September 12, 2006

The First Battle Has Finally Been Won but the War is Far from Over

After seventeen years or crippling children's math skills with nonsensical "standards" that had absolutely no research base, the National Council of Teacher's of Mathematics (NCTM) has finally seen the light and issued currciulum guidelines for PreK to grade 8: Curriculum Focal Points : A Quest for Coherence.

The subtitle says it all, don't you think?

The WSJ is already on the case. Some excerpts.
The nation's math teachers, on the front lines of a 17-year curriculum war, are getting some new marching orders: Make sure students learn the basics.
That's because learning the basics is the only reliable way to teach children how to do math. Whether you like it or not, before kids can do more advanced math they need to know how to do basic math. No, strike that. They need to know basic math so well it is automatic for them. That's one of the many things that the NCTM's previous standards so badly lacked.
In a report to be released today, the National Council of Teachers of Mathematics, which represents 100,000 educators from prekindergarten through college, will give ammunition to traditionalists who believe schools should focus heavily and early on teaching such fundamentals as multiplication tables and long division.
Shame on you WSJ. It's not just a "belief" at this point. It's been proven time and time again in the research base. It's not a debate between opposing viewpoints at this point. It's a debate between crackpots who have nothing but a legacy of failure and no research base and those that do. Pardon the ad hominems.

Here's a good example of that failure in the very next paragraph:
The council's advice is striking because in 1989 it touched off the so-called math wars by promoting open-ended problem solving over drilling. Back then, it recommended that students as young as those in kindergarten use calculators in class.
Downplaying practice and advocating the use of calculators in K before student's have mastered the basics would have been stupid. Nonetheless, our faddish no-nothing educators and textbook writers jumped feet first onto the NCTM bandwagon. You'd be hard pressed to find a decent textbook in widespread use nowadays that is based on learning math basics to mastery.
Those recommendations horrified many educators, especially college math professors alarmed by a rising tide of freshmen needing remediation. The council's 1989 report influenced textbooks and led to what are commonly called "reform math" programs, which are used in school systems across the country.
Did you think I was lying?

Problem was, it didn't horrify enough math educators below the college level. Go to almost any school's website and you will see how they've been fawning over the NCTM's standards for years. Let's see how many admit they were wrong after today's NCTM reversal.
Infuriated parents dubbed it "fuzzy math" and launched a countermovement. The council says its earlier views had been widely misunderstood and were never intended to excuse students from learning multiplication tables and other fundamentals.
Mostly parents who rely on math to make a living, no doubt. But, these parents didn't know anything according to sneering educators because the almighty NCTM, who've never successfully educated any kid, said they didn't know how to teach math.
If states adopt the new standards and teachers adjust their methods, "we'll be more competitive," says Prof. Fennell, who teaches at McDaniel College in Westminster, Md.
And, there goes the big IF. The big IF that'll likely sabotage the whole thing. Between the children and a math education stands a large ominous obstacle. That obstacle is our math educators who don't know how to teach math effectively today and need to "adjust their methods" to conform to the new standards. There will be much gnashing of teeth, pulling of hair, and other forms of adult tantrums along the way I assure you. Witness their reaction to NCLB and the changes it requires.
According to their report, "Curriculum Focal Points," which is subtitled "A Quest for Coherence," students, by second grade, should "develop quick recall of basic addition facts and related subtraction facts." By fourth grade, the report says, students should be fluent with "multiplication and division facts" and should start working with decimals and fractions. By fifth, they should know the "standard algorithm" for division -- in other words, long division -- and should start adding and subtracting decimals and fractions. By sixth grade, students should be moving on to multiplication and division of fractions and decimals. By seventh and eighth grades, they should use algebra to solve linear equations.
DUH! To think that this is in any way controversial boggles the mind.

A significant problem remains. Setting coherent standards is one thing-- a necessary first step if you will. Actually, getting that information into the heads of children, novices in math, is quite a different story.

Here's the dirty little secret in math instruction: constructivist pedagogy may have been patently silly, but traditional math pedagogy wasn't much more successful. Sure, using a rigorous traditional math program will help the top 25% of the class. But, what about the bottom 75%, the kids that didn't seem to learn math all that well in traditional programs either? It's one thing to mandate that kids learn "multiplication and division of fractions and decimals" it's another to actually teach it so that 99% of the kids can do it. There are few math programs that are capable of doing that.
Supporters of the council's previous views worry that the new report may lead to a return to the kind of rote learning they say left many children without any understanding of concepts. They say few adults spend much time doing long division, and students are better served getting a grounding in real-life problem solving.
Jackasses. I can't begin to count the ways that those two sentence are wrong on so many levels. First, they don't know the difference between rote learning and inflexible knowledge. Second, no one teaches by rote in any program --they don't even understand what rote learning really is. Third, for all their blather they did an horrendous job teaching "understanding of concepts" since most of their students didn't understand even basic math as demonstrated by their inability to solve basic math problems. Fourth, the ability to perform the long division algorithm accurately demonstrates that the child has become automatic in many basic math skills that are critical to performing well in algebra and engaging in "real-life problem solving."

Those two sentences are a good litmus test. If the math educator teaching your child math agrees with them, your child is being mistaught math. Don't wait to take action.
"The risk is that we end up with students who have no idea what math is all about or how to use it," says Joseph Rosenstein, a math professor at Rutgers University in New Jersey who reviewed the new guidelines.
As it turns out, that risk is the reality today under the NCTM's old standards. So pot kettle black, Prof Rothstein. It's easy to determine if kids know what math is all about or know how to use it: See how well they can solve math problems. The ones who can solve the most math problems, by definition, know what math is all about and know how to use math.

