Abstract
Ritual teaching, which provides students with ritual opportunities to learn, is common worldwide, notwithstanding extensive research calls for more reform-oriented teaching. Such resilience to change suggests that there are gains for ritual teaching. Therefore, in this study, we search for possible goals of ritual teaching. For this purpose, we suggest two notions: ritual-enabling and exploration-requiring opportunities to learn and seeking possible goals that could be achieved by ritual-enabling opportunities to learn. We adopted the commognitive framework and developed a methodological tool for analyzing lessons using the ritual-exploration lens. We analyzed 11 videos and transcripts of eighth-grade mathematics lessons from the 1999 TIMSS study. Our findings suggest that ritual teaching is essential both for object-level and meta-level learning as it serves as a basis for explorations, and for helping students in their initial steps of entering a new discourse.
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Notes
For convenience, in this article, Hong Kong SAR is referred to as a country. Hong Kong SAR is a Special Administrative Region (SAR) of the People’s Republic of China (Hiebert et al., 2005 , p. 129).
The situation here is a bit more complex. The teacher required her students to prove whereas the narrative a0 = 1 is a definition. The reasons for endorsing such a definition should be discussed yet this was not how the teacher framed the OTL.
Such communication-pattern is often referred to as funneling (e.g., Wood, 1998) which includes teacher’s well-intentioned questioning to guide students through a procedure. Wood claims that this type of communication-pattern gives an illusion of student-learning actually occurring, although it is not.
References
Brown, S. I., Cooney, T. J., & Jones, D. (1990). Mathematics teacher education. In W. R. Houston, M. Haberman, & J. Sikula (Eds.), Handbook of research on teacher education (pp. 639–656). New York: Macmilian.
Brown, K. L. (2003). From teacher-centered to learner-centered curriculum: Improving learning in diverse classrooms. Education, 124(1), 49–55.
Cazden, C. (2001). Classroom discourse: The language of learning and teaching. Portsmouth, NH: Heinemann.
Cicchelli, T. (1983). Forms and functions of instruction patterns: Direct and nondirect. Instructional Science, 12(4), 343–353.
Draper, R. J. (2002). School mathematics reform, constructivism, and literacy: A case for literacy instruction in the reform-oriented math classroom. Journal of Adolescent & Adult Literacy, 45(6), 520–529.
Gregg, J. (1995). The tensions and contradictions of the school mathematics tradition. Journal for Research in Mathematics Education, 26, 442–466.
Hancock, D. R., Bray, M., & Nason, S. A. (2003). Influencing university students’ achievement and motivation in a technology course. The Journal of Educational Research, 95, 365–372.
Heyd-Metzuyanim, E., Tabach, M., & Nachlieli, T. (2016). Opportunities for learning given to prospective mathematics teachers – between ritual and explorative instruction. The Journal of Mathematics Teacher Education, 16(6), 547–574.
Heyd-Metzuyanim, E., & Graven, M. (2016). Between people-pleasing and mathematizing: South African learners’ struggle for numeracy. Educational Studies in Mathematics, 91(3), 349–373.
Hiebert, J., Stigler, J. W., Jacobs, J. K., Givvin, K. B., Garnier, H., Smith, M., … Gallimore, R. (2005). Mathematics teaching in the United States today (and tomorrow): Results from the TIMSS 1999 video study. Educational Evaluation and Policy Analysis, 27(2), 111–132.
Kilpatrick, J., Swafford, J., & Findell, B. (Eds.). (2001). Adding It Up: Helping Children Learn Mathematics. Washington, D.C.: National Academic Press.
Lavie, I., & Sfard, A. (2016). How children individualize numerical routines – Elements of a discursive theory in making (in Hebrew). Studies in Mathematics Education, 4, 22–68.
Lavie, I., Steiner, A., & Sfard, A. (2018). Routines we live by: From ritual to exploration. Educational Studies in Mathematics. https://doi.org/10.1007/s10649-018-9817-4
Mascolo, M. F. (2009). Beyond student-centered and teacher-centered pedagogy: Teaching and learning as guided participation. Pedagogy and the Human Sciences, 1(1), 3–27.
Nachlieli, T., & Sfard, A. (2003). The Activity of Defining. International Group for the Psychology of Mathematics Education, 3, 349–356.
Nachlieli, T., & Katz, Y. (2017). Ritual vs. explorative classroom participation of pre-service elementary school mathematics teachers. Proceedings of CERME 10 – Tenth Conference of European Research in Mathematics Education. Dublin: CERME.
Nachlieli, T., & Tabach, M. (2012). Growing mathematical objects in the classroom – the case of function. International Journal of Educational Research, 51&52, 10–27.
Sfard, A. (2007). When the rules of discourse change, but nobody tells you: Making sense of mathematics learning from a commognitive standpoint. The Journal of the Learning Sciences, 16(4), 565–613.
Sfard, A. (2008). Thinking as communicating: Human development, the growth of discourses, and mathematizing. Cambridge: Cambridge University Press.
Sfard, A. (2012). Introduction: Developing mathematical discourse—some insights from communicational research. International Journal of Educational Research, 51&52, 1–9.
Sfard, A. (2018). Commognition. In S. Lerman (Ed.), Encyclopedia of mathematics education. New York, NY: Springer.
Sfard, A., & Lavie, I. (2005). Why cannot children see as the same what grown-ups cannot see as different? Early numerical thinking revisited. Cognition and Instruction, 23(2), 237–309.
Stigler, J. W., & Hiebert, J. (2009). The teaching gap: Best ideas from the world’s teachers for improving education in the classroom. New York, NY: Simon and Schuster.
Strauss, A., & Corbin, J. (1998). Basics of qualitative research: Techniques and procedures for developing grounded theory (2nd ed.). Thousand Oaks: Sage.
Tabach, M., & Nachlieli, T. (2015). Classroom engagement towards definition-mediated identification: The case of functions. Educational Studies in Mathematics, 90(2), 163–187.
Tabach, M., & Nachlieli, T. (2016). Communicational perspectives on learning and teaching mathematics: Prologue. Educational Studies in Mathematics, 91(3), 299–306.
Wood, T. (1998). Alternative patterns of communication in mathematics classes: Funneling or focusing. In H. Steinbring, M. G. Bartolini Bussi, & A. Sierpinska (Eds.), Language and communication in the mathematics classroom (pp. 167–178). Reston, VA: National Council of Teachers of Mathematics.
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Nachlieli, T., Tabach, M. Ritual-enabling opportunities-to-learn in mathematics classrooms. Educ Stud Math 101, 253–271 (2019). https://doi.org/10.1007/s10649-018-9848-x
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DOI: https://doi.org/10.1007/s10649-018-9848-x