Sfard’s Commognitive Framework as a Method of Discourse Analysis in Mathematics
This paper discusses Sfard’s commognitive approach and provides an empirical study as an example to illustrate the theory as method. Traditionally, research in mathematics education focused on the acquisition of mathematical knowledge and the didactic process of knowledge transfer. Through attending to a distinctive form of language in mathematics, as well as mathematics as a discursive subject, alternative views of making meaning in mathematics have emerged; these views are therefore “critical,” as in critical discourse analysis. The commognitive discourse analysis method has the potential to bring more clarity to our understanding of students’ mathematical thinking and the process through which students are socialized into school mathematics.
[1] A. Sfard, “On two metaphors for learning and the dangers of choosing just one,” Educational Researcher, vol. 27, no. 2, pp. 4-13, 1998.
[2] A. Sfard, Thinking as communicating: Human development, the growth of discourses, and mathematizing. New York, NY: Cambridge University Press, 2008.
[3] L. S. Vygotsky, Thought and language. Cambridge, MA: MIT Press, 1986.
[4] L. Wittgenstein, Philosophical investigations: The German text, with a revised English translation (3rd ed., G. E. M. Anscombe, Trans.). Malden, MA: Blackwell, 1953/2003.
[5] M. Bloor, and T. Bloor, The Practice of Critical Discourse Analysis: An Introduction. London: Hodder Arnold, 2007.
[6] J. P. Gee, An introduction to discourse analysis: Theory and method. New York, NY: Routledge, 1999.
[7] D. Kim, J. Ferrini-Mundy, and A. Sfard, “How does language impact the learning of mathematics? Comparison of English and Korean speaking university students’ discourses on infinity,” International Journal of Educational Research, vol. 51, no. 52, pp. 86-108, 2012.
[8] S. H. Choi, D. J. Kim, and J. Shin, “Analysis on characteristics of university students’ problem solving processes based on mathematical thinking styles,” Journal of Educational Research in Mathematics, vol. 23, no. 2, pp. 153-171, 2013.
[9] S. H. Choi, J. M. Ha, and D. J. Kim, “A communicational approach to mathematical process appeared in a peer mentoring teaching method,” Communications of mathematical education, vol. 30, no. 3, pp. 375-392, 2016.
[10] Y. H. Choi, S. H. Choi, and D. J. Kim, “An investigation of beginning and experienced teachers’ PCK and teaching practices - middle school functions,” Journal of the Korean school mathematics society, vol. 17, no. 2, pp. 251-274, 2014.
[11] J. H. Cha, S. H. Choi, and D. J. Kim, “Effects of a peer tutoring method on mathematical problem solving and class satisfaction,” Journal of the Korean school mathematics society, vol. 18, no. 2, pp. 203-221, 2015.
[12] D. Kim, Comparison of native-English and native-Korean speaking university students’ discourses on infinity and limit (Doctoral dissertation). East Lansing, MI: Michigan State University, 2009.
[1] A. Sfard, “On two metaphors for learning and the dangers of choosing just one,” Educational Researcher, vol. 27, no. 2, pp. 4-13, 1998.
[2] A. Sfard, Thinking as communicating: Human development, the growth of discourses, and mathematizing. New York, NY: Cambridge University Press, 2008.
[3] L. S. Vygotsky, Thought and language. Cambridge, MA: MIT Press, 1986.
[4] L. Wittgenstein, Philosophical investigations: The German text, with a revised English translation (3rd ed., G. E. M. Anscombe, Trans.). Malden, MA: Blackwell, 1953/2003.
[5] M. Bloor, and T. Bloor, The Practice of Critical Discourse Analysis: An Introduction. London: Hodder Arnold, 2007.
[6] J. P. Gee, An introduction to discourse analysis: Theory and method. New York, NY: Routledge, 1999.
[7] D. Kim, J. Ferrini-Mundy, and A. Sfard, “How does language impact the learning of mathematics? Comparison of English and Korean speaking university students’ discourses on infinity,” International Journal of Educational Research, vol. 51, no. 52, pp. 86-108, 2012.
[8] S. H. Choi, D. J. Kim, and J. Shin, “Analysis on characteristics of university students’ problem solving processes based on mathematical thinking styles,” Journal of Educational Research in Mathematics, vol. 23, no. 2, pp. 153-171, 2013.
[9] S. H. Choi, J. M. Ha, and D. J. Kim, “A communicational approach to mathematical process appeared in a peer mentoring teaching method,” Communications of mathematical education, vol. 30, no. 3, pp. 375-392, 2016.
[10] Y. H. Choi, S. H. Choi, and D. J. Kim, “An investigation of beginning and experienced teachers’ PCK and teaching practices - middle school functions,” Journal of the Korean school mathematics society, vol. 17, no. 2, pp. 251-274, 2014.
[11] J. H. Cha, S. H. Choi, and D. J. Kim, “Effects of a peer tutoring method on mathematical problem solving and class satisfaction,” Journal of the Korean school mathematics society, vol. 18, no. 2, pp. 203-221, 2015.
[12] D. Kim, Comparison of native-English and native-Korean speaking university students’ discourses on infinity and limit (Doctoral dissertation). East Lansing, MI: Michigan State University, 2009.
@article{"International Journal of Engineering, Mathematical and Physical Sciences:76606", author = "Dong-Joong Kim and Sangho Choi and Woong Lim", title = "Sfard’s Commognitive Framework as a Method of Discourse Analysis in Mathematics", abstract = "This paper discusses Sfard’s commognitive approach and provides an empirical study as an example to illustrate the theory as method. Traditionally, research in mathematics education focused on the acquisition of mathematical knowledge and the didactic process of knowledge transfer. Through attending to a distinctive form of language in mathematics, as well as mathematics as a discursive subject, alternative views of making meaning in mathematics have emerged; these views are therefore “critical,” as in critical discourse analysis. The commognitive discourse analysis method has the potential to bring more clarity to our understanding of students’ mathematical thinking and the process through which students are socialized into school mathematics.
", keywords = "Commognitive framework, discourse analysis, mathematical discourse, mathematics education. ", volume = "11", number = "11", pages = "481-5", }
