Here's Dan Meyer blogging about a common teacher misconception: the supposed instructional value of allowing/encouraging students to struggle:
The good teacher knows if the learner learns through the ears, the eyes, or the hands just like the good spotter knows where the lifter wants support — at the wrists or under the elbows or on the bar. The good spotter is unhelpful; the good spotter doesn't intervene at the first sign of struggle but realizes that the struggle is essential, that the struggle is the entire reason they are there, and waits as long as possible before intervening.
The good teacher puts weight on the student's intellectual bar and lets her struggle under that weight as long as possible, asking questions to help her cut through the confusion, just like the spotter shouts encouragement at the lifter. (emphasis added)
I hate to ruin a colorful analogy, but the theory is wrong. Students struggling with material is not good for learning, retention, or motivation. Here's Engelmann on the topic:
Always place students appropriately for more rapid mastery progress. This fact contradicts the belief that students are placed appropriately in a sequence if they have to struggle—scratch their head, make false starts, sigh, frown, gut it out. According to one version of this belief, if there are no signs of hard work there is no evidence of learning. This belief does not place emphasis on the program and the teacher to make learning manageable but on the grit of the student to meet the “challenge.” In the traditional interpretation, much of the “homework” assigned to students (and their families) is motivated by this belief. The assumption seems to be that students will be strengthened if they are “challenged.”
This belief is flatly wrong. If students are placed appropriately, the work is relatively easy. Students tend to learn it without as much “struggle.” They tend to retain it better and they tend to apply it better, if they learn it with fewer mistakes.
The prevalence of this misconception about “effort” was illustrated by the field tryouts of the Spelling Mastery programs. Over half of the tryout teachers who field tested the first and second levels of Spelling Mastery with lower performers indicated on their summary forms that they thought the program was too easy for the children. Note that most of these teachers were not DI teachers and had never taught DI programs before. When asked about whether they had ever used a program that induced more skills in the same amount of time, all responded, “No.” Nearly all agreed that the lower performers had learned substantially more than similar children had in the past. When asked if students were bored with the program, all responded, “No.”
What led the teachers to believe that the programs were too easy? All cited the same evidence: students didn’t have to struggle. For them, it wasn’t appropriate instruction if it wasn’t difficult for the lower performers. (p. 17)
This is the danger for a would-be-profession that eschews empiricism in favor of individual intuition.
23 comments:
Do you have some citations in support of what you say about struggle? Your advocacy of DI is least persuasive when it just consists of references to stuff that's published in DI-specific journals or presented at DI-specific conferences. Those things just remind me of stuff like anti-fluoridation conspiracy theorists referencing "journals" that publish nothing but anti-fluoridation articles.
Stick to citing stuff that's been subject to rigorous peer-review - which you sometimes do. But sometimes (e.g., now) don't. "Engelmann thinks Engelmann is awesome" is teh weak sauce.
Paul, further along in the article I cited you'll see:
In working with the ASAP schools in Utah, we had several demonstrations that tested this formula. During the first two years of the project, these schools had great concern over the math placement of fifth- and sixth-grade students. Very few sixth graders placed in the sixth level or even the fifth level of Connecting Math Concepts. Some barely passed the placement test for the fourth level of the program—Level D. This level assumes that students have mastery of a wide range of math facts and operations. Therefore, we were reluctant to place new students in D unless they had a strong performance on the placement test. The schools, like the teacher in the example above, assumed that the fastest way to get sixth graders into sixth-grade material was to start them as close to that material as possible.
On three occasions, we had the opportunity to split groups that were fairly homogeneous in performance and to place half the group at the beginning of D and the other half at the beginning of C, where they would learn the facts and operations that are assumed by Level D. The strategy for these students was to make sure they performed according to the ideal percentages of first-time performance and to move as quickly as possible. If students were clearly firm on something, we would either direct the teacher to skip it in half the lessons or present the problems as independent work. As soon as the percentages started to drop, we would return to presenting full lessons and continue at that pace until it was clear that the students could be safely accelerated. (Note: We tend not to skip material when we accelerate students. We simply go through the material faster. We’ve discovered that when teachers start skipping material, they often skip too much or skip material that should not be skipped even if students perform at acceptable percentages.)
