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27 Oct 2006 - 03:49
excerpt from: Standards and Mastery Learning
outputs, not inputs from the Preface: (pdf file)
The history of standards also reflects federal government versus states’ rights skirmishes, competition among professional organizations (for what will be required and what will be optional for graduation), religious versus secular issues, as well as numerous other political issues beyond the scope of this book. What does seem relevant, however, is an apparent shift in the goals of standards from inputs to outputs, in Marzano and Kendall’s (1996) shorthand. Whereas previous standards emphasized what had to go into a course (specifics of the curriculum, how material was to be taught, how many credits or Carnegie units it was worth), current standards emphasize what comes out (what students know or can do and how to assure accountability). As Marzano and Kendall (1996) summarized, “The new, more efficient and accountable view of education is output-based; success is defined in terms of students learning specific standards” (p. 17). Whether the “outputs” view is better or worse, we cannot be sure, though it certainly created a firestorm of rhetoric over the high-stakes testing, perhaps a too-narrow view of accountability that has become linked to the standards movement beginning in the 1980s. Interestingly, the input/output categories have rough parallels with fundamental variables in John Carroll’s (1963) model of school learning, which provides some of the theoretical underpinnings of mastery learning. Those variables are opportunity and perseverance. Opportunity, in rough parallel to input, is the time allowed or scheduled by the teacher to cover the material and induce students to learn. Perseverance, in rough analogy to output, is the time the students spend or are willing to spend to learn. Although both of these are important to and predictive of achievement, perseverance becomes the bottom line: Teachers have been successful to the extent that they induce students to do what they need to do to learn. We bring this up here to point out that the mastery philosophy on which this book is based is potentially compatible with current views of standards, but it has developed methods for measuring and motivating students to persevere until they achieve those standards. Sadly, many advocates of standards, not to mention those who are charged with implementing them, know little or nothing about implementing mastery learning: its philosophy, its evolution, what makes it work or undermines it, its varieties. [ed.: don't know of don't care to know?] Thus, although the movement toward higher academic standards carries with it assumptions about learning, development, and measurement that have traditionally been central to the theory and philosophy of mastery learning, the standards movement has neither embraced mastery learning nor shown evidence of having learned from its successful or unsuccessful practices.
learning & forgetting
from the first chapter: (pdf file)
Learning, in other words, occurs in phases or episodes, and this original learning phase includes (a) the readiness component (described above), (b) learning to initial mastery, and (c) forgetting. Although forgetting has not been mentioned up to now, it is clear that forgetting is the inevitable result of initial learning, even when a high mastery standard of, say, 80% to 100% correct is required. [ed.: which is why it makes so much sense to spend one day teaching dimensional analysis going into the state test, assign no homework problems, and never mention the topic again] When the degree of original learning is less than mastery, say, 60% to 80%, then forgetting is likely to occur more rapidly or be more complete. If it is less than 60%, it is questionable to speak of forgetting at all, because learning was inadequate in the first place.1 Students show that they understand this principle implicitly when they ask, “Why do we have to learn this stuff anyway? We’ll only forget it.” Our typical answers, “Because it will be on the test” or “Because I said so,” are not satisfactory. In fact, we have been able to find only one satisfactory answer to the question, and it was supplied in one of the first empirical studies of learning/forgetting (Ebbinghaus, 1885/1964). The answer is that relearning is faster—that is, there is a considerable savings of time in relearning compared with original learning. Furthermore, there is a positive relationship between amount of time saved in relearning and the degree of original learning, with essentially no savings when original learning is below some acceptable threshold (which we earlier argued was 60% or less). ...[C]onsider the experience we teachers have. The first year of teaching a unit, we have a lot to learn (even though many prerequisites have already been mastered in college and student teaching). The next year, when we reach that unit again, we find we’ve forgotten quite a bit. Fortunately, relearning is faster, and we find ourselves reorganizing the material, coming up with new examples, and so forth. The next year, forgetting has been less yet, and thus there is greater savings in relearning. By the 10th year, the material is almost totally recalled, with examples virtually falling off the tongue. The material seems so easy by this time that many teachers can now be heard complaining, “The students are getting dumber and dumber every year.” Sadly, this is one of the negative effects of becoming expert in something: We lose empathy for the novice. (Note the parallel to what happens once a nonconserver on Piaget’s tasks becomes a conserver: e.g., the 8-year-old who understands that the amount of water does not change when poured into a taller, thinner glass cannot recall that she expected more in the taller, thinner glass when she was 5). This is also what distinguishes a mere expert from a teacher: An expert can do it; a teacher can do it but also remembers what it takes to progress from novice to expert.Beautifully put. I would add that this is what distinguishes an expert nonfiction writer from a nonexpert.
The bottom 3rd learners are probably routinely being put into states of learned helplessness; I would expect to see learned helplessness in a number of the middle 3rd, too. In the case of accelerated math here in Irvington, I believe that we have some children in the top 3rd who have been pushed into states of learned helplessness for doing and learning math. That is what their parents report. The tearful mother who asked, at the Parent Revolt meeing in winter 2005, "What are you going to do to repair my child's self esteem?" deserved an answer. What she got instead was: "I don't understand why your children are so thin-skinned." That was it.
schools creating "comas"
A summary of the long-term effects of the difference between mastery and nonmastery at original learning is provided in Figure 1.2. After four or five episodes, when learners in Part A say to those in Part B, “I forgot more than you ever learned,” the sad fact will be that they are telling the truth. A close look at the curve in Part B shows that after four or five episodes, those persons—they can hardly be called learners—have learning/forgetting curves that resemble the brain waves of comatose patients.learned helplessness, mastery learning, and math
Let’s return for a moment to the students in Figure 1.2B. If their first experience in learning fractions, say, is unsuccessful, they will forget all or most of it. Next year, they may even claim that they “never had this stuff before,” and they will probably believe it. On the second time through, if they are still unsuccessful (which is likely, because teachers usually spend less time reviewing previous material than was spent on initial learning), they will demonstrate little savings and forget again. By the third and fourth exposures to the material, they at least remember they had it before, but may stop trying and explain their lack of motivation with statements such as “I was never very good at math” or “Why do we have to learn this stuff anyway? I’m never going to use it.” Learned helplessness has set in.
