Reflection on the Skemp Article

I find that this article advocates a view point but does not necessarily use the best examples. For example the article stresses on computing the area of a rectangle as an instance of instrumental teaching. It offers however no explanation on why the area of a rectangle is base times height. There is no obvious answer to this; since area from a mathematical stand point is merely the Lebesgue measure on the plane. Of course given the ubiquity of the concept of area across all cultures old and new indicates that something more basic is at play. This of course is that the concept of area is the generalization of the number of objects in an array, where an array of 5 rows and 7 columns would have 35 squares, similar to how a rectangle of length 5 and width 7 will have area 35.