kitchen table math, the sequel: stagnation at the top, part 2: what do teachers think?

Tuesday, June 24, 2008

stagnation at the top, part 2: what do teachers think?

question:

For pubic schools to help the U.S. live up to its ideals of justice and equality, do you think it's more important that they focus on:

All students equally, regardless of their backgrounds or achievement levels -- 86%

Disadvantaged students who are struggling academically -- 11%

Not sure -- 3%

High-Achieving Students in the Era of NCLB (pdf file)

The breakdown on this answer doesn't surprise me at all. Yes, many of these teachers reported that their schools required them to devote the lion's share of their time to low-achieving kids at the expense of high-achieving kids. But they didn't like the situation, and they didn't approve of it.

I stopped buying the "Washington consensus" a couple of years ago.

The Washington consensus -- focus on the low-achieving kids; let the high-achieving kids fend for themselves -- sounds right on the face of it. Limited resources, neediest cases, and so on.

In real life, it's wrong. At least, it's been wrong in my experience.

thought experiment:

Close your eyes and imagine a school administrator telling a large audience of parents at a school board meeting (paraphrasing): "I only care about the low-scoring kids. They're the ones who are struggling."

How do you think the low-scoring kids attending that administrator's school are going to fare?

If no answer springs to mind, ask yourself whether it's conceivable that Siegfried Engelmann could make such a statement. Or Mike Feinberg. Or the Reverend John Foley.

It's possible that equity and excellence are separate and competing interests at the level of policy. I don't know that they are, but I'm willing to concede that they may be.

At the level of human motivation and behavior, however, excellence is excellence and integrity is integrity. An educator who has no problem writing off an entire group of children because he has to bring up the low kids' scores isn't the man for the job.


tracking in a Catholic high school

My favorite passage on the nature of a school where everyone is doing his best comes from Tom Loveless:

Intellectually stimulating low track classrooms do exist, however, and researchers have found the most productive of them in Catholic schools. Margaret Camarena and Adam Gamoran have described low track classrooms where good teaching, lively discussions, and ample learning take place. In 1990, Linda Valli published her study of a heavily tracked Catholic high school in an urban community. The school’s course designations publicly proclaimed each student’s track level. Textbooks and instruction were adapted for each track. Yet Valli discovered that "a curriculum of effort" permeated the entire school, even the lowest tracks. The school culture centered around academic progress, and the tracking system was but another facet of the school that served this aim. Students of all abilities were aggressively pushed to learn as much as they could. Every year, low track students were boosted up a level. By the senior year, the lowest track no longer existed. A judicious tracking system teaches low track students what they need to know and moves them out of the low track as quickly as possible

The Tracking and Ability Grouping Debate
Tom Loveless
07-01-98

Valli's original paper can be downloaded at ERIC.

ability grouping & SAT score decline
ability grouping in Singapore
stagnation at the top - Fordham report
Tracking: Can It Benefit Low Achieving Children?
Linda Valli on tracking in 5 Catholic high schools, 1
Linda Valli on tracking in 5 Catholic high schools, 2
"school commitment" in Valli's study of tracking in Catholic high schools
7th grade depression starts in 1st grade

48 comments:

Anonymous said...

--"I only care about the low-scoring kids. They're the ones who are struggling."

How do you think the low-scoring kids attending that administrator's school are going to fare?

If no answer springs to mind, ask yourself whether it's conceivable that Siegfried Engelmann could make such a statement.


Not sure what you mean, here. Sieg Engelmann specfically says in his peronsal memoir or in essays on his website that he did DI to focus on the struggling kids. He has said that sure, bright kids go screamingly fast with DI, but HE DOESN'T CARE. They don't need it, and that's NOT his focus.

I'll find the quotes...

Anonymous said...

okay, it's Chapter 4 of his memoir on Project Follow Through. Filename FT-Chap4.pdf. Unfortunately, I don't have that pdf on a machine with net access right now, nor do I have any sneakernet capabilities from where I'm at.

but starting on page 2 of Chap 4, with the sentence "Although these children were awesome, their performance showed a critical difference between their potential and that of the at-risk child," and continuing til page 4, you see his argument. I'm not going to abbreviate it here because I don't want anyone deciding I'm misrepresenting it. But it addresses the issue of why they decided not to work with high performers and only work with lower performers. Catherine, you have a copy of this pdf somewhere here on KTM? After reading it, let me know if you think this speaks to the issue you were addressing above.

LynnG said...

More or less, the hypothetical administrator proudly resides in many school districts across the State. I've been to more than one board of ed meeting where administrators said "the cream rises to the top" and things of that nature.

We eliminated our "gifted" program years ago and moved to totally heterogeneous classes because it was beneficial for the top kids to mentor/tutor/teach the lower performing kids. And the high flyers are supposed to gain compassion for their slower peers. Yeah for compassion.

We've hired remedial everything and expanded our remediation teams. They pay lip service to teaching the smart kids by tossing around words like "differentiation" and "enrichment" but for the most part, if a kid is meeting goal on the CMT, they receive little attention or encouragement. There is an inverse relationship between scores on the CMT and attention in the class room.