[ed.: I want to stress that "learned helplessness" is a well-established concept in psychology — and that it was first demonstrated in animals. These experiments, which I studied in college, are wrenching to read. The most upsetting, which couldn't be done today, involved rats who were, iirc, yoked together and shocked. One of the rats could turn off the shock, or escape it somehow. The other rat was helpless. He received the same level of shocks as the "actor" rat, but he couldn't turn them off. After going through this experience, the rats were put in a tub of water with a platform somewhere in the middle. (again, working from memory - details may be wrong) The "actor rates" - the ones who'd been able to turn off the shocks, swam to the platform and scrambled out of the water. The helpless rats didn't even try to save themselves. They sank into the water and drowned. I believe that today, in our schools, spiraling curricula are putting children into states of learned helplessness. Until someone proves me wrong, I stand by that perception.]
Under laboratory conditions, learned helplessness is developed by first exposing animals or humans to a series of experiences in which failure is inevitable and beyond their control (e.g., Peterson, Maier, & Seligman, 1993; Seligman, 1975). Later, when success is now possible and personally controllable, the victim does not even try. On the emotional level, there is a heightened state of fear, which if prolonged, can easily turn into apathy or depression. On the behavioral/motivational level, there is no perseverance or willingness even for trial-and-error searches (because “Nothing I do ever satisfies these people”). On the cognitive level, there is no discovery of what works, no understanding or organization of an information base, and a long list of defensive excuses or causal attributions, such as “I was never very good at this” and “I could do it if I want to, but school sucks” (the former a primarily female attribution, the latter male; e.g., Dweck & Licht, 1980). It is also more self-protective to adopt a strategy of not trying—or pretending not to try—than to try and not succeed. Math seems to be a field particularly vulnerable to learned helplessness, because new topics and courses seem to be quite different from previous ones (from multiplication of whole numbers to fractions, arithmetic to algebra to trigonometry, etc.). Even having great success at earlier levels does not immunize against having difficulty on a new topic. Thus even being a “good” student or having 100% success does not guarantee against learned helplessness later, particularly if what students have been good at is memorizing without understanding. But those primarily at risk for learned helplessness are those who come to school and have not mastered fundamentals (as mentioned earlier). If we teachers cannot diagnose their problems correctly— and early—they are almost destined to fail to master the new tasks. Sadly, to continue the math example, many teachers are not skilled enough themselves to diagnose a child’s problems with addition and subtraction as being a deficit in rational counting or one-to-one correspondence. Thus these students comprise the population in Figure 1.2B. Is there a cure? As in health, prevention is easier than cure.
Didn't Steve H say this? I believe that the phenomenon of learned helplessness explains why it was important for Christopher and Christian both to teach themselves using a Saxon book. Christian is emerging from his state of learned helplessness vis a vis math so fast it's startling. Same thing for Christopher, except with Christopher we're talking about prevention. Even after all the mishegoss of last year, his slow but steady march through Saxon Algebra 1/2 almost certainly prevents him from developing a state of learned helplessness in the first place. His previous work with Saxon Math 6/5 probably innoculated him against developing learned helplessness last year. I think I've told that story. Christopher does not know that Ms. Kahl selected "Finds subject matter difficult" from the Comments Bank. When I mentioned it one day, thinking he'd read his report card, he said indignantly, "She did not put that on my report card!" He doesn't have learned helplessness.
how to cure math anxiety, part 2
With his learned-helpless dogs, Seligman (1975) literally had to drag them across the barrier to escape electric shock, anywhere from 25 to 200 times, before they once again tried to explore and control their environment. With humans, whose patterns of thought (“I was never very good at this”) may reinforce the helpless-behavior patterns, dragging is more figurative than literal. In any case, the cure for helplessness is competence, and only when students are succeeding do feelings of self-efficacy, self-control, and self-esteem begin to follow (see also Bandura, 1977, 1986).
Saxon Math is the answer.
memory & IQ
Table 1.2 shows the remarkable results regarding intellectual traits and memory.5 Under nonmastery conditions—that is, a single exposure for original learning, recall after 7 days, a single relearning opportunity, and then recall after 14 and 28 days—the correlations between intellectual traits and recall are all positive and significant. That is, higher-ability students tend to remember more, as society has come to expect. In stark contrast, imposing a mastery standard of 75% to 90% correct on original learning and then again at relearning renders those standardized intellectual measures nonpredictors of how much is recalled: The correlations hover around zero and are all nonsignificant. What mastery to a high standard can do, in summary, is virtually bypass the effects of IQ for specified educational objectives. What is recalled about educational lessons is more dependent on how well the material is mastered than on such traits as rate of learning or general intellectual abilities.
(wrong) conventional wisdom about mastery
Critics usually cite three points in opposition to mastery learning: 1. It helps slower students at the expense of the faster students. 2. It is too oriented toward basic knowledge and skills at the expense of creativity and higher levels of thinking. 3. It requires too much work of the teachers.
This is where I get off the boat. This passage equates "mastery" (75% to 80% correct on a test) with "expertise." A child who has scored 80% correct on an initial test of mastery has not reached the level at which he is ready to start constructing knowledge, applying principles to real life, or solving "advanced problems." What is happening here — and, again, until someone proves me wrong I'm going to stand by my opinion — is that constructivist teaching practices are being used to mask the fact that the fast kids are being slowed down to the slow kids' pace. It's significant that these authors do not once reference Siegfried Engelmann's work. There's a reason for that. I think the reason is the Siegfried Engelmann directly confronts the question of maximum efficiency of learning for everyone, not just for the slowest third.
