January 19, 2007

More on cognitive ability

The trio of Charles Murray articles has certainly gotten the blogosphere all atwitter. I'd say that Murray's biggest misstep, among many, was his characterization of the left half of the bell curve as a bunch of dullards who are only capable of learning simple things and who are incapable of engaging in sophisticated reasoning skills.

It is not within his power to learn to follow an exposition written beyond a limited level of complexity

This is the problem when you deal with IQ abstractly and make value judgments without taking into account the failings of our horrendous education system. It may be true that the typical low-IQ student with a typical K-12 education exhibits the behaviors consistent with Murray's observations. But, that is as much an indictment of how that child was educated as much as the child's diminished cognitive ability.

In Murray's view, these low-IQ kids are cognitively crippled and incapable of higher learning. This is the conventional wisdom. It is also flatly wrong.

The false belief that characterizes the conventional wisdom about teaching is that lower performers learn in generically different ways from higher performers and should be held to a lower or looser standard. Evidence of this belief is that teachers frequently have different “expectations” for higher and lower performers. They expect higher performers to learn the material; they excuse lower performers from achieving the same standard of performance. Many teachers believe that lower performers are something like crippled children. They can walk the same route that the higher performers walk, but they need more help in walking.

These teachers often drag students through the lesson and provide a lot of additional prompting. They have to drag students because the students are making a very high percentage of first-time errors. In fact, the students make so many mistakes that it is very clear that they are not placed appropriately in the sequence and could not achieve mastery on the material in a reasonable amount of time. The teachers may correct the mistakes, and may even repeat some parts that had errors; however, at the end of the exercise, the students are clearly not near 100% firm on anything. Furthermore, the teacher most probably does not provide delayed tests to assess the extent to which these students have retained what had been presented earlier.

The information these teachers receive about low performers is that they do not retain information, that they need lots and lots of practice, and that they don’t seem to have strategies for learning new material. Ironically, however, all these outcomes are predictable for students who receive the kind of instruction these students have received. High performers receiving instruction of the same relative difficulty or unfamiliarity would perform the same way. Let’s say the lower performers typically have a first-time-correct percentage of 40%. If higher performers were placed in material that resulted in a 40% first-time-correct performance, their behavior would be like that of lower performers. They would fail to retain the material, rely on the teacher for help, not exhibit self-confidence, and continue to make the same sorts of mistakes again.

The primary differences between low-IQ kids and high-IQ kids is that the high-IQ kids learn faster and need less rehearsals (practice) to master the material taught. Low-IQ kids are capable of learning the same material, they just need more time and practice to learn it. The problem is that our schools were not designed to teach low-IQ children. Rosy progressive rhetoric notwithstanding, the song remains the same today.

Murray's observations are inaccurate because he's viewing the cognitive ability of low IQ kids through a filter of poor instruction. He should know better. He should know that you shouldn't draw conclusions from a failed experiment (other than it failed), in this case the failed experiment is the education of low-IQ kids. Let's look at the behaviors exhibited by low IQ kids when they have been successfully educated.

A good example comes from educator Jerry Silbert who wrote the following in response to Murray's article:

When the authors of Reasoning and Writing C and Reasoning Writing D were trying out the programs during their development, we found something very interesting. Reasoning and Writing C is a program that focuses mainly on teaching narrative writing. Reasoning and Writing D is a program that focuses on critical thinking and writing on exercises involving critical thinking. As we looked at the try out feedback for Reasoning and Writing C with second and third grades, we saw significant differences in the paper's of students from more high income populations and those of kids from lower income populations. The differences were in the vocabulary used and sentence structures used by the kids.