Of course, in educationland, that should mean that the way to succeed is to pay no attention to the students. Research will surely demonstrate that lack of teacher attention = higher student achievement, so then we'll all feel good about the shift in resources.

Anonymous said...

It's possible that equity and excellence are separate and competing interests at the level of policy. I don't know that they are, but I'm willing to concede that they may be.

At the level of human motivation and behavior, however, excellence is excellence and integrity is integrity


So am I right to take your point as something like, "low achievers will do better under a system in which all students, including high achievers, excel, than in a system in which most resources are aimed at the lowest achievers?"

It's interesting. It makes sense, but I'm not sure how you reconcile that reality with the fact that a minimally adequate education has essentially been established as a constitutional right (not that I am familiar enough with the specifics of special ed law, but that's the basic idea, isn't it?)

In other words, I can imagine a contradiction, according to which assuring minimum competency, for legal reasons, has to take precedence over assuring highest competency, even if we're solely talking about the lowest achievers. I'm not sure how one would get around that logically.

Catherine Johnson said...

I'll have to check Engelmann -- I remember Ken, a couple of years ago, posting something Engelmann said about high-performers doing well in DI.

If he really did say "I don't care" then I'm off the Engelmann boat.

Catherine Johnson said...

More or less, the hypothetical administrator proudly resides in many school districts across the State.

right

I'll add, here in the comments, that the aforementioned administrator wasn't hypothetical.

Catherine Johnson said...

Here's Engelmann:


Following the remodeling, we opened a learning center, which was designed to serve hard-to-teach children and school failures. One
of the earliest groups, however, was not low, but was composed of six preschoolers whose parents were professionals or professors. One
student was Wes' youngest son. We worked with these children as
four-year-olds and five-year-olds. They went through the reading and
math programs as fast as they could go at mastery, which was
frighteningly fast. (There was no need for the language programs
because these children were very bright.) Even though they worked for only a little more than an hour a day, they went through all four levels of the programs we had for Follow Through classes. Before they
entered first grade, they performed on the fourth-grade level in both
subjects. And they loved school.

We never published anything about the performance of these children, largely because the group had only six children, which meant that experimental purists would "question" the results. (Usually, at least 15 experimental children are needed for establishing outcomes that are recognized as valid.)

Although these children were awesome, their performance
showed a critical difference between their potential and that of the atrisk child. When these advantaged children came to the third and fourth levels of the reading program, where the material becomes entrenched in and decorated with sophisticated language, they did not slow down. The profile for the at-risk child is different. Performance slows considerably when they reach the vocabulary-rich transition. They have parallel problems with math when the word problems become more substantive than a few pared-down sentences that present necessary information in a "familiar" format.

The performance of the high preschoolers pointed out the
terrible paradox of effective instruction. If we accelerated the
performance of all students in a district that had a full performance range of children, the outcomes would suggest that we were not serving the at-risk children well. Their gains would be far less than those of the higher performers. So we would actually be widening the difference in one sense. In another sense, we would be narrowing it if the at-risk children learned a sufficient amount to become "competent learners," which means that they would have the information, the background knowledge, and the learning skills they needed to quickly learn anything we wanted to teach them.

Viewed a third way, we don't have to worry as much about the
performance of higher performers. They will tend to learn from
teaching that is hideous, as many programs for the talented and gifted demonstrate. These programs provide instruction that appears to be purposely designed to teach, explain, and develop skills in the most circuitous and confusing manner possible. Certainly it's cruel to subject students of any skill level to such instruction, but in the larger scheme, far less cruel than subjecting at-risk children to certain failure. Although it would have been possible for us to work with both
populations, we reconfirmed the decision not to work with higher
performers but rather to show the degree to which at-risk children
would catch up to higher performers with careful instruction. We
figured that teaching higher performers effectively is so easy that in time, those who educate them would learn how to do it effectively. It It
FT-Chap4.doc February 13, 2007, kf © 2007, S. Engelmann Page 4 of 81
certainly hasn't happened yet. But we felt that we needed to work with
the lower performers simply because it is not easy and teachers don't
know how to do it. In fact, we believed that if we didn't do it, it wouldn't happen because nobody in or out of Follow Through (with the exception of the University of Kansas) was close.

Somebody could make a strong argument that it is more
important to assure that higher performers achieve their potential
because they will be the leaders that advance science and technology. To us, it seemed to make more sense to assure that at-risk populations generated their share of leaders. Even though this is a far harder job, it may be a far more important one.


Chapter 4 During Follow Through

Catherine Johnson said...

I'll have to post that up front without all the gaps...

Catherine Johnson said...

I don't have a problem with Engelmann's statement - except, possibly, for the final paragraph about which job is more important (educating future scholars & leaders versus making sure underachieving groups produce leaders, too).

If you listen to his language, he has tremendous admiration for these high-achieving kids & he sees, plainly, the miserable teaching to which so many of them are subjected.

When have you ever heard a person say that GATE kids are taught badly?

What I'm seeing, in my own district and in super-expensive private schools, is GATE kids teaching themselves, or trying to. When they try and fail, parents are told the kid just doesn't have what it takes (and it's "sad" that parents "pressure" their kids - Ed and I have been told this directly).

It's a brutal system, and it's cruel. Engelmann is the first educator I've seen use that word: "cruel."

Catherine Johnson said...

I should clarify my comment about private schools.

I haven't seen kids teaching themselves routinely in expensive private schools.

I've seen it in one private school (or perhaps 2?) and it was appalling. The kids were being given college-level assignments and told to deal with it.

Which meant parents hiring tutors & taking research trips to the library themselves.

Catherine Johnson said...

In other words, I can imagine a contradiction, according to which assuring minimum competency, for legal reasons, has to take precedence over assuring highest competency

Hi, Laura!

Well...I'm still developing my "policy brain," but I think that we're talking about "different levels of analysis." (I was going to reference Dan Willingham's video, but wasn't sure whether the analogy held).

Policymakers may need to think of "equity" and "excellence" as separate and conflicting. I'm not able to work out the logic there, especially when we consider SPED & NCLB and when we factor in all the studies showing that money doesn't make a difference to student achievement but teacher IQ does....

Teachers with high SATs are, by definition, a limited resource.

The level of analysis I'm talking about is psychological and probably "organizational" or "institutional" -- I'm not sure what the term would be for the latter.

One critical factor is the inclination of an educator (teacher or administrator) to view children not as individuals with names and histories but as groups with group characteristics.

In my experience, and I know this generalizes to other public schools, an educator who sees groups instead of individuals -- and who is willing to write off an entire group for whose education he is responsible -- is not going to be doing a good job with any child.

For some time now it's been obvious to me that if the low-achieving kids aren't learning (here I'm talking about low-achieving in the NCLB sense of the term), the high-achieving kids aren't going to be learning, either --- not well, not what they could be.

In an affluent school, when the low-achieving kids aren't doing well you're going to find the high-achieving kids being tutored and re-taught be parents -- and teaching themselves once they're "mature" enough to do so. (I now see lots of district talk about "maturity" as a red flag.)

I now believe that this relationship works the other way around, too. If you see (and this isn't easy to see) that high-achieving kids in a district aren't doing as well as they could be, you're going to see that the low-achieving kids are really struggling.

In other words: in my own experience, schools that do any level of education well will do all levels well and vice versa.

Which brings me to the "organizational" or "institutional" level: I'm pretty sure that it's not in the nature of an excellent organization to say, "We'll do a great job at X & a lousy job at Y."

Assuming that Built to Last is a useful book on the nature of longlasting companies, his chapter on the "tyranny of the OR" is what I'm talking about. (I haven't read the book, btw - you can see the chapter on Google Book Search.)

Here's a good line: "Instead of being oppressed by the "Tyranny of the OR," highly visionary companies liberate themselves with the "Genius of the AND"--the ability to embrace both extremes of a number of dimensions at the same time. Instead of choosing between A OR B, they figure out a way to have both A AND B. p. 44

oh!

Here's a section Steve may like:

"As we move into the rich detail of the next eight chapters, you'll encounter, as we did in our research, a series of these paradoxes--apparent contradictions in many of the visionary companies....

We're not talking about mere balance here. "Balance" implies going to the midpoint, fifty-fifty, half and half. A visionary company doesn't seek balance between short-term and long-term, for example. It seeks to do very well in the short-term and very well in the long-term....

To my knowledge, pundits & policy wonks haven't looked to see whether the presumed contradiction between equity and excellence exists in real life.

At the moment, I'm guessing that it doesn't -- or, at least, that it doesn't for the best schools.

Catherine Johnson said...

The reason I don't have a problem with Engelmann is that he isn't running a school or a school district. He is a specialist in curriculum development.

Catherine Johnson said...

The Race between Education and Technology bears on this question.

The authors demonstrate that for the first 75 years of this century educational excellence and equality rose together.

Since 1980 we have had stagnating or falling quality of education and falling equality.

The book is quite radical in its findings and its implications. It may be so radical that our pundits & wonks aren't going to be able to absorb it.

All of our pundits and policy wonks define "equity" and "excellence" as opposites, regardless of their position.

Eduwonk, Hess, et al say, "We can't do both; we have to choose."

Others say, "We should do both."

To the extent that The Race applies to the equity/excellence dichotomy, the book shows that you can't have one without the other.

At least, it hasn't happened in the past 100 years.

This makes the people who say, "We can have both" as wrong as the people who say "We have to choose."

It's not a question of "both." The two "extremes" cause and reinforce each other.

(sorry, can't think of a better way to put that...)

Catherine Johnson said...

One last thing!

Although I don't begrudge Engelmann his decision to specialize in low performers, it's possible that his decision was a tactical mistake. (Tactical? Strategic? Still can't tell the difference.)

The effect has been to associate DI with SPED and with disadvantaged populations.

A couple of demonstration projects showing exactly how fast talented kids could move using DI would have prevented that....

Anonymous said...

. They will tend to learn from
teaching that is hideous, as many programs for the talented and gifted demonstrate. These programs provide instruction that appears to be purposely designed to teach, explain, and develop skills in the most circuitous and confusing manner possible.


