This came up frequently in my time as a mathematical educator. Far too many “word problems”(*) are written in ways that require some words and phrases in the problem to be interpreted in their everyday sense, and others to be strictly interpreted mathematically even when this directly contradicts their usual meanings. Learning which are in each category often turns out to be equivalent to “guessing the password”, often without even the benefit of instructional material or consistency between problems.
In my experience, problems in probability or statistics are by far the worst of this type.
(*) in the pedagogical sense, not the one that means testing identity of semigroup elements.
This came up frequently in my time as a mathematical educator. Far too many “word problems”(*) are written in ways that require some words and phrases in the problem to be interpreted in their everyday sense, and others to be strictly interpreted mathematically even when this directly contradicts their usual meanings. Learning which are in each category often turns out to be equivalent to “guessing the password”, often without even the benefit of instructional material or consistency between problems.
In my experience, problems in probability or statistics are by far the worst of this type.
(*) in the pedagogical sense, not the one that means testing identity of semigroup elements.