This is known as the vocabulary deficit. Low IQ kids know less vocabulary and background knowledge because they learn slower. To compound the problem, these kids typically get far less exposure to language at home (low IQ parents) so it is a bit of a double whammy for them. A deadly combination of both a nature (genetic) and a nurture shortcoming. Ultimately, this vocabulary and background deficit will result in diminished reading comprehension which will do these kids in in the later grades. It's not that these kids are incapable of learning vocabulary and the underlying concepts; it's that such learning is not easily accelerated. And, slow learners need to have their learning accelerated to keep pace with the higher-IQ kids.

Silbert's observations were predictable. The higher IQ kids had picked up significantly more background knowledge, vocabulary, and language familiarity in the five years before they started formal education and the four years of formal education. It was these skills that were being relied upon in the narrative writing exercises. Predictably, they performed better.

But let's see what happened when the playing field was leveled and skills were taught that were new to both the high IQ kids and the low IQ kids.

When we did the try outs of the Reasoning and Writing D programs we saw much less difference between the performance of the kids.

The more advantaged kids initially had a good deal of difficulty writing about the problems involving faulty arguments, misleading statements and advertisements, contradictions and directions that were too general or inaccurate. The kids from more advantaged homes and less-advantaged homes both had little idea of how to clearly express themselves when it came to critical thinking. When we looked at the kids' papers from the tryout, kids from lower income schools learned the content as quickly as kids from higher income schools.

The most important factor seemed to be the quality of teaching. The point here is that though some kids come into school with much more vocabulary and background knowledge than other kids, that good instruction can bring most of the kids who come in behind to high levels of performance on important skills. In the Reasoning and Writing C program, we also saw great and rapid growth of narrative writing skills in low-income schools when the teaching was solid.

I am familiar with level D of Reasoning and Writing. It teaches difficult reasoning and argument making skills that are rarely taught at the undergraduate level, much less at that K-12 level. Certainly, these skills are not taught to young children in the homes of the affluent. So, for these skills, the playing field was leveled and both the low and high IQ kids were capable of learning at a sufficient pace with good instruction. Which is not to say that the performance of the high-IQ kids couldn't have been further accelerated. It most likely could have, but now we are talking at a faster than grade level pace which is outside the bounds of Murray's argument.

Low-IQ kids are not cognitively crippled. They just learn at a slower pace. They are capable of learning sophisticated, complex material at a grade level pace given adequate instruction. At least up to the K-12 level. But the fact of the matter is that these kids aren't getting anything close to adequate instruction at the K-12 level. This instructional inadequacy taints Murray's underlying premise and renders his conclusion spurious.

Had Murray qualified his argument by stating "It is not within his power to learn to follow an exposition written beyond a limited level of complexity given the typically crappy instruction present in most schools," he'd be much closer to the truth. But, then it would be obvious that the defect lies as much in the schools as it does with the cognitive ability of the students. Thus exposing the flaws in Murray's conclusions.

9 comments:

Parentalcation said...

I was going to blog on this, but I have a headache so I will throw out the reference here.

From the conclusion of Time, Equality, and Mastery Learning by Marshall Arlin

"…I suspect many North American educators are incensed by the social inequalities they see about them, and are oppose to programs that hint at elitism, or that seem to perpetuate these inequalities. I suggest that the notions of inequality among students and differences among students are sometimes perceived interchangeably. I suspect that many teachers would like to oppose hereditarian or stable differences positions with an environmentalist position…"

"…But educators, and particularly teachers, are faced with individual differences among students. Not only do these differences remain stable as they appear to in this review, but they often seem to increase with each year of schooling…"

"…Rather, collective leveling functions as an unconscious means to establish an equilibrium between the apparently conflicting ideals of equal time and equal achievement (equal opportunity and equal outcomes) amid the pervasive background of individual differences. By providing more time that the majority of students need, schools can move students toward a lower common denominator…"



It is an excellent review of literature about the paradox of equal results vs equal time of mastery learning.

TangoMan said...

Murray's observations are inaccurate because he's viewing the cognitive ability of low IQ kids through a filter of poor instruction. He should know better.