That's actually pretty funny because it is largely true.

And people will rarely complain about a gifted program because they're so glad that one even exists.

I'm amazed at the number of people, including those who comment here, that have no tracking in middle school and no GATE program.

SusanS

KDeRosa said...

Although I don't begrudge Engelmann his decision to specialize in low performers, it's possible that his decision was a tactical mistake.

I think it was a political and marketing mistake. It would have been better to gain market share by getting (perhaps watered-down) DI accepted by middle-class parents who want to see their children succeed and are familiar with the issues and then expand into the low-SES market with full-immersion DI schools.

Kind of like the restauranteur who runs a chain of olive gardens to fund his fine dining resaurant.

Anonymous said...

Hi Catherine (what a great blog, by the way!),


It's not a question of "both." The two "extremes" cause and reinforce each other.

Oh, I have no trouble believing that, at least according to the model you have described.

I'm just thinking that, from a policy perspective (not that I can pretend to have any expertise in that area), the primary goal would have to be framed explicitly as using the "excellence" model to match or improve on the current model in terms of ensuring minimal adequacy for all (or as close to all as possible). Even if, from a pedagogical perspective, the primary goal would be equality through excellence, or something like that.

In other words (sorry I'm having trouble articulating this), while equality through excellence is probably a realistic and worthwhile goal, I think there is still an extra requirement to show there will be no decrease in the number of students receiving a minimally adequate education (so even if significantly more kids were better off across the board, the priority would still have to be showing that there was no decrease among "low achievers").

I absolutely believe you that this would be possible--I think it would just be necessary to demonstrate first that no extra kids wind up "falling through the cracks" unexpectedly.

(Also, I take your point about NCLB "low achievers" vs the special ed population, but I *think* special ed law is based on the premise that everyone must be guaranteed an adequate education in order to ensure equal protection under the law, right? So, logically, it seems like that should apply to NCLB "low achievers" as well, I think. )

Anonymous said...

I think a lot of the issues raised here have roots in the 800 pound gorilla hiding in the room.

Kids learn at different rates!

Some kids need repetition. Some need to see a concept from multiple directions. Some seem to make no progress (although they are busily doing synthesis) until they burst open like late blooming flowers and some can go much faster than the teacher does. All of these factors contribute to different learning slopes.

It became politically incorrect to bring this up over the last two decades as it was (incorrectly) perceived or correlated as a racial artifact. Now it is really not possible to talk about it in an objective way without someone morphing it into a racial issue. Nobody wants to be a racist so nobody adresses it realistically.

Every single thing we do in our systems of public education ignores this fundamental rate difference. Programs that buck this reality are rare.

When it comes to special ed (a term I loath) the law simply demands equal access to curricula. It does not demand or expect equal outcomes. Therein lies its flaw.

When it comes to equal access, the implementation means that kids with special needs can't be shunted to a poorly qualified teacher or low expectations curricula. Everybody gets the same thing. This seemingly sensible approach to equality locks in the one rate learning slope. Kids on both ends of the spectrum of ability get shafted by this first order solution.

What should happen is that you figure out a kids slope and tailor a program to fit the kid. If that means the child is doing calculus in the sixth grade, great! If it means some are still working on addition in the sixth grade, well that's great too.

Instead of writing a law that created a one size fits all solution the expectation should be that each child achieves their potential, where ever this leads.

Anything less is not just cruel, it's child abuse.

Anonymous said...

Catherine Said:--Although I don't begrudge Engelmann his decision to specialize in low performers, it's possible that his decision was a tactical mistake.

Ken said: --I think it was a political and marketing mistake. It would have been better to gain market share by getting (perhaps watered-down) DI accepted by middle-class parents who want to see their children succeed and are familiar with the issues and then expand into the low-SES market with full-immersion DI schools.

But at the time that he was doing this, for the first time, were middle class parents up in arms about their children needing something different to succeed? Probably not. Who knew those problems were on the horizon then? But they already knew that disadvantaged kids were being lost. Hindsight looks a bit different, assuredly.

Catherine Johnson said...

Ken - I'm glad you weighed in - I was wondering what you thought about this question in particular.

That's kind of my "take"...but I'm uncertain.

Allison's question is on point; and believe it or not I actually have the data on when middle class parents lost confidence in the schools. I've got to look it up, but I think it's around the same time that keeps popping up here -- around 1980.

The SAT decline went on for 17 years and was covered constantly in newspapers so by the end of that period people were so aware of it that Charles Murray could publish an article calling the SAT chart showing the decline "famous."

I suspect, though, that regardless of whether middle class parents were up in arms, everyone was more sympathetic to direct instruction at that point.

Direct instruction (small caps) was still being taught in ed schools then, too.

On balance I come down on the side that it was probably a political and marketing mistake to focus on low achieving kids.

Catherine Johnson said...

Hi Laura, thanks!

You're right about SPED ---- we once met with a major SPED attorney who told us that NCLB is a SPED law. He wasn't using the term metaphorically, either.

I can't quite think my way through your comment....possibly because I still don't know enough about policy per se.

