Advertisement

Mathematics Education Research Journal

, Volume 27, Issue 3, pp 311–330 | Cite as

Tense and aspect in word problems about motion: diagram, gesture, and the felt experience of time

  • Elizabeth de Freitas
  • Betina Zolkower
Original Article
First Online:

Abstract

Word problems about motion contain various conjugated verb forms. As students and teachers grapple with such word problems, they jointly operationalize diagrams, gestures, and language. Drawing on findings from a 3-year research project examining the social semiotics of classroom interaction, we show how teachers and students use gesture and diagram to make sense of complex verb forms in such word problems. We focus on the grammatical category of “aspect” for how it broadens the concept of verb tense. Aspect conveys duration and completion or frequency of an event. The aspect of a verb defines its temporal flow (or lack thereof) and the location of a vantage point for making sense of this durational process.

Keywords

Word problems Time Tense Motion Diagram Gesture 
This is a preview of subscription content, log in to check access.

References

  1. Alibali, M., & Nathan, M. J. (2007). Teachers’ gestures as a means of scaffolding students’ understanding: evidence from an early algebra lesson. In R. Goldman, R. Pea, B. Barron, & S. J. Derry (Eds.), Video research in the learning sciences (pp. 349–365). Mahwah, NJ: Erlbaum.Google Scholar
  2. Alibali, M. W., Kita, S., & Young, A. (2000). Gesture and the process of speech production: we think, therefore we gesture. Language and Cognitive Processes, 15(6), 593–613.CrossRefGoogle Scholar
  3. Armstrong, A. & Sinclair, N. (2011). Tell a piecewise story.Mathematics Teaching in the Middle Grades, 16(9), 474–479.Google Scholar
  4. Bach, E. (1981). On time, tense, and aspect: an essay in English metaphysics. In P. Cole (Ed.), Radical pragmatics (pp. 63–81). New York: Academic.Google Scholar
  5. Bhattacharya, T., & Hidam, M. (2011). Space-machine. Conference proceedings for the international conference to review research on science, technology and mathematics education. Episteme-4 (pp. 277–281). Mumbai, India: Macmillan.Google Scholar
  6. Bremigan, E. G. (2001). Dynamic diagrams. Mathematics Teacher, 94(7), 566–575.Google Scholar
  7. Chen, C.-L., & Herbst, P. (2013). The interplay among gestures, discourse, and diagrams in students’ geometrical reasoning. Educational Studies in Mathematics, 83(2), 285–307.CrossRefGoogle Scholar
  8. de Freitas, E. (2012). The diagram as story: unfolding the event-structure of the mathematical diagram. For the Learning of Mathematics, 32(2), 27–33.Google Scholar
  9. de Freitas, E., & Zolkower, B. (2010). Discursive authority in the mathematics classroom: developing teacher capacity to analyze interactions in terms of modality and modulation. In U. Gellert, E. Jablonka, & C. Morgan (Eds.), Proceedings of the 6th International Conference on Mathematics Education and Society (pp. 229–239). Availabe at: http://www.ewi-psy.fu-berlin.de/en/v/mes6/research_papers/index.html.Google Scholar
  10. de Freitas, E., & Zolkower, B. (2011). Developing teacher capacity to explore non-routine problems through a focus on the social semiotics of mathematics classroom discourse. Research in Mathematics Education, 13(3), 229–247.CrossRefGoogle Scholar
  11. Edwards, L. D. (2009). Gestures and conceptual integration in mathematical talk. Educational Studies in Mathematics, 70(2), 127–141.CrossRefGoogle Scholar
  12. Gerofsky, S. (1996). A linguistic and narrative view of word problems in mathematics education. For the Learning of Mathematics, 16(2), 36-45.Google Scholar
  13. Gol Tabaghi, S. & Sinclair, N. (2011). Student diagramming motion: a discursive analysis of visual images. Proceedings of the Annual Meeting of the Association for the Psychology of Mathematics Education.Google Scholar
