Teresa makes a simple and also profound point in the video. If multiplication facts are committed to heart there are no “steps” — one has the answer and moves on. These are called “basics” for a reason: continually breaking simple, repetitious actions into tiny subtasks oversells the trivial and misses the point of mathematics, which is the accumulation of more and more sophisticated procedures, always building on what was learned before, until powerful, complex things can be done with fluency. How many times must one justify, two or three different ways, that 9×6=54?
Mathematics is about more than “getting to an answer, one way or another, in basic arithmetic problems”.
Indeed, it seems that the advocates of fuzzy math want precisely that: for children to get hung up on elementary arithmetic and devote as much time and energy as possible to it. The WNCP framework stipulates multiple-step procedures for obtaining multiplication facts in Grade 5, with mastery of those facts … never!
It is not acceptable for students to obsess over elementary building blocks of mathematics for five years of their lives. They should be moving on and doing interesting things. This would be like a 6 week cooking class in which the first three weeks are spent learning how to turn on the stove. Those math facts should fully automatized so that they do not get in the way by cluttering up more complex tasks with unnecessary, purely elementary steps.
It is a common misconception promoted by some in the Educational Establishment that those who talk about emphasizing “basics” in early years want children’s lives consumed with routine, elementary, mindless “basic” tasks. Nothing could be further from the truth. We advocate for the basics to be done — finished and mastered — as early as possible, enabling students to move on in their mathematical education, to the greater things for which that foundation is laid. “Back to basics” is not about more basics, but less, more efficiently covered, and more solidly learned.
In the final analysis it is the advocates of fuzzy math who are about “basics”: years of tedious, multiple-step ad-hoc procedures to calculate what should be committed to memory and reinvested as single steps in more engaging and worthwhile uses of their time.
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