Is there a distinction between policy "writ large" and the assessment or conditions of a policy???

I'm not sure that question even makes sense.

Catherine Johnson said...

Kids learn at different rates!

[snip]

It became politically incorrect to bring this up over the last two decades as it was (incorrectly) perceived or correlated as a racial artifact.


The whole thing is a gigantic mess.

I have to post the article I found about the project method as the solution to our woes ---- nightmare.

It pretty much amounts to saying, "Put the low kids in with the high kids and let the low kids clean up the paste & put away the scotch tape after the high kids wrote and created the project."

No discrimination there!

Catherine Johnson said...

What should happen is that you figure out a kids slope and tailor a program to fit the kid. If that means the child is doing calculus in the sixth grade, great! If it means some are still working on addition in the sixth grade, well that's great too.

Absolutely.

Also...I can speak to this issue from a DEEP WELL of experience from the parents' side at this point.

Our situation (I know I've endlessly brought this up) is that algebra-in-8th-grade is considered to be appropriate only for mathematically gifted students.

Which means that ambitious (aka "pushy") parents who want their non-mathematically gifted kids to take algebra in 8th grade hire tutors, teach the course themselves, etc.

NO ONE ENJOYS THIS.

It is HORRIBLE having your kid constantly have to be "the dumb one" or "the struggling one" in a class of math stars.

This whole idea that if you put the slower students in with the fast ones you're doing the slow kids a big favor is cr**.

Catherine Johnson said...

Instead of writing a law that created a one size fits all solution the expectation should be that each child achieves their potential, where ever this leads.

Anything less is not just cruel, it's child abuse.


That's where I am.

Everyone should go-go-go.

End of story.

We need a Knowledge School.

Anonymous said...

About 40 years ago I had the pleasure of spending a week in the upper Mekong River delta. My boat was working out of this little village that was basically a mud island covered with tall grass. The 'business' of the village was selling sticks retrieved from the river to villages down stream. Every morning all the men got into little canoes and went foraging all day for sticks.

While they were gone every single person in the village, down to and including infants still nursing, spent the day squatting in a big circle knocking the waterlogged bark off yesterday's sticks. It was fascinating to watch. I can still remember thinking, "I'm over here in this hell hole of a war and I'm the lucky one."

My second most often thought was, "If these poor bastards ever get an education, we're (U.S.A) screwed." Well, I think that's happened, figuratively at least.

While we spent my lifetime Guccing and Dioring our politically correct asses off, the rest of the world has been figuring out how to get the max out of their assets, all of them. I fear they are poised to eat our lunch and we still don't get it.

My kids have two and three pairs of sneaks; one for the hood, one for school, and one for gym. They have Xboxes at home and two free meals a day at school. They can't compete with the stick kids from the mud island.

I remember having a class conversation once about why knowing percentages and how to apply them was important to good shoppers. My class thought me a fool. They just hand over the EBT card (our welfare debit card) and don't worry about discounts. They truely didn't give a hoot about discounts.

I keep hoping for some kind of perfect storm to wake people up but my instincts tell me we have passed a tipping point where there's just not enough people that give a rip about this.

KDeRosa said...

But at the time that he was doing this, for the first time, were middle class parents up in arms about their children needing something different to succeed? Probably not. Who knew those problems were on the horizon then? But they already knew that disadvantaged kids were being lost. Hindsight looks a bit different, assuredly.


I'm going to disagree slightly.

DI would have been sold as an acceleration program, which it was and still is. It can accelerate the performance of any student because it is a more efficicent way to teach.

Knowing more is always better than knowing less. That's something middle-class parents could relate to and would want for the advanatge of their children, especially since some of the sharper edges of DI could be rounded off for many middle-class students with little sacrifice in performance.

Are there any new problems that didn't exist 30 years ago or is it just our awareness that has increased because of our greater access to educational opinions/research thanks to the internet.

I rember back in 1998 -- there was very little available to your average parent and what was available was dificult to find. And when you did look, you had to get past the mountain of bad opinion/research that could easily send an uninformed parent down the wrong path.

Today, information related to education is much more readily available. both sides of the issues are well represented and argued.

Anonymous said...

"Are there any new problems that didn't exist 30 years ago or is it just our awareness that has increased because of our greater access to educational opinions/research thanks to the internet."

One of the things I often wonder about is if there has been a change in 'homogeneity' over those 30 years. I'm not talking about diversity in the common vernacular. I'm talking about our increasingly transient population, especially in the inner city.

My previous school had about a 40% turnover every year. I did a study based on MAP scores from NWEA testing and our cohort that was 'stable' (in district 4 years) was about 2 years above our transient (in district 1 year or less) population.

It makes me think that DI is especially appropriate in these high turnover situations as its tight feedback loops address this by focusing on where kids are academically instead of chronologically. So if you come into a district and are radically out of sync with your age group, DI is going to recognize this quickly and inherently correct it.

Non DI, you just generate another frustrated student that has no way to catch another rung.

Anonymous said...

we once met with a major SPED attorney who told us that NCLB is a SPED law. He wasn't using the term metaphorically, either.

Wow, that is so interesting.

