Teaching Elementary Math

Recruiting math professionals into teaching at all levels is a big challenge. But few people realize the kind of math smarts you need to get elementary students grounded in basic skills. It turns out a lot of elementary teachers do not really consider themselves math people, and the math gap is a particular concern in early grades.

I wrote a story for today's paper about how some schools are looking to math coaches to help their teachers and students get up to speed. Here's the link.

By Michael Alison Chandler  |  November 6, 2008; 10:25 AM ET  | Category:  Math Education Reform , Math Resources
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The article was interesting and it's good to see people are making, what seem to be, positive and sensible steps toward better mathematical education.

At one point in the article, they say the kids don't understand 'borrowing' in subtraction.

My reaction was that this isn't strictly necessary to performing a subtraction. One doesn't have to know what to do in order to know how to do it. The mechanics of a subtraction are completely irrelevant to the notion of subtraction. For someone, who feels that the mechanism of subtracting 3,842 from 5,342 is important ... what would: x - y or f(x) - f(y) mean?

Posted by: mathlete | November 6, 2008 11:27 AM | Report abuse

Mathlete is correct but off target in saying that "the mechanics of a subtraction are completely irrelevant to the notion of subtraction." The mechanics of subtraction may not be relevant to the "notion" of subtraction, but one had better be able to perform some sort of mechanics (and there are multiple valid algorithms) in order to actually DO a subtraction.

Consider this analogy. I understand the "notion" of shooting a sub-par round of golf as well as Tiger Woods does. All you have to do is hit all of the greens in regulation, and then make some putts. Easy, right? Actually performing the mechanics, however, is what makes the difference between Tiger's game and the game of mediocre players.

Posted by: BradJolly | November 6, 2008 11:37 AM | Report abuse

I just read the article you linked to. What an embarrassing indictment of teachers! Apparently, nothing much has changed in ed. schools in the quarter century since Damerell wrote his classic book, _Education's Smoking Gun_.

How sad.

Posted by: BradJolly | November 6, 2008 11:48 AM | Report abuse

Thanks for the article, Michael.

I don't see this an an indictment of teachers but an acknowledgment that some abstract topics are difficult to convey to young children with different degrees of readiness.

But I also wonder is this effort may in some way miss the boat.

My child is in 3rd grade and the math textbooks she brings home do a relatively good job in presenting concepts in a careful way. Having a teacher trained to present the concept in a careful way is also helpful but I don't think this is what is usually the issue when problems arise.

Even with a good textbook and teacher there are times that some kids just don't 'get it' no matter how clear the presentation may be. At that point the kid (or someone close to them) needs to direct the child's focus to figuring out what they don't understand, rather than making another passive, one-sided presentation of the material. I guess I'm saying more interactive, two-sided discussion of what is not understood is necessary sometimes. Ideally this would be self-directed (by the student) or family directed but it could be in the form of tutoring. This type of exploration requires more effort from the student and their supporters but is ultimately necessary for performing well, I think.

Posted by: fedbert | November 6, 2008 1:19 PM | Report abuse

It's an interesting article, and I think it goes back to the blog on forgetting, and the discussion on memorization vs understanding.

If you don't understand, you can't teach. You may be able to recite a lesson from a book, and a few students may be naturally insightful enough to really learn, but most of them will end up in the same situation you are in, and probably dislike math and doubt their own ability as a result.

But elementary schools aren't structured that way. One teacher is typically responsible for teaching every subject, and I don't think we can reasonably expect all our teachers to be Renaissance men and women with both broad and deep knowledge. So to me, the idea of a math specialist in a school, to assist or teach class, is a very good idea. Come to think of it, we had a "music specialist" at our elementary school, and one for gym class, too.

Off on a tangent, why aren't elementary schools set up for kids to change classes during the day? Is it too much logistical trouble to have a school full of 5-10 year olds moving around four or five times a day? Why not have teachers move while the kids stay put?

Posted by: tomsing | November 6, 2008 1:30 PM | Report abuse

Thanks for highlighting mathematics education, Michael. The role of a mathematics specialist is muti-faceted. Teachers are constantly learning more about how to improve their practice of teaching mathematics. Through this process, mathematics specialists serve as coaches to provide job-embedded,meaningful,staff development in order to improve student learning. Our goal as mathematics educators is to teach students to "think deeply" and "to understand" the mathematics so they are able to later access higher level mathematics. Thanks for visiting us at McNair Elementary to see how we are making mathematics more meaningful for our students.

