I’ve had a rough week. We just came from a doctor’s appointment where both kids were stuck with needles, then the oldest was dropped off at school and the youngest was taken to his speech therapy. I came home to a message from the school district about Ian’s IEP meeting. We haven’t seen his evaluations yet. They were supposed to give us ten days to review them before the meeting, but we’re going to let it go. Ugh. It’s all boring and time consuming, and you don’t need to hear about it. I’m just glad the semester is over, because this transition to Kindergarten stuff has meant meeting after meeting, test after test all month. We’re all jangly and stressed and worried. It’s seriously difficult to transition back to thinking about my research, after hearing what’s in store for our poor kid next year.
To better make a decision about what’s best for Ian for next year, I set up a meeting with the local elementary school principal and one of the teachers earlier this week. The talk turned to Jonah, and they mentioned how impressed they were with his exposure to different ideas and experiences, which set him apart from other kids in the school. They said that this had major benefits for Ian as well.
We’ve been talking about the relationship between class and education in this blog lately. Our aggressive approach to the special education bureaucracy and Steve’s long talks with Jonah about history are certainly a factor of our background. It’s also coming into play in a town just five minutes from here.
The schools in , New Jersey have been the center of a battle over math curriculum. Parents are rebelling against “new math,” which emphasizes the comprehension of math concepts over rote memorization of math facts. We have the same program in our town. Jonah’s math work is boring and silly. He hasn’t been taught to just memorize 6+7 and 8+9. But curriculum issues don’t stress me out as a parent. When Jonah was taking too long to compute, we did flash cards over breakfast for a couple of weeks and he was cool.
The curriculum issues are super important to my mom, who has been clipping out articles for me on this topic, and to commenter, Amy P, who has been forwarding me articles on this issue. I am fascinated by the politics of this battle.
While I am still absolutely convinced that money makes a difference in schools, so does human capital. Active, annoying, assertive parents make a difference, and those parents are concentrated in high socio-economic towns and neighborhoods. For those of us who are concerned about equity in schools, this is a harder problem to overcome.
Apt. 11d 
I’d hesitate to describe the conflict as being between “comprehension of math concepts” versus “rote memorization of math facts,” because once you phrase it that way, it’s pretty clear who you sympathize with.
Making math facts part of a child’s internal hardware is a sine qua non (unless the child is a weird mathematical genius who doesn’t need it), but even two digit arithmetic isn’t “rote.” It’s not like you separately memorize the answers to 10 + 12, 11 + 18, 16 + 15, etc. The procedures may be learned by rote, but you can’t simply memorize the answers to an infinite array of arithmetic problems.
Enemies of reform math want children to achieve the following in the elementary years (I may be missing a few items):
1. instant recall of math facts
2. knowledge of efficient algorithms
3. quick and accurate computation
They believe that current reform math pedagogy and textbooks are an obstacle to achieving these goals. They prefer curricula such as Singapore Math, which is oriented towards story problems and problem-solving.
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Is the new “New Math” the same as the old “New Math” they were teaching in the 1960s? It sounds the same — at least based on the 1965 Tom Lehrer song “New Math.” Can it still be the “New Math” if the kids’ parents learned from it to?
Also, as I pointed out in the thread last week, and can easily be looked up on the NJ Dept. of Ed. website, Ridgewood paid $12,133 per pupil for the 2006-7 school year, against a state average of $12,098. While I understand that you were making the point that “Human Capital” is important also, I think you are still overplaying the importance of money. Ridgewood is not “buying” a better education through high taxes.
Meanwhile, the incompetents in your district and the experts next door are probably making pretty close to the same amount.
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“because once you phrase it that way, it’s pretty clear who you sympathize with”
Quite honestly, Amy, I confess complete ignorance about curriculum issues and feel totally unqualified to take any side.
I’ve seen Ridgewood schools. They’ve got a lot. Ridgewood may appear to spend only slightly more per pupil, but in reality they have a lot more to play around with. They have almost zero kids from lower income groups. That means less special education and less remedial work, which are very costly for a school system. The PTA donates a ton of money. They have volunteers up the wazoo, because they have a ton of stay at home parents. They have wealthy people in the community donating money. The staff is adept at getting grants. The per pupil amounts don’t tell the full story.
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In response to Ragtime, the key issue in school achievement is not money spent, it’s the school’s intake. British research indicates that intake accounts for at least 75% of a school’s test results. A school with, as Laura notes, almost no low-income children and almost no children of non-educated parents, is going to do infinitely better on 12k a year than is a school with a more challenging intake. There’s loads of robust research from all around the world supporting this point.
There’s no overplaying the importance of money here – the money that matters is in the home. When money isn’t in the home, then loads more money needs to be dumped into the school. More money to support extra staff to deal with problem kids, behaviour issues, wasted time, lack of cultural capital in the home, etc. The Dutch attempt to address this through giving schools more money for low-income pupils (something like 1.9x for kids from the lowest quintile, I believe). Not sure how successful they are – I’ve not seen any relevant studies – but it strikes me as a damn good idea.
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Of course money matters – both in school and at home – but surely teachers, curriculum and parents are even more important. A curious, smart child will learn gobs of stuff, no matter what, just as a less curious child who doesn’t like to read or feels that school is a big bunch of pressure will resist, no matter what. Again: the teachers and the parents are hugely important. And what about teaching math with some of “this” and some of “that”? It’s dandy to understand basic concepts (adding is combining, for example) but if implementing is never learned, too, then what’s the point? Conversely, if you memorize multiplication tables, and spout them all day long but don’t understand what they mean, then that’s pointless too. Why not both?!
Just as an aside: why do even smart people still use the word “weird” about people who are easily good at math? It isn’t any weirder than being good at French or Geography, is it??
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anne,
As it happens, I had my husband in mind. He has a PhD in probability and a very imperfect recall of basic arithmetic. So despite being 100% anti-reform math, in all honesty, I have to put in an exception for people like him. And yes, mathematicians are weird. Philosophers, too. Not that there’s anything wrong with that!
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My kids have spent the last 8 years being taught the “new math”. It was frustrating and scary to me they couldn’t as easily regurgitate their times tables as easily as friends in a traditional school. However they always were in the advanced areas on the standardized tests – and our school does no kill and drill. Then when my two oldest got to high school algebra and geometry were a piece of cake. The new math really plays well into the math skills our kids will need in high school and college.
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Lisa V,
A few thoughts:
1. Someone is always going to wind up with the highest test scores, no matter what. And someone else is going to get the lowest scores.
2. A number of those state exams are aligned with reform math, so the states are playing the hand they dealt themselves.
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My 7 year old is being taught with the “new” math – and I’ve been simply amazed. She has started to understand math concepts that I didn’t quite grasp until I was in Jr. High.
A few nights ago, we were putting together some “Math Arrays” for her teacher. I paused for a moment, because I couldn’t remember what 12 x 8 was. (I learned by memorization…as I get older, my 12s times tables are hiding deep in the cobwebs of my brain.) But my daughter just piped up with the answer. She didn’t have it memorized, but had figured it out. So far, her math education has been focused on concepts rather than memorization and for us, it has worked well.
I suppose like everything else, this varies child by child.
In our community, the city schools are getting more and more low income kids. (Our elementary school is 66% low income) while the suburb schools are full of kids who are lily-white and wealthy.
But we are sticking with our school. I have to believe that there is more to life than test scores…
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Amy, I really don’t put the highest value on standardized tests. That’s why I chose a school for my children that de-emphasizes them. Our state’s test is still very much about the basics- not the new math. I was concerned in general that my children would be lacking because of the way they were being taught. Turns out my fears were without merit. Critical thinking in math has served my children well, they do fine when required to apply basic math concepts (just one way is testing) and later on in life they have the ability to understand higher math in a way that many of my generation struggled with.
