# Using the academic literacy in mathematics framework to uncover multiple aspects of activity during peer mathematical discussions

## Abstract

This paper illustrates how the academic literacy in mathematics framework (Moschkovich, J Math Behav 40:43–62, 2015) can be used to uncover the multiple layers of work bilingual learners accomplish during mathematical discussions. Using this framework allows researchers to examine students’ joint mathematical activity in terms of mathematical proficiency, mathematical practices, and mathematical discourse. The use of the framework is illustrated through analysis of two mathematical discussions among middle school students. We conclude with reflections on the utility of the framework and consider possible pedagogical implications of this work.

## Keywords

Mathematical discourse Peer discussions Academic literacy in mathematics Multilingual mathematics classrooms## Notes

### Acknowledgements

This research was supported by grants from the National Science Foundation (#0424983 and 0096065). Any opinions, findings, and conclusions or recommendations expressed in this paper are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.

## References

- Cobb, P., Stephan, M., McClain, K., & Gravemeijer, K. (2001). Participating in classroom mathematical practices.
*Journal of the Learning Sciences, 10*, 113–164. https://doi.org/10.1207/S15327809JLS10-1-2_6.CrossRefGoogle Scholar - Cobb, P., Wood, T., & Yackel, E. (1993). Discourse, mathematical thinking, and classroom practice. In E. 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 - Crowhurst, M. (1994).
*Language and learning across the curriculum*. Scarborough: Allyn and Bacon.Google Scholar - Forman, E. (1996). Learning mathematics as participation in classroom practice: Implications of sociocultural theory. In L. Steffe, P. Nesher, P. Cobb, G. A. Goldin & B. Greer (Eds.),
*Theories of mathematics learning*(pp. 115–130). Mahwah, NJ: Lawrence Erlbaum.Google Scholar - Gee, J. (1999).
*An introduction to discourse analysis: Theory and method*. New York: Routledge.Google Scholar - Gutiérrez, K. D., Baquedano-López, P., & Tejeda, C. (1999). Rethinking diversity: Hybridity and hybrid language practices in the third space.
*Mind, Culture, and Activity, 6*(4), 286–303.CrossRefGoogle Scholar - Halliday, M. A. K. (1978). Sociolinguistic aspects of mathematical education. In M. A. K. Halliday (Ed.),
*Language as a social semiotic: The social interpretation of language and meaning*(pp. 194–204). Baltimore: University Park Press.Google Scholar - Hiebert, J., & Carpenter, T. P. (1992). Learning and teaching with understanding. In D. Grouws (Ed.),
*Hanbook of research in mathematics teaching and learning*(pp. 65–97). New York: Macmillan.Google Scholar - Hiebert, J., & Grouws, D. (2007). The effects of classroom mathematics teaching on students’ learning. In F. Lester (Ed.),
*Second handbook of research on mathematics teaching and learning*(pp. 371–404). Reston: National Council of Teachers of Mathematics.Google Scholar - Hymes, D. (1972). On communicative competence. In J. B. Pride & J. Holmes, (Eds.)
*Sociolinguistics*(pp. 269–293). London: Penguin.**(Reprinted in Duranti, A. (Ed.). (2009). Linguistic anthropology: A reader (Vol. 1). John Wiley & Sons)**Google Scholar - Kilpatrick, J., Swafford, J., & Findell, B. (2001). Adding it up: Helping children learn mathematics.In J. Kilpatrick, J. Swafford & B. Findell (Eds.), National Research Council. Washington, DC: National Academy Press.Google Scholar
- Lamon, S. (1996). The development of unitizing: Its role in children’s partitioning strategies.
*Journal for Research in Mathematics Education, 27*(2), 170–193.CrossRefGoogle 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*, 29–64.CrossRefGoogle Scholar - Lappan, G., Fey, J. T., Fitzgerald, W. M., Friel, S. N., & Phillips, E. D. (1998).
*Connected mathematics*. White Plains: Dale Seymour Publications.Google Scholar - Leinhardt, G., Zaslavsky, O., & Stein, M. K. (1990). Functions, graphs and graphing: Tasks learning and teaching.
*Review of Educational Research, 60*(1), 1–64.CrossRefGoogle Scholar - Moschkovich, J. N. (1999). Supporting the participation of English language learners in mathematical discussions.
*For the Learning of Mathematics, 19*, 11–19.Google Scholar - Moschkovich, J. N. (2002). A situated and sociocultural perspective on bilingual mathematics learners.
