kitchen table math, the sequel: "accessible" math, grouping, & IQ

Wednesday, January 2, 2013

"accessible" math, grouping, & IQ

from a friend:
Education Next has made the Jacob Vigdor article (released online in October 2012) the lead story in the current Winter 2013 issue.

He argues that the achievement gap and generally dwindling math performance of US students has been addressed by making the math curriculum "more accessible" (i.e., it has been dumbed down). He then argues that it need not be dumbed down if the curriculum were differentiated between low and high performing students.

In fact, this is pretty much how it was in the 50's and 60's. Students did not need the 3 or 4 years of math in high school to get admitted into colleges. What he leaves out, however, is the quality of math education in the lower grades and how this has affected the number of students who might otherwise be high performing students.
There’s no disagreement that some kids are smarter than others. Most people know that you can’t just set a standard (like algebra in 8th grade) and do nothing else. But Vigdor overlooks overlooks that issue and then claims that the failed initiative defines some IQ/algebra correlation. There are many other variables to consider–which he doesn’t.

The “Math Wars” are about curriculum and teaching methods, but this article skips over that analysis. Most schools separate kids starting in 7th grade. In affluent areas, since “enough” students get onto the top math track in high school, (often due to tutors, learning centers, or help from parents), educators will not look for any fundamental issues in K-6. They only assume that it’s a relative problem.

Why not interview parents to see what is done (or not) at home and try to find out how the best students got there? There may see an IQ connection, but it’s not that simple. There are things one can do to separate the variables. But too many authors of the recent spate of articles about math, algebra and its need, either can’t or won’t.

In his report, he pooh poohs the idea of introducing Singapore Math into classrooms, citing the usual cultural differences argument which is specious. (Teachers in Singapore have better math background; students go to school all year round, so there’s no forgetting concepts during the summer; the culture promotes education and hard work, etc). He neglects the fact that Singapore’s texts present the material clearly and succinctly and that there have been successes in schools in the US that have used it.
I remember one day back in middle school, when C. had done well on one of his death-march-to-algebra math tests, we were taking a walk & discussing his triumph. At some point we got to talking about where he would now rank in Singapore terms. We figured probably on par with Singapore kids who have developmental disabilities.

I'm (half) serious.

Remember the Singapore Math pilot project in New Milford, Connecticut?

The SPED kids were ahead of the general ed kids.


Jo in OKC said...

More anecdata with n=1, but Saxon math (standard math around here in many elementary schools) made my math-y kiddo feel like she had forgotten how to do math.

Singapore Math (at home), on the other hand, really challenged her and helped her get her confidence back.

There are tons of other reasons why she's good at math and was extremely subject accelerated, but I do think that it all started with us playing with math manipulatives and then doing Singapore Primary Math.

Catherine Johnson said...

I believe it!

SteveH said...

It's hard to believe that we keep struggling to get past the same simple arguments and strawmen, even with people in power. We keep hearing the same reasons and justifications over and over. We hear the problems of traditional "rote" math even though it's been gone from K-6 for at least 20 years and rigorous, traditional high school math has won the battle for the most able students. K-8 educators talk about critical thinking and problem solving, but they never examine their rigor and expectations or whether it works or not.

This makes me think of top-down versus bottom up analysis. There are many problems in education and some of them interact. If you approach the problem from the top, you are bound to think that there are only one or two problems. It's also easy to filter the problems through your own philosophy. Educators see rote learning and assume that the solution is to drive skills and mastery from the top using real world problems. If this doesn't fix the problem, then something else must be going on.

But what is the error? What number or numbers cause people to think that there is a problem? Is it NAEP, PISA, or TIMSS? Where does this number come from? What is the formula and what are the assumptions? What is the test and what, exactly are the questions that are missed? Who are these kids and what, exactly, goes on in the classroom? That is a bottom up analysis.

I tried to do that once with our state math test and there was no way that I could trace the formula they used. On top of that, the test questions used real world, thinking problems. This required someone to figure out how to separate skill or number prolbems from problem solving problems. I was on a teacher/parent analysis committee once where data came back saying that our score in problem solving went down. What was the solution? More problem solving even though they had no idea what that meant.

It's tough when you believe that there is no linkage between skills and understanding. If you believe that success in math is driven by some magical (Professor Hill) Think System, then you might as well give up on designing tests that give you corrective feedback information.

However, if you work backwards from key "errors", even though they might be anecdotes of n=1, your analysis will be on clear grounds, AND, you will probably find that the problem/solution applies to a very large class of students. You don't fix education with a top down analysys. You fix it by finding the anecdotes at the bottom and fixing them one-by-one.

palisadesk said...

The SPED results don't surprise me one bit. Back in the day when I taught a class for "Learning Disabled" students (Grades 3-6) I had the same experience.

Most of the students were severely reading disabled (that is, they were either complete non-readers or they were several years behind their age expectations). I had just discovered Engelmann's Direct Instruction programs and was using Corrective Reading. My students -- who were not all that "disabled" clearly -- made spectacular gains. They went up from 2-6 YEARS on norm-referenced measures in one school year. One boy who couldn't write his name in September was reading Lord of the Rings in June.

Naively, I thought the powers that be would be pleased with the results. Wrong!! The Supt. of special ed had a meltdown at the IEP meetings, screaming and pounding on the table, "We didn't put them in this program to get ahead!"

