Social interactions and instructional artifacts: Emergent socio-technical affordances and constraints for children's geometric thinking

Journal of Educational Computing Research

Volumn 44, Issue 2, 2011, Pages 141-171

  Evans, Michael ^a   Wilkins, Jesse ^a  

^a VIRGINIA POLYTECHNIC INSTITUTE AND STATE UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 79955157839     PISSN: 07356331     EISSN: None     Source Type: Journal    
DOI: 10.2190/EC.44.2.b     Document Type: Article

References (59)

1. Ares, N., Stroup, W., & Schademan, A. (2009). The power of mediating artifacts in group-level development of mathematical discourse. Cognition and Instruction, 27(1), 1-24.
2. Barab, S. A., & Roth, W.-M. (2006). Curriculum-based ecosystems: Supporting knowing from an ecological perspective. Educational Researcher, 35(5), 3-13.
3. Battista, M. T. (2007). The development of geometric and spatial thinking. In F. K. Lester, Jr. (Ed.), Second handbook of research on mathematics teaching and learning (pp. 843-908). Reston, VA: NCTM.
4. Burger, W. F., & Shaughnessy, J. M. (1986). Characterizing the van Hiele levels of development of geometry. Journal for Research in Mathematics Education, 17(1), 31-48.
5. Cannon, L. Dorward, J., Duffin, J., Heal, B., & Foletta, G. (2004). National Library of Virtual Manipulatives. Mathematics Teacher, 97(2), 158-159.
6. Clements, D. H., & Sarama, J. (2000). The earliest geometry. Teaching Children Mathematics, 7(2), 82-86.
7. Clements, D. H. (2004). Geometric and spatial thinking in early childhood education. In D. H. Clements, J. Sarama, & A. M. DiBiase (Eds.), Engaging young children in mathematics: Standards for early childhood mathematics education (pp. 267-297). Mahwah, NJ: Lawrence Erlbaum.
8. Clements, D. H., & Sarama, J. (2007). Effects of a preschool mathematics curriculum: Summative research on the Building Blocks Project. Journal for Research in Mathematics Education, 38(2), 136-163.
9. Clements, D. H., Sarama, J., & DiBiase, A.-M. (2004). Engaging young children in mathematics: Standards for early childhood mathematics education. Mahwah, NJ: Lawrence Erlbaum.
10. Cobb, P. (1995). Cultural tools and mathematical learning: A case study. Journal for Research in Mathematics Education, 26(4), 362-385.
11. Cobb, P., Wood, T., & Yackel, E. (1993). Discourse, mathematical thinking, and classroom practice. In N. M. E. Forman & C. A. Stone (Ed.), Contexts for learning: Sociocultural dynamics in children's development (pp. 91-119). New York: Oxford University Press.
12. Cobb, P., Stephan, M., McClain, K., & Gravemeijer, K. (2001). Participating in classroom mathematical practices. The Journal of the Learning Sciences, 10(1&2), 113-163. (Pubitemid 33625754)
13. Dillenbourg, P. (1992) The computer as a constructorium: Tools for observing one's own learning. In M. Elsom-Cook & R. Moyse (Eds), Knowledge negotiation (pp. 185-198). London: Academic Press.
14. Enyedy, N. (2003). Knowledge construction and collective practice: At the intersection of learning, talk, and social organizations in a computer-mediated mathematics classroom. The Journal of the Learning Sciences, 12(3), 361-407. (Pubitemid 36853159)
15. Fails, J. A., Druin, A., Guha, M. L., Chipman, G., Simms, S., & Churaman, W. (2005). Child's play: A comparison of desktop and physical interactive environments. In IDC '05: Proceedings of the 2005 conference on Interaction Design and Children (pp. 48-55). New York: ACM.
16. Feltovich, P. J., Spiro, R. J., Coulson, R. L., & Feltovich, J. (1996). Collaboration within and among minds: Mastering complexity, individually and in groups. In T. Koschmann (Ed.), CSCL: Theory and practice of an emerging paradigm. Mahwah, NJ: Lawrence Erlbaum Associates.
