I see two problems here.

The first issue, and perhaps the most significant one, is that Common Core is teaching kids to think in a way that their parents did not. Back when I learned this stuff, we started with “counting by n’s”, and then extended this to memorising the multiplication table. In the days before ubiquitous pocket calculators, this made perfect sense.

The second issue, and I think this is the one that catches a lot of people (even mathematicians like myself) is that just about every week an example is posted to social media which seems to contradict the principle that Common Core actually is about teaching number sense. Most of these criticisms miss the point, but occasionally you see an example where any disinterested observer who understands anything about mathematics and education has to admit that the student was right and someone (whether the teacher, the unthinking bureauracracy, or Common Core) was wrong.

The example that I saw last week went like this. The question asked: “Use the repeated addition strategy to solve: 5×3.” The student said: “5+5+5 = 15”. This was marked wrong; the expected answer was “3+3+3+3+3 = 15”.

(As an aside, one of the problems on the same image was to use an “array” to solve a similar problem, and the student drew the array transposed from what was expected. Sorry, Redditors, Common Core was correct about that one for reasons which I won’t get into now, though I would have given the student half marks. I digress.)

Unless “the repeated addition strategy” is one of those memorise-it-exactly-or-else algorithms which Brett rightly points out is inappropriate in the modern era, the student’s answer was not only correct, but better than the expected answer; 5+5+5 is an easier problem to solve than 3+3+3+3+3. If the purpose is to develop number sense, the student’s answer demonstrates that.

Now, I know that confirmation bias is at work here. Only the weird cases which violate our sensibilities tend to get shared on social media, so we tend to assume that this is the common case, and I don’t think it is. Nonetheless, when you do see things like that, and you do on rare occasions, it doesn’t inspire confidence.