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The Number Line in the Elementary Classroom as a Vehicle for Mathematical Thinking

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Mathematical Cognition and Understanding
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Abstract

This chapter builds on research related to the number line by exploring it as a vehicle for mathematical understanding in the naturalistic setting of Grade 2 and Grade 3 elementary classrooms. Starting from pupils’ embodiment of the number line, and explicitly giving emphasis on the nature of the number line, an instructional sequence was designed and organized around number sequence and recognition, addition and subtraction in the domain from 1 through 1000. Using evidence from pupils’ own productions, this chapter points to the role the number line plays in supporting pupils’ sense making, the elaboration of informal strategies, leading to the development of more sophisticated ones.

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References

  • Ball, D. L. (2003). Mathematical proficiency for all students: Toward a strategic research and development program in mathematics education. RAND Science and Technology Policy Institute.

    Google Scholar 

  • Beishuizen, M. (1993). Mental strategies and materials or models for addition and subtraction up to 100 in Dutch second grades. Journal for Research in Mathematics Education, 24, 294–323.

    Article  Google Scholar 

  • Beishuizen, M. (2010). The empty number line. In I. Thompson (Ed.), Issues in teaching Numercay in primary school (2nd ed., pp. 174–186). Open University Press.

    Google Scholar 

  • Beishuizen, M., Van Putten, C. M., & Van Mulken, F. (1997). Mental arithmetic and strategy use with indirect number problems up to one hundred. Learning and Instruction, 7(1), 87–106.

    Article  Google Scholar 

  • Bobis, J. (2007). The empty number line: A useful tool or another procedure? Teaching Children Mathematics, 13(8), 410–413.

    Article  Google Scholar 

  • Booth, J. L., & Siegler, R. S. (2006). Developmental and individual differences in pure numerical estimation. Developmental Psychology, 41, 189–201.

    Article  Google Scholar 

  • Booth, J. L., & Siegler, R. S. (2008). Numerical magnitude representations influence arithmetic learning. Child Development, 79, 1016–1031.

    Article  Google Scholar 

  • Burns, M. (2004). Writing in math. Educational Leadership, 62(2), 30–32.

    Google Scholar 

  • Dabell, J., Keogh, B., & Naylor, S. (2008). Concept cartoons in mathematics education. Millgate House.

    Google Scholar 

  • Dickinson, P., & Eade, F. (2004). Using the number line to investigate the solving of linear equations. For the Learning of Mathematics, 24(2), 41–47.

    Google Scholar 

  • Diezmann, C. M., & Lowrie, T. J. (2007). The development of primary students’ knowledge of the structured number line. In J. H. Woo, H. C. Lew, K. S. Park, & D. Y. Seo (Eds.), Proceedings of the 31st annual psychology of mathematics education conference (Vol. 2, pp. 201–208) PME.

    Google Scholar 

  • Diezmann, C. M., Lowrie, T. J., & Sugars, L. (2010). Primary students’ success on the structured number line. Australian Primary Mathematics Classroom, 15(4), 24–28.

    Google Scholar 

  • Ernest, P. (1985). The number line as a teaching aid. Educational Studies in Mathematics, 16, 411–424.

    Article  Google Scholar 

  • Freudenthal, H. (1973). Mathematics as an educational task. Reidel Publishing Company.

    Google Scholar 

  • Frykholm, J. (2010). Learning to think mathematically with the number line: A resource for teachers, a tool for young children. The Math Learning Center.

    Google Scholar 

  • Gagatsis, A., Shiakalli, M., & Panaoura, A. (2003). La droite arithmétique comme modéle géométrique de l’addition et de la soustraction des nombres entiers. Annales de Didactique et de Sciences Cognitives, 8, 95–112.

    Google Scholar 

  • Gravemeijer, K. (1999). How emergent models may Foster the constitution of formal mathematics. Mathematical Thinking and Learning, 1(2), 155–177.

    Article  Google Scholar 

  • Gravemeijer, K. (2004). Learning trajectories and local instruction theories as means of support for teachers in reform mathematics education. Mathematical Thinking and Learning, 6(2), 105–128.

    Article  Google Scholar 

  • Gravemeijer, K. (2020). A socio-constructivist elaboration on realistic mathematics education. In M. Van den Heuvel-Panhuizen (Ed.), National reflections on the Netherlands didactics of mathematics ICME-13. Monographs (pp. 217–233). Springer.

    Chapter  Google Scholar 

  • Gray, E., & Doritou, M. (2008). The number line: Ambiguity and interpretation. In O. Figueras, J. Cortina, S. Alatorre, T. Rojano, & A. Sepúlveda (Eds.), Proceedings of the 32nd conference of the international group for the psychology of mathematics education (Vol. 3, pp. 97–104). PME.

    Google Scholar 

  • Hartnett, J. (2007). Categorisation of mental computation strategies to support teaching and to encourage classroom dialogue. In J. Watson & K. Beswick (Eds.), Mathematics: Essential research, essential practice (Vol. 1, pp. 345–352). MERGA.