17. Hammersley, M., & Atkinson, P. (1983). Ethnography, principles in practice. London/New York: Tavistock.
18. Healy, L., Pozzi, S., & Hoyles, C. (1995). Making sense of groups, computers, and mathematics. Cognition and Instruction, 13(4), 505-523.
19. Hershkowitz, R., & Schwartz, B. B. (1999). Reflective processes in a mathematics classroom with a rich learning environment. Cognition and Instruction, 17(1), 65-91.
20. Hundhausen, C.D. (1998). Toward effective algorithm visualization artifacts: Designing for participation and negotiation in an undergraduate algorithms course. Proceedings of the International Conference on Computer-Human Interaction, USA, 54-55.
21. Kaptelinin, V., & Nardi, B. (2006). Acting with technology. Boston, MA: MIT Press.
22. Khandewal, M., & Mazalek, A. (2007). Teaching table: A tangible mentor for Pre-K math education. Proceedings of the First International Conference on Tangible and Embedded Interaction, USA, 1910194.
23. Kuntz, K. J., Mcaughlin, T. F., & Howard, V. F. (2001). A comparison of cooperative learning and small group individualized instruction for math in a self contained classroom for elementary students with disabilities. Educational Research Quarterly, 24(3), 41-54.
24. Lee, C.-Y., & Chen, M.-P. (2008). Taiwanese junior high school students' mathematics attitudes and perceptions towards virtual manipulatives. British Journal of Educational Technology, 39(5), 1-5.
25. Lesh, R., Post, T., & Behr, M. (1987). Representations and translations among representations in mathematics learning and problem solving. In C. Janvier (Ed.), Problems of representation in the teaching and learning of mathematics (pp. 33-40). Hillsdale, NJ: Erlbaum.
26. Lesh, R., & Harel, G. (2003). Problem solving, modeling, and local conceptual development. Mathematical Thinking and Learning: An International Journal, 5(2/3), 157-190.
27. Lincoln, Y. S., & Guba E. G. (1985). Naturalistic inquiry. Newbury Park, CA: Sage.
28. Martin, W. (1999). The social and cultural shaping of educational technology: Toward a social constructivist framework. AI & Society, 13, 402-420.
29. McNeill, D. (2006). Gesture and thought. Chicago, IL: University of Chicago Press.
30. Meira, L. (1998). Making sense of instructional devices: The emergence of transparency in mathematical activity. Journal for Research in Mathematics Education, 29(2), 121-142.
31. Moyer, P. S. (2001). Are we having fun yet? How teachers use manipulatives to teach mathematics. Educational Studies in Mathematics, 47(2), 175-197. (Pubitemid 33808248)
32. Moyer, P. S., Bolyard, J. J., & Spikell, M. A. (2002). What are virtual manipulatives? Teaching Children Mathematics, 8, 372-377.
33. National Council of Teachers of Mathematics (NCTM). (2000). Principles and standards for school mathematics. Reston, VA: Author.
34. National Council of Teacher of Mathematics (NCTM). (2006). Curriculum focal points for prekindergarten through grade 8 mathematics: A quest for coherence. Reston, VA: Author.
35. Nickerson, R. S. (1993). On the distribution of cognition. In G. Salomon (Ed.), Distributed cognitions: Psychological and educational considerations (pp. 229-261). New York: Cambridge University Press.
36. Nickerson, R. S. (1993). On the distribution of cognition: Some reflections. In G. Salomon (Ed.), Distributed cognitions, psychological and educational considerations (pp. 229-261). Cambridge: Cambridge University Press.
37. Núñez, R. E., Edwards, L. D., & Matos, J. F. (1999). Embodied cognition as grounding for situatedness and context in mathematics education. Educational Studies in Mathematics, 39(1/3), 45-65.
38. Olkun, S. (2003). Comparing computer versus concrete manipulatives in learning 2D geometry. Journal of Computers in Mathematics and Science Teaching, 22(1), 43-56.