I'm fast reaching the point where I don't want to hear "challenging" and I don't want to hear "enrichment":
A commonly held belief regarding mastery is that for it to be successful, there must be a highly effective, if not innovative, remediation component. Although we do not underestiet the importance of remediation, it is our assertion that the strength of any mastery program is contingent on its enrichment component. The reasoning behind this assertion is at least twofold. The first issue is that a common criticism of mastery is that it focuses on those students who initially fail to master the objectives at the expense of moe capable students who often easily master those same objectives. One can certainly find examples of this. However, we suggest that poor planning, rather than mastery learning, is at fault. Teachers need to develop engaging enrichment assignments that are pertinent to their objectives and not seen as busy work by students…Contrarily, students in need of remediation will often need to simply revisit and revise previous assignments and not be in need of additional materials. However, what they likely will need is additional instruction from the teacher or classroom aide. These resources will only be available to these students if other students are engaged in appropriate enrichment activities....
...which, presumably, "other students" will be engaged in entirely on their own! Because they've reached mastery! So they can zip right through Bloom's Taxonomy without further ado!
Thus a comprehensive enrichment program is not only a critical component of a mastery learning system but also an effective classroom management tool. Furthermore, enrichment activities need not be narrowly defined as something that occurs following mastery. When scheduling permits, it is appropriate to allow students who have yet to master the critical objectives to engage in enrichment activities. This seems appropriate for at least two reasons: (a) The enrichment activities may assist the student in achieving the critical objectives, and (b) the enrichment activities may provide motivation for that student’s learning.
enrichment = classroom management
in conclusion.... ....first of all, the thing to remember here is that no one is currently doing this in U.S. public schools. No one is "teaching to mastery." That's the rhetorical purpose of the book, to persuade educators to start teaching to mastery. Why aren't schools teaching to mastery now? Because everyone and his brother knows that if you teach to mastery in a mixed-ability class — and mixed-ability classes are taken as a given — you're going to be moving very, very slowly:
"The fast learners ranged from 3 to 7 trials (median = 5), whereas the slow learners ranged from 12 to 33 trials (median = 15)...[for a ratio of] 1:3 (fast:slow).The fastest third of the class masters material 3 times as quickly as the slowest third. (We're not even talking gifted here. Just top third, middle third, bottom third — which is the way a real class "falls out" in the real world,* leaving aside a tiny number of genuinely gifted children.) So say you're studying two-digit multiplication, and the fastest third has got it after a median of 5 trials, which we can probably define as lessons-with-practice. The slowest third still has another 10 trials (lessons-with-practice) to go while the fastest third does — what? Investigates two-digit addition? Solves real-world problems using addition? Teaches two-digit addition to the slowest third? Gentile & Lalley's answer to all of these questions is yes. The fastest third has got two-digit addition after a median of 5 trials, so now they spend the next 10 trials investigating, solving real-world problems, and tutoring their slower peers. This is what Gentile & Lalley are proposing. That is a huge drag on the wheel for the fast kids, one not likely to go unnoticed by parents who are going to come in loaded for bear. Why do real-world teachers and schools not "teach to mastery," as teaching to mastery is defined by Gentile & Lalley? Real-world teachers and schools do not "teach to mastery" for exactly the reason they give: teaching to mastery in a mixed-ability classroom, and the mixed-ability classroom is a given, would slow the entire class down to the pace of the slowest third of students. Almost certainly real-world teachers and schools are splitting the difference by teaching to the middle. Gentile & Lalley don't tell us how much faster the middle group learns than the slowest group, so let's split the difference ourselves. Let's assume they're literally in the middle; let's assume that the same material it takes the fastest learners a median of 5 trials to learn takes the middle learners a median of 10 trials and the slowest learners a median of 15. If you have the fast-thirds, who've hit mastery after 5 trials, sit around enriching themselves while you teach another 5 trials to the middle, and then you move on, you might reach something like mastery with 2/3 of the kids, without inciting the fast-thirds (or their parents) to riot. Meanwhile the spiraling philosophy apparently allows everyone to tell himself that the slow-thirds will see the material again next year so it's OK they didn't master it this time; the constructivist philosophy tells educators nobody should be committing anything to memory anyway; and Bloom's taxonomy tells us (or can be interpreted to tell us) that the important thing is for everyone to comprehend-apply-analyze-synthesize-evaluate....and the entire judicial system of the United States of America has spent the past god-only-knows how many years ruling that the school isn't responsible for getting content inside kids' heads, because "it could be something about the child" — and there you have it. Nobody is "teaching to mastery," nobody apart from teachers who close their doors and try to do it anyway, in spite of the towering odds stacked against them. Worse still, if people did start teaching to mastery, this is what it would look like. "Teaching to mastery" would mean the fastest third learn at exactly the same pace as the slowest third, then spend 2/3 of their class & homework time being enriched. Not "being" enriched; enriching themselves. The teacher and her aide, if she has an aide (questionable) is going to be busy with the slower-thirds while enrichment is taking place. The fast-thirds are going to be spending 2/3 of their class & homework time enriching themselves, and the middle-thirds will spend 1/3 of class & homework time doing the same. No wonder parents (and teachers) want smaller class size.
So this is where we get differentiated instruction, now the essence of an Irvington public school education and part of our strategic plan. Our teachers are all to teach 3 different groups of kids in each and every class & in each and every subject. That is their job. We're not going to have formative assessment or teaching to mastery (except, again, from teachers who buck the odds, or try to). We're just going to have differentiated instruction. Three different levels of classroom instruction delivered to three different groups of kids. Plus a whopping big load of enrichment for the fast-thirds and the 1 or 2 truly-gifteds. Parents have no say — none — in these decisions, which profoundly affect our children's lives. The district is the decider.