I disagree with the thesis of your post, specifically that Murray doesn't know what he's writing about. The level, and quality, of instruction is immaterial to his thesis, for if instruction is improved the student performance gains will not be restricted to just the struggling students.

Low-IQ kids are capable of learning the same material, they just need more time and practice to learn it.

You're describing only a subset of experiences, specifically the material which is below a threshold. Much of the material taught in the most basic stream of public education can be mastered by students above XX IQ, where XX is below mean IQ of a population. As we increase the complexity of the knowledge the IQ floor will rise. You can try this experiment in rudimentary form with your own young children. We know that very young children have a difficult time in conceptualizing many abstract concepts, that is their processing hardware is the limiting factor. Where a normal 15 year old may take 15 minutes to understand your abstract concept, a struggling 15 year old student may take 60 minutes to understand, you'll likely have no success at all in getting the 5 year old to understand no matter how much time you spend on the task nor how many different approaches you try in your effort to make the concept relevant to them.

Murray pointed this out in his essay. He acknowledges that his hardware limitations make it impossible for him to comprehend the complexity of thought represented in cutting-edge mathematics.

Murray's point stands. The only criticism that has any bite is whether the public school curriculum can be mastered by anyone with an IQ over 80, or 85, or 90.

But let's see what happened when the playing field was leveled and skills were taught that were new to both the high IQ kids and the low IQ kids.

You make an inadvertent switcheroo here by equating high IQ and low IQ to Silbert's respective categories of "high income populations" and "lower income populations." While there certainly is significant correlation between the two categories of terms they are not synonyms. This is an important distinction because the performance disparities that Silbert reports between the levels can be attributed to either environment or IQ, and you're going to have a hard time finding people who actually contend that exposure to an environment of enriched vocabulary is a strict function of IQ. So, Silbert isn't seeing a difference in performance based on IQ, rather he's reporting a difference based on environment.

I do take issue with this quotation from Silbert:

"The kids from more advantaged homes and less-advantaged homes both had little idea of how to clearly express themselves when it came to critical thinking. When we looked at the kids' papers from the tryout, kids from lower income schools learned the content as quickly as kids from higher income schools."

I have no problem with the unbolded statement but I really want to see the data on the claim that the children of high income parents and the children of low income parents mastered the relatively high g-loading task of reasoning at the same rate. (that's assuming that the reasoning exercise has some similarity to the high g-loaded Ravens Advanced Progressive Matrice which is a measure on non-verbal reasoning.) If the test they administered has a very low g-loading then the IQ of the children would be immaterial, for instance, we see far less performance differentiation when children are tested on Digit Span tests (recalling numbers in a forward sequence) but a noticeable performance difference on Reverse Digit Span tests (recalling numbers in a reverse sequence) that is significantly correlated to IQ.

Low-IQ kids are not cognitively crippled. They just learn at a slower pace. They are capable of learning sophisticated, complex material at a grade level pace given adequate instruction.

As I already stated, this only applies if the student's IQ is sufficient to achieve cognitive mastery. You're not going to get the same appreciation of the subtlety of Shakespearean sonnets from a student with an IQ of 85 as you would from a student with an IQ of 145, no matter how much time the teacher devotes to expounding on material. The higher IQ student will make more connections, draw more inferences, and have broader insights than his low IQ peer.

Lastly, the impression I get is that you're chastising Murray for not writing the essay that you wanted him to write, which is a topic that you frequently address on your blog, that is, that poor education practices hinder the performance of students and an improvement in teaching practice can make a big difference in student outcome. I'm quite certain that Murray agrees with your point but that really is immaterial to the point of his essay, which makes a well grounded larger point, namely that IQ matters in society.

Tracy said...

The level, and quality, of instruction is immaterial to his thesis, for if instruction is improved the student performance gains will not be restricted to just the struggling students.

