D., Saldanha, L., & Guzmán, J. (2006). Learning about equivalence, equality and equation in a CAS environment: The interaction of machine techniques, paper-and-pencil techniques, and theorizing. In C. Hoyles, J.-B. Lagrange, L. H. Son, & N. Sinclair (Eds.), Proceedings of the 17th ICMI Study Conference, Technology revisited. Hanoi, Vietnam: ICMI-Study-17 Program Committee. 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 31st PME Conference (Vol. 3, pp ). Seoul, Korea: PME

4 Kunkle, Dan and Charles I. Burch Jr. (1984). Symbolic Computer Algebra: The Classroom Computer Takes a Quantum Jump. Mathematics Teacher 77, 3, Kutzler, Bernhard. Technology and the Yin&Yang of Teaching and Learning Mathematics. Leonding, Austria: b.kutzler.com, Losse, John. Lafacroft: TI-Nspire Files Retrieved March 10, 2010 from Lott, Johnny (2002). A Static Mathematics Curriculum Is Unhealthy! NCTM News Bulletin, July/August. President s Corner. Retrieved March 11, 2010 from Mahoney, John. (2002) Computer Algebra Systems in Our Schools: Some Axioms and Some Examples. Mathematics Teacher 95, 8, McCarthy, John et al. LISP 1.5 Programmer s Manual. Cambridge, MA: MIT Press, Media4Math. TI-Nspire Mini-Tutorials: Quadratic Graphs in Standard Form Using Sliders Retrieved April 6, 2010 from National Council of Teachers of Mathematics. Curriculum and Evalution Standards for School Mathematics. Reston, VA: NCTM, Özgün-Koca, S. A., and Thomas G. Edwards (2008). The New Generation of Handheld Calculators. Mathematics Teacher 102, 1, Palmiter, Jeanette R. (1991). Effects of Computer Algebra Systems on Concept and Skill Acquisition in Calculus. Journal for Research in Mathematics Education 22, 2, Rich, Albert and David Stoutemyer. mumath-80 Symbolic Math System for the Apple II Computer. Bellevue, WA: Microsoft, Ronau, Robert N., Niess, M. L., Browning, C., Pugalee, D., Driskell, S. O., & Harrington, R. Framing the research on digital technologies and student learning in mathematics. In Framing Research on Technology and Student Learning in the Content Areas: Implications for Educators, Edited by L. Bell, L. Schrum, & A. D. Thompson, pp Charlotte, NC: Information Age Publishing, Smithsonian American History Museum. Slates, Slide Rules and Software: Teaching in America. Retrieved March 10, 2010 from

5 Scher, Daniel (2000). Lifting the Curtain: The Evolution of The Geometer s Sketchpad. The Mathematics Educator 10, 1, pp Schwartz, Judah and Michal Yerushalmy. Geometric Supposer (Software). Pleasantville NY: Sunburst, South Carolina Department of Education. South Carolina Academic Standards for Mathematics. Columbia, SC: South Carolina Department of Education, Stoutemyer, David R (1979). Computer Symbolic Math & Education: A Radical Proposal. ACM SIGSAM Bulletin 13, 3, pp Steen, Lynn Arthur. Computer Calculus. Science News, April 18, 1981, pp Waits, B. K. and Frank Demana (1992). A Case Against Computer Symbolic Manipulation in School Mathematics Today. Mathematics Teacher 85, 3, Zbiek, R. M., et. al., (2009) Using Computer Algebra Systems to Develop Big Ideas in Mathematics. Mathematics Teacher 102, 7, Zbiek, Rose Mary, M. Kathleen Heid, Glendon Blume, and Thomas P. Dick. Research on Technology in Mathematics Education. In Second Handbook of Research on Mathematics Teaching and Learning edited by Frank K. Lester, Jr., pp Charlotte, NC: IAP and NCTM,