39. Olkun, S., Altun, A., & Smith, G. (2005). Computers and 2D geometric learning of Turkish fourth and fifth graders. British Journal of Educational Technology, 36(2), 317-326. (Pubitemid 43906601)
40. Piaget, J. Inhelder, B, & Szeminska, A. (1960). The child's conception of geometry. New York: Basic Books.
41. Reimer, K., & Moyer, P. S. (2005). Third-graders learn about fraction using virtual manipulatives: A classroom study. Journal of Computers in Mathematics and Science Teaching, 24(1), 5-25.
42. Roschelle, J. (1992). Mediated collaborative inquiry: Toward a practical philosophy of learning technology. In M. Ryan (Ed.), Classrooms: Where ideas meet reality. Brisbane, Australia: Queensland Society for Information Technology in Education.
43. Roschelle, J. (1994). Debating for cognitive communication: Epistemic fidelity or mediating collaborative inquiry? The Arachnet Electronic Journal on Virtual Culture, 2(2). Available: http://dli.lib.ncsu.edu/stacks/serials/aejvc- v2n02-roschelle-designing.txt
44. Roschelle, J. (1996). Designing for cognitive communication: Epistemic fidelity or mediating collaborating inquiry. In D. L. Day & D. K. Kovacs (Eds.), Computers, communication & mental models (pp. 13-25). London: Taylor & Francis.
45. Roschelle, J. (1998). Activity theory: A foundation for designing learning technology? The Journal of the Learning Sciences, 7(2), 241-255.
46. Sabena, C. (2004). The transparency of instruments as index of perceptive and cultural relation to concepts. Paper presented at the ICME 10 Conference.
47. Sarama, J. (2004). Technology in early childhood mathematics: Building Blocks as an innovative technology-based curriculum. In D. H. Clements, J. Sarama, & A. M. DiBiase (Eds.), Engaging young children in mathematics: Standards for early childhood mathematics education (pp. 361-375). Mahwah, NJ: Lawrence Erlbaum.
48. Sfard, A. (1998). On two metaphors for learning and the dangers of choosing just one. Educational Researcher, 27(2), 4-13. (Pubitemid 128056715)
49. Slavin, R. E. (1996). Research on cooperative learning and achievement: What we know, what we need to know. Contemporary Educational Psychology, 21(1), 43-69. (Pubitemid 126163925)
50. Stacey, K., Helme, S., Archer, S., & Condon, C. (2001). The effect of epistemic fidelity and accessibility on teaching with physical materials: A comparison of two models for teaching decimal numeration. Educational Studies in Mathematics, 47, 199-221. (Pubitemid 33808249)
51. Stake, R. E. (1995). The art of case study research. Thousand Oaks, CA: Sage.
52. Suh, J. M., Moyer, P. S., & Heo, H.-J. (2005). Examining technology uses in the classroom: Developing fraction sense using virtual manipulative concept tutorials. The Journal of Interactive Online Learning, 3(4), 1-22.
53. Suthers, D. D. (2006). Technology affordances for intersubjective meaning making: A research agenda for CSCL. International Journal of Computer-Supported Collaborative Learning, 1(3), 315-337. (Pubitemid 44394679)
54. Van de Walle, J. A. (2001). Elementary and middle school mathematics: Teaching developmentally (4th ed.). New York: Longman.
55. van Hiele, P. M. (1986). Structure and insight: A theory of mathematics education. Orlando, FL: Academic Press.
56. van Hiele, P. M. (1999). Developing geometric thinking through activities that begin with play. Teaching Children Mathematics, 5(6), 310-316.
57. Vygotsky, L. (1978). Mind and society: The development of higher psychological processes. Cambridge, MA: Harvard University Press.
58. Wenger, E. (1987). Artificial intelligence and tutoring system. Los Altos, CA: Morgan Kaufman.
59. Wertsch, J. V. (1985). Vygotsky and the social formation of mind. Cambridge, MA: Harvard University Press.