So? There are absolute benefits as well as relative ones to an education. If, as a result of an improved education system, person X learns to make change and understand Shakespearean sonnets where they didn't before, those gains are worthwhile, even if person Y can now, as a result of an improved education system, not only make change and understand Shakespeare but also solve differential equations and understand Tolstoy in Russian.

Much of the material taught in the most basic stream of public education can be mastered by students above XX IQ, where XX is below mean IQ of a population. As we increase the complexity of the knowledge the IQ floor will rise.

I'm curious. How do you know this? How do you rule out the possibility that there's a way of teaching any subject that can be understood by students with an IQ lower than XX?

He acknowledges that his hardware limitations make it impossible for him to comprehend the complexity of thought represented in cutting-edge mathematics.

How does Murray know this? How can he rule out the possibility that if he went back to school and started at whatever point he is shaky at maths, and then worked on it steadily for the next 5, or 10, or 20 years (depending on how early his maths problems were) with good teachers, he couldn't comprehend cutting-edge mathematics?

You're not going to get the same appreciation of the subtlety of Shakespearean sonnets from a student with an IQ of 85 as you would from a student with an IQ of 145, no matter how much time the teacher devotes to expounding on material. The higher IQ student will make more connections, draw more inferences, and have broader insights than his low IQ peer.

How do you know this?

TangoMan said...

So? There are absolute benefits as well as relative ones to an education.

Murray and I are not disputing this which is why, for the purpose of his essays, the quality of instruction issue is immaterial to his thesis but seems to be the central complaint of Ken's postings. No matter the absolute gains made by the troubled students the relative distance between them and the more able students would remain and would serve as the basis for life outcome disparity. Individuals who are more capable and better prepared usually accrue greater levels of success in life. Moving the goalposts 10 yards for each group does little to address the initial problems.

How do you rule out the possibility that there's a way of teaching any subject that can be understood by students with an IQ lower than XX?

I see this tactic quite often when I debate creationists. "Sure, all these points you raise about evolution are indeed persuasive but how do you rule out the possibility that GOD or a Flying Spaghetti Monster isn't a force behind everything. You see, you can't rule that out so I'm going to ignore evolution and cling to my liferaft of faith." Check out the Negative Proof Fallacy.

KDeRosa said...

Hi Tangoman

I had a feeling you'd be chiming in sooner or later on this issue.

Did you happen to see my post on Murray's first article?

I pointed out there that I agree with Murray's underlying premise. I'm only taking issue with his judgment about how much low IQ kids can learn. This, I think, is dependent on the quality of their education. As I pointed out in this post, had Murray qualified his statement we would be in agreement.

i actually think we are mostly on the same page and that our disagreements are largely semantic.

The level, and quality, of instruction is immaterial to his thesis, for if instruction is improved the student performance gains will not be restricted to just the struggling students.


I agree with this statement and the distribution of performance based on IQ. However, what I'm talking about is a shift in the performance distribution to the right based on improvement in education. What I'm saying is that with better education, we can get kids with an IQ of 120 to perform like they have an IQ of 135, kids with an IQ of 100 to perform like they have an IQ of 115, and kids with an IQ to perform like they have an IQ of 100. And, in all likelihood, the higher IQ kids would perform even better if we allowed them to accelerate.

As we increase the complexity of the knowledge the IQ floor will rise.

This is likely the case, however, I don't think we get to this level in K-12. Plus, the perceived complexity of the new material is often affected by the student's knowledge of prior material.

For example, it is easy to assume that low IQ kids are too dull to learn calculus because, as they are educated today, the frequently fail to learn to calculus when taught. But, if you look at the actual problems these kids are having, you see that the problems are frequently the result of a lack of algebra skills, which are aften the result of a lack of fraction manipulation skills. With better instruction, they could learn these pre-skills, and, as a result, they'd probably find learning calculus that much easier, especially if the calculus instruction is also improved.

