For some reason, I have always found mnemonics to be irritating. Perhaps this is based on a worry that understanding was being condensed to a ‘word’ that referenced a ‘phrase’ that had no connection to the mathematics involved. Because we cover order of operations prior to algebra (questionable), we introduce one mnemonic to almost all students — PEMDAS. Something about Aunt Sally (we all have one?) being excused. The mathematical statement might be Grouping, Powers, Products and Quotients L to R, then Sums and Differences L to R. Somehow, we don’t see “GP(P/Q)(S/D)”, even though it is better mathematically.
Another idea is reduced to a mnemonic — SOAP, for ‘same, opposite, always positive’ in factoring binomials involving two cubes. This one at least refers to a memory process; this factoring is essentially a formula application. The mathematics that is lost is ‘binomials of cubes’. Perhaps this one should be ‘cubic SOAP’. Of course, cubic-SOAP still is incomplete … it fails to capture the binomial going with the ‘Same’, and the trinomial first term (another always positive).
However, I wonder about the MATH mnemonic. Perhaps you’ve heard it:
Man, Anything That Helps!! (“MATH”)
Are we so desperate that we offer incomplete or inaccurate memory aids? Perhaps we confuse correct answers with understanding mathematics.
Instead, I would like us to consider what this means:
Students should learn good mathematics in every math course.
A list of nice topics does not create a set of good mathematics. In conversations, I usually find a good amount of consensus on the phrase ‘good mathematics’; we might have trouble articulating a single definition, but we have a good idea what it looks like at various levels of student mastery in various domains of mathematics.
Not everybody in the world uses ‘math’ as a label. The label ‘maths’ is better, since our field has a plural nature; there is not one mathematic … there are fields of mathematics. Perhaps if we kept using the word ‘mathematics’ instead of the inaccurate ‘math’ it would help us maintain our focus on why we are here … what we are helping our students WITH. We are not here to get students to produce a minimal number of correct answers; we are here to help them learn mathematics with value.
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