Mathematical Knowledge and Practices Resulting from Access to Digital Technologies

• Abbott, E. A. (1884). Flatland: A Romance of Many Dimensions. London: Seeley.

  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.

  Article  Google Scholar 

• Arzarello, F., Micheletti, C., Olivero, F., Robutti, O., Paola, D., & Gallino, G. (1998a). Dragging in cabri and modalities of transition from conjectures to proofs in geometry. In A. Olivier & K. Newstead (Eds.), Proceedings of the 22nd Annual Conference of the International Group for the Psychology of Mathematics Education (PME 22) (Vol. 2, pp. 32–39). Stellenbosch, South Africa.

  Google Scholar 

• Arzarello, F., Micheletti, C., Olivero, F., Robutti, O., & Paola, D. (1998b). A model for analyzing the transition to formal proofs in geometry. In A. Olivier & K. Newstead (Eds.), Proceedings of the 22nd Annual Conference of the International Group for the Psychology of Mathematics Education (PME 22) (Vol. 2). Stellenbosch, South Africa.

  Google Scholar 

• Australian Academy of Science. (2006). Mathematics and Statistics: Critical Skills for Australia's Future. National Strategic Review of Mathematical Sciences Research. Canberra, ACT, Australia: Author.

  Google Scholar 

• Balacheff, N. (1994). Artificial intelligence and real teaching. In C. Keitel & K. Ruthven (Eds.), Learning Through Computers: Mathematics and Educational Technology (pp. 131–158). Berlin: Springer.

  Google Scholar 

• Balacheff, N., & Sutherland, R. (1994) Epistemological domain of validity of microworlds. The case of Logo and Cabri-géomètre. Paper to IFIP, the Netherlands.

  Google Scholar 

• Ball, D. L. (2002). Mathematical proficiency for all students: toward a strategic research and development program in mathematics education. Santa Monica, CA: RAND Education/Science and Technology Policy Institute.

  Google Scholar 

• Baroody, A. J., Feil, Y., & Johnson, A. R. (2007). Research commentary: an alternative reconceptualization of procedural and conceptual knowledge. Journal for Research in Mathematics Education, 38(2), 115–131.

  Google Scholar 

• Biddlecomb, B. D. (1994). Theory-based development of computer microworlds. Journal of Research in Childhood Education, 8, 87–98.

  Article  Google Scholar 

• Bienkowski, M., Hurst, K., Knudsen, J., Kreikemeier, P., Patton, C., Rafanan, K., & Roschelle, J. (2005). Tools for Learning: What We Know About Technology for K-12 Math and Science Education. Menlo Park, CA: SRI International.

  Google Scholar 

• Boaler, J. (1997). Experiencing School Mathematics: Teaching Styles, Sex and Setting. Buckingham, England: Open University Press.

  Google Scholar 

• Boon, P. (2006). Designing didactical tools and microworlds for mathematics educations. In C. Hoyles, J.-b. Lagrange, L. H. Son, & N. Sinclair (Eds.), Proceedings of the Seventeenth Study Conference of the International Commission on Mathematical Instruction. Hanoi Institute of Technology and Didirem Université Paris 7.

  Google Scholar 

• Borba, M. C., & Villarreal, M. E. (2006). Humans-with-Media and the Reorganization of Mathematical Thinking: Information and Communication Technologies, Modelling, Experimentation and Visualization. New York: Springer.

  Google Scholar 

• Buchberger, B. (1989). The white-box/black-box principle for using symbolic computation systems in math education. http://www.risc.uni-linz.ac.at/people/buchberg/white_box.html. Accessed 5 February 2008.

• Buteau, C., & Muller, E. (2006). Evolving technologies integrated into undergraduate mathematics education. In C. Hoyles, J.-b. Lagrange, L. H. Son, & N. Sinclair (Eds.), Proceedings of the Seventeenth Study Conference of the International Commission on Mathematical Instruction (pp. 74–81). Hanoi Institute of Technology and Didirem Université Paris 7.

  Google Scholar 

• Cabri 3D. (2005). [Computer Software, Version 1.1], Grenoble, France: Cabrilog.

  Google Scholar 

• Chiappini, G., & Bottino, R. M. (1999). Visualisation in teaching-learning mathematics:the role of the computer. http://www.siggraph.org/education/conferences/GVE99/papers/GVE99.G.Chiappini.pdf. Accessed December 2007.

• Chinnappan, M. (2001). Representation of knowledge of fraction in a computer environment by young children. In W. C. Yang, S. C. Chu, Z. Karian, & G. Fitz-Gerald (Eds.), Proceedings of the Sixth Asian Technology Conference in Mathematics (pp. 110–119). Blacksburg, VA: ACTM.

  Google Scholar 

• Chinnappan, M. (2006). Role of digital technologies in supporting mathematics teaching and learning: rethinking the terrain in terms of schemas as epistemological structures. In C. Hoyles, J.-b. Lagrange, L. H. Son, & N. Sinclair (Eds.), Proceedings of the Seventeenth Study Conference of the International Commission on Mathematical Instruction (pp. 98–104). Hanoi Institute of Technology and Didirem Université Paris 7.

