Friday, December 20, 2013

How to divide 90 by 18 in 108 steps

… and other wonders of Common Core
A mother speaking to the Arkansas Board of Education on 16 December is being hailed on many websites for “obliterating” the Common Core curriculum by posing a simple fourth-grade math problem to the board members.  (Video here; math problem read out starting around 1:45.)
The board members are able to solve the problem instantaneously by dividing 90 by 18 and coming up with 5.  Granted, this was some years ago for me, but I do remember that in fourth grade, I could have solved the problem that way too.  (Problems one digit bigger than that, in the dividend and/or the divisor, would have caused me to get out pencil and paper.)
Common Core students will have their work counted wrong, however, if they simply solve the problem by dividing 90 by 18.  The Common Core solution involves drawing 18 circles and using 90 hash marks – and 108 steps (presumably, drawing each circle plus making each hash mark).

Now, I get that kids are taught different principles of math operations as they go through school.  In grade school, we were periodically taught to cast out 9s, for example; an operation for which I have never found a single use after passing my last quiz on it, somewhere ca. fifth grade.
But translating word problems into math was always a hunt for the quickest and most elegant solution: the one that identified the elements of a math problem accurately and processed them efficiently.  That in itself was an education about logic, thinking, and mental power.  The idea of “every day math” was that it would apply sensibly to problems that might need solving in the life of a sane person.  (If, to be sure, a person who unaccountably spent a lot of time picking apples, or dividing pieces of candy among friends.)
By fourth grade, it’s hard to imagine any student benefiting from drawing a group of 18 circles and then working his way around them, distributing hash marks, in order to understand that that’s one way of seeing what he does when he divides 90 by 18.  Which presumably is the object of this bizarre exercise; although I remember “getting” the hash-mark concept in first grade, and fully understanding its relationship to multiplication (and consequently division) well before the halfway point in second grade.
I can imagine educators explaining that many children’s brains envision math problems “differently.”  That the lengthy exercise of distributing hash marks makes the most sense to them, validates their natural approach, and makes them feel better about themselves.  Perhaps the educators just feel, for some reason, that it’s important to present this perspective on division.  I would have to wonder why: I can easily imagine my attention span being utterly defeated in the process, largely because it’s a lengthy process, a tedious process, assigned for no reason other than to demonstrate a concept the average person would master inside 4 seconds, and then be ready to move on from for the rest of his entire life.  If I had been told to work a problem this way in fourth grade, I would have wondered if the teacher had some hidden motive.  If it happened a lot, I might have concluded that the teacher was an idiot.
But regarding the potential argument that some students’ brains are attuned to the hash-mark distribution concept:  that’s fine, but is catering to that education?  For me, and I suspect for many readers out there, math was a subject whose rules and best practices I had to learn.  Not all of the concepts seemed natural to my mind.  I still remember failing a math quiz in fifth grade because I was “borrowing” in the wrong way doing long-division problems.  I never started out as the student who was quickest at translating word problems into math expressions.  At each step along the way, I had to learn the concept first, get my mind around it.
Once I did, I functioned well.  And the whole process was in itself an education for me, about education: about why I was there.  I felt a natural ownership of subjects like writing and history, a confidence in my instincts that turned out, over and over again, to be well-founded.  I never felt that way about math.  With math, I was plugging in to something my civilization defined for me, and – for the purposes of the education project – knew better about than I did.
And I am better now for having had to work a little harder, to learn concepts as an apprentice rather than start out by judging them, and to not just adapt my methods of thinking, but to recognize that I was having to, and see the value in it.
The reason this happened for me is that I was not treated to simplified, tedious distribution exercises, but was instead required to learn, at a fairly rapid pace, the patterns and rules of math, as my civilization conceives them.  I was challenged, rather than being handed things to do that were manifestly stupid.  I went on to master calculus, trigonometry, and advanced statistics, approaching each one with the well-earned assumption that I knew how to learn whatever didn’t come naturally.
There seems to be plenty of justification for suspecting that Common Core won’t foster this kind of attitude in students.  Consider this account of an excruciating Common Core lesson module for ninth-graders, on a short story from a 2007 collection by Karen Russell.  (H/t: Schools Matter.)  The story itself, “St. Lucy’s Home for Girls Raised by Wolves” (excerpt here), sounds intriguing, like something about werewolves that ninth-graders would enjoy.
But the module runs for 17 days on the one short story, some of it moving at the stately pace of two pages’ worth of textual analysis per day – and Day 1 involving only the opening paragraph.  Here’s how the blogger at Perdido Street School describes the reaction of students (italics and [sics] in original):
The first day, they’re excited to start a new lesson and read a story that seems to be about werewolves.
By the third day, they’re bored by reading and discussing the same story for three days straight and starting to get antsy.
By the sixth day, they’re outwardly hostile to the lessons and the teacher for teaching the lessons.

By the ninth day, they’re totally disengaged from class and talk openly about how much they hate English.

By the twelve day, they no longer give a s*** about anything – not the class, not the story, not the teacher, not the “assessment” (i.e., “test” for those of you who aren’t fluent in reformy geekspeak) that is coming up on Day Seventeen.

By the seventeenth day, students complete the “assessment” with little regard to how they do on it because they stopped caring about the entire process somewhere between the end of Day Four and the beginning of Day Five.
I’m with the students.  That’s cruel and unusual punishment.  I’m pretty sure that in ninth grade, we covered Brave New World, Nineteen Eighty-Four, and Anthem in about 17 class days (we read them outside of class, of course), and had time to spare for oral book reviews of our individual selections of futuristic novels (for which approximately half the class chose Atlas Shrugged, as I recall).
“Dumbing down” is too simple and linear a concept for what these Common Core approaches to math and literature seem to do.  It’s more like lining math and literature up as watermelons before a firing squad armed with shotguns.  I’ll get back to you if a better formulation occurs to me.
Meanwhile, there are some things the Common Core curriculum is prepared to be brief, no-nonsense, and rote-learn-y about.  You won’t be surprised to hear that students are not invited to intuit, distribute, parse, deconstruct, or question the concept or reality of global warming.  In fifth grade, they are simply given a reading assignment that presents it to them, from the standpoint of the future, as a historical fact.
No pointless elliptical teaching processes for this one.  Some things are too important to leave to chance.
J.E. Dyer’s articles have appeared at Hot Air, Commentary’s “contentions,Patheos, The Daily Caller, The Jewish Press, and The Weekly Standard online. She also writes for the new blog Liberty Unyielding.

No comments: