The authors state “An Unsolved Question,” namely “whether this phenomenon is essentially
inevitable for most children of this age, or whether it is a consequence of an excessively
`algorithmic’ (and meaningless) program of instruction.” I can think of perhaps a thousand
other reasons why these children do not apply other things that they know in order to spot
errors in subtraction. Having taught at the college level for many years, I have always been
struck by how few students can apply material that they learn in one course to the problems
of another course. It seems that people compartmentalize what they learn, and it seems
very hard for them (us) to break down those compartment walls and use things that we learn
in, say, calculus, to do things in, say, physics. So I think the “unsolved question” is childish
in the extreme, the observed phenomenon being neither of the two possibilities that are
offered, but instead a complex mixture of about one million human factors that couldn’t
possibly be analyzed in a meaningful way with questionnaires and sample problems and logic and other irrelevancies like that.