  Google Scholar 

• Cuban, L. (2001). Oversold and Underused: Computers in the Classroom. Cambridge, MA: Harvard University Press.

  Google Scholar 

• Cuoco, A. A., & Goldenberg E. P. (1997). Dynamic geometry as a bridge from euclidean geometry to analysis. In J. R. King & D. Schattschneider (Eds.), Geometry Turned On!: Dynamic Software in Learning, Teaching, and Research (pp. 33–46). Washington, DC: The Mathematical Association of America.

  Google Scholar 

• Dana-Picard, T., & Kidron, I. (2006). A pedagogy-embedded computer algebra system as an instigator to learn more mathematics. In C. Hoyles, J.-b. Lagrange, L. H. Son, & N. Sinclair (Eds.), Proceedings of the Seventeenth Study Conference of the International Commission on Mathematical Instruction (pp. 128–143). Hanoi Institute of Technology and Didirem Université Paris 7.

  Google Scholar 

• de Villiers, M. (1997). The role of proof in investigative, computer-based geometry: some personal reflections. In J. R. King & D. Schattschneider (Eds.), Geometry Turned On!: Dynamic Software in Learning, Teaching, and Research (pp. 15–24). Washington, DC: The Mathematical Association of America.

  Google Scholar 

• de Villiers, M. (1998). An alternative approach to proof in dynamic geometry? In R. Lehrer & D. Chazan (Eds.), Designing Learning Environments for Developing Understanding of Geometry and Space (pp. 369–394). Mahwah, NJ: Lawrence Erlbaum.

  Google Scholar 

• de Villiers, M. (1999). Rethinking Proof with the Geometer's Sketchpad. Emeryville, CA: Key Curriculum Press.

  Google Scholar 

• de Villiers, M. (2006). Rethinking Proof with the Geometer's Sketchpad, 2nd edition. Emeryville, CA: Key Curriculum Press.

  Google Scholar 

• Dick, T., & Shaughnessy, M. (1988). The influence of symbolic/graphic calculators on the perceptions of students and teachers toward mathematics. In M. Behr, C. Lacampagne, & M. Wheeler (Eds.), Proceedings of the Tenth Annual Meeting of PME-NA (pp. 327–333). DeKalb, IL: Northern Illinois University.

  Google Scholar 

• Drijvers, P., & Doorman, M. (1996). The graphics calculator in mathematics education. Journal of Mathematical behavior, 15(4), 425–440.

  Article  Google Scholar 

• Duke, R., & Pollard, J. (2004). Case studies in integrating the interactive whiteboard into secondary school mathematics classroom. In W.-C. Yang, S.-C. Chu, T. de Alwis, & K.-C. Ang (Eds.), Proceedings of the 9th Asian Technology Conference in Mathematics (pp. 169–177). NIE, Singapore: ATCM Inc.

  Google Scholar 

• Farrell, A. M. (1990). Teaching and learning behaviours in technology-oriented precalculus classrooms. Doctoral Dissertation, Ohio State University. Dissertation Abstracts International, 51, 100A.

  Google Scholar 

• Fernandes, E., Fermé, E., & Oliveira, R. (2006). Using robots to learn functions in math class. In C. Hoyles, J.-b. Lagrange, L. H. Son, & N. Sinclair (Eds.), Proceedings of the Seventeenth Study Conference of the International Commission on Mathematical Instruction. Hanoi Institute of Technology and Didirem Université Paris 7.

  Google Scholar 

• Fey, J. T., & Good, R. A. (1985). Rethinking the sequence and priorities of high school mathematics curricula. In C. R. Hirsch & M. J. Zweng (Eds.), The Secondary School Mathematics Curriculum (Yearbook of the National Council of Teachers of Mathematics) (pp. 43–52). Reston, VA: NCTM.

  Google Scholar 

• Fey, J., & Heid, K. (1995). Concepts in Algebra: A Technological Approach. Dedham, MA: Janson.

  Google Scholar 

• Finzer, W. (2007). Fathom ^TM Dynamic Data^TM Software (Version 2). Emeryville, CA: Key Curriculum Press.

  Google Scholar 

• Finzer, W., Erickson, T., Swenson, K., & Litwin, M. (2007). On getting more and better data into the classroom. Technology Innovations in Statistics Education, 1(1), Article 3, 1–10. http://repositories.cdlib.org/uclastat/cts/tise/vol1/iss1/art3.

• Fuys, D., Geddes, D., & Tischler, R. (1988). The van Hiele model of thinking in geometry among adolescents. Journal for Research in Mathematics Education Monograph, No. 3.

  Google Scholar 

• Gage, J. (2002). Using the graphics calculator to perform a learning environment for the early teaching of algebra. The International Journal of Computer Algebra in Mathematics Education, 9(1), 3.

  Google Scholar 

• Galbraith, P., Goos, M., Renshaw, P., & Geiger, V. (2001). Integrating technology in mathematics learning: what some students say. In J. Bobis, B. Perry, & M. Michael Mitchelmore (Eds.), Numeracy and Beyond. Proceedings of the 24th Annual Conference of the Mathematics Education Research Group of Australasia (pp. 223–230). Sydney: MERGA.

