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There is data that you can improve individual children's rate of learning in specific areas. The general rule of thumb is that the rate of improvement will be about x2 : i.e., if a certain concept or discrimination required 100 trials to master, the next similar learning task will take 50 trials, then 25, etc up to an individual's ceiling. This is nicknamed the "learning curve," although on a semilog graph it will be a straight line. Individuals do have ceilings -- in this as in most things. Learning rate, like IQ, is a range rather than a point, and something that is modifiable by environmental variables.Can a school that slows learning to a crawl via heterogeneous grouping, required collaboration, discovery, problem-solving, whole-to-part teaching and all the rest of it reduce a student's rate of learning?
Several early studies (1960's-1970's) were with severely handicapped children who needed THOUSANDS of repetitions to learn something. Their learning rate improved, under experimental conditions, to a much more normal (but still slow) rate. Thus, you will never turn a tortoise into a cheetah, but the tortoise might end up similar to an average dachshund. I have the cites on some of those articles but they are very recherché items in Sp. Ed. journals and not easy to look up. I'll see whether Catherine can run them down for me. Engelmann was a partner in some of them.
With more "normal" learners, there is lots of data in the PT [precision teaching] literature about improvement in learning rate. The Great Falls project (a school implementation of rate-building instruction in North Dakota in the 70's or 80's) collected quite a lot of data on this. The students' abilities generalized to many areas of the curriculum and the project was finally pulled, in part because too many kids ended up being classified as "gifted." One of the project managers was Ray Beck, who subsequently (and perhaps still) went to work for Sopris West. You could consult him for data on the project -- I know it has been published, but I don't know where.
PT practioners and their clinics also have a great deal of data on individuals and their rate of learning improvements. You could consult Elizabeth Haughton, the Center for Advanced Learning (CAL) in Las Vegas (can't remember the name of the person in charge), Dr. Kent Johnson at Morningside, Dr. Joe Layng who implemented many rate-building procedures both with stroke victims and with low-SES college students in his years in Chicago, Dr. Carl Binder and others for specifics of publications, data, etc. There's plenty out there, but you have to try hard to find it since it is in opposition to mainstream thinking.
Since my concern is with teaching students, not with convincing naysayers (I ignore them), I have made use of the lessons from these people to successfully get "hopeless" cases -- not only "dumb" kids but kids who learn at a slow rate -- functioning at higher levels so that they can compete in the mainstream successfully. Very few end up at the top of the heap (only one so far), but numerous others end up in the average range and that's what excites me, since they were initially regarded as too dyslexic, too stupid, too slow, too disadvantaged, too whatever, to succeed. At least once or twice a year I hear from one who has finished university, started a business, is successful in some field of study or application that I would never have thought of when he/she was a student (designing solar -powered homes in one case, marine biology in another, co-ordinating seniors' services for a community agency in a third). The point is that these students' can learn effectively (with DI, among other things) and their rate of learning can be maximized so that they are empowered to achieve meaningful goals.
In a perfect DI environment, you do periodically regroup students based on rate, but rate-building per se is not something DI people typically focus on, and its largest application has been with people in Special Ed populations (autism, developmental disabilities, LD). For people currently doing cutting edge work in the field, google Michael Fabrizio, Alison Moors, Richard McManus, Kent Johnson (I can probably think of others).
It's hard work, but it can be done. Will it be done routinely in the school system? Not in our lifetime I suspect.
If IQ decreases in mediocre-to-bad schools, does learning speed decrease as well?
on not teaching to mastery
how to build a fast learner (one-trial learning in rats)
19 comments:
So,
it's an achievable goal to build someone's rate to where they can handle college level material with proficiency, as long as that's not above their ceiling. And we don't know how to tell what someone's ceiling is.
But it's not an achievable goal to close the rate gap--because if you worked this hard with DI on the bright students, they too would double the rate gap.
Therefor, dispersion over time is not the way to measure if what is happening in a classroom is good or bad. One hypothesis perfectly consistent with growing dispersion over the years is that all students are increasing their learning rates.
