Skip to main content
Log in

What’s the problem? Meaning making and learning to do mathematical word problems in the context of digital tools

  • Published:
Instructional Science Aims and scope Submit manuscript

Abstract

The general background of this study is an interest in how digital tools contribute to structuring learning activities. The specific interest is to explore how such tools co-determine students’ reasoning when solving word problems in mathematics, and what kind of learning that follows. Theoretically the research takes its point of departure in a sociocultural perspective on the role of cultural tools in thinking, and in a complementary interest in the role of the communicative framing of cognitive activities. Data have been collected through video documentation of classroom activities in secondary schools where multimedia tools are integrated into mathematics teaching. The focus of the analysis is on cases where the students encounter some kind of difficulty. The results show how the tool to a significant degree co-determines the meaning making practices of students. Thus, it is not a passive element in the situation; rather it invites certain types of activities, for instance iterative computations that do not necessarily rely on an analysis of the problems to be solved. For long periods of time the students’ activities are framed within the context of the tool, and they do not engage in discussing mathematics at all when solving the problems. It is argued that both from a practical and theoretical point of view it is important to scrutinize what competences students develop when using tools of this kind.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4

Similar content being viewed by others

Notes

  1. VETA (literally: KNOW) is a Swedish commercial company specialising in offering education in mathematics, physics, language and nursing- and healthcare-education through web-based educational software (cf. http://www.veta.com/).

  2. In mathematics text books and exercise books in Sweden, there is generally an Answer book section (Swedish: Facit) at the end of the book. This implies that Swedish students are used to checking their calculations by comparing them with the answer given in the Facit. What the students are discussing in several of the excerpts we will present is the possibility if there is a mistake in the Facit.

  3. The data are taken from a larger project which contains extensive additional material, including interviews with teachers and participants, additional recordings from uses of web-based learning software in other subjects etc.

References

  • Bishop, A., Clements, M., Keitel, C., Kilpatrick, J., & Leung, F. (Eds.). (2003). Second international handbook of mathematics education. Cornwall, Great Britain: Kluwer.

    Google Scholar 

  • Blumenfeld, P., Soloway, E., Marks, R., Krajcik, J., Guzdal, M., & Palincsar, A. (1991). Motivating project-based learning: Sustaining the doing, supporting the learning. Educational Psychologist, 26, 369–398.

    Article  Google Scholar 

  • Brosseau, G. (1997). Theory of didactical situations in mathematics. Dordrecht, The Netherlands: Kluwer.

    Google Scholar 

  • Carpenter, T. P., Lindquist, M. M., Matthews, W., & Silver, E. A. (1983). Results of the third NAEP mathematics assessment: Secondary school. Mathematics Teacher, 76, 652–659.

    Google Scholar 

  • Goffman, E. (1986). Frame analysis: An essay on the organization of experience. Boston, MA: Northeastern University Press.

    Google Scholar 

  • Greeno, J. G., Collins, A., & Resnick, L. B. (1996). Cognition and learning. In D. C. Berliner & R. C. Calfee (Eds.), Handbook of educational psychology (pp. 15–46). London: Prentice-Hall.

    Google Scholar 

  • Greer, B. (1993). The modeling perspective on wor(l)d problems. Journal of Mathematical Behavior, 12, 239–250.

    Google Scholar 

  • Griffin, P., Belyaeva, A., & Soldatova, G. (1993). Creating and reconstituting contexts for educational interactions, including a computer program. In E. A. Forman, N. Minick, & C. A. Stone (Eds.), Contexts for learning—sociocultural dynamics in children’s development. New York: Oxford University Press Inc.

    Google Scholar 

  • Guin, D., Ruthven, K., & Trouche, L. (Eds.) (2005). The didactical challenge of symbolic calculators. Turning a computational device into a mathematical instrument. New York, USA: Springer.

    Google Scholar 

  • Hatano, G., Miyake, Y., & Binks, M. G. (1977). Performance of expert abacus operators. Cognition, 5, 47–55.

    Article  Google Scholar 

  • Jordan, B., & Henderson, A. (1995). Interaction analysis: Foundations and practice. The Journal of the Learning Sciences, 4, 39–103.

    Article  Google Scholar 

  • Lafer, S., & Markert, A. (1994). Authentic learning situations and the potential of Lego TC Logo. Computers in the School, 1, 79–94.