  Google Scholar 

• Gawlick, T. (2001). Zur mathematischen Modellierung des dynamischen Zeichenblattes. In H.-J. Elschenbroich, T. Gawlick, & H.-W. Henn (Eds.), Zeichnung - Figur - Zugfigur (pp. 55–68). Hildesheim: Franzbecker.

  Google Scholar 

• Geiger, V. (2006). More than tools: mathematically enabled technologies as partner and collaborator. In C. Hoyles, J.-b. Lagrange, L. H. Son, & N. Sinclair (Eds.), Proceedings of the Seventeenth Study Conference of the International Commission on Mathematical Instruction. Hanoi Institute of Technology and Didirem Université Paris 7.

  Google Scholar 

• Goldenberg, E. P., & Cuoco, A. A. (1998). What is dynamic geometry? In R. Lehrer & D. Chazan (Eds.), Designing Learning Environments for Developing Understanding of Geometry and Space (pp. 351–368). Mahwah, NJ: Lawrence Erlbaum.

  Google Scholar 

• Goldenberg, E. P., Cuoco, A. A., & Mark, J. (1998). A role for geometry in general education. In R. Lehrer & D. Chazan (Eds.), Designing Learning Environments for Developing Understanding of Geometry and Space (pp. 3–44). Mahwah, NJ: Lawrence Erlbaum.

  Google Scholar 

• Gray, E., & Tall, D. (1994). Duality, ambiguity, and flexibility: a “Proceptual” view of simple arithmetic. Journal for Research in Mathematics Education, 25(2), 116–140.

  Article  Google Scholar 

• Hackenburg, A. (2007). Units coordination and the construction of improper fractions: a revision of the splitting hypothesis. Journal of Mathematical behavior, 26, 27–47.

  Article  Google Scholar 

• Hadas, N., Hershkowitz, R., & Schwarz, B. B. (2000). The role of contradiction and uncertainty in promoting the need to prove in Dynamic geometry environments. Educational Studies in Mathematics, 44(1–3), 127–150.

  Article  Google Scholar 

• Hancock, C., & Osterweil, S. (2007). InspireData (Computer Software). Beaverton, OR: Inspiration Software.

  Google Scholar 

• Hatano, G. (2003). Foreword. In A. J. Baroody & A. Dowker (Eds.), The Development of Arithmetic Concepts and Skills: Constructing Adaptive Expertise (pp. xi–xiii). Mahwah, NJ: Lawrence Erlbaum.

  Google Scholar 

• Healy, L. (2006). A developing agenda for research into digital technologies and mathematics education: a view from Brazil. In C. Hoyles, J.-b. Lagrange, L. H. Son, & N. Sinclair (Eds.), Proceedings of the Seventeenth Study Conference of the International Commission on Mathematical Instruction. Hanoi Institute of Technology and Didirem Université Paris 7.

  Google Scholar 

• Heid, K. (2005). Technology in mathematics education: tapping into visions of the future. In W. J. Masalski & P. C. Elliot (Eds.), Technology-Supported Mathematics Learning Environments: NCTM 67th Yearbook. Reston, VA: NCTM.

  Google Scholar 

• Hiebert, J., & Lefevre, P. (1986). Conceptual and procedural knowledge in mathematics: an introductory analysis. In J. Hiebert (Ed.), Conceptual and Procedural Knowledge: The Case of Mathematics (pp. 199–223). Hillsdale, NJ: Lawrence Erlbaum.

  Google Scholar 

• Hitt, F. (Ed.) (2002). Representations and mathematics visualization (presented in the working group of the same name at PME-NA, 1998–2002). CINVESTAV-IPN, Mexico City.

  Google Scholar 

• Hollebrands, K. (2007). The role of a dynamic software program for geometry in the strategies high school mathematics students employ. Journal for Research in Mathematics Education, 38(2), 164–192.

  Google Scholar 

• Hollebrands, K., Laborde, C., & Sträßer, R. (2007). The learning of geometry with technology at the secondary level. In M. K. Heid & G. Blume (Eds.), Handbook of Research on Technology in the Learning and Teaching of Mathematics: Syntheses and Perspectives. Greenwich, CT: Information Age Publishing.

  Google Scholar 

• Howson, A. G., & Kahane, J.-P. (Eds.) (1986). The Influence of Computer and Informatics on Mathematics and its Teaching (ICMI Study Series #1). New York: Cambridge University Press.

  Google Scholar 

• Hoyles, C., & Healy, L. (1999). Linking informal argumentation with formal proof through computer-integrated teaching experiments. In O. Zaslavsky (Ed.), Proceedings of the 23rd Conference of the International Group for the Psychology of Mathematics Education (pp. 105–112). Haifa, Israel.

  Google Scholar 

• Hoyos, V. (2006). Functionalities of technological tools in the learning of basic geometrical notions and properties. In C. Hoyles, J.-b. Lagrange, L. H. Son, & N. Sinclair (Eds.), Proceedings of the Seventeenth Study Conference of the International Commission on Mathematical Instruction. Hanoi Institute of Technology and Didirem Université Paris 7.