Standards and Mastery Learning: ERIC abstract * Mrs. Panitz told Ed and me about this back when Christopher was in 4th grade. She said every classroom falls naturally into 3 groups; teachers expect this. She said that the Phase 3 classes all had 3 such groups; so did the Phase 4 classes. That was one of the main reasons why, as she thought about it a bit, she realized Christopher should move to Phase 4. He was at the top of the top 3rd of his Phase 3 class, which meant that at a bare minimum he ought to be able to hold his own in the bottom third of the Phase 4 class. We figured he could probably be in the middle of the pack with the extra work we gave him at home, and in fact he probably did quite a bit better than that when he moved to Mrs. Woeckener's class. I think he may have been in the top third of her Phase 4 class in 5th grade. I would guess he was towards the "bottom of the top," but I think he was in the top third.
on not teaching to mastery - Gentile & Lalley
Engelmann on diversity and teaching to mastery
IQ is a range, not a point
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"Didn't Steve H say this?" I can't take the credit. However, remember when we talked about diagnosing math weaknesses? I have seen cases where once a few misconceptions have been cleared up, the student really takes off. It's quite amazing. But, then again, there are some who just need to go back to the basics and grind it out. My son's fifth grade EM math teacher started an after school "club" to help kids struggling with their "grades". (I hope she doesn't see the problem as grades rather than understanding and skills.) They will work on problems and do some peer tutoring. She wanted my son to be one of the tutors, but fortunately, he has piano lessons that afternoon. And my son is the one who, last weekend, had to stop and think about the answer to 7 times 8. Peer tutoring. Kill two birds with one stone. Right. I felt like telling her to drop the (cough-losers-cough) "club" and do one-on-one tutoring. -- SteveH - 25 Oct 2006
"Table 1.2 shows the remarkable results regarding intellectual traits and memory." This shoots Everday Math completely out of the water. If you don't hit a high mastery mark on the initial teaching, then it will be almost impossible to achieve mastery. I don't know if I agree with this completely, but I like how it shows the up and down path to long term mastery. My son is in one of those valleys regarding some of his basic facts. Of course, this is a great justification for doing lots of long division by hand. When I was growing up, I don't remember using flash cards after third grade. But we did have lots of multiplication and division. -- SteveH - 25 Oct 2006
A friend of mine has a daughter that really struggled through 3rd grade math. She was really devasted (she had done Abeka math in private school for grades 1-2) and lost all her confidence. This summer her grandmother set her up with a tutor. This tutor is a retired math teacher. The tutor worked with this child on memorizing her multiplication facts through flashcards and games. Now, this child is getting A's on all her math this year (4th grade). It was a simple as getting her through this ONE concept. Mastering it. Now she has regained her confidence and loves math. I wonder how far she would have fallen in math before someone identified this weakness, if it weren't for her grandmother persisting that she memorize her facts -- no matter what the school said. -- NicksMama - 25 Oct 2006
"What is happening here — and, again, until someone proves me wrong I'm going to stand by my opinion, is that constructivist teaching practices are being used to mask the fact that the fast kids are being slowed down to the slow kids' pace." My take is that the driving forces in the lower grades are full-inclusion and child-centered mixed ability groupings, with the teacher as guide-on-the-side. Constructivism is their theoretical cover for doing this. Higher order thinking! Conceptual understanding! They would drop constructivism in an instant if it meant no child-centered group learning. To allow for very wide ability levels, the pace has to be slowed and the expectations reduced. Spiraling the curriculum allows them to eliminate hard year-to-year expectations that would separate kids by ability. Mastery is considered "rote" learning and the spiraling curriculum gives them cover. Mastery also requires hard work and that also separates kids by ability. When parents complain about the slow pace, they introduce "Differentiated Instruction". This means that the more willing or able kids get their own projects or tasks to work on. This is usually for homework or for short periods during the day. It consists of variations on the same material rather than accelerating on to new material. They don't teach to the middle. They teach to the low end. At a minimum, the expectations are set to the low end. They expect these natural learning darlings will rise to their potential rather then just meet (low) expectations. But they can't tell the difference between the child who is having real difficulties and the one who just needs a swift kick in the rear. In any case, they will not change the low cut-off expectations. Our schools use rubrics (of course) that go from 1 - 4. It's very easy to get 3's (meeting expectations). Remember that the expectations are set very low. All of the kids find out that to get a 4 requires a huge jump in work. Most don't bother. And some complain that this work is mostly busy work; quantity over quality and skill level. The school has difficulty dealing with kids that won't do more on their own. But the schools will not raise the level of expectations. Schools might take different paths in 7th and 8th grades, but this is what I see in the lower grades. -- SteveH - 25 Oct 2006
I felt like telling her to drop the (cough-losers-cough) "club" and do one-on-one tutoring. yeah -- CatherineJohnson - 25 Oct 2006
This shoots Everday Math completely out of the water. If you don't hit a high mastery mark on the initial teaching, then it will be almost impossible to achieve mastery. I don't know if I agree with this completely, but I like how it shows the up and down path to long term mastery. I don't think this stuff is controversial in any way. One of the best lines in their chapter is the one about how a person with below 60% mastery can't be said to have learned at all. You MUST achieve a certain level of mastery to be able to "pick up where you left off." Otherwise you start all over again at square one. I've seen it too many times myself - and experienced it too many times - not to know this from common sense as well as from decades of research on memory and forgetting. -- CatherineJohnson - 25 Oct 2006
Everyday Math isn't based on actual research with actual people. They've just followed an abstract principle of "distributed practice," without spending a second figuring out how distributed practice actually works. Distributed practice without attaining 80% mastery to start is worthless. btw, all autism programs are based on this principle it's extremely well-known -- CatherineJohnson - 25 Oct 2006
My best example from my own life, which I mentioned on another thread, is the tennis scoring system, which I have never managed to learn. I've never managed to learn it because I go to the U.S. Open once a year, at which time Ed explains the scoring system. Then I don't watch tennis again for another year, when I again attend the U.S. Open and discover that I have forgotten everything I "learned" about the scoring system the year before. Our schools are putting the bottom thirds in this position. They may be putting a lot of the middles in this position, too. -- CatherineJohnson - 25 Oct 2006
