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Understanding Negative Numbers

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Part of the book series: Research in Mathematics Education ((RME))

Abstract

This chapter focuses on the development of concepts that children draw on as they work toward understanding negative numbers. Framed from a conceptual change lens, I discuss different interpretations children have of minus signs, numerical order, numerical values, and addition and subtraction operations and how children draw on these varied conceptions to solve addition and subtraction problems involving negative numbers. Children’s unconventional attempts at solving these problems reflect their efforts to make sense of negatives in light of their whole number understanding.

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Notes

  1. 1.

    If we only consider the negative integer sequence, the starting point is −1, just as 1 is the starting point of the positive integer sequence.

  2. 2.

    Students will pick a large negative number to start their negative sequence.

  3. 3.

    In colored chip models, one color of counters (i.e., chips) represents positives and another color of counters represents negatives. A positive counter cancels out a negative counter. For −3 + 4, one would put out three negative chips and four positive chips. Three of the positive and negative chip pairs would cancel out, leaving one positive chip, or an answer of 1.

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Acknowledgements

Some of the work discussed here was supported by NSF CAREER award DRL-1350281. Many thanks to Mahtob Aqazade, Sherri Farmer, and the children with whom we have worked for their willingness to engage in the world of negative numbers with me.

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  1. Department of Curriculum & Instruction, Purdue University, West Lafayette, IN, USA

    Laura Bofferding

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  1. Department of Mathematics, Virginia Tech, Blacksburg, VA, USA

    Anderson Norton

  2. Department of Psychology, University of Wisconsin–Madison, Madison, WI, USA

    Martha W. Alibali

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Bofferding, L. (2019). Understanding Negative Numbers. In: Norton, A., Alibali, M.W. (eds) Constructing Number. Research in Mathematics Education. Springer, Cham. https://doi.org/10.1007/978-3-030-00491-0_12

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