We know that very young children have a difficult time in conceptualizing many abstract concepts, that is their processing hardware is the limiting factor. ... you'll likely have no success at all in getting the 5 year old to understand no matter how much time you spend on the task nor how many different approaches you try in your effort to make the concept relevant to them.

I'm not so sure about this. Assuming the 5 year old's cognitive ability remains constant, it's not the hardware but the lack of skills, which is a function of education. It likely is not the case that the smart 5 year old can't understand the concept but that he lacks many prerequisite skills to understand the concept. It might take me three years to teach these preskills, but at the end of those three years the kid will understand the abstract concept.

Murray pointed this out in his essay. He acknowledges that his hardware limitations make it impossible for him to comprehend the complexity of thought represented in cutting-edge mathematics.

Is is the hardware deficiencies or the five years of math education he might be lacking to get him to that level? It could be both. Murray's a smart guy, given enough effort and motivation and the right teacher, he probably could learn it (though there'd probably be smarter students with better hardware that learned it faster and better than he could). But, this doesn't detract from his ability to learn it, though it could contribute to his lack of motivation to engage in such an endeavor.

The only criticism that has any bite is whether the public school curriculum can be mastered by anyone with an IQ over 80, or 85, or 90.

That was really the only one I was making. this was a serious misstep on Murray's part, in my opinion. He opened up himself to easy criticism by doing this. This is already a controversial topic and he gave his real critics lots of ammunition. This was the camel's nose under the tent for many of the loonier critics which allowed them to overreach and criticize his entire argument.

I really want to see the data on the claim that the children of high income parents and the children of low income parents mastered the relatively high g-loading task of reasoning at the same rate.

This goes to the crux of my argument. The object of the field test was to teach the material at a grade-level pace so that the entire class learned the material. This they accomplished. Now, the smart kids probably got better grades and could have learned the material at a faster than grade level pace, but this doesn't detract from the fact that the low performers managed to learn the material at an acceptable pace. This is the critical distinction that Murray gets wrong.

When the material is taught effectively, at merely a grade level pace (i.e., slow) cogntive ability is much less of a limiting factor. The low IQ kids may be pushing against their limits at even this pace and the high IQ kids proabably have lots of capacity to spare. That's the ultimate point of my posts, we (and Murray) underestimate just how much we all could accomplish with better instructional techniques.

You make an inadvertent switcheroo here by equating high IQ and low IQ to Silbert's respective categories of "high income populations" and "lower income populations."

Actually, it was an intentional switcheroo. Here's my reasoning. The high income group will likely have a higher average IQ than the lower income group. The higher income group would also likely have been exposed to a better environment, thus, further increasing the amount of background knowledge they had acquired.

Thus, we see in the level C course, where background knowledge has a greater effect, the higher income group learns significantly faster and performs better. But, in level D, where background knowledge plays less of a role, the performance differential between the groups has decreased even though the material has gotten much more complex and difficult. Yes, performance differences based purely on cognitive ability likely remain between the groups, but those differences are significantly less when the higher income group couldn't rely on its incresed background knowledge (which is also a function of cognitive ability).

Don't get me wrong, background knowledge is still a huge problem for low performers due to both genetic (the learn slower and this material is not easily accelerated) and environmental (the have less exposure and opportunity tp learn).

You're not going to get the same appreciation of the subtlety of Shakespearean sonnets from a student with an IQ of 85 as you would from a student with an IQ of 145, no matter how much time the teacher devotes to expounding on material. The higher IQ student will make more connections, draw more inferences, and have broader insights than his low IQ peer.

I don't disagree with this statement. But recognize that if a skilled educator developed a sequence of instruction that pre-taught the background knowledge needed to make these inferences and insights, the lower performers might approach a sufficient level of understanding needed to appreciate the materialon an acceptable level of performance which is lacking in today's education system.

I'm quite certain that Murray agrees with your point but that really is immaterial to the point of his essay, which makes a well grounded larger point, namely that IQ matters in society.

