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Enhancing classroom discourse about measure to foster a conceptual understanding of geometrical practices

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Abstract

The research project partly presented in this paper aims at investigating the potential of the design of learning environments based on research to enhance language for mathematics learning in order to foster conceptual and language development. In this paper I present a collaboratively designed learning environment on angles, with a focus on enhancing classroom discourse to adapt to the conceptual development of most students in 6th grade. The theoretical background of the research combines Vygotskian and Bakhtinian points of view on language, and relies on the idea of a secondarising process of discourse. An empirical investigation of the enacted learning environment revealed its potential to enhance classroom discourse and students’ conceptual and language development by introducing an explicit distinction between empirical and theoretical aspects of measurement concepts. The findings include the identification of conditions and limitations to be addressed in the design and instructional practices of mathematics- and language-integrated interventions, in general, and for the next steps of the current project.

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Notes

  1. This happens for different reasons, including their home language not being the same as the school language or because of their socio-economic status.

  2. Author of this paper.

  3. TXM was developed at the University of Lyon. https://sourceforge.net/projects/textometrie.

  4. We interpret this ‘no’ as meaning ‘it is the contrary’, as the use of ‘but’ indicates, and the fact that he answered ‘yes and no’.

References

  • Adler, J. (1997). A participatory-inquiry approach and the mediation of mathematical knowledge in a multilingual classroom. Educational Studies in Mathematics, 33, 235–258.

    Article  Google Scholar 

  • 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 

  • Bakhtin, M. M. (1981). In M. Holquist (Ed.), The dialogic imagination: Four essays (C. Emerson & M. Holquist, Trans.). University of Texas Press.

  • Barwell, R. (2016). Formal and informal mathematical discourses: Bakhtin and Vygotsky, dialogue and dialectic. Educational Studies in Mathematics, 92, 331–345.

    Article  Google Scholar 

  • Barwell, R., Ingram, J., Prediger, S., & Planas, N. (2018). ETC4 Panel—Opportunities and challenges of classroom-based research on mathematics and language. In N. Planas & M. Schütte, (Eds.), Proceedings of the fourth ERME topic conference ‘classroom-based research on mathematics and language’ (pp. 17–25). Technical University of Dresden/ERME.

  • Barwell, R., & Pimm, D. (2016). Bakhtin and some dilemmas of mathematics—Language. In M. Phakeng & S. Lerman (Eds.), Mathematics education in a context of inequity, poverty and language diversity (pp. 7–18). Springer.

    Chapter  Google Scholar 

  • Bernié, J.-P. (2002). L’approche des pratiques langagières scolaires à travers la notion de «communauté discursive»: un apport à la didactique comparée? [Approaching school language practices through the notion of “discursive community”: enriching compared didactic?]. Revue Française de Pédagogie, 41, 77–88.

    Article  Google Scholar 

  • Chesnais, A. (2012). L’enseignement de la symétrie orthogonale en sixième: des contraintes, des ressources et des choix [Teaching orthogonal symmetry in 6th grade: Constraints, resources and choices]. Recherches en didactique des mathématiques, 32(2), 229–278.

    Google Scholar 

  • Chesnais, A. (2018). Diversity of teachers’ language in mathematics classrooms about line symmetry and potential impact on students’ learning. In N. Planas, & M. Schütte (Eds.), ETC 4 : fourth ERME Topic Conference ‘Classroom-based research on mathematics and language’ (pp. 41–48). ERME. http://www.mathematik.uni-dortmund.de/~prediger/ERME/18-ETC4_Proceedings-Complete.pdf.

  • Chesnais, A., & Constantin, C. (2020). Developing new discourses to deepen students’ conceptual understanding in mathematics. In Communication at the 7th ETC ‘Language in the Mathematics Classroom’ (Montpellier, February, 18th–21th).

  • Chesnais, A., & Munier, V. (2016). Mesure, mesurage et incertitudes: une problématique inter-didactique mathématiques/physique. In A.-C. Mathe & E. Mounier (Eds.), Actes du séminaire national de didactique des mathématiques (pp. 212–237). IREM de Paris.

    Google Scholar 

  • Chesnais, A., & Munier, V. (2021). Differentiating empirical and theoretical measures in mathematics and physics: A powerful idea for learning, teaching and researching (submitted).

  • Coulange, L., & Train, G. (2020). School mathematical discursive community: The diversity and the role of language for meaning making. Communication at the 7th ETC “Language in the Mathematics Classroom” (Montpellier, February, 18–21th).

  • Erath, K., Ingram, J., Moschkovich, J., & Prediger, S. (2021). Designing and enacting instruction that enhances language for mathematics learning. ZDM Mathematics Education, 53(2), in this issue.

  • Fishbein, E. (1993). The theory of figural concepts. Educational Studies in Mathematics, 24(2), 139–162.

    Article  Google Scholar 

  • Hanna, G. (2000). Proof, explanation and exploration: An overview. Educational Studies in Mathematics, 44(1–2), 5–23.

    Article  Google Scholar 

  • Houdement, C. (2007). Geometrical working space, a tool for comparison. Proceedings CERME, 5, 972–981.

    Google Scholar 

  • Houdement, C., & Kuzniak, A. (2000). Formation des maîtres et paradigmes géométriques [Teachers education and geometrical paradigms]. Recherches en Didactique des Mathématiques, 20(1), 89–116.

    Google Scholar 

  • Jaubert, M. (2007). Langage et construction de savoirs à l’école: un exemple en sciences [Language and knowledge construction in school: an example about sciences]. PUB.