In all cases, groups that started in C performed much better and actually passed up groups that started in D. In two cases, this occurred before the end of the first year. For the last case, it occurred in the middle of the second year. The students who started in D tended not to perform near the ideal first-time percentages. They often failed the ten-lesson tests, and teachers had to spend a great deal of time reviewing and reteaching things the students were expected to have learned. In contrast, the students who had been placed in C were able to do more than one lesson a day (until they reached about lesson 30 in D) and had a very high rate of passing the ten-lesson tests. For these students, the sequence of the program was congruous with their skill level, and the steps in the program were small; for the students who started in D, the program steps were too large and the climb too steep. The overall effect was that the D-starting students didn’t like math as much as the other students did and had far less confidence about their ability to learn math. We later adopted the practice of starting all students with marginal understanding in Level C, not D.
So, Zig does have some empirical support for what he claims. It's not a formal experiment or peer-reviewed (like that matters in education research) but it is based on a one variable variation experiment of a rigorously researched curriculum.
I fail to see why the standard shouldn't be peer-review and rigorous experimentation. Just because you often don't see it in educational research doesn't mean it doesn't matter. Don't dodge the standards of scientific inquiry; that's shady. DI advocacy - like all educational advocacy - should be much less insular than that.
Additionally, the situation you're describing isn't really isolating and evaluating "struggle" in any meaningful way. Part of the issue is that "struggle" is a vague term to begin with, but then so much the worse of the argument that struggle is categorically bad.
Nobody denies that struggle is bad in some situations; constructivists just want to say that kids should struggle within their proximal zones of development. Nothing in Engelmann's example contradicts this. (Granted, I haven't read the whole thing end to end because, again, it's just Engelmann talking about how awesome he is.)
As somebody who's not particularly enamored of constructivism in the first place, I'm not crazy about pointing these things out, but, I mean, the problems and straw men here are pretty obvious.
Paul, you can rest easy on this point.
It's a very old topic in the psychology of learning that goes under the topic of "proactive inhibition," Related matters are "spaced and massed practice," and "behavior under stress," and "schedules of positive and negative reinforcement"--to name a few.
But it's a tricky matter in terms of instructional execution. There is no merit in "struggle," particularly by novices. Experts at the other end can say they are "struggling with a problem," but their struggle is not in anyway the total confusion the novice experiences.
Ever get off the freeway on the wrong exit ramp in a strange city? You're lost.Without GPS or a detailed roadmap, the only way to find your way back is to wander. That's not very effective, because there are more ways to go wrong than to go right. A better bet is to ask for direction from someone who knows the territory.
In learning any complex skill, there are going to be "errors." The handling of these "errors" is the stuff of what an effective instructional program is made. Zig chooses to use a tight script and defined instructional protocols to guide the learning.
That's one legitimate way to go about it. There are other ways.
One can present in situ successive expansions and approximations of the larger skill at issue.
Work is being done at the high school level to develop simulations that give students guided experience in different types of work situations.
After a child has been taught to read, and to handle arithmetic algorithms, a whole host of self-and guided instruction via the Internet is opened up.
"Discovery learning"/constructivism ideology is the most unreliable instructional architecture imaginable. Ken has been around this block many times and the dialog quickly degenerates into a "tis" "taint" disagreement. But the science of learning and the science of acquiring expertise are on Ken's side.
Zig does think highly of himself, but it's not undeserved. DI proponents at times are zealous, but I don't see anything wrong with that either. I fault Zig and his acolytes for relying on standardized achievement tests and comparative experimental research methodology. But they have a lot of company.
I agree with Paul, your post(s) is not the least bit compelling. I was initially interested and looked for a list of references. Who cares what Englemann thinks, that's nothing but an argument from authority. Stick to peer-reviewed, experimental data. Until the the body of research points to a particular theory, I'll use my own observations and inferences.
The field of education is a joke when it comes to experimentation and intellectual rigor, but let's try to raise the bar (challenge our peers, if you will).
Lack of peer review is a specious argument.
1. Biologists review biology papers. On occasion they might review a physics paper that deals with biology. When Englemann writes about how to waste educational resources, then he can be reviewed by school of ed professors. Until then, his peers are other DI practitioners and others who understand the science behind the method.
2. @NMahoney -- on your blog you have a video of Bill Gates talking about malaria and you want to criticize this blog for lack of references? Really?
3. If Bill Gates wanted to talk about the Windows OS, I wouldn't need his speech to be peer-reviewed in order to "use my own observations and inferences" to figure out that he knows what he's talking about. Same with Englemann and DI.
@Paul This is not Englemann talking about how great he is. Perhaps UC Berkeley has not provided you with enough knowledge to be within the proximal zone required to understand the paper.