That's utimately my biggest beef with Murray's article -- I'm not so sure that Murray agrees with my point based on what he actually wrote. He has too many statements that imply that low IQ are simply not capable of learning basic material. If Murray's intention was to simply point out that IQ matters in society, he picked a lousy way to express this opinion.

TangoMan said...

Hi Ken,

Yes, I do think that we're mostly on the same page, but quibbling can be fun :)

Assuming the 5 year old's cognitive ability remains constant, it's not the hardware but the lack of skills, which is a function of education.

But that's just it, the wetware, the brain, is not constant. There is a difference in brain development between a 5 year old and a 15 year old. Meep's comment over at Joanne Jacobs reinforces this point. It appears as though folks like Tracy don't accept that a continuum of wetware sophistication exists. What I get from her comments is that they model brains as reaching a sufficient stage of development and thereafter there are no performance limitations present other than environmental factors.

The object of the field test was to teach the material at a grade-level pace so that the entire class learned the material. This they accomplished. Now, the smart kids probably got better grades and could have learned the material at a faster than grade level pace, but this doesn't detract from the fact that the low performers managed to learn the material at an acceptable pace. This is the critical distinction that Murray gets wrong.

Compare your statement above, which allows for learning rate to be a function of IQ to the statement from Silbert's paper, he writes:

When we looked at the kids' papers from the tryout, kids from lower income schools learned the content as quickly as kids from higher income schools.

Note the bolded text, "as quickly." He's pulling the learning rate distinction out from under you. Now, if the task truly was a measure of reasoning ability then that would be a task with a high g-loading. If, OTOH, the task was simply a regurgitation of some basic rules then it's likely that the task was not very cognitively demanding. In the case of the former we should see a learning rate differential that favors those children with higher IQ. In the case of the latter the learning rate differential would be flatter.

Think of it this way. Once we teach children how to count to 10 we should expect there to be no performance difference, based on IQ, when we ask the children to recite the number sequence. Then, we put a puzzle in front of them and ask them to trace a route out of a maze and here we should see a performance difference based on IQ.

My point is that I suspect Silbert's Level D involved the children applying simple rules rather than engaging in reasoning. If this is in fact what transpired then we're back to the basic formulation - everyone above IQ XX is capable of mastering the course content that is taught and the reason we have a content failure problem is because of poor instruction.

Recall Murray's invocation of the NAEP statistics where he noted the failure rate and made the equivalence to the proportion of student body that had an IQ lower than XX. What you're saying, which he and I fully acknowledge, is that if teaching process was reformed then we would expect to see many of those students who are presently failing will be boosted to a higher performance level, likely a level that is above the current pass rate. Boosting performance in such a manner is simply the opposite of the administrator tactic of lowering proficiency benchmarks so that everyone can pass the hurdle. Here though, the proficiency hurdle remains constant and the improved instructional process gets more kids across the hurdle. This begs the question of how satisfied we are with proficiency levels where everyone passes? Are we content with minimum standards or do we want to extract as much performance from each student as they are capable of giving. I'm sure that you recognize that improved instructional process will yield performance boosts across the IQ range so that better instruction will yield low performers improving and likely high performers improving at an even faster rate, thus enlarging the performance gap. The implications here remain the same as when administrators lower the proficiency level to a point where more students can pass muster.

He has too many statements that imply that low IQ are simply not capable of learning basic material.

The take I get is that while Murray is constructing his thesis on a relativist position you are constructing your criticism on the basis of an absolutist position. You're defining "learning basic material" as a fixed measure of content mastery while Murray is defining "learning basic material" as a relative point along the bell curve. For Murray, if you improve instructional process all that you've done is move the goalposts 10 yards down the field for everyone, and possibly increased the gap somewhat. Think of it like inflation. If you get a raise of $2/hr that means that you can afford to buy $4,000 more goods per year. If everyone gets at least a $2/hr raise then all of the price metrics reset and you're really not much better off.

