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Developing fluency in the mathematical register through conversation in a tenth-grade classroom

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Abstract

The purpose of this study was to identify the interactional strategies that one teacher used in a discourse-rich tenth-grade classroom to develop her students’ facility with the mathematical register. Viewing the mathematical register as multi-semiotic and having a specific grammatical patterning, we used discourse analysis (Sinclair & Coulthard, 1975) to examine the teacher’s initiation and feedback moves that supported students in using symbolic and natural language in mathematical ways during three consecutive lesson episodes. Our findings suggest that, while teacher interactional strategies which focus or probe student thinking are effective for supporting students’ learning of the mathematical register, strategies that funnel or lead student contributions towards predetermined answers may also serve that purpose through creating opportunities for meaningful language practice.

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Notes

  1. The Romanian term used by the teacher and the students was “versor.” We chose to translate it as “versor” rather than “unit vector” because the students’ difficulty in grasping the concept might be partly due to the fact that the meaning of the word cannot be inferred from its form.

References

  • Adler, J. (1999). The dilemma of transparency: Seeing and seeing through talk in the mathematics classroom. Journal for Research in Mathematics Education, 30(1), 47–64.

    Article  Google Scholar 

  • Cazden, C. B. (2001). Classroom discourse: The language of teaching and learning. Portsmouth, NH: Heinemann.

    Google Scholar 

  • Chapman, A. (1997). Towards a model of language shifts in mathematics learning. Mathematics Education Research Journal, 9(2), 152–172.

    Article  Google Scholar 

  • Christie, F. (2002). The development of abstraction in adolescence in subject English. In M. J. Schleppegrell & M. C. Colombi (Eds.), Developing advanced literacy in first and second languages: Meaning with power (pp. 45–67). Mahwah, NJ: Erlbaum.

    Google Scholar 

  • Cobb, P., Boufi, A., McClain, K., & Whitenack, J. (1997). Reflective discourse and collective reflection. Journal for Research in Mathematics Education, 28(3), 258–277.

    Article  Google Scholar 

  • Cobb, P., Wood, T., & Yackel, E. (1991). A constructivist approach to second grade mathematics. In E. von Glasersfeld (Ed.), Radical constructivism in mathematics education (pp. 157–176). Dordrecht, NL: Kluwer.

    Google Scholar 

  • Cobb, P., Wood, T., & Yackel, E. (1993). Discourse, mathematical thinking, and classroom practice. In E. A. Forman, N. Minick, & C. A. Stone (Eds.), Contexts for learning: Sociocultural dynamics in children’s development (pp. 91–119). New York: Oxford University Press.

    Google Scholar 

  • Coffin, C. (2006). Historical discourse: The language of time, cause, and evaluation. London, UK: Continuum.

    Google Scholar 

  • Cope, B., & Kalantzis, M. (Eds.). (2000). Multiliteracies: Literacy learning and the design of social futures. New York: Routledge.

    Google Scholar 

  • Delpit, L. (1989). The silenced dialogue: Power and pedagogy in educating other people's children. Harvard Educational Review, 58, 280–298.

    Google Scholar 

  • Dowling, P. (1998). The sociology of mathematics education: Mathematical myths/pedagogic texts. London, UK: The Falmer Press.

    Google Scholar 

  • Edwards, D., & Mercer, N. (1987). Common knowledge: The growth of understanding in the classroom. London: Routledge.

    Google Scholar 

  • Fang, Z., Schleppegrell, M. J., & Cox, B. E. (2006). Understanding the language demands of schooling: Nouns in academic registers. Journal of Literacy Research, 38(3), 247–273.

    Article  Google Scholar 

  • Franke, M. L., Webb, N. W., Chan, A. G., Ing, M., Freund, D., & Battey, D. (2009). Teacher questioning to elicit students’ mathematical thinking in elementary classrooms. Journal of Teacher Education, 60, 380–392.