My son is in one of those valleys regarding some of his basic facts. Of course, this is a great justification for doing lots of long division by hand. When I was growing up, I don't remember using flash cards after third grade. For what it's worth, I'll remind you that several of us found flash cards not to work very well. I don't know why that should be. Christopher really got hold of his math facts when we did paper-and-pencil Saxon Fast Facts sheets. (You can order those separately if you want to - or just join edhelper.com for $15 a year and print out facts worksheets.) Christopher learned his facts to mastery VERY quickly once we started paper and pencil worksheets. I saw that with another child, too. This child actually has an IEP, I think. -- CatherineJohnson - 25 Oct 2006
Now, this child is getting A's on all her math this year (4th grade). It was a simple as getting her through this ONE concept. Mastering it. Now she has regained her confidence and loves math. I wonder how far she would have fallen in math before someone identified this weakness, if it weren't for her grandmother persisting that she memorize her facts -- no matter what the school said. Parents simply have to be on the lookout. Period. Parents & grandparents. -- CatherineJohnson - 25 Oct 2006
My take is that the driving forces in the lower grades are full-inclusion and child-centered mixed ability groupings, with the teacher as guide-on-the-side. Absolutely. Child-centered mixed ability grouping is gospel. It is a religion. In the bad sense of the word. -- CatherineJohnson - 25 Oct 2006
To allow for very wide ability levels, the pace has to be slowed and the expectations reduced. Spiraling the curriculum allows them to eliminate hard year-to-year expectations that would separate kids by ability. Mastery is considered "rote" learning and the spiraling curriculum gives them cover. Mastery also requires hard work and that also separates kids by ability. When parents complain about the slow pace, they introduce "Differentiated Instruction". This means that the more willing or able kids get their own projects or tasks to work on. This is usually for homework or for short periods during the day. It consists of variations on the same material rather than accelerating on to new material. perfect -- CatherineJohnson - 25 Oct 2006
When parents complain about the slow pace, they introduce "Differentiated Instruction". and enrichment don't forget enrichment -- CatherineJohnson - 25 Oct 2006
I love it that here I sit in this wealthy community and I'm hearing the word "enrichment" all the time. Meanwhile the IEF can only raise money for enrichment, not for activities the school "should be paying for itself" (something like that). -- CatherineJohnson - 25 Oct 2006
7th and 8th, so far, are worse that's what I'm seeing more on that later — -- CatherineJohnson - 25 Oct 2006
Actually, this year, for us, is great. -- CatherineJohnson - 25 Oct 2006
The rationing kicks in next year. -- CatherineJohnson - 25 Oct 2006
Wow! Another one hit right out of the park! Excellent post. -- JdFisher - 25 Oct 2006
thanks! I LOVED getting the figures on what the exact difference in learning speed is. I'd like to get the analogous figure for mathematically gifted kids. I'm guessing they master material after 1 or 2 trials. -- CatherineJohnson - 25 Oct 2006
_"The fast-thirds are going to be spending 2/3 of their class & homework time enriching themselves, while the middle-thirds spend 1/3 of class & homework time doing the same."_ enrichment = wasting time Maybe not exactly wasting time, but the fast-thirds could get through 12 years of education in four years, and the middle-thirds could get through in eight... if they could cover the material at their optimum speed. This explains the occasional "9th grader who got admitted to Harvard;" a fast-third who was allowed and encouraged to achieve mastery at his own pace, and then allowed and encouraged to proceed with the next step, instead of waiting for everyone else. And also why schools seem to need kids for more days-per-year, more hours-per-day, and more years (all-day kindergarten, anyone?): Gotta pace everybody to the slow-thirds. And they're still not teaching to mastery. -- OldGrouch - 25 Oct 2006
"time spent doing enrichment" = "time to forget the material you just learned" -- OldGrouch - 25 Oct 2006
There is a resourcing problem for primary schools when it comes to providing maths acceleration. My primary school did it by all classes having maths at the same time and sending kids around classes to various levels. It was a small school and there were about 1 1/2 teachers per year. This meant that there were limited maths teachers. So once you got into the standard four maths class the school had nothing further to offer. And, lets face it, resources for faster learners are always going to be under pressure from the claims from disabled kids and slower learners. -- TracyW - 25 Oct 2006
Maybe not exactly wasting time, but the fast-thirds could get through 12 years of education in four years, and the middle-thirds could get through in eight... if they could cover the material at their optimum speed. wow I hadn't even gone that far.... The whole thing is horrifying. A 1 to 3 ratio - unbelievable. There are various studies out there showing our kids making zero gains between, say, 7th & 8th grade math (that's a real one cited in McEwan). The sole virtue of this approach is that the lower thirds actually get to learn content. -- CatherineJohnson - 25 Oct 2006
Catherine Johnson on the NoOneToWaste thread: "A group of parents fought 8 years for a foreign language program in the lower grades. The district fought back for 8 years on grounds that foreign languages would be too hard to schedule." Would scheduling still be a problem if they had 1/3-2/3 more time to work with? -- OldGrouch - 25 Oct 2006
Everything about this is just nuts These guys are talking about grade school kids - so these kids are just going to sit there and enrich themselves 2/3 of the school year, year-in & year-out??? -- CatherineJohnson - 25 Oct 2006
This explains the occasional "9th grader who got admitted to Harvard;" a fast-third who was allowed and encouraged to achieve mastery at his own pace, and then allowed and encouraged to proceed with the next step, instead of waiting for everyone else. sure does -- CatherineJohnson - 25 Oct 2006
And they're still not teaching to mastery. I KNOW! I KNOW! AAAUUUGGGHHHH ! -- CatherineJohnson - 25 Oct 2006
"time spent doing enrichment" = "time to forget the material you just learned" snort actually, that raises a point: I'm not sure they do say much about when the fast-thirds are supposed to get their distributed practice in....(they may; not sure) -- CatherineJohnson - 25 Oct 2006
And, lets face it, resources for faster learners are always going to be under pressure from the claims from disabled kids and slower learners. That's true, but on the other hand we're talking about one-third of the kids here. This book doesn't address the needs of the 1 or 2% of kids who are gifted. Actually, we're not talking about 1/3 of the class; we're talking about 2/3. These psychologists are recommending radically slowing down fully 2/3 of the class, on grounds that they can spend all that time cruising Bloom's. -- CatherineJohnson - 25 Oct 2006
