Stuff like this is entirely arbitrary: > Notice that the second problem is marked incorrect as well. Why is it important that 4 x 6 is 4 rows of 6, instead of

Stuff like this is entirely arbitrary: > Notice that the second problem is marked incorrect as well. Why is it important that 4 x 6 is 4 rows of 6, instead of 6 rows of 4? Not only does this adhere to the definition, it also teaches students the correct order for diagramming matrices, which is rows times columns. This sort of slavish devotion to arbitrary conventions is really tiresome, and I think it promotes the wrong sort of thinking about math. Every time I see one of those questions going around like "4+8÷3(5)=?", it drives me nuts. People look at these equations and point to rules taught in school, or examples in textbooks. They see math as a set of rules, rather than a means of communicating. The fact is, an equation should never be written that way, because as shown by all the arguments about it, the intent of the author is not understood by all readers. The problem is that these sorts of questions just demand that students mechanically follow a bunch of rules.