I don't mean this as a snark. I suggest you develop a stronger foundation of the scientific theory and body of knowledge about mastery learning and then come back to Englemann's article and try reading it all the way through.
If you need specific articles (peer-reviewed at that), then let me know and I will list some here. Otherwise, start with:
Thorndike's Laws
Bloom's mastery learning
Gagne's 9 events of instruction
There's nothing scientifically invalid with using an "ask and check" approach for identifying instructional variables in education programs that have scientific validation. These successful education programs were created by design (in this case by Zig), not by accident. The designer of the program knows the instructional variables that the education program controls for (in the case, student placement). And, Zig's answers can be easily investigated. As Dick has pointed out, there is plenty of evidence that Zig's assertions are accurate. More evidence can be found in Kirschner's paper Why Minimal Guidance During Instruction Does Not
Work.
The Kirschner et al paper should be required reading for every parent to immunize themselves (and hopefully their child) against the toxic instruction their child is likely to receive in school. Also by every college student before taking their first Education course to immunize them against the constructivist ideology that permeates most Ed courses.
That kind of boot would do more to "reform" the el-hi enterprise than "reboot" squared.
The only question worth pursuing re "guidance" is "what kind of guidance." And as the article notes "The advantage of guidance begins to recede only when learners have sufficiently high
prior knowledge to provide 'internal' guidance."
That's what makes the skill of reading, and to a lesser extent math, so vitally important to deliver the kind of independent learning, that constructivists and everyone else strive to to equip students with.
Kirchner is a good collection of research and presents some compelling arguments, but I do not believe that the paper proves that minimal instruction doesn't work. It may prove that no/very little guidance doesn't work very well and that minimal guidance often is less effective, but these, opponents will argue, are straw men.
That kind of boot would do more to "reform" the el-hi enterprise than "reboot" squared.
I doubt that it will because there is not incentive for any one to change or adopt the practices set forth in Kirschner. That's the problem.
dweir - I think it's telling that your position is that DI advocates just shouldn't engage with the rest of the educational research community. That illustrates my point about insularity quite nicely. You see similar kinds of arguments from tin-foil hat types like the anti-fluoridation folks I mentioned before, and it hurts the movement's credibility pretty severely.
As for my UC Berkeley education, I don't have any particular confidence that I'm more or less well-versed in these things than, say, yourself. However, I'd say, I seem to be no less well-versed in some of the mastery-learning theory than you seem to be in constructivism. Otherwise, you'd see how Ken's post sets up a silly straw man.
And, not to be snarky, but I'd suggest you develop a stronger background in formal and informal logic (something Cal trained me in fairly well), since it can be helpful in understanding how arguments are structured and how they can fail. The fact that you think my objection to the post's Engelmann reference has to do with some lack of relevant domain knowledge shows that you miss the point - Engelmann isn't really engaging, there, with the notion of "struggle" in a way that is relevant to the argument Ken wants to make. (And that's not a knock against Engelmann.) The ability to identify when terms - like "struggle" - are being used in vague or inconsistent ways is important when assessing arguments, and requires a certain amount of training and/or practice. (It also, of course, requires domain knowledge, in this case, for example, knowledge about constructivism.)
Something I mentioned briefly but should have been clearer about is that I think there is considerable evidence suggesting that mastery-learning type interventions can be quite valuable. But bad arguments are bad arguments, and I see no reason to pretend they're good arguments just because their conclusions happen to be appealing. Ken, apparently, wants to dismiss "opponents" who "will argue" that he's setting up a straw man but, I mean, it really is a straw man, since nobody's bothering to define "struggle" in a useful way.
"since nobody's bothering to define 'struggle' in a useful way."
I'd define it in the context that is being discussed as "thoroughly confused regarding heuristic next steps." How would a Berkeley-educated guy define it, Paul?
@Paul
Would evolutionary biologist support your argument of insularity if there work wasn't reviewed by creationists?
If creationists were the biology professors, would say that evolutionary biologists were wearing tin-foil hats if they didn't engage with these professors?
It is interesting that you go after a term like "struggle." Human technological advances (and here I use the broad term of technology as tools and process) come alongside a change in the lexicon. Dick has already pointed you to some of the history which makes it possible for us to use the word "struggle" with sufficient accuracy.
You suggest if I had more understanding of constructivism that I'd better understand your struggle with "struggle." I find this interesting as constructivism itself is an imprecise term. This imprecision, I believe, has come as a result of a poor translation from theory into practice.