  Google Scholar 

• Hoyos, V., & Capponi, B. (2000). Increasing the comprehension of function notion from variability and dependence experienced within Cabri-II. Proceedings of Workshop 6: Learning Algebra with the Computer, a Transdiciplinary Workshop-ITS2000. Montreal (Canada): UQAM.

  Google Scholar 

• Hunscheidt, D., & Koop, A. P. (2006). Tools rather than toys: fostering mathematical understanding through ICT in primary mathematics classrooms. In C. Hoyles, J.-b. Lagrange, L. H. Son, & N. Sinclair (Eds.), Proceedings of the Seventeenth Study Conference of the International Commission on Mathematical Instruction. Hanoi Institute of Technology and Didirem Université Paris 7.

  Google Scholar 

• Jackiw, N. (2001). The Geometer's Sketchpad [Computer Software, Version 4.0]. Berkeley, CA: Key Curriculum Press.

  Google Scholar 

• Kahn, K., Noss, R., & Hoyles, C. (2006). Designing for diversity through web-based layered learning: a prototype space travel games construction kit. In C. Hoyles, J.-b. Lagrange, L. H. Son, & N. Sinclair (Eds.), Proceedings of the Seventeenth Study Conference of the International Commission on Mathematical Instruction. Hanoi Institute of Technology and Didirem Université Paris 7.

  Google Scholar 

• Kaput, J. J. (1987). Representation systems and mathematics. In C. Janvier (Ed.), Problems of Representation in the Teaching and Learning of Mathematics (pp. 19–26). Hillsdale: Lawrence Erlbaum.

  Google Scholar 

• Kaput, J. J. (1992). Technology and mathematics education. In D. A. Grouws (Ed.), Handbook of Research on Mathematics Teaching and Learning (pp. 515–556). New York: Macmillan.

  Google Scholar 

• Kaput, J. J. (1996). Overcoming physicality and the eternal present: cybernetic manipulatives. In R. Sutherland & J. Mason (Eds.), Technology and Visualization in Mathematics Education (pp. 161–177). London: Springer.

  Google Scholar 

• Kaput, J. J. (1998). Commentary: representations, inscriptions, descriptions and learning - a kaleidoscope of windows, Journal of Mathematical behavior, 17, 265–281.

  Article  Google Scholar 

• Keyton, M. (1997). Students discovering geometry using dynamic geometry software. In J. King & D. Schattschneider (Eds.), Geometry Turned on! Dynamic Software in Learning, Teaching, and Research (pp. 63–68). Washington, DC: The Mathematical Association of America.

  Google Scholar 

• Kieran, C., & Drijvers, P. (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 Seventeenth Study Conference of the International Commission on Mathematical Instruction (pp. 278–287). Hanoi Institute of Technology and Didirem Université Paris 7.

  Google Scholar 

• King, J., & Schattschneider, D. (Eds.) (1997). Geometry Turned on! Dynamic Software in Learning, Teaching, and Research. Washington, DC: The Mathematical Association of America.

  Google Scholar 

• Konold, C., & Miller, C. (2005). Tinkerplots: Dynamic Data Exploration [Computer software]. Emeryville, CA: Key Curriculum Press.

  Google Scholar 

• Konold, C., Robinson, A., Khalil, K., Pollatsek, A., Well, A., Wing, R., & Mayr, S. (2002). Students' use of modal clumps to summarize data. Paper presented at the Sixth International Conference on Teaching Statistics: Developing a Statistically Literate Society. Cape Town, South Africa.

  Google Scholar 

• Kor, L. K. (2004). Students' attitudes and reflections on the effect of graphing technology in the learning of statistics. In W.-C. Yang, S.-C. Chu, T. de Alwis, & K.-C. Ang (Eds.), Proceedings of the 9th Asian Technology Conference in Mathematics (pp. 317–326). NIE, Singapore: ATCM Inc.

  Google Scholar 

• Kor, L. K. (2005).Impact of the Use of Graphics Calculator on the Learning of Statistics. Unpublished PhD Thesis.

  Google Scholar 

• Kor, L. K., & Lim, C. S. (2004). Learning statistics with graphics calculators: students' viewpoints. In Y. A. Hassan, A. Baharum, A. I. M. Ismail, H. C. Koh, & H. C. Chin (Eds.), Integrating Technology in the Mathematical Sciences (pp. 69–78). USM, Pulau Pinang: Universiti Sains Malaysia.

  Google Scholar 

• Kor, L. K., & Lim, C. S. (2006). The impact of the use of graphics calculator on the learning of statistics: a Malaysian experience. In C. Hoyles, J.-b. Lagrange, L. H. Son, & N. Sinclair (Eds.), Proceedings of the Seventeenth Study Conference of the International Commission on Mathematical Instruction. Hanoi Institute of Technology and Didirem Université Paris 7.