The best way to tell, then, if what is happening in a classroom is good or bad is with absolute valued tests, against objective metrics.
it's an achievable goal to build someone's rate to where they can handle college level material with proficiency, as long as that's not above their ceiling
Correct. In many cases it would be a matter of identifying missing component skills, teaching those to mastery, moving up to more complex/composite skills, etc. until the student was at the required level. In fact there are people doing this at the college level; I just don't follow the developments there, because it's not my area of concern. The principles are the same, but I don't know about time frames.
we don't know how to tell what someone's ceiling is.
That's not quite true. Of course we don't know exactly, especially at the start. But we can make some reasonable hypotheses, and by keeping data on what the student learns and how quickly in a variety of areas, we will soon learn what that individual's ceiling is in terms of rate of new learning.
At some point the student's learning rate will stop accelerating. There are various steps to take when this happens, but if the student consistently meets a wall at that point, despite the recommended steps, s/he has probably reached the ceiling in that area of learning. The ceilings might be different in different cognitive domains.
I take a flexible approach and figure the student's ceiling is likely within 2 standard deviations. Getting student performance (even IQ) up one standard deviation is not all that uncommon, and getting improvements of two standard deviations is less frequent but a regular occurrence. I suspect this is easier with younger students than older ones, but I do not have data on that. The SD range is what I keep in mind myself. Thus, I would not be trying to get a student with a diagnosed developmental delay and an assessed IQ of 55 into a college-prep program (4 SD).I would try to get this student functioning in the low average range. The data would tell me when a student had reached the ceiling on performance improvement in something specific.
But it's not an achievable goal to close the rate gap--because if you worked this hard with DI on the bright students, they too would double the rate gap.
Correct. We are never going to make everyone equal. The gifted students would also achieve more and faster.
One hypothesis perfectly consistent with growing dispersion over the years is that all students are increasing their learning rates.
By dispersion, do you mean a wider scatter? An increase in the gap? If so, that would not be an hypothesis consistent with all students increasing their rate of learning. If in fact all students did this, the gap would stabilize -- it would look like parallel lines, rather than like the blades of an opened set of garden shears -- farther and farther out the greater the distance from the handle. Typically students' achievement becomes more divergent the longer they stay in school. If, however, by some miracle of instructional manna they were all well taught and their native talents coaxed to the top end of their range, the gap would remain but the intervals would be narrower and the lines more nearly parallel.
The best way to tell, then, if what is happening in a classroom is good or bad is with absolute valued tests, against objective metrics.
Objective tests are part of the answer, but so is observation. There is plenty of data on what effective teaching looks like -- observations that can be gathered and assessed in a scientific way. The late Dr. Michael Pressley has written extensively on this; I recommend his Motivating Primary Grade Students for a well-written look at this question. He wrote more technical articles in journals; this one is an astute analysis of what makes early grade teachers effective, with examples and non-examples, and (for teachers) some workable suggestions that one can start to use right away. .
"The students' abilities generalized to many areas of the curriculum and the project was finally pulled, in part because too many kids ended up being classified as 'gifted.'"
Great critical thinking here. When confronted with a clear example of their low expectations, they ignore the results.
I can understand this effect when an individual child is studied, but I don't understand this effect when you apply it to large populations. Why isn't it bad teaching or low expectations, rather than slow learning? When people talk about slow learners statistically, it sounds like another form of blame the student. Slow learning implies that you have done a careful study of an individual child and made this determination.
"PT practioners and their clinics also have a great deal of data on individuals and their rate of learning improvements."
Are these clearly "slow learners", or are these any kids who appear to learn slowly? How many kids have high ceilings but hit learning speed bumps?
"There is plenty of data on what effective teaching looks like -- observations that can be gathered and assessed in a scientific way."
Is effective teaching the same for true slow learners and for average kids? (I suppose you could say that effective means effective.) I wouldn't think so. My nephew was considered to be a slow learner, but my sister worked to provide him with better skills for approaching new material. She had the same issue when she was young. Now that he is grown up (with a degree in computer science), he is anything but a slow learner.
Slow learning is a vague term. If a child is truly slow, then it seems to me that there could be a variety of reasons and solutions that should be customized for the child.
I can understand this effect when an individual child is studied, but I don't understand this effect when you apply it to large populations. Why isn't it bad teaching or low expectations, rather than slow learning?