We keep wanting our children to have more math and science before college, but the truth is they just need better math and science.
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I am sure, based on your “Mommy E-Mails”post, that you’ve got one (or a dozen) of the forwarded e-mails that tells you how much money a Stay-at-Home-Mom’s job is “worth” by looking at all of the jobs she combines — guidance counselor, CFO, laudromat, etc. Depending on the e-mail, you will probably get a total somewhere between $137,000 and $13.7 million as the “value” of a mother.
While, as you say, the e-mails themselves are simply junk, there is the grain of truth that the value of good parenting is really worth a whole lot of money. In New Jersey, the poorer (Abbott) districts get about 25% more per pupil than the richer districts. That doesn’t make a heck of a lot of difference, for all the reasons you have given. I think if the poorer districts got twice as much, it still wouldn’t make much of a difference, because the value of a well-off, well-informed, and involved populace is worth a lot more than $12K per pupil per year just by itself. Beyond what you point out yourself, they will be more active in identifying waste and mis-management, thus allowing for better use of the money provided.
So, yes, I agree that the “problems” with the schools have to do with stratified neighborhoods, so that the kids of the rich all go to the same school, and their parents efforts are therefore concentrated in a single district. But between the relative importance Human Capital and actual cash, I’d put the split much closer to 90/10.
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Totally agree, Ragtime. Parenting is really important, and I do think that parents who have more time and resources to spend on their kids, definitely provide a great service for their kids and for the entire community. My only gripe about those e-mails was that the silent suffering thing.
And yeah, money + human capital makes the difference, but I’m sure they can be separated. Human capital seems to follow those who have a lot of money. And communities without a lot of human capital need more money to make up for that deficit.
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From what I understand of the new math philosophy, the main goal is to make sure that all children can reach their potential in math. Interestingly, my mom is an 8th grade math teacher, and starting next year she is going to implement a similar program. In the program the children won’t be required to memorize anything, and they can always refer back to their notes, but the questions are much harder and more complex and they have to complete a problem perfectly (and be able to explain exactly how and why they got the answer they did) before they move on to new material. That way the teacher knows that the student has actually internalized the lesson. My mom is putting this system in place for several reasons. The first is that most kids don’t naturally “get” math, and those that do will succeed regardless of whether the new math is taught. For the kids who can’t memorize and regurgitate well, they get frustrated easily, assume they just can’t do math, and give up. It’s those kids that this program is targeting. It is designed to meet each kid where they are at, and bring them along as far as possible during the school year. It’s not about teaching to standardized tests, but actually learning something. Which, for many schools, is a novel idea.
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Call me cynical, but over time I’ve come to realize that one of the reasons various attempts to “equalize” education fail is because many parents are working as hard as they can to not equalize.
This is not to say people don’t think poor kids deserve a better education. (Some believe that, some don’t.) It’s a more basic thing: people are worried about their *own* kids’ ability to compete in the future economy. And as such, they want their *own* kids to have every advantage. This involves their kids getting some things other kids don’t have, simple as that. People work hard to differentiate their children. I don’t think any policy is going to change that.
One of the primary flaws of NCLB, in my view, is that it’s so focused on reducing test score gaps between groups of kids. I think a more laudable, and reasonable, goal would be to focus on every child reaching a certain baseline level of skill. Being so focused on the general spread of test scores is counterproductive … it can just as easily end with everyone’s scores going down — note the gap is gone, and according to NCLB it’s a success.
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Re social background, I thought you might be interested in this graphic showing how socio-economic status affects cognitive score development from the age of 22 months up to 10 years (in the UK). Part of what it traces are the average trajectories of two very different children: the first a low-income child who scores in the 90th percentile on a test of cognition at age 22 months, the second a high-income child who scores in the 10th percentile at the same age. (Click on the graphic to make it larger.)