    Article  Google Scholar 

  • Gee, J. P. (1996). Social linguistics and literacies: Ideology in Discourses (2nd ed.). London: Taylor & Francis.

    Google Scholar 

  • Gutierrez, K. D., Baquedano-Lopez, P., Alvarez, H., & Chiu, M. M. (1999). Building a culture of cooperation through hybrid language practices. Theory Into Practice, 38, 87–93.

    Article  Google Scholar 

  • Halliday, M. A. K. (1978). Language as social semiotic. London: Edward Arnold.

    Google Scholar 

  • Halliday, M. A. K., & Martin, J. R. (Eds.). (1993). Writing science: Literacy and discursive power. Pittsburgh, PA: University of Pittsburgh Press.

    Google Scholar 

  • Heath, S. B. (1983). Ways with words: Language, life, and work in communities and classrooms. New York: Teachers’ College Press.

    Google Scholar 

  • Hedge, T. (1993). Key concepts in ELT: Fluency. ELT Journal, 47, 275–276.

    Article  Google Scholar 

  • Herbel-Eisenmann, B. A. (2002). Using student contributions and multiple representations to develop mathematical language. Mathematics Teaching in the Middle School, 8, 100–105.

    Google Scholar 

  • Herbel-Eisenmann, B. A., & Breyfogle, M. L. (2005). Questioning our patterns of questioning. Mathematics Teaching in the Middle School, 10(9), 484–489.

    Google Scholar 

  • Lampert, M. (1990). When the problem is not the question and the solution is not the answer: Mathematical knowing and teaching. American Educational Research Journal, 27(1), 29–63.

    Google Scholar 

  • Lemke, J. (1990). Talking science: Language, learning, and values. Norwood, NJ: Ablex.

    Google Scholar 

  • Lyster, R., & Ranta, L. (1997). Corrective feedback and learner uptake: Negotiation of form in communicative classrooms. Studies in Second Language Acquisition, 19(1), 37–61.

    Article  Google Scholar 

  • Martin, J. R., & Veel, R. (Eds.). (1998). Reading science: Critical and functional perspectives on discourses of science. London, UK: Routledge.

    Google Scholar 

  • Meaney, T., Fairhall, U., & Trinick, T. (2007). Te Reo Tätaitai: Developing rich mathematical language in Mäori immersion classrooms. Teaching and Learning Research Initiative. Wellington, NZ. Retrieved from: http://www.tlri.org.nz/school-sector/#developingMeaney

  • Mehan, H. (1979). Learning lessons. Cambridge, MA: Harvard University Press.

    Google Scholar 

  • Mercer, N. (1995). The guided construction of knowledge: Talk between teachers and learners. Clevedon: Multilingual Matters.

    Google Scholar 

  • Moje, E. B. (2007). Developing socially just subject-matter instruction: A review of the literature on disciplinary literacy teaching. Review of Research in Education, 31(1), 1–44.

    Article  Google Scholar 

  • Moje, E. B., Ciechanowski, K. M., Kramer, K. E., Ellis, L. M., Carrillo, R., & Collazo, T. (2004). Working toward third space in content area literacy: An examination of everyday funds of knowledge and discourse. Reading Research Quarterly, 39(1), 38–71.

    Article  Google Scholar 

  • Morgan, C. (1998). Writing mathematically: The discourse of investigation. London: Palmer.

    Google Scholar 

  • Morgan, C. (2007). Who is not multilingual now? Educational Studies in Mathematics, 64(2), 239–242.

    Article  Google Scholar 

  • Moschkovich, J. N. (2010). Recommendations for research on language and mathematics education. In J. N. Moschkovich (Ed.), Language and mathematics education (pp. 151–170). Charlotte, NC: Information Age Publishing.

    Google Scholar 

  • Nation, I. S. P. (2001). Learning vocabulary in another language. Cambridge, UK: Cambridge University Press.