I do not profess to understand the mind of the education administrator. I do know that good results are always attributed to what the school is doing (even though the results may be the outcome of actions by parents and tutors) while bad results are usually attributed to characteristics of students and families. It seems to be the way it is.
Are these clearly "slow learners", or are these any kids who appear to learn slowly? How many kids have high ceilings but hit learning speed bumps?
I can't say. I would hypothesize that many students have high ceilings (or at least much higher than we assume) and most hit speed bumps in various areas along the way. Most of us can think of examples of such in our own lives.
Learning centers such as the ones I cited serve a widely varied clientele, so I would be wary of overgeneralizing . What I know from my own research is that they set goals, develop detailed plans to meet those goals, and are successful with a wide variety of learners of different ages. It's probably a safe statement to posit that MOST people could learn much more and faster than they currently do, given the appropriate application of learning science and technology. Much is known now about cognitive processes and how learning occurs and how to work around various obstacles, but very little of this knowledge has trickled down to the grass roots -- schools in particular.
Is effective teaching the same for true slow learners and for average kids? (I suppose you could say that effective means effective.)
General principles of teaching effectiveness seem to apply across the board. For instance, effective teaching is highly interactive. Teacher and students(s) are interacting at a high rate -- teachers may model, give examples, pose questions, clarify distinctions, scaffold tasks, provide feedback, etc. while students may listen, ask questions, demonstrate, practice, compare/contrast, respond orally, by actions or written output, etc. The key thing is lots of interaction -- ON TASK interaction, not chit-chat; learning is active, not passive. Think of an orchestra conductor, or an athletics coach --the relationship of those people with their team/orchestra is highly interactive. Lots of back and forth. Engagement is high (another important component).
Pressley developed something like a checklist of behaviors of effective teachers . What these behaviors would look like and the specifics of application would vary of course (the type of interactive teaching that is effective in first grade would not be appropriate for seventh grade), but the general case would be the same. Pacing -- another important characteristic of effective teachers -- also varies by population. You speak faster and can move things along quicker in a group in middle school than in K. But appropriate pacing as a characteristic of effective teaching remains constant.
Slow learning is a vague term.
Rather than vague, I think it is a confusing term because it is frequently used to refer to separate issues -- cognitive ability and/or processing speed.
"Slow learners" are often (in educational jargon) those students who are deemed rather low in academic ability but not low enough to be considered intellectually disabled. They are very low average, and they take longer to reach the same levels of achievement as same-age peers (their physical development is sometimes slower as well). Then there can be students whose academic ability is average or even high but who are slow processors -- they may have difficulty with word finding, working memory, lexical access, various types of memory, co-ordination, motor skills. Typically these students need more repetitions to mastery and more distributed practice over time to become automatic on fundamental skills which they may *grasp* easily (conceptually) but not be able to apply reliably. The evidence is that some of these difficulties are neurologically determined, but again, we are working with a range -- so the individual can improve his or her own performance level and while s/he may never be "fast," s/he can meet average expectations. I think this is worth striving for, as it gives the individual many more choices in life and much more sense of competence.
If a child is truly slow, then it seems to me that there could be a variety of reasons and solutions that should be customized for the child
I agree, but realistically this is seldom done in school and in many cases I've seen, it is not realistic to expect it to be entirely done in school. We can only customize so far for individuals -- which is why homogeneous instructional grouping is so important in key areas.
I'm really an amateur in these matters myself, but I recommend people interested in the issues go to the excellent site maintained by an amazing self-educated parent activist:PT Wiki
Some of the items in the bar along the right -- "Why frequency matters," "Why celeration matters" etc. are a good place to start.
It's kind of a seeing is believing thing. When you see kids (or adults) make HUGE, sudden, dramatic leaps forward in their learning that change their lives, you can't help saying to yourself, Holy cow! WHAT was THAT? and trying to learn more to make it happen again.
If you haven't seen it you may not think it's possible and you certainly won't see what the fuss is about.
I have fun introducing as many of my colleagues as possible to that HOLY COW!! moment. They never look back.
it's an achievable goal to build someone's rate to where they can handle college level material with proficiency, as long as that's not above their ceiling. And we don't know how to tell what someone's ceiling is
This is what makes me crazy about public schools -- and people in general -- assuming a ceiling.
