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Historical objections against the number line

Albrecht Heeffer UGent (2011) SCIENCE & EDUCATION. 20(9). p.863-880
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.
Please use this url to cite or link to this publication:
author
organization
year
type
journalArticle (original)
publication status
published
subject
keyword
MATHEMATICS
journal title
SCIENCE & EDUCATION
Sci. Educ.
volume
20
issue
9
pages
863 - 880
Web of Science type
Article
Web of Science id
000293398200002
JCR category
HISTORY & PHILOSOPHY OF SCIENCE
JCR impact factor
0.702 (2011)
JCR rank
14/56 (2011)
JCR quartile
2 (2011)
ISSN
0926-7220
DOI
10.1007/s11191-011-9349-0
language
English
UGent publication?
yes
classification
A1
copyright statement
I have transferred the copyright for this publication to the publisher
id
1891046
handle
http://hdl.handle.net/1854/LU-1891046
date created
2011-08-19 16:03:11
date last changed
2016-12-19 15:46:39
@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},
}

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.