    Google Scholar 

  • O’Connor, M. C., & Michaels, S. (1996). Shifting participant frameworks: Orchestrating thinking practices in group discussion. In D. Hicks (Ed.), Discourse, learning, and schooling (pp. 63–104). New York: Cambridge University Press.

    Chapter  Google Scholar 

  • Pimm, D. (1987). Speaking mathematically: Communication in mathematics classrooms. London: Routledge & Kegan Paul.

    Google Scholar 

  • Schleppegrell, M. J. (2004). The language of schooling: A functional linguistics perspective. Mahwah, NJ: Lawrence Erlbaum.

    Google Scholar 

  • Schleppegrell, M. J. (2007). The linguistic challenges of mathematics teaching and learning: A research review. Reading and Writing Quarterly, 23, 139–159.

    Article  Google Scholar 

  • Sfard, A. (2000). On reform movement and the limits of mathematical discourse. Mathematical Thinking and Learning, 2(3), 157–189.

    Article  Google Scholar 

  • Sfard, A. (2001). There is more to discourse than meets the ears: Looking at thinking as communicating to learn more about mathematical learning. Educational Studies in Mathematics, 46, 13–57.

    Article  Google Scholar 

  • Sfard, A. (2007). When the rules of the 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.

    Article  Google Scholar 

  • Sfard, A., Nesher, P., Streefland, L., Cobb, P., & Mason, P. (1998). Learning mathematics through conversation: Is it as good as they say? [1]. For the Learning of Mathematics, 18(1), 41–51.

    Google Scholar 

  • Sinclair, J. M., & Coulthard, R. M. (1975). Towards an analysis of discourse: The English used by teachers and pupils. London: Oxford University Press.

    Google Scholar 

  • Temple, C. (2008). Teaching and learning mathematical discourse in a Romanian classroom: A critical discourse analysis. Unpublished doctoral dissertation. Syracuse University, New York

  • Unsworth, L. (1998). “Sound” explanations in school science: A functional linguistic perspective on effective apprenticing texts. Linguistics and Education, 9(1), 199–226.

    Google Scholar 

  • Unsworth, L. (1999). Developing critical understanding of the specialized language of school science and history texts: A functional grammatical perspective. Journal of Adolescent and Adult Literacy, 42(7), 508–521.

    Google Scholar 

  • Wells, G. (1993). Reevaluating the IRF sequence: A proposal for the articulation of theories of activity and discourse for the analysis of teaching and learning in the classroom. Linguistics and Education, 5, 1–37.

    Article  Google Scholar 

  • 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.

    Google Scholar 

  • Yackel, E., & Cobb, P. (1996). Sociomathematical norms, argumentation, and autonomy in mathematics. Journal for Research in Mathematics Education, 27(4), 458–477.

    Article  Google Scholar 

  • Zevenbergen, R. (2000). “Cracking the code” of mathematics classrooms: School success as a function of linguistic, social, and cultural background. In J. Boaler (Ed.), Multiple perspectives on mathematics teaching and learning (pp. 201–223). Westport, CT: Ablex.

    Google Scholar 

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Authors and Affiliations

  1. State University of New York College at Cortland, Cortland, NY, USA

    Codruta Temple

  2. Syracuse University, Syracuse, NY, USA

    Helen M. Doerr

Authors
  1. Codruta Temple
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  2. Helen M. Doerr
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Correspondence to Helen M. Doerr.

Appendix

Appendix

Initiation moves

  1. 1.

    Comparing—tasks that require comparing two or more mathematical objects. Example: Teacher: “So how is adding two complex numbers similar to adding two vectors?”

  2. 2.

    Defining—tasks that require a definition. Example: Teacher: “What’s an equation?”

  3. 3.

    Describing—tasks that require a description of a mathematical object. Example: Teacher: “What are the characteristics of the points in the first quadrant?”

  4. 4.

    Evaluating—tasks that require that students evaluate the truth of a proposition expressed in natural or symbolic language. Example: Teacher: “Is this equality always true?”

  5. 5.