  Google Scholar 

• Kosheleva, O., & Giron, H. (2006). Technology in K-14: what is the best way to teach digital natives? Proceedings of the 2006 International Sun Conference on Teaching and Learning. El Paso, TX. http://sunconference.utep.edu/SunHome/2006/proceedings2006.html Accessed December 2007.

• Kosheleva, O., Rusch, A., & Ioudina, V. (2006). Analysis of effects of tablet PC technology in mathematical education of future teachers. In C. Hoyles, J.-b. Lagrange, L. H. Son, & N. Sinclair (Eds.), Proceedings of the Seventeenth Study Conference of the International Commission on Mathematical Instruction. Hanoi Institute of Technology and Didirem Université Paris 7.

  Google Scholar 

• Laborde, C. (1992). Solving problems in computer based geometry environments: the influence of the features of the software. Zentrablatt für Didactik des Mathematik, 92(4), 128–135.

  Google Scholar 

• Laborde, C. (1993). The computer as part of the learning environment: the case of geometry. In C. Keitel & K. Ruthven (Eds.), Learning from Computers: Mathematics Education and Technology (pp. 48–67). Berlin: Springer.

  Google Scholar 

• Laborde, C. (1995). Designing tasks for learning geometry in a computer-based environment. In L. Burton & B. Jaworski (Eds.), Technology in Mathematics Learning - A Bridge Between Teaching and Learning (pp. 35–68). London: Chartwell-Bratt.

  Google Scholar 

• Laborde, C. (1998). Factors of Integration of Dynamic Geometry Software in the Teaching of Mathematics. Paper presented at theENC Technology and NCTM Standards 2000 Conference . Arlington, VA, June 5–6.

  Google Scholar 

• Laborde, C. (2001). Integration of technology in the design of geometry tasks with Cabri-geometry. International Journal of Computers for Mathematical Learning, 6, 283–317.

  Article  Google Scholar 

• Laborde, C., Kynigos, C., Hollebrands, K., & Sträßer, R. (2006). Teaching and learning geometry with technology. In A. Gutierrez & P. Boero (Eds.), Handbook of Research on the Psychology of Mathematics Education: Past, Present and Future (pp. 275–304). Rotterdam: Sense Publishers.

  Google Scholar 

• Lakatos, I. (1976). Proofs and Refutations. Cambridge: Cambridge University Press.

  Google Scholar 

• Lakatos, I. (1978). What does a mathematical proof prove? Mathematics, Science and Epistemology. Cambridge, UK: Cambridge University Press.

  Chapter  Google Scholar 

• Lehrer, R., Jenkins, M., & Osana, H. (1998). Longitudinal study of children's reasoning about space and geometry. In R. Lehrer & D. Chazan (Eds.), Designing Learning Environments for Developing Understanding of Geometry and Space (pp. 137–168). Mahwah, NJ: Lawrence Erlbaum.

  Google Scholar 

• Leung, A., Chan, Y., & Lopez-Real, F. (2006). Instrumental genesis in dynamic geometry environments. In C. Hoyles, J.-b. Lagrange, L. H. Son, & N. Sinclair (Eds.), Proceedings of the Seventeenth Study Conference of the International Commission on Mathematical Instruction (pp. 346–353). Hanoi Institute of Technology and Didirem Université Paris 7.

  Google Scholar 

• Lobato, J., & Siebert, D. (2002). Quantitative reasoning in a reconceived view of transfer. The Journal of Mathematical behavior, 21, 87–116.

  Article  Google Scholar 

• Lubienski, S. T. (2000). Problem solving as a means toward mathematics for all: an exploratory look through a class lens. Journal for Research in Mathematics Education, 31(4), 454–482.

  Article  Google Scholar 

• Lyublinskaya, I. (2004). Connecting Mathematics with Science: Experiments for Precalculus. Emeryville, CA: Key Curriculum Press.

  Google Scholar 

• Lyublinskaya, I. (2006). Making connections: science experiments for algebra using TI technology. Eurasia Journal of Mathematics, Science and Technology Education, 2(3), 144–157.

  Google Scholar 

• MacFarlane, A., & Kirriemuir, J. (2005). Computer and Video Games in Curriculum-Based Education. Report of DfES. England: NESTA Futurelab.

  Google Scholar 

• Mackrell, K. (2006). Cabri 3D: potential, problems and a web-based approach to instrumental genesis. In C. Hoyles, J.-b. Lagrange, L. H. Son, & N. Sinclair (Eds.), Proceedings of the Seventeenth Study Conference of the International Commission on Mathematical Instruction. Hanoi Institute of Technology and Didirem Université Paris 7.

  Google Scholar 

• Makar, K., & Confrey, J. (2004). Secondary teachers' reasoning about comparing two groups. In D. Ben-Zvi & J. Garfield (Eds.), The Challenges of Developing Statistical Literacy, Reasoning, and Thinking (pp. 353–373). Dordrecht: Kluwer.

  Google Scholar 

• Makar, K., & Confrey, J. (2005). “Variation-talk”: articulating meaning in statistics. Statistics Education Research Journal, 4(1), 27–54.