My principal took me aside later and said, "Keep it up -- we just won't tell Special Ed how well they are doing after this. We can be selective in what we choose to report."

I think this is called "tall poppy syndrome," but I've kept it in mind ever since. The bureaucracy is resistant to any suggestion that something else -- no matter what it is -- works significantly better. Even worse if it was "not invented here."

palisadesk said...

Where the math issues are concerned, I've seen a shift in thinking over the past few years, locally at least. This is not only what I observe from colleagues (in several different schools recently) but also from math curriculum people and district-level meetings.

The idea that students will develop solid math skills through a discovery approach seems to have slowly died a natural death, quietly but surely. The emphasis now is on teaching them skills, including math facts and algorithms (yes, the traditional ones) along with activities that promote problem solving and require students to use those math facts and algorithms.

We have time allotted every day for basic math skills -- yes, rote learning, including mental math, number facts, times tables. Kids also engage in problem-solving activities that are quite teacher directed," at least at first, and remind me of the Morningside Academy "talk aloud problem solving" strategy they use which has a lot of supporting data re effectiveness.

We have meetings of our school math improvement committee where we look at specifics from the standardized tests -- what items are missed, by what students, what patterns suggest things we should target instructionally in a focused way? We attempt to develop plans that address identified weaknesses in a comprehensive, schoolwide manner so that we're all on the same page, not just "lone rangers" in our individual classrooms, doing our own thing.

"Differentiation" remains a problematic area. In K-2, there is so much developmental difference among children that teachers routinely devise lessons and activities that are multi-level or can be applied at whatever level the child is at. This becomes harder and harder as you move up through the grades, so we try to address this by grouping students, not by "ability" (which we can't reliably assess), but by instructional level, which we CAN reliably assess. Timetabling can be an obstacle here, because teachers at the same grade level may not be able to schedule math at the same time, enabling cross-class instructional groups. However, we can do it to some extent, and this benefits both higher and lower achievers.

One problem to which we have no real solution is that of providing enough practice and drill for the children who need it most. In a low-SES community, you can't outsource to parents and tutors. We can and do provide extra tutoring before and after school, but then students who take the bus are excluded. Some of the neediest kids simply don't follow through with extra practice at home, and we can't force them to do it -- besides which, practice without feedback is not very effective.

We have some students who are perfectly capable of learning, but who need much more instructional time and directed practice than we can provide during the school day and I am frankly stumped as to how to solve THAT problem. It applies to areas other than math of course, but is easy to identify in math.

Technology could be part of the solution here -- I've had students do very well with Timez Attack and other CAI, but most kids don't have internet access at home, and we don't have much technology in the classrooms either.

Engelmann's early research showed that some children needed many thousands of repetitions to mastery, and these were not necessarily the low-IQ students (my genius-level-IQ student who couldn't learn the alphabet comes to mind), but the challenge remains, how to provide that kinds of practice in school?.

Crimson Wife said...

Now that I've taught grades 1-7 of Singapore Math, I think the real issue with getting it into American schools is that most of the elementary school teachers here in the U.S. don't have a good enough understanding of math to teach it without a LOT of self-remediation.

My mother-in-law is a retired 3rd grade teacher, and when we were visiting her one time, she offered to teach my DD her 4th grade Singapore Math lesson. She wound up not being able to do it because she didn't have a solid enough understanding of the concept being taught. My MIL is a bright woman, but it did not inspire much confidence to see her struggle with 4th grade mat.

Unknown said...

Crimson Wife - That's the crux of adopting Singapore's Primary Mathematics...Most teachers lack the deep number sense to teach it.

I had a (very young) second grade teacher confess to me this year that the first year she taught Primary Math at her school, she just taught the way she had learned. And the kids struggled.

The next year, she studied the teacher's manual and tried very hard to do things the "Singapore" way. And her students soared. Good for her. Bummer for her first 24 kids, though. They then went to a third grade group of teachers who told me this year that they weren't going to teach any long division because fourth grade taught it and it was too hard for their third graders. (Yes-Allison, my jaw dropped to the ground when they told me this!)

If you know anything about Singapore Math, you know there's no way you can take a skill/concept like long division out of the curriculum - it is practiced continually afterward. And they don't teach long division in fourth grade, they practice and review. It's part of the sequence that students get a year and 3/4 to practice with single digit divisors before 5th grade introduces two-digit divisors.

The school has used the U.S. Edition of Primary Mathematics for 6+ years and for the last 3-4 years, fourth grade has been complaining that the kids don't know long division when they come in. Now we know why.

Allan Folz said...

BTW, this is probably as good a post as any for me to say thanks Catherine and all the KTM readers that took the time to download, and especially review, our app going into Christmas.

He had a huge jump in Amazon downloads Christmas Day (over 500 of the free demo) and kept the momentum up through the week following. By Monday we had moved into the #1 slot for "Hot New Apps" in the Educational segment and have maintained #1 so far this week.

The hardest part is getting one's app noticed among the hundreds that are out there, so this has been a great help, both to us and, I'm sure, to the kids and parents that are using it.

Again, thanks everyone so much.

Allan Folz said...

At the risk of hijacking the thread, we have a few polishing touches we want to add to Blackboard Math, then will be prioritizing development for our next app.

I'm trying to decide between fractions and story problems. If anyone has an opinion they'd like to share, please email me (, since I don't want to hijack the thread.

Then again, Catherine is on vacation right? What's the saying... "forgiveness is easier to get than permission." :-)