You know, I'm not even sure what I was trying to get at--something like your question, I think. I'll think about it some more.

Anonymous said...

--What should happen is that you figure out a kids slope and tailor a program to fit the kid... If it means some are still working on addition in the sixth grade, well that's great too.

NO NO NO NO NO NO NO!

It is NOT GREAT. It is NOT OKAY that some kids are still working on addition in sixth grade. It is a DISASTER for THOSE KIDS.

"work on your own slope" CANNOT become "some kids will NEVER MAKE IT PASSED arithmetic." That is relegating them to failure.

The slope argument is correct. But the answer is obvious. If you have a lower slope, you are going to need to move farther in X so you can be at a reasonable place on Y.

The kids with lower slopes need MORE instruction. Saying it's okay to let them be on addition in 6th grade and we'll go "at his pace" means he's falling farther and farther behind. That's PRECISELY the problem the Race between Ed and Tech is pointing out. If you have to start there, then you start there, with the EXPLICIT statement and consequent understanding that "this is NOT okay. You are behind. You will need a LOT more time and a LOT more effort to be in a place that is okay." And then you provide that. That's what DCP did. That's why it worked.

SteveH said...

Who gets to decide on slope? Many K-6 educators believe in letting nature take its course. That's the basis of Everyday Math. Most people (in hindsight) think that the best teachers they had were the ones who pushed their slope, so to speak.

I really don't see it as an equity/excellence dichotomy. I see it as a goal A versus goal B problem and a low versus high expectation problem. My son's school is going in the wrong direction and sets low expectations for the kids and the teachers.

I look at the NAEP questions and results and don't think about slopes or equity. I think about what the heck are schools doing for 6+ hours a day. Talking about tradeoffs between equity, excellence, and money assumes that this is the problem. I agree with the teacher of the year in the other thread. Schools can't even make sure that two teachers of the same grade are teaching the same thing.

It makes me think about an episode of Arthur where Arthur realizes that he is glad to be in tough, Mr. Ratburn's third grade class when he sees the teacher in the other class singing songs ("I like fudge.") and using hand puppets to teach. My son has outgrown Arthur but I loved the high expectations viewpoint. I also liked the fact that Arthur was starting to play Bach's Two Part Inventions in third grade. When Arthur didn't try hard enough, his piano teacher "fired" him.

In our town, the stagnation at the top starts with low expectations in K-8. Bad habits are hard to overcome.

Anonymous said...

Yes, Yes, Yes! Teaching addition to a sixth grader is absolutely OK and NECESSARY, if that's what they need. I'm not saying this is a desirable thing. Of course this is not PLANNED.

You don't get to choose who is in your class. We have a highly mobile world wide population and, have you noticed, open borders. My district has 9th graders that need addition work.

What's outrageous is putting such a student in a system that is totally designed to teach to the median child of age grouped cohorts. It happens every day!

Anonymous said...

"Many K-6 educators believe in letting nature take its course"

Can you provide a citation for that?

Of course it is the child that determines the slope. It's a naturally occuring independent variable.

Anonymous said...

Education policy at the state and federal level is driven in large part by the neediest students. It's what governments do. Think FEMA, U.S. Military, welfare, food programs, etc.

Even at the local level this is true to a lesser extent. Think about fire and police services. Governments either help those in need or regulate those who need it. There's no agency set up to help you rake your leaves in the fall.

As long as localities partake of the public funding trough they are drinking from the equity stew no matter what it's called. Unfortunately this stew is always delivered via an infrastructure built around one size fits all systems.

It doesn't follow from this that all teachers are communists, or hate gifted kids, or are stupid, or don't know how to do their jobs. Many of them, perhaps most, are no more in love with this than the parents who get sucked into this vortex. They're simply working inside a dysfunctional system. If a few are extrodinarily good at it, you should look at it as a miracle.

My belief is that there are ways to provide for excellence across the board but not in the current infrastructure. It's incapable of realistic, effective differentiation because it's stuck on arbitrary cohort formation and 'median' curricula delivery to match the cohorts. The only short term fix for a parent is the opt out, to private, parochial, or home schooling.

When you opt out think about what you're doing at a really high meta level (higher than the level that addresses quality of instruction). One, you are cutting off drinking of the stew. Two, you are finding your child's ZPD. Three, you are engaged and for me this implies that you are now tuning the child's slope. This is especially true with home schoolers.

This combination has far more effect on learning than the type of math program employed. If you want a long term fix inside a publicly funded structure then it has to look more like the opt out than not.

SteveH said...

"Many K-6 educators believe in letting nature take its course"

"Can you provide a citation for that?"

Developmentally appropriate. But how do they determine that? How can schools tell the difference between bad teaching, low expectations, and developmentally appropriate?


"Of course it is the child that determines the slope. It's a naturally occuring independent variable."

Independent of teachers, curricula, and expectations? Then I don't know what you're referring to.

Anonymous said...

There are two components at work on the slope. One is a sort of cyclical variation around a mean slope. This can range from causes as simple as a child having a bad bout of daydreaming to missing some key days through illness. The daily measure looks like a low slope on some days and high on others.