Posted by: bethrodriguez | November 6, 2008 2:59 PM | Report abuse

Interesting article, and one of my pet peeves. It seems as though we spend so much time focusing on why our high schoolers are falling behind in math, whether 7th-8th graders should be taking algebra, etc. -- but the foundation for all of that is in elementary school. And in my own experience (both as a kid and what I see with my own kids), most elementary school teachers were liberal arts types, who either didn't much like math or were intimidated by it. (Hey, don't get me wrong -- I'm one of those liberal arts types myself!). So we end up with some fairly watered-down math early on, which leaves the kids who don't naturally pick it up flailing by the time they get a little older.

We have a great school, great teacher, etc. this year (2nd grade). But the math is really, really easy for my daughter. On the one hand, I can see how the school is introducing concepts that the kids will build on later -- when the teacher asks, say, 7 + __ = 10, I feel comfortable that my kid won't panic in a few years when the blank is replaced with "X." But on the other hand, my daughter picked up multiplication pretty much on her own at 5; we just explained that 3 x 2 is the same as adding two three times, and she was off. And yet, in school they're barely doing two-digit addition and subtraction.

Sometimes I think our kids can handle more than we think they can, if we'd only present it to them in a way that gets them engaged with it. It's frustrating to see math get such relatively short shrift at the elementary level (my daughter's school spends 3+ hrs every morning on reading and writing, and maybe an hour in the afternoon on math and science) -- especially with all the whining about how we're falling behind at the higher grades. If you want kids to really learn math and science, you need to make it a priority in the teachers (and specialists) you hire, in the curriculum, and in the classroom.

Posted by: laura33 | November 6, 2008 4:59 PM | Report abuse


"One doesn't have to know what to do in order to know how to do it."

I messed up this sentence. I meant to say: "one doesn't have to know what(in a deep sense) one is doing in order to know how to do it." I don't have to know newtonian mechanics in order to play volley ball.

My feeling is after doing enough subtractions, you'll just know why borrowing works spontaneously because you can visualize what you are doing much more easily and you can visualize how the parts of the method work.

In terms of the Tiger Woods analogy, I get these sense that we probably agree. I think 'understanding' isn't how you get good at arithmetic. The way is to memorize the routines and repeatedly perform them.


"why not have teachers move while the kids stay put?"

My primary school worked like this and that worked fine. Perhaps it's about saving money. One teacher per class is a lower bound but if all teachers were specialists then the number would have to necessarily be greater than or equal to the aforementioned lower bound.

Posted by: mathlete | November 6, 2008 10:59 PM | Report abuse

Thank you for the clarification, mathlete. Your revised sentence makes a lot more sense.

Posted by: BradJolly | November 6, 2008 11:46 PM | Report abuse

Building a conceptual understanding of mathematics will provide students with the metacognitive skills necessary for actual application in real world problem solving cases.

Posted by: mrod_mancha | November 7, 2008 1:44 PM | Report abuse

My kids go to a excellent private school, but many of the otherwise excellent teachers are not confident in math, and it is their least favorite subject. I supplement their math education at home.

A peeve of mine about getting qualified teachers in Pennsylvania is the state's new requirement to get FBI fingerprints of all new educators. I understand the need for background checks, which I support, but fingerprinting smacks of a police state and assumption of criminality. I have thought about teaching, but balk at this requirement. I wonder how many good teachers the state is losing. Probably not a huge portion, but enough to make a noticeable difference. This new requirement started last year.

Posted by: ConcernedMom2 | November 11, 2008 10:42 AM | Report abuse

Hi ConcernedMom, Thanks for your comments! I think that most school systems (and work places) do background checks.. I actually had to get fingerprinted before I could take this Algebra class! When you are working with children, schools want to err on the side of caution...

Posted by: Michael Alison Chandler | November 11, 2008 11:00 AM | Report abuse

Re: math specialists in elementary school.
I ran a program for math specialists in the 60's at Teachers College, Columbia U. A Masters program for experienced el ed teachers, its courses consisted of a good deal of math, and much grounding in the use of concrete materials. We ran this unusual program (for its time) for several years, hoping graduates would find positions as specialists. Sooner or later, many did. All stayed in the math teaching, a few in the middle school, a few at college.

Specialists are a key to a successful elementary math program to provide continuity over the grades and to keep abreast of the changes taking place in the field.

Jerry Kaplan, Professor Emeritus, Seton Hall University

Posted by: jerrykap | November 12, 2008 5:03 PM | Report abuse

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