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We identify two ways of introducing negative numbers. In the first one, a totally ordered set (L, $\prec $) is presupposed, an element 0 in L is arbitrarily taken, and a number a is negative when a 0. In the second one, a negative number is defined by the formula a + (−a) = 0. From a mathematical perspective, the first method involves the idea of a totally ordered group (G,+, 0,<), while the second...
This article presents the author’s reflections, comments and problems that arise in relation to the issue of defining the subject matter knowledge a teacher should have in the context of Even’s theoretical framework. They incline to start working on a considerable modification of this conception in order to explore its adaptability in other contexts. This paper also includes initial results of this...
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