TY - JOUR UR - http://lib.ugent.be/catalog/pug01:1891046 ID - pug01:1891046 LA - eng TI - Historical objections against the number line PY - 2011 JO - (2011) SCIENCE & EDUCATION SN - 0926-7220 PB - 2011 AU - Heeffer, Albrecht LW01 001960248142 801000575690 0000-0003-0583-7988 AB - 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. ER -Download RIS file
00000nam^a2200301^i^4500 | |||
001 | 1891046 | ||
005 | 20180813141149.0 | ||
008 | 110819s2011------------------------eng-- | ||
022 | a 0926-7220 | ||
024 | a 000293398200002 2 wos | ||
024 | a 1854/LU-1891046 2 handle | ||
024 | a 10.1007/s11191-011-9349-0 2 doi | ||
040 | a UGent | ||
245 | a Historical objections against the number line | ||
260 | c 2011 | ||
520 | a 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. | ||
598 | a A1 | ||
100 | a Heeffer, Albrecht u LW01 0 001960248142 0 801000575690 0 0000-0003-0583-7988 | ||
650 | a Philosophy and Religion | ||
653 | a MATHEMATICS | ||
773 | t SCIENCE & EDUCATION g Sci. Educ. 2011. 20 (9) p.863-880 q 20:9<863 | ||
856 | 3 Full Text u https://biblio.ugent.be/publication/1891046/file/6760712 z [open] y Numberline-ScienceAndEducation-rev.pdf | ||
920 | a article | ||
852 | x LW b LW01 | ||
922 | a UGENT-LW |
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