We don't know what or where the ceilings are, and for tenured professionals to be arbitrarily deciding they've spotted one resting on top of your kid's head: bah humbug.
(I think I've written a Comment or two about the meeting last school year at which the science department chair & the Earth Science teacher told us C. "can't think inferentially. That was a Shining Moment of tenured tomfoolery, for sure.)
But it's not an achievable goal to close the rate gap--because if you worked this hard with DI on the bright students, they too would double the rate gap.
How does this work logically?
Let's see.... if all students had terrific DI or PT instruction.... what would occur?
Offhand, I'm thinking that the rate gap would stay the same but the knowledge gap would widen -- BUT, since acquisition of organized knowledge influences rate of learning, one might expect to see the rate gap widen -- ?
I'd love to know if there's a "ceiling" on schema formation. Is there a point of diminishing returns in schema formation? Is there a "Perfect Schema," or a "Good Enough Schema," which, after one has acquired it, is all you need to learn new material as quickly as you possibly can? (Or, perhaps, is all you need to move to one-trial learning?)
The fundamental point seems to be that once you know something quite well, you can learn new aspects of that field or domain extremely rapidly.
I guess my feeling is that although it's logical to reason that the rate gap can't be closed, reality could be different. (I don't know or assume that it's different.)
In many cases it would be a matter of identifying missing component skills, teaching those to mastery, moving up to more complex/composite skills, etc. until the student was at the required level.
What do you think about teaching to fluency instead?
oops -- should have read palisadesk's comment first!
I take it all back.
I do still have a question about teaching to fluency as opposed to mastery.
My nephew was considered to be a slow learner, but my sister worked to provide him with better skills for approaching new material. She had the same issue when she was young. Now that he is grown up (with a degree in computer science), he is anything but a slow learner.
right
we went through something like this in the middle school
at the end of 5th grade, C was 1 of 2 students awarded "Student of the Year," which was an academic award
suddenly, in middle school, he was considered maybe average or a bit above average & we had teachers selecting "finds subject matter difficult" and "weak inferential thinking" from the Comment Bank on his report card
flash forward to Hogwarts & he's been placed in all Honors courses, which he is easily able to manage without help from parents or tutors (NO RETEACHING!)
this is the same kid
there's been no change in his personal circumstances or his motivation, and "maturity" isn't the explanation because these changes happened so abruptly: each change happened when he changed schools
I do not profess to understand the mind of the education administrator.
Have you ever noticed that, while we have a lot of teachers reading & writing for ktm, we don't seem to have attracted any education administrators?
I've been thinking about that lately.
I do know that good results are always attributed to what the school is doing (even though the results may be the outcome of actions by parents and tutors) while bad results are usually attributed to characteristics of students and families. It seems to be the way it is.
ditto that!
It's probably a safe statement to posit that MOST people could learn much more and faster than they currently do, given the appropriate application of learning science and technology.
That's exactly my view - and it's the reason why I'm impatient with Charles Murray-type arguments about IQ limitations on learning & the like.
It's not that I think IQ doesn't exist, or that I believe there aren't ceilings or limits -- it's that having dealt with public schools for lo these many years now, I'm interested in hearing how my kids & everyone else's kids are going to be taught.
As I see it, Vicki Snider is right: we need a science of teaching.
We don't know what level of achievement will become possible once we have that.
(I should say 'if,' I suppose.)
re: gaps in learning rates, and dispersions:
I didn't mean to confuse. I was referring to the dispersions Paul B noted in his school district's aggregated performance--the dispersion being the spread in the variance over time.
Yes, the learning rate gaps would stabilize over time, and become parallel in your graphing of them. But since distance = rate X time, over time, those constant differences in rate yield linear differences in learned content. That is, if we've achieved parallel learning rate lines, then I'm learning, say, twice as much as you, and therefore, twice as much as you can in an hour, so a graph like Paul's (ignoring the X axis values) could occur even in an ideal district that accelerated everyone up to their highest possible learning rates. (And that graph fits other hypotheses, too, including the hypothesis "teaching is irrelevant.")
I'll look into the above testing and observations to know what's a good classroom; thanks for those pointers.
for those of us who haven't seen PT or something similar work, how do you suppose we get such religion? How would we see such an acceleration in ourselves, or someone else, to believe in it?
