> If the teacher has not covered the commutative property, then it might be unwise to let a student continue with this line of thought.<p>Built in to this is the idea that only the teacher provides knowledge to the student. Consider that the student may have learned it from a parent or someone else, or from a book.<p>Thus, the author regards this not as a test of the student's math skills, but as a test of being able to repeat a specific teacher's math pedagogy.<p>I like (and agree with) some the comments:<p>> I have to disagree with this. Your intepretation of the Wikipedia article is fallacious: Wikipedia says “The multiplication of two whole numbers is equivalent to adding as many copies of one of them, as the value of the other one.” They did not define “one” as being the first number in the problem a x b, nor “other one” as being the second.<p>> Whoa, so now we’re making first graders confused about the commutative property because of category theory? Nice
I disagree with the author. He confuses Math with Computer Science. In Math, a x b and b x a are both equal and equivalent. The division example with switching places is ridiculous. Learning from mistakes is part of the process. Even kids who suck at Math won't switch places when dividing or subtracting!