Warning, an edu-technical polemic, wrought by frustrations with new students and their skill deficits, follows...
Teachers, it’s 10-12 weeks until testing, do you know where your kids are…in their facts?
Everyday, as I focus on teaching math, I grow more and more convinced that the facts are the sine qua non of elementary math. We have invested hugely in building facts fluency at our school and I cannot fathom how this is not done at others. I suspect the rhetoric of “drill and kill” has given some teachers a handy excuse to escape the need for students to be absolutely fluent in their facts. Certainly, students should be taught the facts in fun and engaging ways that do not poison their enjoyment of math. Automaticity in arithmetic is a standard, not an instructional practice; students should have lots of fun developing their fluency in the facts but teachers must make sure they achieve complete competency.
I have also heard some teachers say that they believe their students will develop their facts fluency through their daily use embedded in higher-level material. They liken developing facts fluency through math to developing oral fluency through wide-reading. This is a tempting but erroneous analogy. A fifth-grader unable to fluently multiply is not simply slowed but crippled. Following a reading analogy, arithmetic is more akin to decoding than fluency. You would not expect a student to read a 5th grade story without knowing phonics, you cannot expect a student to even understand much of 5th grade math without multiplication. What sense does it make to teach that one-fourth is equivalent to two-eighths, if the “4 x 2 = 8” fact is not automatic in the students’ minds? Likewise, the most difficult aspects of area and volume are not memorizing formulas, it is doing long-division by two and multiplication with multiple digits. Next year, if I teach 5th grade again, I plan to start with algebra and coordinate geometry, teaching no number sense standards until my students have mastered their facts. I suspect that “lowest common denominators” and “simplest form” will cease to be such a struggle when students can intuitively perceive the links between the numbers and I suspect that long division will be much less of a challenge when the students can easily subtract.
Further, I was recently told by our second-grade teachers that about 40% of their students had mastered subtraction. Funny, little more than that had mastered those facts when they came to me in fifth grade. Teachers: do not be deceived by students who can “quickly” subtract on their fingers, or speedily count multiples to finish a ten or twenty question fact exam. The arithmetic bar must be set at automaticity, instantaneous recall, not conceptual understanding. It is good for students to know that four times five is 5 + 5 + 5 + 5, but they must also know that four times five is twenty, without stopping to think.
Our math curriculum, and I suspect most, offers no remedial lessons for the majority of students who rise to fourth or fifth grade without being fluent in subtraction and multiplication. It certainly offers none of the resources needed to track students’ progress, an equally essential element. But that does not excuse teachers from preparing and including activities and lessons that teach the facts, and from taking the time to assure that all students learn them. Teachers, if there is only one thing you force yourself to go outside of the curriculum and do, I suggest that this be it.
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