  Google Scholar 

• Makar, K., & Confrey, J. (2006). Dynamic statistical software: how are learners using it to conduct data-based investigations? In C. Hoyles, J.-b. Lagrange, L. H. Son, & N. Sinclair (Eds.), Proceedings of the Seventeenth Study Conference of the International Commission on Mathematical Instruction. Hanoi Institute of Technology and Didirem Université Paris 7.

  Google Scholar 

• Makar, K., & Confrey, J. (2007). Moving the context of modeling to the forefront: preservice teachers' investigations of equity in testing. In W. Blum, P. Galbraith, H.-W. Henn, & M. Niss (Eds.), Modelling and Applications in Mathematics Education: The 14th ICMI Study (pp. 485–490). New York: Springer.

  Chapter  Google Scholar 

• Mariotti, M.-A. (2006). New artefacts and the mediation of mathematical meanings. In C. Hoyles, J.-b. Lagrange, L. H. Son, & N. Sinclair (Eds.), Proceedings of the Seventeenth Study Conference of the International Commission on Mathematical Instruction (pp. 378–385). Hanoi Institute of Technology and Didirem Université Paris 7.

  Google Scholar 

• Marrades, R., & Gutiérrez, A. (2000). Proofs produced by secondary school students learning geometry in a dynamic computer environment. Educational Studies in Mathematics, 44(1–3), 87–125.

  Article  Google Scholar 

• MASCOS. (2004). Centre of excellence for mathematics and statistics of complex systems. http://www.complex.org.au.

• Meletiou-Mavrotheris, M., Lee, C., & Fouladi, R. (2007). Introductory statistics, college student attitudes and knowledge: a qualitative analysis of the impact of technology-based instruction. International Journal of Mathematical Education in Science and Technology, 38(1), 65–83.

  Article  Google Scholar 

• Nabors, W. K. (2003). From fractions to proportional reasoning: a cognitive schemes of operation approach The Journal of Mathematical behavior, 22(2), 133–179.

  Article  Google Scholar 

• Norton, A. (2005). The power of operational conjectures. Paper presented at the annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education. Virginia Tech University, Roanoke, VA.

  Google Scholar 

• Noss, R., & Hoyles, C. (1996). Windows on Mathematical Meanings: Learning Cultures and Computers. Dordrecht, the Netherlands: Kluwer.

  Google Scholar 

• Olive, J. (1999). From fractions to rational numbers of arithmetic: a reorganization hypothesis. Mathematical Thinking and Learning, 1(4), 279–314.

  Article  Google Scholar 

• Olive, J. (2000a). Implications of using dynamic geometry technology for teaching and learning. Plenary paper for the Conference on Teaching and Learning Problems in Geometry . Fundão, Portugal, May 6–9.

  Google Scholar 

• Olive, J. (2000b). Computer tools for interactive mathematical activity in the elementary school. The International Journal of Computers for Mathematical Learning, 5, 241–262.

  Article  Google Scholar 

• Olive, J. (2002). Bridging the gap: interactive computer tools to build fractional schemes from children's whole-number knowledge. Teaching Children Mathematics, 8(6), 356–361.

  Google Scholar 

• Olive, J., & Biddlecomb, B. (2001). JavaBars [Computer program]. Available from the authors (January, 2008): http://math.coe.uga.edu/olive/welcome.html.

• Olive, J., & Çağlayan, G. (2008). Learners' difficulties with quantitative units in algebraic word problems and the teacher's interpretation of those difficulties. International Journal of Science and Mathematics Education, 6, 269–292.

  Article  Google Scholar 

• Olive, J., & Lobato, J. (2007). The learning of rational number concepts using technology. In K. Heid & G. Blume (Eds.), Research on Technology in the Learning and Teaching of Mathematics, Greenwich, CT: Information Age Publishing.

  Google Scholar 

• Olive, J., & Steffe, L. P. (1994). TIMA: Bars [Computer software]. Acton, MA: William K. Bradford Publishing Company.

  Google Scholar 

• Olive, J., & Steffe, L. P. (2002). The construction of an iterative fractional scheme: the case of Joe. Journal of Mathematical behavior, 20, 413–437.

  Article  Google Scholar 

• Olive, J., & Vomvoridi, E. (2006). Making sense of instruction on fractions when a student lacks necessary fractional schemes: the case of Tim. Journal of Mathematical behavior, 25, 18–45.

  Article  Google Scholar 

• Olivero, F. (2006). Students' constructions of dynamic geometry. In C. Hoyles, J.-b. Lagrange, L. H. Son, & N. Sinclair (Eds.), Proceedings of the Seventeenth Study Conference of the International Commission on Mathematical Instruction. Hanoi Institute of Technology and Didirem Université Paris 7.

  Google Scholar 

• Pacey, A. (1985). The Culture of Technology. Cambridge, MA: The MIT Press.

  Google Scholar 

• Papert, S. (1970). Teaching Children Thinking (AI Memo No. 247 and Logo Memo No. 2), Cambridge: MIT Artificial Intelligence Laboratory.