My ed school courses covered Piaget, Dewey and Vygotsky. This was part of the "traditional" pedagogy that we learned. I don't believe it was referred to as constructivism. It was just "this is how you teach."
You can clearly write circles around me and have a stronger background in logic. Nonetheless, here's what I see as the flow of this discussion:
1. Ken cites a post by Meyer.
2. Meyer draws an analogy between struggling to build muscle and struggling to build knowledge.
3. Ken calls this theory about learning wrong.
4. Ken cites an Englemann paper published in a peer-reviewed DI journal.
5. You dismiss this because it's a DI journal
I'm curious which journal you think it should be published in? How about AERA's Educational Researcher? It can be alongside scientifically rigorous research such as:
"The Economic Payoff to Investing in Educational Justice"
"Taking a Stand on Standardization"
"Energizing Learning: The Instructional Power of Conflict"
> Students tend to learn it without as much “struggle.” They tend to retain it better and they tend to apply it better, if they learn it with fewer mistakes.
If you are merely teaching students to retain facts, then you may as well simply present students facts and be done with it. That's what the work you cite suggests.
If, on the other hand, you are also attempting to teach the student to reason through difficult solutions where the answer may not be easy, apparent, or even exist, then you give the student practice in struggling and working things out for him or her choice.
> This is the danger for a would-be-profession that eschews empiricism in favor of individual intuition.
Your tendency to irony never fails to amuse me, as the one work you reference cites no empirical research at all.
If you are merely teaching students to retain facts, then you may as well simply present students facts and be done with it. That's what the work you cite suggests.
The work I'm citing does far more that teach facts. I can provide a detail list of exactly what is taught; it's mostly problem solving.
If, on the other hand, you are also attempting to teach the student to reason through difficult solutions where the answer may not be easy, apparent, or even exist, then you give the student practice in struggling and working things out for him or her choice.
No, you would give the student practice reasoning through difficult problems. Remember, we're talking about K-12 students who are novices. We're not talking about the education of experts at this level because the K-12students are far from experts at this level. To the extent that your comment has any merit, it applies to the learning of experts.
the one work you reference cites no empirical research at all.
The owrk is based on emperical research, juts not formalized emperical research. Plus, if you had read through the comments, you would have learned (actually, you already know this point from past disputes), that there is ample empirical support for this point.
No, you would give the student practice reasoning through difficult problems. Remember, we're talking about K-12 students who are novices. We're not talking about the education of experts at this level because the K-12students are far from experts at this level. To the extent that your comment has any merit, it applies to the learning of experts.
Here the term 'expert' is used far too loosely; K-12 students are not flat-out mathematical 'novices'. If you want to stick with the claim that for some reason mental 'struggle' is only valuable for 'experts', then at least recognize that young students can be experts within certain subareas of knowledge that they can apply in using problems specifically designed to create an appropriate amount of 'struggle'. No one is an expert of everything.
While I agree that in many cases content is most easily absorbed via tiered or scaffolded instruction so that each progressive 'step' can be reached without inhibitive amounts of struggle (particularly in urban environments such as the one that I work in), I also feel that introducing students to 'struggle' is a necessity in order to fairly prepare them for the 'real-world' and challenging careers where problems will not be tiered/scaffolded. With-holding experiences of struggle from students creates a body of people who will simply give up when faced with these situations later in life.
This is something that I struggle with as a teacher; I want to make things easy for my students to learn because my urban students have a huge propensity for 'giving up' or refusing to work when things get challenging. However, I also want to gradually build them up into individuals who have the confidence and desire to struggle through problems so that they will not just learn content, but be competent and innovative adults in the future.
A kid's biggest problem in school is "school." Human beings are dealing with "problems" from the time they are born. A child doesn't need to be taught "problem solving." It's built in, but it's highly situational.
Some instruction labels matters "problems." If a kid has been taught how to handle a given "problem" it's not a problem. If a kid hasn't been taught how to handle it "struggling" isn't going to increase the child's expertise. It will only have unintended negative consequences.
What is "content" for instructors is just "more school" for kids. Do they have to memorize it? Can they add to previous learning? Can they ignore or reject it? And so on.
"to teach the student to reason through difficult solutions"... "you would give the student practice reasoning through difficult problems."
That's easier said than done, because "problems" are situational.
Sorting these matters out is the business of instructional design.
