#
Studying Online Participation and its Impact on the Development of Mathematical Content Knowledge for Teaching
PROCEEDINGS

## Jason Silverman, Drexel University, United States

Society for Information Technology & Teacher Education International Conference, in Nashville, Tennessee, USA ISBN 978-1-880094-84-6 Publisher: Association for the Advancement of Computing in Education (AACE), Chesapeake, VA

## Abstract

In this paper, we report on our efforts to support teachers’ development of mathematical knowledge for teaching through online professional development. In particular, we report on our investigation into the relationship between online interaction in teacher development activities and teachers’ development of mathematics content for teaching. Through the integration of content analysis and social network analysis, we identify underlying relationships between aspects of online interaction – the function and content of particular posts and the relative importance of individuals in the interaction – and teacher learning. Results indicate that while interaction, broadly speaking, was not correlated with teacher learning, particular combinations of content and the centrality of an individual in the interaction were. Implications of these significant correlations for mathematics teacher education are discussed.

## Citation

Silverman, J. (2011). Studying Online Participation and its Impact on the Development of Mathematical Content Knowledge for Teaching. In M. Koehler & P. Mishra (Eds.), Proceedings of SITE 2011--Society for Information Technology & Teacher Education International Conference (pp. 746-753). Nashville, Tennessee, USA: Association for the Advancement of Computing in Education (AACE). Retrieved November 12, 2019 from https://www.learntechlib.org/primary/p/36366/.