As you see, the bright low-income kid son falls into a quick and steep plummet, while the not so bright high-income kid’s scores begin to rise. By the age of six, both are scoring around the 50th percentile. By the age of 10, the high-income kid has made it to the 60th percentile, while the low-income child – the one who appeared so bright as a baby – has fallen to the 40th.
It’s one of the saddest pictures of what education is up against that I’ve ever seen.
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I think Ragtime’s 90/10 estimation of the value of capital inside the home versus cash in the school is probably pretty good – correct in spirit if impossible to quantify in practice.
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Laura,
We can actually separate human capital from financial capital. There are many immigrants to the US
from places like Eastern Europe who have very modest means, but who benefited from excellent math and science education in the Soviet bloc, where higher education was largely technical. These parents are of modest means in the US, but their children often excel in American schools. I’m less familiar with other immigrant groups, but I think one does often encounter this scenario in other groups.
Lindsey,
Your mom’s emphasis on mastery is quite admirable.
Jen,
You make some interesting points. I have heard that you can decrease the achievement gap by depressing achievement across the board. So, first thing we do, we kill the gifted program!
Reuben,
That’s very interesting. There’s also something called the Matthew effect, by which the educationally poor get poorer and the rich get richer. There’s a short article on it on wikipedia, and another short piece at balancedreading.com/matthew. Balancedreading.com has a chart up, showing the educational development from kindergarten to third grade of children who start school with foundational pre-reading skills, versus those who don’t. The children with foundational skills make rapid progress (represented by a steep upward trend), while those without foundational skills end third grade at the same level they were at when they started kindergarten.
The idea is, I suppose, the lack of foundational skills forms a bottleneck and makes it very difficult to acquire new information. On a personal note, I taught my daughter to read this winter at around 4.5, using the Bob books and a pile of “phonics” books featuring Clifford, Dora, and the Backyardigans. I left her alone after that, and have lately been astonished by how “sticky” her mind is now that she’s nearly 5. It seems like nowadays, she only needs to hear things once to remember them, and she has started reading books for information, for instance about caves or volcanoes. I feel like I’ve just witnessed some sort of snowball effect, or that after a bit of pushing her uphill, she’s rolling quickly downhill (but in a good way!) and picking up momentum with every second.
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Thanks Amy, but it’s early yet, and we’ll see how it turns out! She’s changing it up because the old way of teaching just hasn’t been working, at least not for enough students. But it may not work, in which case she’ll have to go back to the old method. And unfortunately, she’s already starting to prepare for the inevitable backlash from parents and the high school teachers who tend to fight viciously against curriculum changes (though they already complain that the freshman come in ill-prepared, so it can’t hurt to try).
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Reuben:
Interesting graph; I was going to complain that it was flawed by the “regression to the mean” problem, but the complete graph actually addresses that question by comparing the trajectory of low & high income kids who are identified in the same group at 22 months.
Jen:
I really concur with you on failures in educational systems resulting from the fact that those with power/resources do everything they can to gain their children _relative_ advantage, not just an appropriate education.
But, I’m not sure that means that one shouldn’t focus on the differences. The reason to focus on the differences among groups and populations is that the higher achieving groups tell us what is possible for children to achieve. The danger with setting minimum standards, rather than comparative ones is that the standard will be set too low. Combined with the race for _relative_ advantage, this will continue to exacerbate the problems we hope to treat with education.
bj
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Catherine Johnson of kitchentablemath.blogspot.com has praised the “Gambill Method” of teaching algebra. (Gambill is an award-winning math teacher.) She has a summary at:
http://www.kitchentablemath.net/twiki/bin/view/Bloggers/GambillNutshell
There’s nothing amazing in the method Johnson describes, just a lot of consistency, accountability, and focus on mastery.
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It looks like the URL somehow got chopped–it should end “Bloggers/GambillNutshell.”
