Common Core math: deep or dull?

According to a New York Times article by Motoko Rich, parents and students are finding Common Core math not only confusing but tedious and slow.

To promote “conceptual” learning, many Core-aligned textbooks and workbooks require steps that may be laborious for students who already get it. A second-grade math worksheet, pictured in the article, includes the question: “There are 6 cars in the parking lot. What is the total number of wheels in the parking lot?” To answer the question, the student drew six circles with four dots within each. (Actually, this doesn’t seem new; it reminds me of “New Math” and “constructivist” math.)

One nine-year-old, apparently weary of this kind of problem, stated that she grew tired of “having to draw all those tiny little dots.”

Students with good understanding may be put through steps that seem redundant to them. If they skip those steps, they may be penalized.

“To make a student feel like they’re not good at math because they can’t explain something that to them seems incredibly obvious clearly isn’t good for the student,” said W. Stephen Wilson, a math professor at Johns Hopkins University.

One reason for emphasizing “conceptual” learning is that employers apparently are demanding critical thinking. Several questions remain to be answered, though: (a) whether Common Core math–in its current forms–really is promoting conceptual learning; (b) if so, whether it also promotes math proficiency; (c) whether the current approach is benefiting students at the upper and lower ends–and those in between, for that matter–or holding them back; and (d) whether this is the kind of “critical thinking” that will serve students well in college, the workplace, and elsewhere.

I will comment briefly on the first question; I welcome others’ insights.

Tedium and depth are not the same. One can go through a long explanation of a problem without gaining any understanding; one can solve a problem quickly and come to understand a great deal.

In sixth grade, in the Netherlands, I learned mental arithmetic: I learned to add, subtract, multiply, and divide double-digit numbers in my head, using all kinds of tricks that the teacher taught. Those tricks enhanced my understanding of what I was doing. I enjoyed the swiftness and ingenuity of it; I would have detested it, probably, if I had to write it all out, step by step, and illustrate the steps with circles and dots.

Detailing and explaining your steps is a worthwhile exercise. But part of the elegance of math has to do with its mental leaps. Sometimes, when you do steps in your head, or when you figure out which steps in a proof are assumed, you not only understand the problem at hand, but also see its extensions and corollaries. Sometimes this understanding is abstract, not visual or even verbal.

There seems to be an unquestioned assumption that one comes to understand math primarily through applying it to real-life situations; hence the Common Core emphasis on word problems. While word problems and practical problems can lead to insights, so can abstract reasoning, and so can models that bridge the abstract and the concrete, like the multiplication table.

Yes, the multiplication table–horrors, the multiplication table!–abounds with concepts. If you look at it carefully (while committing it to memory), you will see patterns in it. You can then figure out why those patterns are there (why, for instance, any natural number whose digits add up to a multiple of 3, is itself a multiple of 3). (Something similar can be said for Pascal’s triangle: one can learn a lot from studying the patterns.)

In other words, conceptual learning can happen in the mind and away from “real-life situations”; it need not always be spelled out at great length on paper or illustrated in terms of cars and wheels. Nor should students be penalized for finding shortcuts to solutions. Nor should memorizing be written off as “rote.” Yes, it’s good to understand those memorized things, but the memorization itself can help with this.

In ELA see a similar tendency toward laboriousness (that likewise long predates the Common Core). Students are required to “show their thinking” in ways that may not benefit the thinking itself. For example, they may be told to explain, at great length, how a supporting quotation or detail actually supports their point–even when it’s obvious. Students with economy of language (and, alas, clarity of thought) may lose points if they don’t follow instructions. Instead of being at liberty decide whether an explanation is needed, they receive a message along the lines of “Explain, and explain again, and then explain that you have explained what you set out to explain.”

Critical thinking is important–and one should think critically about how it is conveyed and taught.

That’s Mathematics

Math isn’t just for math class sings Tom Lehrer in That’s Mathematics.

The new math

Tom Lehrer’s song, The New Math, shows that the Common Core didn’t invent the idea of teaching math for understanding.