    Google Scholar 

  • Herbst, P. (1997). The number-line metaphor in the discourse of a textbooks series. For the Learning of Mathematics, 17(3), 36–45.

    Google Scholar 

  • Kilpatrick, J., Swafford, J., & Findell, B. (2001). Adding it up. Helping children learn mathematics. National Academy Press.

    Google Scholar 

  • Lemonidis, C. (2016). Mental computation and estimation: Implications for mathematics education, teaching and learning. Routledge.

    Google Scholar 

  • Lemonidis, C. E., & Gkolfos, A. (2020). Number line in the history and the education of mathematics. Inovacije U Nastavi, 33(1), 36–56.

    Article  Google Scholar 

  • Moone, G., & Groot, C. (2005). Time is of the essence. Teaching Children Mathematics, 12(2), 90–98.

    Article  Google Scholar 

  • Murphy. (2011). Comparing the use of the empty number line in England and The Netherlands. British Educational Research Journal, 31, 147–161.

    Article  Google Scholar 

  • Naylor, S., & Keogh, B. (2013). Concept cartoons: What have we learnt? Journal of Turkish Science Education, 10(1), 3–11.

    Google Scholar 

  • Novick, L. R. (1990). Representational transfer in problem solving. Psychological Science, 1(2), 128–132.

    Article  Google Scholar 

  • Onslow, B., Adams, L., Edmunds, G., Waters, J., Chapple, N., Kealey, B., & Eady, J. (2005). Are you in the zone? Teaching Children Mathematics, 11(9), 458–463.

    Google Scholar 

  • Pelczer, I., Singer, F., & Voica, C. (2011). Between algebra and geometry: The dual nature of the number line. In M. Pytlak, T. Rowland, & T. Swoboda (Eds.), Proceedings of the seventh congress of the european society for research in mathematics education (pp. 376–385). University of Rzesów.

    Google Scholar 

  • Reys, R. E., Lindquist, M. M., Lambdin, D. V., Smith, N. L., Rogers, A., Falle, J., & Frid, S. (2012). Helping children learn mathematics. Wiley.

    Google Scholar 

  • Selter, C. (1998). Building on children’s mathematics – A teaching experiment in Grade three. Educational Studies in Mathematics, 36, 1–27.

    Article  Google Scholar 

  • Sexton, M., Gervasoni, A., & Brandenburg, R. (2009). Using a concept cartoon to gain insight into children’s calculation strategies. Australian Primary Mathematics Classroom, 14(4), 24–28.

    Google Scholar 

  • Sidney, P. G., Thompson, C. A., & Rivera, F. D. (2019). Number lines, but not area models, support children’s accuracy and conceptual models of fraction division. Contemporary Educational Psychology, 58, 288–298.

    Article  Google Scholar 

  • Siegler, R. S., & Booth, J. (2005). Development of numerical estimation in young children. Child Development, 75(2), 428–444.

    Article  Google Scholar 

  • Skoumpourdi, C. (2010). The number line: An auxiliary means or an obstacle? International Journal for Mathematics Teaching and Learning, 270, 1–12.

    Google Scholar 

  • Teppo, A., & Van den Heuvel-Panhuizen, M. (2014). Visual representations as objects of analysis: The number line as an example. ZDM Mathematics Education, 46, 45–58.

    Article  Google Scholar 

  • Thompson, Ι. (2010). Issues in teaching numeracy in primary schools (2nd ed.). Open University Press.

    Google Scholar 

  • Threlfall, J. (2000). Mental calculation strategies. Research in Mathematics Education, 2(1), 77–90.

    Article  Google Scholar 

  • Umiltà, C., Priftis, K., & Zorzi, M. (2010). Visuo-spatial representation of number magnitude. In V. Coltheart (Ed.), Tutorials in visual cognition (pp. 337–348). Psychology Press.

    Google Scholar 

  • Van den Heuvel-Panhuizen, M. (2003). The didactical use of models in realistic mathematics education: An example from a longitudinal trajectory on percentage. Educational Studies in Mathematics, 54(1), 9–35.

    Article  Google Scholar 

  • Van den Heuvel-Panhuizen, M. (2008). Learning from “Didactikids”: An impetus for revisiting the empty number line. Mathematics Education Research Journal, 20(3), 6–31.

    Article  Google Scholar 

  • Yang, D. C. (2005). Developing number sense through mathematical diary writing. Australian Primary Mathematics Classroom, 10(4), 9–14.

    Google Scholar 

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Correspondence to Maria Pericleous .

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Pericleous, M. (2023). The Number Line in the Elementary Classroom as a Vehicle for Mathematical Thinking. In: Robinson, K.M., Dubé, A.K., Kotsopoulos, D. (eds) Mathematical Cognition and Understanding. Springer, Cham. https://doi.org/10.1007/978-3-031-29195-1_9

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  • DOI: https://doi.org/10.1007/978-3-031-29195-1_9

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-29194-4

  • Online ISBN: 978-3-031-29195-1

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