Steve, I understand your comments that such aggregated data is a way to blame the student. It certainly can be, but that's probably because of the bias to blame the student in the first place. I can also use such aggregated data as Paul's to blame the school, and in fact, to argue that the school had no effect whatsoever on the students' learning. (the "Fast learners" being accelerated by their own internal IQ, their parents' hep, additional tutoring, etc. and slow learners being hampered by never being actually taught anything...)
That's the problem with the aggregated data that I think you were getting at: it's consistent with at least three hypotheses:
1. current teaching is improving the knowledge of all students, the "better" students more than the "worse" students,
2. current teaching is improving the knowledge of the "better" students, but leaving the "Worse" students behind,
3. current teaching has no effect whatsoever on the knowledge of the students--the "better" learn it largely somewhere else, and the "Worse" barely learn it somewhere else.
If you can't produce aggregated data than can distinguish the above 3 cases, then your aggregated data is completely useless.
And certainly, you're right that the most obvious aggregated data would be matched data--where you match not just the population, but the individuals in it against themselves over time to see what's happening.
for those of us who haven't seen PT or something similar work, how do you suppose we get such religion? >How would we see such an acceleration in ourselves, or someone else, to believe in it?
I can't help you there. I'm not into "getting religion" or "believing in" things where empirical methods are concerned. Although there are many important aspects of learning that can't be measured, I like measurable phenomena and practices and technologies that will reliably deliver a superior return on time and effort invested. Once you've seen things that work, repeatedly, far better than other things, you have no desire to go back to twiddling your thumbs waiting for children to discover the decimal system or the conventions of written English. There are Aha! moments of an empirical kind.
A little off topic, but I recently (being a fan of Dr. Richard Feynman) watched the video of the movie Infinity and went back and reread one of his biographies about that time period -- the Manhattan Project and the development of the atomic bomb. When the test was successful, the team of scientists had reactions ranging from awe to exhilaration. They had a party afterward. No, they weren't callous jerks -- they had seen something that they knew was going to change the world in unpredictable ways -- good and bad. It was a turning point moment -- none would ever see the world in the same way again because their knowledge and their sense of the possible were both changed by something empirical and measurable.
Not the best analogy but as good as I can come up with at the moment. I was lucky enough to run across this phenomenon of a huge and sudden non-linear leap in learning in a "hopeless" case very early in my career (in that case it was DISTAR reading and some PT techniques, before I had even heard of PT) and it was so dramatic I couldn't ignore it. I had to find out why it occurred and how to make it occur again. This was much more a case of the scientist at work than a religious orientation (we have too much of the latter in education, where "beliefs" guide practice, rather than proven observation and scientific testing). PT is a branch of applied behavior analysis, not a teaching method but a system of measurement and recording of data relative to learning and changes in behavior on the way. Once you realize some basic things, such as the importance of frequency, the non-linear nature of learning, the way new skill sets can be acquired more quickly and easily,how to do component/composite analysis, you try to apply these principles as much as possible to set the stage for future quantum leaps for kids (or adults, if you're working with adults).
I was lucky, I just tripped over an amazing "miracle" case early on, and it set me on the path of following up on effective teaching as much as I possibly could. Of course not every student is a miracle but there are enough miracles that it keeps me steadily on the path to learn as much about effective practices as I can. Because of course these are not miracles at all, these would be routine learning outcomes if effective teaching was the norm. "Belief" has nothing to do with it,I *know* I can get good outcomes for students. I can show others how to do the same. If I were properly trained myself, I could do it even better. Having to put up with the {bleep}that routinely goes on drives me nuts -- but that's another story.
okay, sorry that I spoke in a way that didn't address it scientifically. I was responding to what you said--Seeing is believing...holy cow...-being not the way I'd talk about science..
It's kind of a seeing is believing thing. When you see kids (or adults) make HUGE, sudden, dramatic leaps forward in their learning that change their lives, you can't help saying to yourself, Holy cow! WHAT was THAT? and trying to learn more to make it happen again.
So, for those of us that aren't teachers, how do we get to see kids make these leaps so that we can see that PT works?
Do we have to be in a classroom to see it happen? Will seeing a working classroom do it, or do we have to see it over a long period of time? How do we find a PT classroom to observe?