PLUS WHICH.....how much synthesis & analysis & etc. are top-third 8 year olds going to be doing during the 2/3 of the year they spend enriching themselves??? Precious little. -- CatherineJohnson - 25 Oct 2006
Unless they're demon readers. Then they can spend the time reading their way through the World Book and accumulating information. -- OldGrouch - 25 Oct 2006
Doodlers and demon readers. I love it. You can't imagine the artwork I find in all the margins of my kids schoolwork. Any relationship to the top 1/3 of kids developing ADD? If there's nothing to pay attention to, bad habits develop, which are eventually labeled something, right? I wonder if anyone has looked at ADD from this angle. -- LynnGuelzow - 26 Oct 2006
"Gotta pace everybody to the slow-thirds. And they're still not teaching to mastery." Exactly. This is not just a philosophical trade-off decision on their part. They are not just spreading resources differently. They are doing less work and accepting less responsibility for learning. After coming home from our 4th/5th grade First Lego League Robotics after-school teams, I want to comment on another problem. (before I shoot myself) I know these are 10 and 11 year-olds, but they have very little self-control and very short attention spans. Perhaps it's the years of not having to pay attention to a teacher in front of the room for more than 5 minutes at a time. They are used to noisy child-centered groups and only occasionally hearing the teacher shout instructions above the noise. From all I have heard from my son and other parents, many teachers have little knowledge of how to control a class without yelling at, lecturing (see, they do know how to do this), and threatening them. Maybe they should have the kids get in a group and discover their bad behavior. At this age, kids struggle with focus and staying on task. Child-centered groups do not help this one bit. This is just another thing we have to do it at home. -- SteveH - 26 Oct 2006
I'm tired of the implication that the Everyday Math spiral is for the slow learners. Here is what Professsor James Milgram, math professor at Stanford, says about EM: "For very bright kids and extremely well prepared teachers, it would be a very good thing ... But for the vast majority of teachers and kids it's a total disaster." In our district, it's the parents of the top third who like EM. They see their kids scoring advanced proficient on state standardized tests. The director of our gifted program also likes EM. I have a friend whose son is a "mathbrain" and she likes EM too. She says that by jumping around from topic to topic, it keeps him interested. It's the parents of children who struggle who are complaining about EM. Quick learners don't need a lot of practice before mastering material. They can keep up with the spiral. It's the bottom third of the class that gets lost because they don't spend enough time on any given subject. The parents of those kids are spending a fortune on tutoring, and no one seems to care. Teaching to mastery in math makes sense. I agree that that's what schools ought to be doing. That's what Kumon does and I think it works. I think kids should be separated according to ability, but only for math. There are drawbacks to tracking, and it's probably not necessary for reading and writing. In those subjects, it's easier for kids to work at their own levels. But in math, it doesn't make sense for every child to move through the curriculum at the same speed. -- RobynW - 26 Oct 2006
Is there any benefit at all to child centered, mixed ability groupings in any subject? Setting aside your other points, Robyn, should I interpret your point about mixed ability groupings in reading, social studies, or science to be that it doesn't do any harm? By 5th grade, kids are beginning to really separate themselves by their ability to abstract and analyze, rather than digest. It is not easily tested. Kids that can engage in discussions of ethics and causality are held back by those still very much in the concrete stage, or worse, they can't yet read and understand the material. Ability groupings are generally positive in all subject areas, I believe. But you may be confusing separating by ability with older forms of tracking, which was no better than segregation. -- LynnGuelzow - 26 Oct 2006
In our district, it's the parents of the top third who like EM. Interesting. Not true here. Parents of the top kids quietly teach at home or hire tutors. We know we face ridicule if we complain that our kid, who is getting top scores on a poorly designed, low level state exam, is not well served by EM. The problems with the state tests are just to complicated for most people's patience. If your child isn't given a norm-referenced exam, you won't discover the gaps until its too late. -- LynnGuelzow - 26 Oct 2006
My cousin thought EM was for the kids who were good at math. That was the way she and her friends saw it. -- CatherineJohnson - 26 Oct 2006
Here's my cousin's story: first person -- CatherineJohnson - 26 Oct 2006
resources for faster learners are always going to be under pressure from the claims from disabled kids and slower learners I just realized why this shouldn't matter, in theory: the fast learners really, truly don't need as many resources The really fast kids "breathe it in" (that's my neighbor's description of what it's like to teach a math brain); the top third are fairly easy to teach. Ed's complaint about all schools (not ours in particular; he's said this for years) is that schools and some teachers prefer the kids who don't need teaching. That is absolutely the case in the Phase 4 math class; it may be the governing though unstated principle of all of the Irvington school district as a whole - and it's an assumption made by most Americans I think: a smart person doesn't need teaching. They "pick it up" etc. To some extent this is true. I have developmentally disabled kids & I have one smart kid & teaching the smart kid takes WAY less resources than teaching the smart kid. Remember when Susan said she told her district they needed to let her gifted child soar (I don't remember her exact words)? As far as I can tell, the fastest kids really do need significantly fewer resources to learn very well. Since they're already (probably) consuming fewer resources than everyone else, why put weights on their feet? -- CatherineJohnson - 26 Oct 2006
Unless they're demon readers. Then they can spend the time reading their way through the World Book and accumulating information. Actually, that might even be worthwhile. If you're going to make the fast-thirds enrich themselves for 2/3 of the school year, you should have a high-quality, stepped reading program in place for all of them. Those kids would be scoring 800 on the SATs by the time they hit junior high. -- CatherineJohnson - 26 Oct 2006
If there's nothing to pay attention to, bad habits develop, which are eventually labeled something, right? I wonder if anyone has looked at ADD from this angle. There certainly does seem to be a class of smart kids who just can't take it. My sister's 8th grader is classified gifted. The GATE program they have in their town was a mess, so she went back to her regular school this fall. Now she's leaving that and will be on Independent Studies for the rest of the year. CA has Independent Studies. -- CatherineJohnson - 26 Oct 2006
I want to comment on another problem (before I shoot myself) Steve?