  14. Halliday, M. A. K. (1978). Language as social semiotic: the social interpretation of language and meaning. Maryland: University Park Press.Google Scholar
  15. Halliday, M. A. K. (2004). In C. Matthiessen (Ed.), An introduction to functional grammar (3rd ed.). London: Hodder Arnold.Google Scholar
  16. Kita, S. (2000). How representational gestures help speaking. In D. McNeill (Ed.), Language and gesture (pp. 162–185). Cambridge: Cambridge University Press.CrossRefGoogle Scholar
  17. Kordemsky, B.A. (1992/1956). The Moscow puzzles: 359 mathematical recreations. Dover Publications.Google Scholar
  18. Martin, J. R. (1993). Genre and literacy: modeling context in educational linguistics. Annual Review of Applied Linguistics, 13, 141–72.CrossRefGoogle Scholar
  19. McNeill, D. (2000). Language and gesture. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
  20. McNeil, D. (1992). Hand and mind: What gestures reveal about thought. Chicago: University of Chicago Press.Google Scholar
  21. Morgan, C. (2006). What does social semiotics have to offer mathematics education research? Educational Studies in Mathematics, 61(1–2), 219–245.CrossRefGoogle Scholar
  22. Netz, R. (1998). Greek mathematical diagrams: their use and their meaning. For the learning of Mathematics, 18(3), 33–39.Google Scholar
  23. O’Halloran, K. L. (1999). Towards a systemic functional analysis of multisemiotic mathematics texts. Semiotica, 124(1), 1–29.CrossRefGoogle Scholar
  24. O’Halloran, K. L. (2000). Classroom discourse in mathematics: a multisemiotic analysis. Linguistics and Education, 10(3), 359–88.CrossRefGoogle Scholar
  25. O’Halloran, K. L. (2003). Intersemiosis in mathematics and science: grammatical metaphor and semiotic metaphor. In M. Taverniers, L. Ravelli, & A. M. Simon-Vandenbergen (Eds.), Grammatical metaphor: views from systemic functional linguistics (pp. 337–65). Amsterdam: John Benjamins.CrossRefGoogle Scholar
  26. O’Halloran, K. L. (2005). Mathematical discourse: language, symbolism and visual images. Australia: Continuum Press.Google Scholar
  27. O’Halloran, K. (2007). Mathematical and scientific forms of knowledge: a systemic functional multimodal grammatical approach. In F. Christie & J. R. Martin (Eds.), Language, knowledge, and pedagogy: functional linguistic and sociological perspectives (pp. 205–235). Australia: Continuum International Publishing Corp.Google Scholar
  28. Pimm, D. (2004). Discourse analysis and mathematics education: an anniversary of sorts (Paper presented at international congress on mathematics education, 10). Denmark: Copenhagen.Google Scholar
  29. Radford, L. (2009). Signifying relative motion: time, space and the semiotics of Cartesian graphs. In Ed. M-W. Roth. Mathematical representation at the interface of body and culture (pp. 45–69). Information Age Publishing.Google Scholar
  30. Roth, M.-W. (2008). The dawning of signs in graph representation. In L. Radford, G. Schubring, & F. Seeger (Eds.), Semiotics in mathematics education: epistemology, history, classroom and culture. Rotterdam: Sense Publishing.Google Scholar
  31. Sherin, B. L. (2000). How students invent representations of motion: a genetic account. Journal of Mathematical Behavior, 19, 399–441.CrossRefGoogle Scholar
  32. Solomon, Y., & O’Neill, J. (1998). Mathematics and narrative. Language and Education, 12(3), 210–221.CrossRefGoogle Scholar
  33. Staats, S., & Batteen, C. (2009). Stretching, sliding and strategy: indexicality in algebraic explanations. Research in Mathematics Education, 11(1), 57–71.CrossRefGoogle Scholar
  34. Van Leeuwen, T. (2005). Introducing social semiotics. New York: Routledge.Google Scholar

Copyright information

© Mathematics Education Research Group of Australasia, Inc. 2014

Authors and Affiliations

  1. 1.Ruth S. Ammon School of EducationAdelphi UniversityGarden CityUSA
  2. 2.Department of Education, Brooklyn CollegeCity University of New YorkNew YorkUSA

Personalised recommendations

Cite article

Buy options