    Google Scholar 

  • Jaubert, M., & Rebière, M., (2012). Communautés discursives disciplinaires scolaires et construction de savoirs: l’hypothèse énonciative [School disciplinary discursive communities and knowledge construction: the hypothesis of enunciation] (with the collaboration of J.-P. Bernié). Forum lecture.ch, 2012–3. https://www.forumlecture.ch/archiv.cfm?issue=3&year=2012#.

  • Lebesgue, H. (1966). Measure and the integral. Translated and edited with a bibliographical essay by Kenneth O. May. San Francisco: Holden-Day, Inc.

  • Lhoste, Y., Boironv, V., Jaubert, M., Orange C., Rebière, M. (2011). Le récit: un outil pour prendre en compte le temps et l’espace et construire des savoirs en sciences? [The narration: A tool for taking time and space into account and constructing scientific knowledge?] Recherches en didactique des sciences et des technologies, 4, 57–82.

  • Moschkovich, J. (2010). Language(s) and learning mathematics: Resources, challenges, and issues for research. In J. Moschkovich (Ed.), Language and mathematics education. Multiple perspectives and directions for research (pp. 1–28). Information Age.

    Google Scholar 

  • Parzysz, B. (1988). “Knowing” vs “seeing”. Problems of the plane representation of space geometry figures. Educational Studies in Mathematics, 19(1), 79–92.

    Article  Google Scholar 

  • Perdijon, J. (2012). La mesure, histoire, sciences et technique. Vuibert.

    Google Scholar 

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

    Google Scholar 

  • Pimm, D. (2004). Discourse analysis and mathematics education: An anniversary of sorts. Paper presented at the ICME-10 Conference, Copenhagen, Denmark, 2004, July 4–10.

  • Pöhler, B., & Prediger, S. (2015). Intertwining lexical and conceptual learning trajectories—A design research study on dual macro-scaffolding towards percentages. Eurasia Journal of Mathematics, Science & Technology Education, 11(6), 1697–1722. https://doi.org/10.12973/eurasia.2015.1497a

    Article  Google Scholar 

  • Prediger, S. (2019). Investigating and promoting teachers’ expertise for language-responsive mathematics teaching. Mathematics Education Research Journal, 31, 367–392.

    Article  Google Scholar 

  • Prediger, S., & Şahin-Gür, D. (2020). Eleventh graders’ increasingly elaborate language use for dis-entangling amount and change—A case study on the epistemic role of syntactical language complexity. Journal für Mathematikdidaktik, 41(1), 43–79. https://doi.org/10.1007/s13138-019-00155-x

    Article  Google Scholar 

  • Prediger, S., & Wessel, L. (2013). Fostering German language learners’ constructions of meanings for fractions—Design and effects of a language- and mathematics-integrated intervention. Mathematics Education Research Journal, 25(3), 435–456. https://doi.org/10.1007/s13394-013-0079-2

    Article  Google Scholar 

  • Prediger, S., & Zindel, C. (2017). School academic language demands for understanding functional relationships: A design research project on the role of language in reading and learning. EURASIA Journal of Mathematics, Science and Technology Education, 13(7b), 4157–4188.

    Google Scholar 

  • Radford, L., & Barwell, R. (2016). Language in mathematics education research. Second handbook of PME (pp. 275–313). Sense.

    Google Scholar 

  • Schleppegrell, M. J. (2010). Language in mathematics teaching and learning. A research review. In J. Moschkovitch (Ed.), Language and mathematics education (pp. 73–112). Information Age Publishing.

    Google Scholar 

  • Sfard, A., & Linchevski, L. (1994). The gains and the pitfalls of reification—The case of algebra. Educational Studies in Mathematics, 26, 191–228.

    Article  Google Scholar 

  • Vergnaud, G. (1998). Towards a cognitive theory of practice. In A. Sierpinska & J. Kilpatrick (Eds.), Mathematics education as a research domain: A search for identity. ICMI Study Book 1 (pp. 227–240). Dordrecht: Kluwer.

    Google Scholar 

  • Vygotsky, L. S. (1934/1986). Thought and language. Translated and reprinted 1986. MIT Press.

  • Wood, D., Bruner, J., & Ross, G. (1976). The role of tutoring in problem solving. Journal of Child Psychiatry, 17, 89–100.

    Article  Google Scholar 

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Correspondence to Aurélie Chesnais.

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Appendices

Appendix 1

See Table 6.

Table 6 Details of analysed classroom sessions’ transcripts

Appendix 2: Proportion of the usages of the three locutions by students

See Figs. 10, 11 and 12.

Fig. 10
figure 10

Distribution of the usages of theoretical measure among students and teachers per class

Fig. 11
figure 11

Distribution of the usages of theoretical value among students and teachers per class

Fig. 12
figure 12

Distribution of the usages of measured value among students and teachers per class

Appendix 3: Evolution of the usages of the three locutions in each of the classrooms

See Figs. 13, 14, 15, 16 and 17.

Fig. 13
figure 13

Cumulative evolution of the usages of the three locutions in class Cel1

Fig. 14
figure 14

Cumulative evolution of the usages of the three locutions in class Cel2

Fig. 15
figure 15

Cumulative evolution of the usages of the three locutions in class Dor1

Fig. 16
figure 16

Cumulative evolution of the usages of the three locutions in class Dor2

Fig. 17
figure 17

Cumulative evolution of the usages of the three locutions in Jus’s class

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Chesnais, A. Enhancing classroom discourse about measure to foster a conceptual understanding of geometrical practices. ZDM Mathematics Education 53, 337–357 (2021). https://doi.org/10.1007/s11858-021-01255-0

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