I can see both sides of this argument, with the "show work" side in a sort-of kind-of way.

I get that the teacher needs to know that my DD understands a concept. But IMO, "following the algorithm" does not necessarily mean "understanding the concept." And I'm certain that her teacher's OCD-level requirements for showing work are detrimental to DD's ability to understand said concepts. As an example, let us take "What is 15% of 50?" They have to write it out as follows, mental math (5 + 2.5) being BANNED:


What is 15% of 50?

n= the number that is 15% of 50. (it has to be n)

n = (0.15)(50)           Do calculation on the right.

n = 7.5

The number 7.5 is 15% of 50.

7.5 (Answer must be at the bottom, not circled)

Problems are marked wrong if they don't follow her recipe exactly, including lack of capitals in sentences and so on. Even work for 12*4 must be shown. DD gets so wound up about following the steps, she gets into a muddle about how to obtain the answer. I get that she's trying to teach them to be tidy, but she goes overboard and just sows confusion.

IMO, there are only two valid arguments about showing work. The first is that it shows that you know how to do the algorithm (value of which is noted above). But teachers can keep a list of who gets it and allow algorithm-savvy kids to start taking shortcuts (which will presumably lead to increased understanding of the material). The other argument is that it helps you learn how to explain things to other people. This skill is important in adult life, especially at work if you want to convince someone about your cool new idea or teach a subordinate how to do something. Fine. But this doesn't mean a student should be required to write out each step on 72 problems that all require the same steps.

The other side of the argument is that by not forcing a student to show steps that are trivial to her, you allow her to focus on the meat of the problem. Which I think is a more important consideration for gifties. But teachers don't generally get gifties, which brings us back to

12
*4
48