*Mathematical Thinking and Learning, 4*, 189–212. https://doi.org/10.1207/S15327833MTL04023_5.CrossRefGoogle Scholar - Moschkovich, J. N. (2004). Appropriating mathematical practices: A case study of learning to use and explore functions through interactions with a tutor.
*Educational Studies in Mathematics, 55*, 49–80.CrossRefGoogle Scholar - Moschkovich, J. N. (2007). Examining mathematical discourse practices.
*For the Learning of Mathematics, 27*, 24–30.Google Scholar - Moschkovich, J. N. (2008). “I went by twos, he went by one:” Multiple interpretations of inscriptions as resources for mathematical discussions.
*The Journal of the Learning Sciences, 17*(4), 551–587. https://doi.org/10.1080/10508400802395077.CrossRefGoogle Scholar - Moschkovich, J. N. (2013). Issues regarding the concept of mathematical practices. In Y. Li & J. N. Moschkovich (Eds.),
*Proficiency and beliefs in learning and teaching mathematics: Learning from Alan Schoenfeld and Günter Toerner*(pp. 257–275). Rotterdam: Sense Publishers.CrossRefGoogle Scholar - Moschkovich, J. N. (2015). Academic literacy in mathematics for English learners.
*The Journal of Mathematical Behavior, 40*, 43–62. https://doi.org/10.1016/j.jmathb.2015.01.005.CrossRefGoogle Scholar - Moschkovich, J. N., & Brenner, M. E. (2000). Integrating a naturalistic paradigm into research on mathematics and science cognition and learning. In A. E. Kelly & R. A. Lesh (Eds.),
*Handbook of research design in mathematics and science education*(pp. 457–486). Mahwah: Lawrence Erlbaum.Google Scholar - O’Connor, M. C., & Michaels, S. (1996). Shifting participant frameworks: Orchestrating thinking practices in group discussion.
*Discourse, Learning, and Schooling, 63*, 103.Google Scholar - Pimm, D. (1987).
*Speaking mathematically: Communication in mathematics classrooms*. New York: Routledge.Google Scholar - Pirie, S., & Schwarzenberger, R. (1988). Mathematical discussion and mathematical understanding.
*Educational Studies in Mathematics, 19*, 459–470.CrossRefGoogle Scholar - Rasmussen, C., Zandieh, M., King, K., & Teppo, A. (2005). Advancing mathematical activity: A practice-oriented view of advanced mathematical thinking.
*Mathematical Thinking and Learning, 7*, 51–73. https://doi.org/10.1207/s15327833mtl0701_4.CrossRefGoogle Scholar - Schleppegrell, M. (2007). The linguistic challenges of mathematics teaching and learning: A review.
*Reading Writing Quarterly, 23*, 139–159. https://doi.org/10.1080/10573560601158461.CrossRefGoogle Scholar - Scribner, S. (1984). Studying working intelligence. In B. Rogoff & J. Lave (Eds.),
*Everyday cognition: Its development in social context*(pp. 9–40). Cambridge: Harvard University Press.Google Scholar - Sfard, A. (2008).
*Thinking as communicating: Human development, the growth of discourses, and mathematizing*. Cambridge: Cambridge University Press.CrossRefGoogle Scholar - Star, J. R. (2005). Reconceptualizing procedural knowledge.
*Journal for Research in Mathematics Education, 36*(5), 404–411. https://doi.org/10.2307/30034943.Google Scholar - Thompson, A. G., Philipp, R. A., Thompson, P. W., & Boyd, B. A. (1994). Calculational and conceptual orientations in teaching mathematics. In A. Coxford (Ed.),
*1994 yearbook of the NCTM*(pp. 79–92). Reston: NCTM.Google Scholar - Vygotsky, L. S. (1978).
*Mind in society: The development of higher psychological processes*. Cambridge: Harvard University Press.Google Scholar - Zahner, W. (2015). The rise and run of a computational understanding of slope in a conceptually focused bilingual algebra class.
*Educational Studies in Mathematics, 88*(1), 19–41. https://doi.org/10.1007/s10649-014-9575-x.CrossRefGoogle Scholar - Zahner, W., & Moschkovich, J. N. (2010). Talking while computing in groups: The not-so private functions of computational private speech in mathematical discussions.
*Mind Culture and Activity, 17*, 265–283.CrossRefGoogle Scholar - Zahner, W., & Moschkovich, J. N. (2011). Bilingual students using two languages during peer mathematics discussions: ¿Qué significa? Estudiantes bilingües usando dos idomas en sus discusiones matemáticas: What does it mean? In K. Tellez, J. N. Moschkovich & M. Civil (Eds.),
*Latinos and mathematics education: Research on learning and teaching in classrooms and communities*(pp. 37–62). Charlotte: Information Age Publishing.Google Scholar - Zahner, W., Velazquez, G., Moschkovich, J. N., Vahey, P., & Lara-Meloy, T. (2012). Mathematics teaching practices with technology that support conceptual understanding for Latino/a students.
*Journal of Mathematical Behavior, 31*, 431–446. https://doi.org/10.1016/j.jmathb.2012.06.002.CrossRefGoogle Scholar