The war is far from over. Look out for "balanced math" to come to a classroom near you; it'll be the latest way our math educators will attempt to salvage their desire to keep doing things as they've been doing them. Mark my words.


John Dewey said...

The focal points may be hailed as an improvement, but they are still too much of a Rorhschach test. We can still end up with fuzzy math. Case in point: 2nd grade focal point for number and operations states as the title: "Developing quick recall of addition facts and related subtraction facts and fluency with multidigit addition and subtraction."

The first sentence says "Children use their understanding of addition to develop quick recall of basic addition facts and related subtraction facts."

Now I, and probably KDR and others read that as kids will memorize the addition and subtraction facts. Others however, may hang on the words "Developing quick recall" and "use their understanding of addition to develop..." NCTM can't bear to say the word memorization; to do so is akin to Communist party members saying that a little Capitalist competition might be necessary to sustain the economy.

So I'll hope for the best, and interpret the ink blot the way I see fit, and hope I can convince others to see it my way. But I agree with Ken. The war is far from over.

KDeRosa said...

I'm sure our educators will try their hardest to weasel their way out of these focal points. In the WSJ article, the TERC nutters already claim their program complies. They have no shame.

I don't understand why the word "develop[ing]" is an any standards document. It would have been preferable to know when the students should have that skill developed. Then the "quick recall of [math] facts" standard may have meant something.

Catherine said...

I'm willing to go on record as to how this will be sabotaged, based in our experience of "Phase 4 math" last year.

This paragraph is key:

Francis Fennell, the council's president, says the latest guidelines move closer to the curriculum of Asian countries such as Singapore, whose students tend to perform better on international tests. There, children focus intensely on a relative handful of topics, such as multiplication, division and algebra, then practice by solving increasingly difficult word and other problems. That contrasts sharply with the U.S. approach, which the report noted has long been described as "a mile wide and an inch deep."

Check this against a passage from the NEA website Barry quoted in his forthcoming article:

My child's teacher says that the mathematics curriculum is problem-based. What does that mean?

Teachers are now designing mathematical tasks that ask students to think deeply about math and how that math is part of their real lives. The problems students encounter won't be the two problems at the end of the lesson page that we all remember, but they'll be "real" problems that use math in a "real" way. It may be a problem that takes the children an hour, or perhaps several, to solve. There may be multiple ways to solve the problem. (See sample problems.)

Sample problem here here.

What we'll have now is far fewer topics taught to non-mastery, which will allow teachers like Ms. K to give kids two-hour homework assignments consisting of just one problem the kids have no idea how to do.

A Quest for Coherence indeed.

As far as I can tell, a "problem-based" curriculum is even more demanding in terms of coherence and "deliberate practice" than a "rote" curriculum.

I'm glad this report is out.

But the fact that educators are giving quotes to the press saying "Parents don't understand" tells me nothing has changed.

In fact, things may get worse.

Catherine said...

MATH TRAILBLAZERS has already blazed this trail. (sorry)

The teacher manual (I'm sure it's not called "manual") says that all kids must have "fluency" in math facts, but it's destructive for kids to memorize math facats in order to achieve fluency.

TRAILBLAZERS explicitly states that children will gain fluency incidentally, not via memorization or drill.

Catherine said...

It's not a manual.

It's a Teacher Implementation Guide.

Catherine said...

Here's the salient passage from the Math Trailblazers Teacher Implementation Guide:

The MATH TRAILBLAZERS approach to the basic facts differs from that in traditional textbooks. We seek a careful balance between strategies and drill, an approach based on research and advocated by the NCTM in the Curriculum and Evaluation Standards for School Mathematics (1989). Our approach is
characterized by these elements:

•Early emphasis on problem solving. Students first approach the basic facts as problems to be solved rather than as facts to be memorized. They invent their own strategies to solve these problems or learn appropriate strategies from others through class discussion. Children’s natural strategies,
especially counting strategies, are explicitly encouraged.

• De-emphasis of rote work. We believe that children must indeed learn their math facts, but we de-emphasize rote memorization and the frequent administration of timed tests. Both of these can produce undesirable results. Instead, our primary goal is that students learn that they can find answers using strategies they understand.

• Ongoing practice. Work on the math facts is distributed throughout the
curriculum, especially in the Daily Practice and Problems and in the
games. This practice for facility, however, takes place only after students have a conceptual understanding of the operations and have achieved proficiency with strategies for solving basic fact problems. Delaying practice in this way means that less practice is required for facility with
the number facts.

• Gradual and systematic introduction of facts. Students study the facts in small groups that can be solved by a single strategy. Early on, for example,they study facts that can be solved by counting on 1, 2, or 3. Students first work on simple strategies for easy facts, and then progress to more sophisticated strategies and harder facts.

• Appropriate assessment. Students are assessed on the facts through
teacher observation as well as through the appropriate use of written tests and quizzes.

• Facts are not gatekeepers. Students are not prevented from learning more complex mathematics because they do not perform well on fact tests.

The MATH TRAILBLAZERS approach to the math facts is discussed more fully in the TIMS Tutor: Math Facts.

TIMS Tutor
Section 9

Catherine said...

Students will learn math facts via problem solving.

Anonymous said...

That "implementation guide" sounds even worse then a year ago especially since I've now seen some of the results of their philosophy. It ain't pretty, folks.


rightwingprof said...

"Students will learn math facts via problem solving."

Please cite any research that confirms this -- and by research I mean that, not some pointless qualitative study.

Students can't tackle problem-solving until they KNOW the math. That's reality.

Catherine Johnson said...

I think the NEA may have removed the "A Parent’s Guide to Helping Your Child with Today’s Math" from its site.

If so, I applaud the decision.

You can still see the original here