Although I'm a fan of DI, I'm with Paul on this. I don't think we have enough evidence to conclude that struggle is unimportant. Engelmann's work may be a good start, but it's only a start and not enough to support confidently saying that the theory is wrong. Although on the other hand Dan Meyer doesn't cite *any* experiments in his argument for struggle.
I also am inclined to think that teaching kids to persist with problems by struggling is valuable, though I don't have any evidence on this (and probably no one has, a longitudinal study covering say 20 years after finishing school that tries to see how valuable experience in struggling is would be expensive and I don't know how it could be properly controlled). I however have two caveats - firstly, if the skill is really important in its own right (eg reading, arithmetic) my fears about motivation being destroyed takes over and I say go for the easy way of learning. Struggle should be learnt in less-essential skills. Secondly, I think that if we want schools to teach the skills of struggling through problems we should do it properly. Start off with a decent amount of field-testing, so we can say how much struggle students can endure and a set of tested guidelines for when and how teachers should intervene, develop a set of problems so that teachers have problems lined up for those kids who are "naturals" at both sports and academics, and see what unexpected problems such a teaching approach throws up.
There's plenty of support for the efficacy of Worked Problem Examples for teaching novices. And, within that spectrum there is plenty of room for presenting increasingly difficult problems for the student to solve. Different types of problems (i.e., those requiring different problem solving strategies) can also be mixed together to present a further challenge to the novice students.
This is a worthwhile discussion so I hope it's not too late to get some responses. This post might seem late, but I've been mulling over the issues Ken DeRosa raised in this thread all week and just tonight had time to join the exchange. Also, I'm glad to see Dick Shutz is active on this forum.
My work is teaching English to Japanese school children. The charm of Constructivism is strong among English as a Foreign Language (EFL) teachers here, and I'm sympathetic to some of its pillars. Most of all, I want clear standards that I can apply for effective teaching.
What is the distinction between 'struggle' and 'stimulation'?
I deal with many students who have been trained to be passive: the teacher will give them the lesson, they listen, and try to memorize it. In my own classes, I want them to produce the language, so a large part of my focus is to get them into situations where they have to make effort to resolve the situation I have arranged.
For example, Taro's classmate hands him a card showing a verb, and asks Taro 'What's he doing?', expecting an answer. If Taro doesn't know how to articulate the verb that is illustrated, I expect him to ask me (or another classmate). I think repeating verbs in chorus to prepare the lesson is a waste of time. Would Kirschner disagree?
One standard guideline for EFL is PPP: Present, Practice, then Produce. I try to minimize the Present portion, and get the students into the Practice as soon as possible. If the Presentation is sufficient enough to get them through (to success) without frustration, is it sufficient? If boredom has been avoided, and some error, pressure, humor (and minor embarrassment) endured to reach eventual solution, isn't the experience and discovery more memorable?
My sense is that with learning SPOKEN language, the ideas of constructivism make practical sense: making sense of spoken language is largely a phsycolinguistic (sp?) guessing game. If pain and frustration can be avoided, isn't a small challenge more stimulating?
However with learning (English) WRITTEN language, I think the ideals of constructivism should not be applied. The Alphabetic Code is a complex phonetic code that should be explicitly and systematically taught in order for most effective learning to occur, in my strong opinion.
Yet even if I've shown Taro that the sound /ssssss/ is encoded with the grapheme 's' and so on, requiring him to articulate and write out the familiar spoken word 'sub' presents a task that he has to work out on his own, providing some level of challenge and stimulation. Isn't that much more effective for developing phonemic awareness and an understanding of the alphabetic code than directly telling him how to spell the word?
I think the best method would be to provide a clear understanding of the basic fundamentals of a subject, then arrange that the student has to apply those given fundamentals in order to resolve an arranged task successfully (and accurately).
What would Zig Englemann say to that?
Best regards, Peter Warner.
Nagoya, Japan.
My comments might belong in the 'To struggle or not to struggle' thread, but let me add this as an edit to my post directly above if I may.
Part of my thoughts on this issue come from reading a book on the Kumon Method at the moment. The book really isn't very clear, but it does mention some of the Kumon teaching philosophy, which stresses repeating a worksheet task until the student gets 'full marks' and can then move ahead 'with mastery'. The idea seems to be that if the student completes a worksheet quickly and with no errors, they build confidence and motivation to pursue higher levels of tasks.
In my own worksheet materials, I have the student repeat a worksheet (after they have corrected it with my hinting assistance) if there was more than 20% errors. I generally expect about 10% errors.
