Commognitive analyses of the learning and teaching of mathematics at university level: the case of discursive shifts in the study of Calculus

References

• Bar-Tikva, J. (2009). Old meta-discursive rules die hard. In F. Lin, F. Hsieh, G. Hanna, & M. de Villiers (Eds.), Proceedings of ICMI Study 19: Proof and Proving in Mathematics Education (vol. 1, pp. 89–93). Taipei, Taiwan: ICMI.
   Google Scholar
• Biza, I., Jaworski, B., & Hemmi, K. (2014). Communities in university mathematics. Research in Mathematics Education, 16(2), 161–176.
   Google Scholar
• Cobb, P. (2009). Learning as the evolution of discourse: Accounting for cultural, group and individual development. Human Development, 52, 205–210. doi:10.1159/000213893
   Web of Science ®Google Scholar
• Felton, M. D., & Nathan, M. (2009). Exploring Sfard's commognitive framework. Journal for Research in Mathematics Education, 40, 572–576.
   Google Scholar
• González-Martín, A. S., Bloch, I., Durand-Guerrier, V., & Maschietto, M. (2014). Didactic Situations and Didactical Engineering in university mathematics: cases from the study of Calculus and proof. Research in Mathematics Education, 16(2), 117–134.
   Google Scholar
• Güçler, B. (2013). Examining the discourse on the limit concept in a beginning-level calculus classroom. Educational Studies in Mathematics, 82, 439–453. doi:10.1007/s10649-012-9438-2
   Web of Science ®Google Scholar
• Ioannou, M. (2012). Conceptual and learning issues regarding undergraduate students' first encounter with group theory: A commognitive analysis (Unpublished PhD thesis). University of East Anglia, UK.
   Google Scholar
• Jablonka, E., & Bergsten, C. (2010). Commentary on theories of mathematics education—Is plurality a problem? In B. Sriraman & L. English (Eds.), Theories of mathematics education: Seeking new frontiers (pp. 111–117). New York, NY: Springer.
   Google Scholar
• Jaworski, A., & Coupland, N. (Eds.). (2005). The discourse reader (2nd ed.). London, UK: Routledge.
   Google Scholar
• Kieran, C., Forman, E., & Sfard, A. (Eds.). (2002). Learning discourse: Discursive approach to research in mathematics education. Dordrecht: Kluwer Academic.
   Google Scholar
• Kim, D.-J., Ferrini-Mundy, J., & Sfard, A. (2012). How does language impact the learning of mathematics? Comparison of English and Korean speaking university students' discourses on infinity. International Journal of Educational Research, 51–52, 86–108. doi:10.1016/j.ijer.2012.01.004
   Google Scholar
• Kjeldsen, T. H., & Blomhøj, M. (2012). Beyond motivation: History as a method for learning meta-discursive rules in mathematics. Educational Studies in Mathematics, 80, 327–349. doi:10.1007/s10649-011-9352-z
   Web of Science ®Google Scholar
• Lemke, J. L. (2009). Learning to mean mathematically. Mind, Culture, and Activity, 16, 281–284. doi:10.1080/10749030902977695
   Web of Science ®Google Scholar
• Nardi, E. (2005). “Beautiful minds” in rich discourses: On the employment of discursive approaches to research in mathematics education. European Educational Research Journal, 4, 145–154. doi:10.2304/eerj.2005.4.2.7
   Google Scholar
• Nardi, E. (2008). Amongst mathematicians: Teaching and learning mathematics at university level. New York, NY: Springer.
   Google Scholar
• Nardi, E. (2011). ‘Driving noticing’ yet ‘risking precision’: University mathematicians' pedagogical perspectives on verbalisation in mathematics. In M. Pytlak, T. Rowland, & E. Swoboda (Eds.), Proceedings of CERME7 (7th Conference of European Research in Mathematics Education) (pp. 2053–2062). Rzeszów, Poland: ERME.
   Google Scholar
• Nilsson, P., & Ryve, A. (2010). Focal event, contextualization, and effective communication in the mathematics classroom. Educational Studies in Mathematics, 74, 241–258. doi:10.1007/s10649-010-9236-7
   Web of Science ®Google Scholar
• Ong, G. (2013). How can we better understand mathematical expositions? An analysis of three online lectures on derivatives using Sfard's discursive framework (Unpublished dissertation [MSc]). University of East Anglia, UK.