I'm still struck by the impression that, as I wrote in my initial comment, "the impression I get is that you're chastising Murray for not writing the essay that you wanted him to write." You're well focused on writing on the efficacy of instructional process as it relates to achievement outcomes but that universe is predicated upon absolute, rather than relative, benchmarks. This important viewpoint is not germaine to Murray's argument, that's all.

Tracy said...

No matter the absolute gains made by the troubled students the relative distance between them and the more able students would remain and would serve as the basis for life outcome disparity. Individuals who are more capable and better prepared usually accrue greater levels of success in life. Moving the goalposts 10 yards for each group does little to address the initial problems.

It depends on what you think the initial problems are. If you think inequalities are the only thing that matters then moving everyone up 10 yards won't address the "initial problems". If you think that life is a positive-sum game and we can all be better off in some senses, even if inequality remains, then moving everyone up 10 yards may do quite a bit to address the initial problems.

For example, I think that humanity is better off if the risk of starving to death drops for everyone.

I also think poeple are better off if everyone is capable of writing love letters to the person they love, even if the cost of this is that more people can write love sonnets as well (an increase in romantic inequality).

How do you rule out the possibility that there's a way of teaching any subject that can be understood by students with an IQ lower than XX?

I see this tactic quite often when I debate creationists. "Sure, all these points you raise about evolution are indeed persuasive but how do you rule out the possibility that GOD or a Flying Spaghetti Monster isn't a force behind everything. You see, you can't rule that out so I'm going to ignore evolution and cling to my liferaft of faith." Check out the Negative Proof Fallacy.


Funny, I thought your argument was an example of a creationist argument. "I can't imagine how to construct an eye/bacterial flagella/etc could evolve, so therefore it can't have."

You're the one making the negative claim. I'm asking your evidence for it.

As for why I think you hold some burden of proof - many things have become possible that weren't thought possible in the past. Some examples are heavier-than-air flight, cellphones, an end to slavery, women having the right to vote. Why shouldn't teaching methods improve as teachers learn to focus more on students' actual learning?

To give an example more specific to teaching, when Roman numerals were used multiplication and divison was a suitable topic for university studies in Europe. Now we have Arabic numerals and multiplication and division are topics for primary school education.

This is why I think your claims that certain topics cannot be taught to someone with an IQ below XX are a bit like a creationist's claims that certain organs (life-forms, etc) are irreduciably complex.

KDeRosa said...

Tangoman, I agree with your argument I just don't think Murray was making this particular argument. He went beyond the points you're making.

With respect to Silbert's comment, he was writing to the DI Listserv and they would have known that what he was talking about was getting the students through about 120 lessons in the school year. At this pace all the kids performed similarly, which is to say they all got through the lessons and learned the material-though I'm sure the scores on the end test were normally distributed as a function of IQ and I'm sure that the higher ability classes could have been accelerated further if that were the object of the tryout. Basically, what I'm saying is that Silbert was implicitly qualifying his statement based on his audience's knowledge. He is aware of this blog so maybe he'll chime in.

I understand your realtive/absolute and goalpost moving arguments and agree with them to extent, but I'd add that there are certain skills we wish all high school graduates to possess to function in modern society no matter what their cognative ability. We should be satisfied if we can shift the goalposts to this condition through better instruction. And, I don't see this goal as getting in the way to eduacting all kids to some place appraoching their cognitive limit which is another desireable goal. Murray seems to see the two as goals as being mutually exclusive, I don't.

Tracy said...

. It appears as though folks like Tracy don't accept that a continuum of wetware sophistication exists. What I get from her comments is that they model brains as reaching a sufficient stage of development and thereafter there are no performance limitations present other than environmental factors.

Really? Interesting inference from my statement.

I can quite happily accept that a continuum of wetware sophistication exists. Can you accept that there might be ways of teaching students that are more effective than other ways and reach students with a lower IQ?