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Lisa V writes:
“My kids have spent the last 8 years being taught the “new math”. It was frustrating and scary to me they couldn’t as easily regurgitate their times tables as easily as friends in a traditional school. However they always were in the advanced areas on the standardized tests – and our school does no kill and drill. Then when my two oldest got to high school algebra and geometry were a piece of cake. The new math really plays well into the math skills our kids will need in high school and college.”
Early standardized tests don’t require instant recall to succeed, as long as they have enough time to figure out the answer, the test will reflect that.
The fact that they did well in Algebra and Geometry is completely irrelevant. It is impossible to do well in Algebra and Geometry without having a firm grasp of multiplication facts. Both subjects require loads of factoring… no amount of skip counting, pictures, or finger tricks can replace knowing the basic math facts.
All this shows is that your kids were able to eventually master their math facts, despite lack of concentrated practice, by the time they took these classes. Just as some kids will learn to read through osmosis, many kids need explicit instruction.
I would also like to point out that income is usually used as an indirect proxy for parents IQ. The correlation between parents IQ and their children’s is significantly higher than the correlation between parents income and children’s IQ.
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There is a whole lot of room between “reform” or “constructivist” math on the one hand, and “back to basics” on the other. But it is hard to advocate for the center, as the extremes generate the outrage and the money.
As a teacher who has been pushing the “center” for a decade, and a bit successfully, there are a few observations I’s like to share:
1) Top-down reform fails. Passively accepted reform fails. All you need is one group to passively resist: students, parents, middle level admin, teachers, and it sinks.
2) It is far easier to add reform elements to a traditional program, than it is to add traditional elements to a reform program.
3) Many good “traditional” teachers routinely add “reform-ish” aspects to their teaching already.
4) Teacher-proof programs stink.
I also know a little about Ridgewood. Did you know that they selected a new superintendent, all tied into reform in a town on Long Island, but that the parents’ firestorm was too hot, and that he withdrew himself from the job?
For all of the cash Ridgewood has, they’ve had the worst of both ends of math: their regular, traditional stuff was hyper-accelerated – everything for stretch, nothing for depth. And their reform math? TERC, the worst out there. Ugh. I think they like literature better than numbers.
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Hello from one of the Math Moms in Ridgewood. We have had quite a battle going on about reform Math here and we haven’t won yet.
It’s hard for people to understand their kids can be straight A students and still not learning key concepts. It’s what is omitted in this curriculum that will harm our children.
We’ve had a hard time educating our “educated” town. Most folks are happy to blindly trust our educators because they have the PHDs in education and we are just lowly Mothers.
So we’ve continue to enlist the help of Math Professors so our PHDs can counter their Phds.
Everyone in New Jersey should look out for TERC Investigations and the Connected Math Program. Even if you decide not to fight your local Board of Education, you should tutor your children or they will be behind when they get to college and perhaps locked out of Math related careers, such as Engineering.
Here’s our website for those who want to read up.
http://www.vormath.info
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Thanks for the link Amy. I think I’ve heard my mom mention the Gambill method, though I’m not quite sure if that’s what she’s using. If you (or anyone else) wants to keep tabs on her project, I’ve convinced her to start a blog so that the parents and her administrators can stay informed with her class’s progress. She won’t start writing in it until fall, but the link is:
http://radical-teaching.blogspot.com
When the time comes, I know she would love helpful comments/tips from any other teachers out there!
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Amy :
“a number of those state exams are aligned with reform math, so the states are playing the hand they dealt themselves.”
yes … and many traditional assessment measures are aligned with traditional maths … so they’re also playing their own hand
the link between assessment and curriculum can a re-inforcing feedback loop either way
the big international studies (PISA etc) that are used to raise concern over relative performance of various countries are also subject to this positioning and alignment
maths curricula is not a neutral set of skills. It can be framed as traditional “exam” mode, or deeper and more productive enquiry.
sooner we realise that the better, or we are comparing apples with comquats
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