As a parent, I don't have the ability to see time elapsed versions of a classroom, so what would it take to see evidence of it working and reach a "seeing is believing" experience?
I think you are asking the wrong questions of the wrong person.
It sounds to me like you want me (or someone) to convince you of something.
I'm not interested in convincing you of anything. I share my own experiences on this blog because Catherine and others find them relevant. I only need to convince people of the importance of doing things a certain way when a kid's well-being and future depend on it. I don't need to convince anyone else; I am an amateur and if you want to learn about things like direct instruction, effective teaching practices, applied behaviour analysis, fluency-based instruction, precision teaching and so forth, you should hunt down people who are experts in those fields and learn from THEM.
That's what I did. It only took about a thousand hours a year, (never mind how many years) and most people are generous with their time and don't charge money for sharing what they know. I attend conferences and workshops to continue to learn more. You don't need to be in a classroom, you have people all around you (including one or more children). You can accelerate their learning, or your own. If I knew you personally, and thought your interest was serious, I would try to line you up to meet someone in your area who might steer you in the right direction (depending on your needs). I don't know you, so I won't.
There is a lot of learning you can do about many of these topics with no help from anyone. There are listserves you can join, organizations that promote effective teaching, journals you can subscribe to. There are conferences to you can go to. There are related activities, like TAGTeach, that you could get involved in. You can read Karen Pryor, Fred Jones, Engelmann, Michael Pressley, Wesley Becker, Michael Maloney, Glen Latham.You can find people to mentor you. There is lots you can do to acquire the information you need if it is important to you.
Is it important? I have no idea. Only you can answer that. If it is, you should go to people in the field who can teach you what you need to know. That's what I did, and it paid off for me and for my students, and for members of my family. What I can tell you or anyone is, it's worth it to work like hell to find out what you need to do to get outstanding results. Don't settle for less.
Happy New Year.
I'm asking for how a parent sees evidence that a school implements something that works. And I don't understand why I need to reinvent the wheel if someone else already knows the answer.
If your point is "I'm am amateur writing about my experience and don't know the answer" they I suggest you reread your posts and comments.
I'm at a loss for why you think I'm asking you to do something other than what you were already doing--you've claimed YOU can accelerate students' learning rates. When I ask how a parent could tell that a classroom can do that, you punt?
Then you tell me that I should become my own expert. I could give you my own parental bona fides: I've read Engelmann and Carnine. I believe their theory of instruction because I've read it and can validate it. But they didn't write curricula in every subject, nor did they claim they can increase learning rates. Everything I've seen about DI and IQ suggests that the modest gains are lost later. But that's not enough? A parent has to be more educated than a teacher because the teacher can't explain how the teacher has evidence of what works?
Really, if the bottom line is that a parent needs to do a thousand hours a year of self study to find out what and how her kid is supposed to be doing in a classroom, then DI and PT and the rest, are and will always be failures.
If someone isn't trying to create an efficiency of scale for the parents, --that is, by teaching parents how they can tell what effective teaching looks like in the classroom--then this effort is really for nothing.
I'm asking for how a parent sees evidence that a school implements something that works. And I don't understand why I need to reinvent the wheel if someone else already knows the answer.
For me, it's when I see that my child is learning what is supposed to be learned and I don't have to re-teach. In fifth grade, for example, my daughter had a teacher who taught English writing skills (including spelling) in a traditional manner. She dictated sentences that had, say, quotes in it, and students were expected to be able to write the sentence with correct punctuation. ALso they were given written sentences without proper punctuation and expected to correct it. My daughter learned punctuation well in that class. Spelling focused not only on a list of words for the week, but students were expected to get the word spelled correctly in a sentence. I.e, the spelling test was not the teacher saying the word and having the students write it, but rather the teacher dictating a sentence and the students reproducing the sentence without error. And words from previous weeks were always in the mix.
In that year, my daughter's spelling and writing improved immensely. It was never followed through in subsequent grades, however, and she fell back to bad habits and her proficiency fell.
I'm sure this example is not definitive nor scientific but it opened my eyes. Her fifth grade teacher retired the year she had her. Too bad!
Sorry, I meant to see that the example I cited above opened my eyes in a "Holy Cow" manner.
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