  Google Scholar 

• Papert, S. (1972). Teaching children to be mathematicians versus teaching about mathematics. International Journal for Mathematical Education, Science, and Technology, 3, 249–262.

  Article  Google Scholar 

• Papert, S. (1980). Mindstorm: Children, Computers and Powerful Ideas. Sussex, England: Harvester.

  Google Scholar 

• Pfannkuch, M., Budgett, S., & Parsonage, R. (2004). Comparison of data plots: building a pedagogical framework. Paper presented at the Tenth Meeting of the International Congress on Mathematics Education. Copenhagen, Denmark.

  Google Scholar 

• Piaget, J. (1970). Genetic Epistemology. Trans. by E. Duckworth. New York: Norton.

  Google Scholar 

• Piaget, J., & Szeminska, A. (1965). The Child's Conception of Number. New York: Norton.

  Google Scholar 

• Polya, G. (1945). Cómo plantear y resolver problemas. Mexico City: Trillas.

  Google Scholar 

• Presmeg, N. (2006). Research on visualization in learning and teaching mathematics. In A. Gutiérrez & P. Boero. (Eds.), Handbook of Research on the Psychology of Mathematics Education: Past, Present, and Future (pp. 205–235). Rotterdam: Sense Publishers.

  Google Scholar 

• Rabardel, R. (2002). People and technology: a cognitive approach to contemporary instruments. Trans. by H. Wood. http://ergoserv.psy.univ-paris8.fr/. Accessed December 2007.

• Raggi, V. (2006). Domino [Electronic board game]. http://descartes.ajusco.upn.mx/html/simetria/simetria.html . Accessed March 2007.

• Rodriguez, G. (2007). Funcionalidad de juegos de estrategia virtuales y del software Cabri-II en el aprendizaje de la simetría. Tesis de Maestría en Desarrollo Educativo. Mexico: Universidad Pedagogica Nacional.

  Google Scholar 

• Roschelle, J., Tatar, D., Schechtman, N., Hegedus, S., Hopkins, W., Knudson, J., & Stroter, A. (2007). Scaling Up SimCalc Project: Can a Technology Enhanced Curriculum Improve Student Learning of Important Mathematics? Menlo Park, CA: SRI International.

  Google Scholar 

• Rosihan, M. Ali, & Kor, L. K. (2004). Undergraduate mathematics enhanced with graphing technology. Journal of the Korea Society of Mathematical Education Series D: Research in Mathematical Education, 8(1), 39–58.

  Google Scholar 

• Rubin, A. (2007). Much has changed; little has changed: revisiting the role of technology in statistics education 1992–2007. Technology Innovations in Statistics Education 1(1), Article 6, 1–33. http://repositories.cdlib.org/uclastat/cts/tise/vol1/iss1/art6. Accessed December 2007.

• Ruthven, K., Hennessy, S., & Deaney, R. (2005). Teacher constructions of dynamic geometry in English secondary mathematics education. Paper presented at the CAL 05 conference . University of Bristol, Bristol, UK.

  Google Scholar 

• Sanford, R. (2006). Teaching with games. Computer Education, the Naace Journal. Issue 112 [Spring]. Nottingham, England: Naace.

  Google Scholar 

• Santos-Trigo, M. (2001). Transforming students' fragmented knowledge into mathematical resources to solve problems through the use of dynamic software. Proceedings of the Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (Vol. 1, pp. 511–517). Snowbird, Utah, October 18–21, 2001..

  Google Scholar 

• Saxe, G., & Bermudez, T. (1996). Emergent mathematical environments in children's games. In L. P. Steffe, P. Nesher, P. Cobb, G. A. Goldin, & B. Greer (Eds.), Theories of Mathematical Learning. Mahwah, NJ: Lawrence Erlbaum.

  Google Scholar 

• Schoenfeld, A. H. (1988). When good teaching leads to bad results: the disasters of well taught mathematics classes. Educational Psychologist, 23(2), 145–166.

  Article  Google Scholar 

• Shaffer, D. W. (2006). Epistemic frames for epistemic games. Computers and Education, 46, 223–234.

  Article  Google Scholar 

• Sinclair, M. P. (2003). Some implications of the results of a case study for the design of pre-constructed, dynamic geometry sketches and accompanying materials. Educational Studies in Mathematics, 52(3), 289–317.

  Article  Google Scholar 

• Sorto, M. A. (2006). Identifying content knowledge for teaching statistics. Paper presented at the Seventh International Conference on Teaching Statistics. Salvador, Brazil.

  Google Scholar 

• Star, J. R. (2005). Reconceptualizing procedural knowledge. Journal for Research in Mathematics Education, 36, 404–411.

  Google Scholar 

• Star, J. R. (2007). Foregrounding procedural knowledge. Journal for Research in Mathematics Education, 38, 132–135.

  Google Scholar 

• Steffe, L. P. (1992). Schemes of action and operation involving composite units. Learning and Individual Differences, 4, 259–309.

  Article  Google Scholar 

• Steffe, L. P. (2002). A new hypothesis concerning children's fractional knowledge. Journal of Mathematical behavior, 102, 1–41.