The other, the one that drives the mean slope is partly due to prior history and partly due to inate abilities. Kids that have 'holes' in prior knowledge exhibit short term memory overload. While a new concept should be gaining relevance in their minds they're busily seeking connections that can't be found so the new stuff doesn't get in when it should. Doesn't mean it won't get in tomorrow or the next day, but it doesn't get in when it 'should'. This appears as a lower slope with more legs than the cyclical stuff.

The other component that can drive the mean slope is the child with a genuine learning disability that might need far more repetition to get it. I've seen kids leave my classroom on a given day completely proficient in something new and the next day have absolutely zero retention of the concept. These kids can sometimes have success with higher repetition than the norm and sometimes not. Sometimes they need a different angle on a concept. Sometimes they get it later in the year.

Think of these as independent of any external stimulus; teaching quality, curricula, environment, parental involvement. This is the childs independent composite slope.

What the externals can do is alter this slope up or down but, and this is my argument, they all need to be working off the existing point in space where the child is actually located, the ZPD. All of these external variables can provide some delta m, if you will, but they are intimately related to the child's underlying slope.

Unfortunately, our existing structures are designed to provide an arbitrary slope or curricula pace and sequence that has nothing to do with anybody in the class. Some kids can hook up to this train ride. Some kids can't. No kids are ideally suited for this hypothetical mean.

There is nothing (structurally) available to build in more repetition or alternative approaches. There is nothing available to objectively measure and respond to where kids are on the plane and nothing that addresses their individual slopes. This is not to say teachers don't give this their best shot but when you have 30 kids in a room in thirty different places on the plane and 30 different slopes it's wishful thinking to think anybody can pull this off for every kid in the room.

Of course if your kids are in a perfectly homogeneous classroom much of what I'm talking about is moot. A good teacher in such an environment can make everybody fly. My experience (and I suppose my strong opinion) comes from extremely heterogeneous classrooms.

I've had 3 (count 'em) kids in 4 years that were above the 50th percentile on a national standardized test. My classrooms have had a central tendancy of about the 25th percentile with a skewed distribution having a strong tail in the 1st percentile.

In this environment my peers and I are asked to teach a program designed for the 50th percentile (or higher). This is insane. My experience is probably an extreme but my conjecture would be that this kind of disconnect exists to varying degrees anywhere you want to look.

I'll even go further and throw out one more conjecture. What if the big educational decline we've seen in the last thirty years has a strong component due to a societal trend from homogeneous to heterogeneous communities? Are we educating heterogeneous kids in a system derived in homogeneous times?

Catherine Johnson said...

One of the things I often wonder about is if there has been a change in 'homogeneity' over those 30 years.

There is a big increase in "homogeneity" in the sense that people are living in communities with other people at exactly their level SES.

Rising inequality in income has led to rising inequality in housing. This is something I've been frustrated over---the little town I live in is way too homogeneous for my tastes (and for a lot of people's tastes).

That is happening everywhere.

Catherine Johnson said...

I believe that we do have problems today we didn't in 1960.

Up until the 1980s ed schools were teaching direct instruction, B.F. Skinner was important enough to appear on the cover of TIME MAGAZINE, the 60s had not yet happened. (The 60s seem to have added a kind of postmodernist relativism to classic Dewey/Kilpatrick progressivism. Talk about a tipping point!)

The decline in SAT scores happened between 1964 and 1980.

Hoxby shows that wage compression & declining SAT scores in teachers occurred during the unionization period (60s, right).

AND: personal evidence...my grandmother went back to teaching in the 1960s, I believe. She said the teachers she had started out with, who were terrific, were gone, replaced by uneducated new young teachers who didn't know what they were doing.

Same thing happened in Ed's school in Levittown PA. When his younger brother got there in the 70s it was a completely different place. It had been an excellent public school when Ed attended; in the 70s it was mediocre.

For a variety of reasons things changed during the 1960s and perhaps part of the 1970s.

Catherine Johnson said...

DI would have been sold as an acceleration program, which it was and still is. It can accelerate the performance of any student because it is a more efficicent way to teach.

WOW -- that is a VERY good point.

I remember, from when I was a kid: people were obsessed with accelerated reading.

People were buying Evelyn Wood's speed reading course.

Catherine Johnson said...

The astonishing thing to me is that my district deliberately slows learning down.

I find it incredible.

The fact that Trailblazers delays some topics by a year or more simply isn't an issue for anyone employed by the district.

Catherine Johnson said...

Many K-6 educators believe in letting nature take its course

oh my gosh, how many times have I been told some version of this

the entire, public rationale for limiting enrollment in Earth Science in 8th grade here to 48 students (exactly 48) is that the rest of the class isn't developmentally ready to take Earth Science.

The first time a teacher told me this I was so flabbergasted it didn't occur to me to say, "So I guess the black kids are always developmentally slower than the white kids, right?"

Catherine Johnson said...

At least a hundred parents were told, in a public setting, that many of the kids simply had not developed the maturity to handle Earth Science in the 8th grade.

Catherine Johnson said...

Willingham has a new article out on "developmental readiness" we can all spend a lot of time quoting from now on.