Anyone heard from Steve?
-- CatherineJohnson - 26 Oct 2006
From all I have heard from my son and other parents, many teachers have little knowledge of how to control a class without yelling at, lecturing (see, they do know how to do this), and threatening them. I take my hat off to teachers who can control a room. From what I gather, you can't learn that in ed school. I did a lousy job with my Singapore Math class. (btw, I lecture Christopher on this at home. He's a talk-to-my-neighbor type kid, although he's not noisy & his attention span seems good to me. So he's not in the top-third disrupter category, but still...) I have what looks like a terrific book on the subject: Reluctant Disciplinarian: Advice on Classroom Management From a Softy who Became (Eventually) a Successful Teacher by Gary Rubinstein
-- CatherineJohnson - 26 Oct 2006
"As part of the training process, future teachers are often sent to obseve dynamic teachers. They scribble notes furiously, as these phenomenons silence chatter by merely asking, "Are you respecting your classmates right now?" After observing one teacher with excellent classroom control, I asked, "What do you do if they throw paper airplanes?" She answered, immediately, "I don't put up with that kind of nonsense!" In my notebook, I jotted, "Don't put up with that kind of nonsense!" [snip] New or future teachers leave a mentor's room delighted with their new collection of foolproof ideas, which they have just witnessed working flawlessly. To assume that these ideas will automatically work for less experienced teachers is like assuming that any golfer can clear the water hole with a five-iron from 200 yards, just because he has seen Tiger Woods do it on television." -- CatherineJohnson - 26 Oct 2006
In our district, it's the parents of the top third who like EM. They see their kids scoring advanced proficient on state standardized tests. The director of our gifted program also likes EM. I have a friend whose son is a "mathbrain" and she likes EM too. She says that by jumping around from topic to topic, it keeps him interested. That's very interesting. I can believe it - as I mentioned, that's what my cousin thought of it. This may also explain Ardsley's high math scores with TERC. I have data I've never gotten around to posting showing that Scarsdale's scores went down with TRAILBLAZERS....and TRAILBLAZERS doesn't seem to do the kind of rapid hopping from one subject to the next that Everyday Math does. At least, that's not my impression, and that's not what I'm hearing from parents in K-5. Those parents are complaining about the slowness & repetitiveness of TRAILBLAZERS. -- CatherineJohnson - 26 Oct 2006
I want to comment on another problem (before I shoot myself) "Steve?" I missed. The robotics team will be fine. It's just not the most productive use of everyone's time. Feel good learning. -- SteveH - 26 Oct 2006
Robyn I don't know what to think about tracking in other subjects, except to say that I would take Siegfried Engelmann's word for it. After reading THE SCHOOLS WE NEED and THE KNOWLEDGE DEFICIT back to back I'm acutely conscious of the need for young kids to acquire information in all the major subject matter areas - and "acquring information" means absorbing it into memory. Since we know kids have different rates of doing that, I'm inclined to think the most efficient path to learning the most content is "flexible achievement grouping" across the board. For me, Hirsch's discussion of reading was paradigm-shifting. Like everyone else, I've always thought of reading as a "formal skill" that can be applied to any subject matter. It turns out that reading - and writing - depends on background knowledge; a superb reader knows a huge amount of stuff. If your goal in every class is to move material from the blackboard (excuse me, whiteboard), textbook, and teacher's brain inside the student's brain then probably flexible achievement grouping is the best way to go. The one aspect of Gentile's & Lalley's argument I absolutely agree with is that everyone has to be taught to mastery because of the savings in relearning time. If your slow-thirds are starting from square one every time they're re-exposed to content, that's wrong. If you're trying to have children memorize the facts and analytical accounts of the American revolution, that's going to happen at different speeds for the 3 different groups..... -- CatherineJohnson - 26 Oct 2006
I suspect that grouping wouldn't be such a distressing and potentially destructive practice if all classes were pegged to content. Suppose teachers, parents, and students all had a list of the material to be learned - learned meaning remembered - in each subject. An annotated scope and sequence - suppose we had this for every subject. The school would be able to show you objectively precisely where your child is in the scope and sequence. The grounds for grouping would be transparent. I suspect that very few parents would insist that their child jump over the Civil War to join the fast-thirds studying the Vietnam War. -- CatherineJohnson - 26 Oct 2006
Kids that can engage in discussions of ethics and causality are held back by those still very much in the concrete stage, or worse, they can't yet read and understand the material. Again, having read back-to-back Hirsch, I want to look closely at "analytical" discussions in classrooms. Many of these conversations seem to be simply opinion-fests. I've been thinking about Ed's course on nationalism last year, where he set out to use formative assessment to teach students how to write a history paper. The students started out with grades in the C to B- range. By the end of the semester they were getting - and deserving - grades of B+ to A. The t.a.'s were doing the grading, then Ed checked it. He said their grading was correct; the improvement was real. We attributed this to his writing instruction, which I'm sure was part of it. But I hadn't read Hirsch at the time. Good writing, as it turns out, depends upon subject matter content knowledge. A good sports writer isn't a good science writer and vice versa. Ed is a good teacher, and by the end of the course those students knew quite a lot about nationalism, about the scholarship on nationalism, and about the debates on the subject of nationalism. They were far better versed in their subject matter, and they wrote far better papers. I'm positive that's a causal relationship. I don't know how to put all this together....but once you know that there is no such thing as a critical thinking skill apart from subject matter knowledge, then what? You wouldn't want to do too much "discussing" and "analyzing".....though on the other hand you do want to make sure the kids are linking what they're learning in class with what they already know.... Also, I feel positive in a Bayesian kind of way that you want to be encouraging kids to ask questions. So: I don't know. This is my conclusion. I don't know. The one thing I do know is that I would always, always focus on getting content inside students' heads - and by "inside students' heads" I mean inside their memories. I want my own child to remember, from one year to the next, as much of what he learned the previous year as possible. -- CatherineJohnson - 26 Oct 2006
