Encrypted objects and decryption processes: Problem-solving with functions in a learning environment based on cryptography

Educational Studies in Mathematics

Volumn 72, Issue 1, 2009, Pages 17-37

  White, Tobin ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

Context; Functions; Multiple representations; Problem solving; Technology

Indexed keywords

EID: 70349923637     PISSN: 00131954     EISSN: 15730816     Source Type: Journal    
DOI: 10.1007/s10649-008-9180-y     Document Type: Article

References (24)

1. Abrahamson, D. (2009) Embodied design: constructing means for constructing meaning. Educational Studies in Mathematics, in press.
2. Boaler, J. (1993). Encouraging the transfer of 'school' mathematics to the 'real world' through the integration of process and content, context and culture. Educational Studies in Mathematics, 25, 341-373. doi:10.1007/BF01273906.
3. Brown, A. (1992). Design experiments: theoretical and methodological challenges in creating complex interventions in classroom settings. Journal of the Learning Sciences, 2(2), 141-178. doi:10.1207/s15327809jls0202_2.
4. Collins, A. (1992). Towards a design science of education. In E. Scanlon, & T. O'shea (Eds.), New directions in educational technology (pp. 15-22). Berlin: Springer.
5. Confrey, J., & Smith, E. (1994). Exponential functions, rates of change, and the multiplicative unit. Educational Studies in Mathematics, 26, 135-164. doi:10.1007/BF01273661.
6. 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. doi:10.2307/749505.
7. Gray, E., & Tall, D. (2001). Relationships between embodied objects and symbolic procepts: An explanatory theory of success and failure in mathematics. In M. van den Heuvel-Panhuizen (Ed.), Proceedings of the 25th Conference of the International Group for the Psychology of Mathematics Education, 3 (pp. 65-72). Utrecht, the Netherlands: PME.
8. Kaput, J. (1992). Patterns in students' formalization of quantitative patterns. In G. Harel, & E. Dubinsky (Eds.), The concept of function: Aspects of epistemology and pedagogy (pp. 290-317). Washington, DC: Mathematical Association of America.
9. Kieran, C. (1992). The learning and teaching of school algebra. In D. Grouws (Ed.), Handbook of Research on mathematics teaching and learning (pp. 390-419). New York, NY: Macmillan.
10. Kieran, C., & Yerushalmy, M. (2004). Research on the role of technological environments in algebra teaching and learning. In K. Stacey, H. Chick, & M. Kendal (Eds.), The future of the teaching and learning of algebra (pp. 99-152). Boston, MA: Kluwer.
11. Moschkovich, J., Schoenfeld, A., & Arcavi, A. (1993). Aspects of understanding: On multiple perspectives and representations of linear relations and connections among them. In T. Romberg, E. Fennema, & T. Carpenter (Eds.), Integrating Research on the Graphical Representation of Functions (pp. 69-100). Hillsdale, NJ: Lawrence Erlbaum Associates.
12. O'Callaghan, B. (1998). Computer-intensive algebra and students' conceptual knowledge of functions. Journal for Research in Mathematics Education, 29(1), 21-40. doi:10.2307/749716.
13. Roschelle, J., Pea, R., Hoadley, C., Gordin, D., & Means, B. (2000). Changing how and what children learn in school with computer-based technologies. The Future of Children: Children and Computer Technology, 10(2), 76-101. doi:10.2307/1602690.
14. Schwarz, B., & Dreyfus, T. (1995). New actions upon old objects: A new ontological perspective on functions. Educational Studies in Mathematics, 29, 259-291. doi:10.1007/BF01274094.
15. Schwartz, J., & Yerushalmy, M. (1992). Getting students to function in and with algebra. In G. Harel, & E. Dubinsky (Eds.), The concept of function: Aspects of epistemology and pedagogy (pp. 261-289). Washington, DC: Mathematical Association of America.
16. Sfard, A. (1991). On the dual nature of mathematical conceptions: Reflections on processes and objects as different sides of the same coin. Educational Studies in Mathematics, 22, 1-36. doi:10.1007/BF00302715.
17. Sfard, A. (1992). Operational origins of mathematical objects and the quandary of reification-The case of function. In G. Harel, & E. Dubinsky (Eds.), The concept of function: Aspects of epistemology and pedagogy (pp. 59-84). Washington, DC: Mathematical Association of America.
18. Singh, S. (1999). The code book: The science of secrecy from ancient Egypt to quantum cryptography. New York, NY: Anchor.
19. Slavit, D. (1997). An alternate route to the reification of function. Educational Studies in Mathematics, 33, 259-281. doi:10.1023/A:1002937032215.
20. Tall, D., Thomas, M., Davis, G., Gray, E., & Simpson, A. (2000). What is the object of the encapsulation of a process? The Journal of Mathematical Behavior, 18(2), 223-241. doi:10.1016/S0732-3123(99)00029-2.
21. Tall, D., & Vinner, S. (1981). Concept image and concept definition in mathematics with particular reference to limits and continuity. Educational Studies in Mathematics, 12(2), 151-169. doi:10.1007/BF00305619.
22. Thompson, P. (1994). Students, functions, and the undergraduate curriculum. In E. Dubinsky, A. Schoenfeld, & J. Kaput (Eds.), Research in collegiate mathematics education, 1 (Issues in Mathematics Education, Vol. 4) (pp. 21-44). Providence, RI: American Mathematical Society.
23. Thompson, P., & Sfard, A. (1994). Problems of reification: Representations and mathematical objects. In D. Kirshner (Ed.), Proceedings of the Annual Meeting of the International Group for the Psychology of Mathematics Education-North America, Plenary Sessions, 1 (pp. 1-32). Baton Rouge, LA: Louisiana State University.
24. White, T. (2008). Debugging an artifact, instrumenting a bug: Dialectics of instrumentation and design in technology-rich learning environments. International Journal of Computers for Mathematical Learning, 13(1), 1-26. doi:10.1007/s10758-007-9119-x.