  Google Scholar 

• Steffe, L. P. (2004). On the construction of learning trajectories of children: the case of commensurate fractions. Mathematical Thinking and Learning, 6, 129–162.

  Article  Google Scholar 

• Steffe, L. P., & Olive, J. (1990). Children's Construction of the Rational Numbers of Arithmetic. Athens, GA: The University of Georgia.

  Google Scholar 

• Steffe, L. P., & Olive, J. (1996). Symbolizing as a constructive activity in a computer microworld. Journal of Educational Computing Research, 14(2), 113–138.

  Article  Google Scholar 

• Steffe, L. P., & Olive, J. (2002). A constructivist approach to the design and use of software for early mathematics learning. Journal of Educational Computing Research, 20, 55–76.

  Article  Google Scholar 

• Steinbring, H. (2005). The Construction of New Mathematical Knowledge in Classroom Interaction: An Epistemological Perspective. New York: Springer.

  Google Scholar 

• Sträßer, R. (1992). Didaktische Perspektiven auf Werkzeug-Software im Geometrie-Untericht der Sekundarstufe I. Zentralblatt für Didaktik der Mathematik, 24, 197–201.

  Google Scholar 

• Sträßer, R. (2001a). Chancen und Probleme des Zugmodus. In H.-J. Elschenbroich, T. Gawlick, & H.-W. Henn (Eds.), Zeichnung - Figur - Zugfigur (pp. 183–194). Hildesheim-Berlin: Franzbecker.

  Google Scholar 

• Sträßer, R. (2001b). Cabri-géomètre: does a dynamic geometry software (DGS) change geometry and its teaching and learning? International Journal for Computers in Mathematics Learning, 6(3), 319–333.

  Article  Google Scholar 

• Sträßer, R. (2002). Research on dynamic geometry software (DGS) - an introduction. Zentralblatt für Didaktik der Mathematik, 34(3), 65.

  Article  Google Scholar 

• Tall, D. (1989). Concepts images, generic organizers, computers and curriculum change. For the Learning of Mathematics. 9(3), 37–42.

  Google Scholar 

• Tall, D., Gray, E., Ali, M. B., Crowley, L., DeMarois, P., McGowen, M., Pitta, D., Pinto, M., Thomas, M., & Yusof, Y. (2001). Symbols and the bifurcation between procedural and conceptual thinking. Canadian Journal of Science, Mathematics and Technology Education, 1(1), 81–104.

  Article  Google Scholar 

• Thompson, P. W. (1995). Notation, convention, and quantity in elementary mathematics. In J. Sowder & B. Schapelle (Eds.), Providing a Foundation for Teaching Middle School Mathematics (pp. 199–221). Albany, NY: SUNY Press.

  Google Scholar 

• Tyack, D. B., & Cuban, L. (1995). Tinkering Toward Utopia: A Century of Public School Reform. Cambridge, MA: Harvard University Press.

  Google Scholar 

• Tzur, R. (1999). An integrated study of children's construction of improper fractions and the teacher's role in promoting the learning. Journal for Research in Mathematics Education, 30, 390–416.

  Article  Google Scholar 

• Utah State University. (2007). National library of virtual manipulatives. http://nlvm.usu.edu/. Accessed December 2007.

• Van Hiele, P. M. (1986). Structure and Insight: A Theory of Mathematics Education. Orlando, FL: Academic.

  Google Scholar 

• Von Glasersfeld, E. (1995). Sensory experience, abstraction, and teaching. In L. P. Steffe & J. Gale (Eds.), Constructivism in Education (pp. 369–383). Hillsdale, NJ: Lawrence Erlbaum.

  Chapter  Google Scholar 

• Vygotsky, L. S. (1978). Mind in Society: The Development of Higher Psychological Processes. Cambridge, MA: Harvard University Press.

  Google Scholar 

• Wijekumar, K., Meyer, B., Wagoner, D., & Ferguson, L. (2005). Technology affordances: the ‘real story’ in research with K-12 and undergraduate learners. British Journal of Educational Technology, 37(2). Oxford: Blackwell.

  Google Scholar 

• Zbiek, R. M., & Glass, B. (2001). Conjecturing and formal reasoning about functions in a dynamic environment. In G. Goodell (Ed.), Proceedings of The Twelfth Annual International Conference on Technology in Collegiate Mathematics (pp. 424–428). Reading, MA: Addison-Wesley.

  Google Scholar 

• Zbiek, R. M., & Hollebrands, K. (2007). Chapter 7: A research-informed view of the process of incorporating mathematics technology into classroom practice by inservice and prospective teachers. In K. Heid & G. Blume (Eds.), Research on Technology in the Learning and Teaching of Mathematics. Greenwich, CT: Information Age Publishing.

  Google Scholar 

• Zbiek, R., Heid, H., Blume, G., & Dick, T. (2007). Chapter 27: Research on technology in mathematics education: a perspective of constructs. In F. K. Lester (Ed.), The Second Handbook of Research in Mathematics Education (pp. 1169–1207). Charlotte, NC: Information Age Publishing and NCTM.

  Google Scholar 

Download references