Catherine Johnson said...

The kids with lower slopes need MORE instruction.

Christopher Jencks had a great line about the achievement gap and what it would take to close or narrow it.

oh!

Here it is:

The thing is that Black students start out behind. So if they're going to catch up, in order to catch up, they've actually got to do more than the White students and, if they're no more academically motivated than most White students and they start out behind, they're going to stay behind. Ron Ferguson uses this wonderful analogy which I think is right. You see a track race. There's a White runner and a Black runner. The White runner is ahead and the White runner isn't running very hard, he's kind of jogging along, and then you look behind and you see the Black runner, but he's not running very hard either, he's just kind of jogging along. Well, in that circumstance you could say well, there's not the fact that the Black runner isn't trying very hard doesn't explain why he's losing, because the White runner isn't trying very hard either. But if you say what would it take for the Black runner to catch up, the answer is pretty obvious, you'd have to run faster. And it wouldn't be that hard to do it. Now, of course, then the White runner might start to run faster too.

interview with Christopher Jencks

I'm a veteran of Heroic Gap Closing efforts, partly because of C., who I accelerated in order to catch him up to the kids in the accelerated math class, and partly because of Jimmy, for whom the gap between him and his typical peers just kept getting wider and wider.

Raising a developmentally disabled child really brings home the nature of what it means to fall behind and get behinder as you go along.

Early on, I used to say that every time I almost caught Jimmy up to his peers (not that I ever did, but still) the peers would take this quantum jump ahead and leave us in the dust.

Anonymous said...

>>What if the big educational decline we've seen in the last thirty years has a strong component due to a societal trend from homogeneous to heterogeneous communities?

http://www.theatlantic.com/doc/200807/memphis-crime is an article that describes two researchers who saw a connection between shifts in crime rate/location and the destruction of public housing & subsequent dispersal of the poor in Memphis. It would be interesting to see how school acheivement was affected, since we know anecdotally that it takes only 2 outspoken anti-school children or one low expectations teacher to ruin a year.

Are we educating heterogeneous kids in a system derived in homogeneous times?

We are zigzagging students between two tracks (low expectations and high expectations) and ending up with students who have major gaps. We need to do what the Dept. of Defense schools do - ensure that each child masters the grade level curriculum.

Catherine Johnson said...

My previous school had about a 40% turnover every year. I did a study based on MAP scores from NWEA testing and our cohort that was 'stable' (in district 4 years) was about 2 years above our transient (in district 1 year or less) population.

This is NO surprise to me.

Hirsch writes about this all the time. He argues that we need a national curriculum for reasons of social justice. If you've got kids moving around all the time - and we do - there's no way on earth they're going to make it through the public school system.

I remember reading about the Finnish schools (I think it was Finland). One of the keys to their success is that the entirely country, apparently, (this isn't fact-checked) is on the same page in the textbook on the same day.

I don't see that happening here, and I don't see it working even if we passed some kind of constitutional amendment saying it's going to happen.

But the principle is built into the brain: you can't start kids in a curriculum ahead of where they are.

DI is the only program I know that could address the issue of catching "itinerant kids" up to their non-itinerant peers.

(There may be other ways - DI is the best thing I know of personally.)

Catherine Johnson said...

My belief is that there are ways to provide for excellence across the board but not in the current infrastructure. It's incapable of realistic, effective differentiation because it's stuck on arbitrary cohort formation and 'median' curricula delivery to match the cohorts. The only short term fix for a parent is the opt out, to private, parochial, or home schooling.

This is the perception we came to.

"Opt out" is the right term for what we're doing.

Catherine Johnson said...

they all need to be working off the existing point in space where the child is actually located, the ZPD

Remember this passage from Engelmann?

Viewed a third way, we don't have to worry as much about the performance of higher performers. They will tend to learn from teaching that is hideous, as many programs for the talented and gifted demonstrate. These programs provide instruction that appears to be purposely designed to teach, explain, and develop skills in the most circuitous and confusing manner possible. Certainly it's cruel to subject students of any skill level to such instruction...

For the past 3 years, C. has taken the only accelerated courses our middle school offers.

He has been chronically in the situation of being "taught" content far outside his ZPD. It's been a nightmare. Damaging, too.

The school's attitude is, Hey. If your kid can't cut it, he should get out. We don't want to teach these courses anyway.

The science chair told us this directly: "If it were up to me we wouldn't offer any accelerated courses in middle school. But this community demands it." She practically spat the last sentence at Ed and me.

Much of the instruction offered to academically talented kids is a scandal. Once again I come back to my perception that the kids at the top of the SES heap and the kids at the bottom have strikingly similar experiences in public school.

Catherine Johnson said...

Are we educating heterogeneous kids in a system derived in homogeneous times?

I just saw this.

It's actually the opposite (except for the Section 8 vouchers) -- and yet we are STILL in the situation of having wildly differing levels of achievement within the same class of kids.

Intentionally so, in the case of many, many school districts.

Next year we'll have the middle school model in full; one of the stated principles is "balanced" classes, which means heterogeneous grouping. This is now a core principle of the district.