The periodic table in song

In The Elements, Tom Lehrer has fun with the periodic table.

Tom Lehrer’s New Math

Still funny after all these years …

Harry Potter and the Periodic Table

“Harry Potter” actor Daniel Radcliffe sings Tom Lehrer’s “The Elements,” on a BBC show.

Via Cosmic Log and Instapundit.

After Superman, what?

Done Waiting hopes to use Waiting for Superman as a catalyst for a grassroots education reform movement.

Education Reform Now is managing the coalition, which will advocate for “greater access to excellent public school options, like high-performing charter schools, for all families; putting a highly-effective teacher in every classroom and treating them as a valued professional; and, above all else, placing the best interests of children ahead of those of politicians and special interest groups.”

These are pie-in-the-sky goals: How should we give all kids access to excellent schools or find an excellent teacher for every class? What does it mean to put children first?

Rick Hess is dubious about the “Take Action” page on Superman‘s site, which is mostly devoted to promoting the movie and a companion book.

The page on “what parents can do” offers five items: “get local school ratings and parent reviews on GreatSchools.org,” “demand world-class standards for all students,” “talk to your teachers,” “do what’s best for kids, not adults,” and “make a teacher’s job easier.” The page on what “you” can do adds: “help students succeed” by supporting “All4Ed.org,” which amazingly “helps ensure every child graduates from high school prepared for college and for life;” “pledge to see the film;” “help your local school;” and “attend a school board meeting.”

This is “vague, tepid, and remarkably inconsistent with their revolutionary declarations,” Hess writes. Those trying to leverage Superman‘s impact should “focus on the concrete and actionable,” he suggests.

GOOD: Getting e-mails of departing viewers who will put up yard signs for reform-minded school board candidates, encouraging supporters to work the phones, their neighbors, and their e-mails to push their state legislators to take the lead on specific changes in statute.

BAD: Pledges to care more, to be “engaged,” or to write letters on behalf of “reform.”

Instead of trying to get everyone to care more, focus on lobbying key decision makers, such as legislators who might vote for “mayoral control of troubled inner-city schools” or stripping down “licensure requirements and tenure protections.”

Voting for reform-minded politicians is all very well, writes Mike Petrilli on Flypaper. But educated, middle-class parents can make a direct impact on the system: Choose a diverse public school for your own children.

In schools with a critical mass of middle-class children, everyone does better. If Davis Guggenheim and his friends all sent their kids to urban schools, those schools “would improve overnight.”

. . . all around the country, affluent families are choosing to send their children to racially and socio-economically integrated schools, in places like Cambridge and Berkeley, but also in less likely spots such as Alexandria, Virginia; Stapleton, Colorado; and Miraloma Park, California.

This is no easy decision, to be sure. I live in Takoma Park, Maryland, a very diverse suburb of DC, and my wife and I are agonizing about whether to stay or go, mostly because of the schools. (Our oldest son is only three, so we have some time.)

As long as reform means fixing the schools of “other people’s children,” it’s not going to get very far, he argues.

It’s a lot easier for middle-class people to buy a Prius than it is to send little Emma and Aidan to a school with a lot of poor kids.

Not everyone predicts a Superman-inspired movement. The NEA decided against $3.5 million campaign to counter “the media propaganda of this summer’s series of anti-teacher union documentaries,” reports the Sacramento Bee.

In the end, union officials decided it wasn’t worth it, said John Wilson, executive director.

“I think the films are a blip. They will come and go, but the union will still be there, our members will still be in these schools,” he said.

Tom Lehrer warned that caring isn’t enough.

Update: “You don’t send your child to a school to improve the school,” writes Checker Finn in response to his colleague, Petrilli. “You send your child to a school that will improve him (or her).”

You should drive past bad schools in search of a better one for your kids — and the great dual crime of American education policy is (1)  there are far too few truly better schools and (2) far too many families lack the means (or, in many places, the right) to opt into those schools.

Improving bad schools and starting great new ones is hard work for educators, policy makers, political leaders and advocates, he writes. Parents’ first job is to do what’s best for their own children.