    Google Scholar 

  • Lave, J. (1988). Cognition in practice: Mind, mathematics and culture in everyday life. Cambridge, MA: Cambridge University Press.

    Google Scholar 

  • Lave, J., & Wenger, E. (1991). Situated learning: Legitimate peripheral participation. Cambridge, MA: Cambridge University Press.

    Google Scholar 

  • Linderoth, J. (2004). Datorspelandets mening: Bortom idén om den interaktiva illusionen. Goteborg: Acta Universitatis Gothoburgensis.

    Google Scholar 

  • Luppinici, R. (2007). Review of computer mediated communication research for education. Instructional Science, 35, 141–185.

    Article  Google Scholar 

  • Masalski, W. (Ed.) (2005). Technology-supported mathematics learning environments: Sixty-seventh yearbook. Reston, VA.: National Council of Teachers of Mathematics.

    Google Scholar 

  • Miller, K. F., & Stigler, J. W. (1991). Meanings of skill: Effects of abacus expertise on number representation. Cognition and Instruction, 8, 29–67.

    Article  Google Scholar 

  • Nunes, T., Schliemann, A. D., & Carraher, D. W. (1993). Street mathematics and school mathematics. Cambridge, England: Cambridge University Press.

    Google Scholar 

  • Papert, S. (1993). The children’s machine. Basic Books: New York.

    Google Scholar 

  • Rogoff, B., & Lave, J. (Ed.). (1984). Everyday cognition: Its development in social context. Cambridge, MA: Harvard University Press.

    Google Scholar 

  • Ruthven, K. (2006). Embedding new technologies in complex ongoing practices of school mathematics Education. International Journal for Technology in Mathematics Education, 13, 161–167.

    Google Scholar 

  • Säljö, R., Eklund, A.-C., & Mäkitalo, Å. (2006). Reasoning with mental tools and physical artefacts in everyday problem solving. In L. Verschaffel, F. Dochy, M. Boekaerts, & S. Vosniadou (Eds.), Instructional psychology: Past, present and future trends (pp. 73–90). Oxford, England: Pergamon.

    Google Scholar 

  • Säljö, R., & Wyndhamn, J. (1988). A week has seven days. Or does it? On bridging linguistic openness and mathematical precision. For the Learning of Mathematics, 8, 16–19.

    Google Scholar 

  • Säljö, R., & Wyndhamn, J. (1993). Solving everyday problems in the formal setting. An empirical study of the school as context for thought. In S. Chaiklin & J. Lave (Eds.), Understanding practice. Perspectives on activity and context (pp. 327–342). Cambridge, MA: Cambridge University Press.

    Google Scholar 

  • Verschaffel, L., De Corte, E., & Lasure, S. (1994). Realistic considerations in mathematical modeling in the elementary school. Learning and Instruction, 4, 273–294.

    Article  Google Scholar 

  • Verschaffel, L., Greer, B., & De Corte, E. (2000). Making sense of word problems. Lisse, The Netherlands: Swets & Zeitlinger.

    Google Scholar 

  • Vygotsky, L. S. (1978). Mind in society: The development of higher psychological processes. Cambridge, MA: Harvard University Press.

    Google Scholar 

  • Wertsch, J. V. (1998). Mind as action. New York, NY: Oxford University Press.

    Google Scholar 

  • Wyndhamn, J., & Säljö, R. (1997). Word problems and mathematical reasoning-a study of children’s mastery of reference and meaning in textual realities. Learning and Instruction, 7, 361–382.

    Article  Google Scholar 

  • Yoshida, H., Verschaffel, L., & De Corte, E. (1997). Realistic considerations in solving problematic word problems: Do Japanese and Belgian children have the same difficulties? Learning and Instruction, 7, 329–338.

    Article  Google Scholar 

Download references

Acknowledgements

The research reported has been funded by LearnIT, the research program on learning and ICT of the Knowledge (KK) foundation. The work has been carried out within the Linnaeus Centre for Research on Learning, Interaction and Mediated Communication in Contemporary Society (LinCS). This article was written while the third author was Finland Distinguished Professor at the University of Turku.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Annika Lantz-Andersson.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Lantz-Andersson, A., Linderoth, J. & Säljö, R. What’s the problem? Meaning making and learning to do mathematical word problems in the context of digital tools. Instr Sci 37, 325–343 (2009). https://doi.org/10.1007/s11251-008-9050-0

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11251-008-9050-0

Keywords

Navigation