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Historical objections against the number line

(2011) SCIENCE & EDUCATION. 20(9). p.863-880
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Abstract
Historical studies on the development of mathematical concepts will help mathematics teachers to relate their students’ difficulties in understanding to conceptual problems in the history of mathematics. We argue that one popular tool for teaching about numbers, the number line, may not be fit for early teaching of operations involving negative numbers. Our arguments are drawn from the many discussions on negative numbers during the seventeenth and eighteenth centuries from philosophers and mathematicians such as Arnauld, Leibniz, Wallis, Euler and d’Alembert. Not only does division by negative numbers pose problems for the number line, but even the very idea of quantities smaller than nothing has been challenged. Drawing lessons from the history of mathematics, we argue for the introduction of negative numbers in education within the context of symbolic operations.
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MATHEMATICS

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Citation

Please use this url to cite or link to this publication:

Chicago
Heeffer, Albrecht. 2011. “Historical Objections Against the Number Line.” Science & Education 20 (9): 863–880.
APA
Heeffer, A. (2011). Historical objections against the number line. SCIENCE & EDUCATION, 20(9), 863–880.
Vancouver
1.
Heeffer A. Historical objections against the number line. SCIENCE & EDUCATION. 2011;20(9):863–80.
MLA
Heeffer, Albrecht. “Historical Objections Against the Number Line.” SCIENCE & EDUCATION 20.9 (2011): 863–880. Print.
@article{1891046,
  abstract     = {Historical studies on the development of mathematical concepts will help mathematics teachers to relate their students{\textquoteright} difficulties in understanding to conceptual problems in the history of mathematics. We argue that one popular tool for teaching about numbers, the number line, may not be fit for early teaching of operations involving negative numbers. Our arguments are drawn from the many discussions on negative numbers during the seventeenth and eighteenth centuries from philosophers and mathematicians such as Arnauld, Leibniz, Wallis, Euler and d{\textquoteright}Alembert. Not only does division by negative numbers pose problems for the number line, but even the very idea of quantities smaller than nothing has been challenged. Drawing lessons from the history of mathematics, we argue for the introduction of negative numbers in education within the context of symbolic operations.},
  author       = {Heeffer, Albrecht},
  issn         = {0926-7220},
  journal      = {SCIENCE \& EDUCATION},
  keyword      = {MATHEMATICS},
  language     = {eng},
  number       = {9},
  pages        = {863--880},
  title        = {Historical objections against the number line},
  url          = {http://dx.doi.org/10.1007/s11191-011-9349-0},
  volume       = {20},
  year         = {2011},
}

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