   Google Scholar
• Park, J. (2013). Is the derivative a function? If so, how do students talk about it? International Journal of Mathematical Education in Science and Technology, 44(5), 624–640. doi:10.1080/0020739X.2013.795248
   Google Scholar
• Pettersson, K. (2008). Växelverkan mellan intuitiva idéer och formella resonemang: En fallstudie av universitetsstudenters arbete med en analysuppgift [Interplay between intuitive ideas and formal justification. A case study of university students' work on a calculus task]. Nordic Studies in Mathematics Education, 13(1), 29–50.
   Google Scholar
• Remillard, K. S. (2010). Exploring the learning of mathematical proof by undergraduate mathematics majors through discourse analysis. Proceedings of the 13th Annual Conference on Research in Undergraduate Mathematics Education. Retrieved from http://sigmaa.maa.org/rume/crume2010/Archive/Remillard.pdf
   Google Scholar
• Ryve, A. (2011). Discourse research in mathematics education: A critical evaluation of 108 journal articles. Journal for Research in Mathematics Education, 42, 167–198.
   Web of Science ®Google Scholar
• Ryve, A., Nilsson, P., & Pettersson, K. (2013). Analyzing effective communication in mathematics group work: The role of visual mediators and technical terms. Educational Studies in Mathematics, 82, 497–514. doi:10.1007/s10649-012-9442-6
   Web of Science ®Google Scholar
• Seel, N. M. (Ed.). (2012). Encyclopedia of the sciences of learning. New York, NY: Springer
   Google Scholar
• Sfard, A. (2002). There is more to discourse than meets the ears: Looking at thinking as communicating to learn more about mathematical learning. In C. Kieran, E. Forman, & A. Sfard (Eds.), Learning discourse: Discursive approaches to research in mathematics education (pp. 13–57). Dordrecht: Kluwer Academic.
   Google Scholar
• Sfard, A. (2008). Thinking as communicating. Human development, the growth of discourse, and mathematizing. New York, NY: Cambridge University Press.
   Google Scholar
• Sfard, A., & Kieran, C. (2001). Cognition as communication: Rethinking learning-by-talking through multi-faceted analysis of students' mathematical interactions. Mind, Culture, and Activity, 8(1), 42–76. doi:10.1207/S15327884MCA0801_04
   Google Scholar
• Sriraman, B. (2009). What's all the commotion over commognition? The Montana Mathematics Enthusiast, 6, 541–544.
   Google Scholar
• Sriraman, B., & Nardi, E. (2013). Theories, models and frameworks. In M. A. K. Clements, A. Bishop, C. Keitel, J. Kilpatrick, & F. Leung (Eds.), Third international handbook of mathematics education (pp. 303–326). New York, NY: Springer.
   Google Scholar
• Stadler, E. (2011). The same but different—Novice university students solve a textbook exercise. In M. Pytlak, T. Rowland, & E. Swoboda (Eds.), Proceedings of CERME7 (7th Conference of European Research in Mathematics Education) (pp. 2083–2092). Rzeszów, Poland: ERME.
   Google Scholar
• Stahl, G. (2008). Exploring thinking as communicating in CSCL. International Journal of Computer-Supported Collaborative Learning, 3(3), 361–368. doi:10.1007/s11412-008-9046-4
   Web of Science ®Google Scholar
• Thurston, W. P. (1990). Mathematical education. Notices of the American Mathematical Society, 37(7), 844–850.
   Google Scholar
• Viirman, O. (2013). The functions of function discourse – University mathematics teaching from a commognitive standpoint. International Journal of Mathematical Education in Science and Technology, 45(4), 512–527. doi:10.1080/0020739X.2013.855328
   Google Scholar
• Walker-Johnson, A. (2009). Book review. Anthropology and Education Quarterly, 40, 323–324. doi:10.1111/j.1548-1492.2009.01051.x
   Google Scholar
• Wing, T. (2011) Purifying the dialect of the tribe. Educational Studies in Mathematics, 76, 363–369. doi:10.1007/s10649-010-9283-0
   Web of Science ®Google Scholar
• Yackel, E. (2009). Book review. Research in Mathematics Education, 11(1), 90–94.
   Google Scholar