“Depending on algorithms we don’t fully understand is what leads to horror stories like this!”

No, sorry, it’s not. This story is about a student NOT taught a key algorithm — possibly the most important algorithm of them all in elementary school arithmetic.

Further this business about “algorithms we don’t understand” is a false dichotomy. Who says that “not understanding” is an essential aspect of learning algorithms? I say that the opposite is true: a student who has no understanding of an algorithm hasn’t been taught it properly. Understanding and procedure ought to go hand-in hand. Indeed, students who have no idea about procedure clearly do not understand arithmetic.

Your mental-math procedure for that result is perfectly functional, and completely beside the point. I am certain this student spend many valuable classroom hours learning (and being expected to construct) numerous variants on that idea in his math class. But he was never taught the one thing he needs most: the single, effective, elegant and easy skill that will enable him to solve any problem of this type and many other types … and also provide the cognitive basis for numerous advanced techniques and concepts.

Re-read my comment: I anticipate you suggesting such a procedure and pointed out why it is not a response to this student’s problem. Given time and less pressure the student could surely have come up with 2 or 3 different ways to do this. But he had only 90 minutes and a fair bit of other work to do. Engineers MUST learn to work under pressure, it goes with the field. It is imperative that they learn the most effective procedures for elementary tasks so that their attention can be focussed on the highest level of meaning — where the critical, life-and-death outcomes are determined. Having to use ad-hoc counting-on-fingers approaches are precisely the thing that holds students back at this level. I am astonished at the level of denial evident in your response.