## References

View References & Citations Map- Ball, D.L. (1993). Halves, pieces, and twoths: Constructing and using representational contexts in teaching fractions. In T. Carpenter, E. Fennema & T. Romberg (Eds.), Rational numbers: An integration of research (pp. 157-195). Hillsdale, NJ: Lawrence Erlbaum Associates.
- Bass, H. (2005). Mathematics, Mathematicians, and Mathematics Education. Bulletin of the American Matheamtical Society, 42(4), 417-430.
- Bransford, J., Brown, A., & Cocking, R. (2000). How people learn. Washington, DC: National Research Council.
- Briedenbach, D., Dubinsky, E., Hawks, J., & Nichols, D. (1992). Development of the process conception of function. Educational Studies in Mathematics, 33, 247-285.
- Carlson, M. (1998). Across sectional investigation of the development of the function concept. Research in collegiate mathematics education, III. Issues in mathematics education, 7, 115-162.
- Carlson, M., Jacobs, S., Coe, E., Larsen, S., & Hsu, E. (2002). Applying covariational reasoning while modeling dynamic events: A framework and a study. Journal for Research in Mathematics Education, 33(5), 352378.
- Corbin, J.M., & Strauss, A.L. (2008). Basics of qualitative research: Techniques and procedures for developing grounded theory (3rd ed.). Thousand Oaks, CA: Sage.
- Cunningham, R. (1992). Beyond educational psychology: Steps toward an educational semiotic. Educational Psychology Review, 4, 165-194.
- Cuoco, A. (2001). Mathematics for teaching. Notices of the American Mathematical Society, 48(2), 68-74.
- England, E. (1985). Interactional Analysis: The missing factor in computer-aided learning design and evaluation. Educational Technology, 25(9), 24-28.
- Glaser, B., & Strauss, A. (1967). The Discovery of Grounded Theory: Strategies for Qualitative Research. Chicago, IL: Aldine Publishing Company.
- Greenberg, J., & Walsh, K. (2008). No Common Denominator: The Preparation of Elementary Teachers in Mathematics. Washington, DC: National Council on Teacher Quality.
- Haythornthwaite, C. (2002). Building social networks via computer networks: creating and sustaining distributed learning communities. In K.A. Renninger & W. Shumar (Eds.), Building virtual communities: Learning and change in cyberspace (pp. 159-190). New York, NY: Cambridge University Press.
- Henwood, K., & Pidgeon, N. (2006). Grounded Theory. In G.M. Breakwell, S. Hammond, S. Fife, Chris & J.A. Smith (Eds.), Research Methods in Psychology (3rd ed.). Thousand Oaks, CA: Sage.
- Hill, H.C., & Ball, D.L. (2004). Learning mathematics for teaching: Results from California's Mathematics Professional Development Institutes. Journal for Research in Mathematics Education, 35(5), 330-351.
- Hill, H.C., Schilling, S.G., & Ball, D.L. (2004). Developing measures of teachers' mathematics knowledge for teaching. The Elementary School Journal, 105, 11-30.
- Jeong, A.C. (2003). The Sequential Analysis of Group Interaction and Critical Thinking in Online Threaded Discussions. American Journal of Distance Education, 17(1), 25.
- Lotman, Y. (1988). Text within a Text. Soviet Psychology, 26(3), 32-51.
- Lowes, S., Lin, P., & Wang, Y. (2007). Studying the Effectiveness of the Discussion Forum in Online Professional Development Courses. Journal of Interactive Online Learning, 6(3), 181-210.
- Ma, L. (1999). Knowing and teaching elementary mathematics: Teachers' understanding of fundamental mathematics in China and the United States. Mahwah, NJ: Lawrence Erlbaum Associates.
- Mercer, N. (2000). Words and Minds: how we use language to think together. New York, NY: Routledge.
- Monk, S. (1992). Students' understanding of a function given by a physical model. In G. Harel & E. Dubinsky (Eds.), The Concept of Function: Aspects of Epistemology and Pedagogy. Washington, DC: Mathematical Association of America.
- National Mathematics Advisory Panel (2008). Foundations for Success: The Final Report of the National Mathematics Advisory Panel. Washington, DC: U.S. Department of Education.
- Paloff, R., & Pratt, K. (1999). Building learning communities in cyberspace. San Fransisco, CA: Jossey-Bass.
- Penuel, W.R., & Riel, M. (2007). The 'new' science of networks and the challenge of school change. [Article]. Phi Delta Kappan, 88(8), 611-615.
- Ravenscroft, A. (2001). Designing E-learning Interactions in the 21st Century: revisiting and rethinking the role of theory. European Journal of Education, 36(2), 133-156.
- Ravenscroft, A. (2007). Promoting thinking and conceptual change with digital dialogue games. Journal of Computer Assisted Learning, 23(6), 453-465.
- Reddy, M.J. (1979). The conduit metaphor-a case of frame conflict in our language about language. In A. Ortony (Ed.), Metaphor and Thought. London, England: Cambridge University Press.
- Renninger, K., Ray, L., Luft, I., & Newton, E. (2006). A comprehension tool for mathematics?: The Math Forum@ Drexel's Online Mentoring Project. Paper presented at the 7th International Conference of the Learning Sciences Bloomington, IN.
- Rovai, A. (2002). A preliminary look at structural differences in sense of classroom community between higher education traditional and ALN courses. Journal of Asynchronous Learning Networks, 6(1).
- Russo, T.C., & Koesten, J. (2005). Prestige, Centrality, and Learning: A Social Network Analysis of an Online Class. Communication Education, 54(3), 254-261.
- Schilling, S.G., Blunk, M., & Hill, H.C. (2007). Test Validation and the MKT Measures: Generalizations and Conclusions. Measurement: Interdisciplinary Research& Perspective, 5(2), 118-128.
- Schilling, S.G., & Hill, H.C. (2007). Assessing Measures of Mathematical Knowledge for Teaching: A Validity Argument Approach. Measurement: Interdisciplinary Research& Perspective, 5(2), 70-80.
- Schlager, M.S., Farooq, U., Fusco, J., Schank, P., & Dwyer, N. (2009). Analyzing Online Teacher Networks: Cyber Networks Require Cyber Research Tools. Journal of Teacher Education, 60(1), 86-100.
- Schwandt, T.A. (1997). Qualitative inquiry: a dictionary of terms. Thousand Oaks: Sage Publications.
- Shale, D., & Garrison, D. (1990). Introduction. In D. Garrison& D. Shale (Eds.), Education at a distance: From issues to practice. Melbourne, FL: Krieger.
- Shulman, L.S. (1986). Those who understand: Knowledge growth in teaching. Educational Researcher, 15(2), 414.
- Shumar, W. (2006). Personalized Identity, Mentoring and Mathematical Conversation: The Math Forum's Online Mentoring Project. Paper presented at the 7th International Conference of the Learning Sciences Bloomington, IN.
- Simon, M.A. (2006). Key Developmental Understandings in Mathematics: A Direction for Investigating and Establishing Learning Goals. Mathematical Thinking& Learning, 8(4), 359-371.
- Steffe, L.P. (1991). The learning paradox. In L.P. Steffe (Ed.), Epistemological foundations of mathematical experience (pp. 26-44). New York: Springer-Verlag.
- Thompson, P.W. (1994). Students, functions, and the undergraduate curriculum. In E. Dubinsky, A. Schoenfeld& J. Kaput (Eds.), Research in Collegiate Mathematics Education, I: Issues in Mathematics Education (Vol. 4, pp. 21-44). Providence, RI: American Mathematical Society.
- Vygotsky, L. (1981). The genesis of higher mental functions. In J. Wertsch (Ed.), The Concept of Activity in Soviety Psychology. Armonk, NY: M.E. Sharpe.
- Vygotsky, L. (1986). Thought and language (A. Kozulin, Trans.). Cambridge, MA: Massachusetts Institute of Technology. (Original work published in 1934).
- Wasserman, S., & Faust, K. (1994). Social network analysis: methods and applications. Cambridge; New York: Cambridge University Press.
- Wegerif, R. (2006). A dialogic understanding of the relationship between CSCL and teaching thinking skills. International Journal of Computer-Supported Collaborative Learning, 1(1), 143-157.
- Wertsch, J., & Toma, C. (1995). Discourse and learning in the classroom: A sociocultural approach. In L. Steffe & J. Gale (Eds.), Constructivism in Education (pp. 159-174). Hillsdale, NJ: Lawrence Erlbaum.

These references have been extracted automatically and may have some errors. Signed in users can suggest corrections to these mistakes.

Suggest Corrections to References