Education, Division &amp; Derivative: Putting A Sky Above A Field Or A Meadow

The sky is a tentative suggestion for extension group theory, that has supervariables with flexible domains, that would allow the formulation of dynamic rational functions, such that division by zero is prevented by manipulation of the domain. This would allow an algebraic approach to the derivative. Meadows are no alternative to such an approach. The world needs Academic Schools in which teaching is merged with empirical research on didactics.

See 10.5281/zenodo.292247 "A potential relation between the algebraic approach to calculus and rational functions", February 2017, for an improved understanding of the notion of "rational function". This new paper on rational functions seems to require an edit of the paper on the "sky".

Keywords

division, quotient, dynamic quotient, simplify, algebraic approach to the derivative, calculus, supervariables, field, meadow, division by zero, abstract data types, computer algebra, rational functions, Pierre van Hiele, levels of abstraction, didactics of mathematics, mathematics education research, research mathematics, academic school

Impact byBIP!

	selected citations These citations are derived from selected sources. This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).	2
	popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.	Average
	influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).	Top 10%
	impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.	Average