My theory is that if a student is proficient with 90% of the material, they will be able to work out the remaining 10%, and that is stimulating challenge. Toru Kumon might call that process 'self-learning'.
If the student understands less than 80%, they will be unable to bridge the gap to full understanding, fail to comprehend the lesson, and consequently will fall further behind in confusion. This is pretty similar to Stanovitch's famous Matthew Principle, I think.
Would these principles identify the distinction of 'stimulate' and 'struggle' as about 90% proficiency/understanding/mastery?
Best regards, Peter Warner.
Peter Warner, there are some sample scripts available for DI at the Special Connections website (and sampe maths and language lessons as well).
Basically the amount of time between the teacher presentation and the students practice is minimised. I understand the goal in designing those lessons is that students should be making about ten responses per minute on average - responses being defined generally (obviously there are some variations, eg there are some games where they are making far more responses, there are some times when the teacher is explaining a bit more).
For example, Taro's classmate hands him a card showing a verb, and asks Taro 'What's he doing?', expecting an answer. If Taro doesn't know how to articulate the verb that is illustrated, I expect him to ask me (or another classmate). Okay, two things going on here. One, you can expect Taro to ask me, or another classmate, if he doesn't know the verb, but what happens if he doesn't live up to your expectations and keeps quiet if he doesn't know a verb? In the DI sampe lesson Language for Thinking exercise 1 has students practising in asking the teacher when they don't know a word. (Students are placed into lessons based on assessments of their prior knowledge, if all the students in the group already knew the words in the sample lesson they would be a different lesson).
Secondly, this process is time-consuming. While it is valuable to teach students to ask questions when they don't know, it does slow things down. If you know that they don't know, based on say pre-tests, why not tell them first a chunk of the time? Kids don't arrive at school knowing everything.
I think repeating verbs in chorus to prepare the lesson is a waste of time.It depends on what you are trying to teach and who you are trying to teach it to. The reason for repeating things is that the students need to practice new skills in order to be able to remember them, as you yourself say. Now if you ask a question of one student in the class then only that student necessarily gets the practice (there may be some kids who listen intently and answer the question to themselves, but this is not necessary), if you ask the question of every student in the class then every student gets the practice. The advantage of asking a question verbally is that it's fast and it works with kids who can't read yet (although adaptations are needed sometimes, say for students who are deaf and obviously this doesn't work for skills that can't be verbalised, for example handwriting or riding a bike). But, if you ask the question of every student in the class then all of them get practice. *But* there is always some variation in how fast children think and speak, so if you just ask the question then some children who are quicker to organise their thoughts and/or their tongues will answer right away, and others will be a bit slower. And how does the teacher then know that the slower ones have actually understood the question or if they are just repeating what the faster students said? Well, a solution is to delay the slightly faster children's answers until the slightly slower ones have had time to figure out the answer and get their tongues in line. Thus the chorus.
If the Presentation is sufficient enough to get them through (to success) without frustration, is it sufficient? If boredom has been avoided, and some error, pressure, humor (and minor embarrassment) endured to reach eventual solution, isn't the experience and discovery more memorable?The number of things a teacher has to get their class to learn in order to be able to read is incredibly long. If every piece of learning involves some error, pressure, humour and minor embarrassment, I don't see how any student will find any particular piece more memorable. If everything is associated with error, pressure, minor embarrassment, etc, then how will any particular thing stand out in their brains? Do you remember every time you made a mistake at school or suffered some mild embarrassment? How about every time you jogged your funny bone?
And how enthusiastic do you think kids will be about school if every piece of learning is associated with minor embarrassment? It sounds to me like a reason for dreading getting out of bed in the morning. I loathed sports at school, I have a minor case of dyspraxia and nearly every PE session for me was associated with minor embarrassment (the one exception was "long"-distance running, which I did with great enthusiasm until a foot injury from infection stopped me).
As for your discussion on proficiency, you appear to be at the same point as Engelmann, presumably by different routes. See this article of his from his website www.zigsite.com on student-Program Alignment and Teaching to Mastery, and in particular page 7. His definition of mastery is that students should be responding "perfectly at least 9 out of 10 times."
Thank you Tracy, for your thoughtful and extensive response. Your comments have given me much to reflect on, and I will pursue the articles you link to. Thank you sincerely for your effort and assistance.
Best regards, Peter Warner.
Nagoya, Japan
And thanks Peter for your lovely reply.
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