In my recent post on vocabulary, I wondered whether what holds for vocabulary words also holds for math facts:
not just that knowing them fosters higher test scores and broader intelligence, but also that they are best learned not as lists of "math facts," but in the course of doing actual, systematically structured math.In an earlier post on the abysmal mastery of math facts seen in children whose only exposure to math is Reform Math, I estimate that Reform Math children are getting less than one tenth the embedded practice with math facts as their traditional and overseas peers are.
It's interesting to see how often Reform Math problem sets skirt the issue of actual calculation in their attempts to nurture number sense. Here below, for example, we have, from 5th grade TERC / Investigations, (1) a problem set that substitutes multiplication for estimation (where Singapore Math would have students do both):
(2) one of many problem sets in a chapter on decimals that simply ask students to put specific decimals in order of size (while ordering of fractions may require actual calculation, ordering of decimals does not).
(3) a multiplication/division "skill check" that almost looks like it's asking for calculations, but carefully STOPS you before you begin:
I'm reminded of those foreign language software programs that promise fluency in a language without making you practice grammar rules. As with language, people would love to think there's a silver bullet for arithmetic mastery and algebra preparedness that avoids the productive drill and practice that so many elemenary school teachers assume is as tedious for their students as it is for them. But what I've seen even with basic number sense suggests that a fair amount of productive drill ("embedded learning" in the best sense of the term) is, for most students, absolutely necessary.