    Hypothesizing—suggestions for solving a problem or for expressing a mathematical relationship. Example: Student: “Can’t we prolong each diagonal by half?”

  6. 6.

    Recounting—tasks requiring that students recount the steps followed in carrying out a task or in solving a problem. Example: Teacher: “How did you determine the slope?”

  7. 7.

    Representing—tasks requiring that students construct a verbal and/or symbolic representation of a mathematical relationship. Example: Teacher: “How can we write the vector OM as the sum of two vectors?”

Feedback moves

  1. 1.

    Clarification request—questions indicating that an utterance is not fully comprehensible. Example: Teacher: “What do you mean by x and y?”

  2. 2.

    Elicitation—unfinished sentences uttered with a rising intonation or questions aimed at eliciting a technical term or additional information. Example 1: Teacher: “Remember that two vectors are equal when they have …” Example 2: Teacher: “What else?”

  3. 3.

    Evaluation request—questions requiring that the truth of a proposition be evaluated. Example: Teacher: “Do you agree with what he wrote on the board?”

  4. 4.

    Expansion—information that expands other participants’ contributions. Example: Student: “R times R.”—Teacher: “R times R or we can say R squared. So the Cartesian product R times R can be represented as R squared.”

  5. 5.

    Explicit correction—provision of the correct form when an error has been committed. Example: Teacher: “y 1 minus y 2 equals zero.”—Student: “y 2 minus y 1 .”

  6. 6.

    Justification request—questions requiring arguments to support a proposition. Example: Student: “Why does it follow from this condition that d 1 is perpendicular on d 2 ?”

  7. 7.

    Metalinguistic feedback—comments signaling that a linguistic/symbolic expression is inaccurate/inappropriate without providing the correct form. Example 1: Student: “The point is x.”—Teacher: “x is a value, not the name of the point.”

  8. 8.

    Recast—reformulation of all or part of another participant’s utterance. Example: Student: “The two vectors are equal only if x 1 –x 2 is zero and if y 2 –y 1 is zero.”—Teacher: “If their coefficients are equal to zero.”

  9. 9.

    Reinforcement—acknowledging the correctness of an utterance through repetition of the utterance with a falling intonation, and/or through explicit value judgments. Example: Student: “Their modules are equal.”—Teacher: “Their modules are equal. Correct.”

  10. 10.

    Repetition—teacher’s partial or complete repetition of a student’s utterance as a question to signal an error. Example: Student: “The slope is the angle between the line and the x-axis.”—Teacher: “The slope is the angle?”

Response-to-feedback moves

  1. 1.

    Clarification—information provided in response to a clarification request. Example: Teacher: “But what do the axes represent?”—Student: “The y-axis represents the price in Euros and the x-axis is the number of items sold.”

  2. 2.

    Evaluation—value judgments made in response to an evaluation request. Example: Teacher: “Do you agree?”—Student: “No.”

  3. 3.

    Extension—information volunteered by a student to complete another student’s response. Example: Teacher: “What’s V (t) ?”—Student 1: “The value.”—Student 2: “As a function of time.”

  4. 4.

    Justification—information provided by teacher or students in response to a justification request. Example: Teacher: “How do you know the graph should be a straight line?”—Student: “They say it’s a linear relationship.”

  5. 5.

    No response—student response to feedback that does not contain the information requested. Example: Teacher: “In that case, x will be…”—Student: “I have no clue.”

  6. 6.

    Repair—reformulation of a previous linguistic and/or symbolic expression based on feedback received. Example: Student 1: “The value of the slope equals the ratio between the difference of the abscissas and…”—Student 2: “The other way around! Of the ordinates.”—Student 1: “The ratio between the difference of the ordinates and the difference of the abscissas.”

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Temple, C., Doerr, H.M. Developing fluency in the mathematical register through conversation in a tenth-grade classroom. Educ Stud Math 81, 287–306 (2012). https://doi.org/10.1007/s10649-012-9398-6

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