"I'm tired of the implication that the Everyday Math spiral is for the slow learners." I don't think I said that. I've always thought and said that it was bad for everyone. It has less impact on the fast learners because they (almost) master the material in the first loop of the spiral. (Most schools supplement EM.) Even my son, who is a straight-A EM student (that's not saying much), is still not fast enough with his basics. The problems get worse in 5th and 6th grades when they get to fractions, decimals, percents, and word problems - not enough practice, even for the math brains. Even Andy Isaacs, one of the authors of EM, says it's not for the elite. "In our district, it's the parents of the top third who like EM. They see their kids scoring advanced proficient on state standardized tests." They are fooling themselves into thinking that good EM grades and good scores on a state's trivial math test are meaningful. These are the parents who will be horrified when little A-student Suzie gets to high school and starts the honors or AP Calculus track. Maybe their middle school can bridge the gap between EM and the high school AP track, but it's not going to be easy. "Parents of the top kids quietly teach at home or hire tutors." "If your child isn't given a norm-referenced exam, you won't discover the gaps until its too late." I agree 100 percent with Lynn. Too late is usually the first year in high school when they get out of the fuzzy world of K-8 education. "The parents of those kids are spending a fortune on tutoring, and no one seems to care." We care a lot here. KTM is all about tutoring at home. We're mad as hell and we're not going to take it anymore! Well, it sounds good anyways - not that the schools care what we think. I would love it if my son's school switched to Singapore (there's now a chance!), Saxon, or some Kumon-like approach. And this is for my son who masters (?) EM on the first loop. EM is structurally flawed. For the slower learners, the no-master spiral is a killer. For the fast learners, they are fooled into thinking that what they know is enough. "I think kids should be separated according to ability, but only for math. There are drawbacks to tracking, ..." We've talked about tracking here before. Tracking (by ability) is a dirty word for many teachers and schools, but it all depends on how you do it. (Some, like at our school, just don't like it any which way.) The big problem is that some forms of tracking in the early grades define which track you will go to in high school. Lower tracks often use a simpler curriculum rather than cover the same material, but just at a slower speed. For example, it's better for kids to go slowly, but still get to honors Algebra II or Trig in high school, rather than go slowly (with a poor curriculum) and end up in "check-book" math in high school. Some schools think that if kids need more time, they are dumber all around and can't handle a rigorous curriculum. Some schools stick with one curriculum (hopefully a good one), but allow kids to go up (or down) a grade level on a subject-by-subject basis. There are problems with this model because a grade level jump is pretty big. Other schools wait until 7th or 8th grade to begin official tracking, usually just for math or languages. There are problems no matter which way you do it, but schools just can't ignore the problem or hope that some magic technique, like differentiated instruction, will save their ass(umptions). -- SteveH - 26 Oct 2006
My experiences with EM have been incredibly frustrating and this website, which I have been reading for a while, has been very helpful to me. After reading this site, for example, I was persuaded to stick with Kumon, even though, at first, it seemed too slow and simple. Let me clarify my point about tracking. When I went to school, during the 1970's, we were tracked by ability in elementary school. We were separated early on into groups and stayed with the same group of kids until we reached junior high. I was in the top group, and I did benefit, but I also see the drawbacks to this type of early separation. I think that at least for early elementary school, tracking can stunt kids' social skills. I was always with the same group year after year. My kids are with different kids each year, and I think they feel more comfortable being around kids they don't know and making new friends. My kids are still in elementary school. I have a child who does very well in school. But I'm glad that he is in class with boys who are not such great students. Those boys have other strengths, and I think it helps my son's social and emotional development to be around them. My other child struggles academically, and benefits from socializing with kids who are good students. Would my son be learning more if he were with kids on his level? Yes. But at least, for now, the kids have separate in-class groups for reading and word study, and that seems to work okay. (Is that flexible achievement grouping or differentiated instruction? Probably the latter). My big concern is really in math. It is in math that my struggling student really is harmed because she is not taught to mastery and can't keep up with the class. I am constantly trying to figure out how and to what extent to supplement her education at home so that she learns basic skills. (Again, this website has been a great help). I guess all I'm saying is that tracking has both costs and benefits. Kids probably do learn more content when they are grouped with kids like themselves, and they all move at the same, suitable pace. But there can be drawbacks to their social development. Maybe the answer is to mix the kids together in K through 3 (except for math) and then separate them as they get into the intermediate grades. Wouldn't "flexible ability grouping" have the same effect as tracking? The strong students are usually strong in math and reading, and the struggling students often have problems in more than one subject. -- RobynW - 26 Oct 2006
SteveH?, I agree that the parents of the better students have a false sense of security from the state standardized tests. Your insights and the insights of others on this site have persuaded me to supplement my strong student, as well as my other child. Both kids are in Kumon and I work with my son on Singapore Math, although it's not always easy to fit in with all the other things we're doing. But I think there are a lot of parents who look at standardized tests scores in math and assume their children are getting a fine education. I know that's our district's defense of EM. Scores are up. The Fordham Foundation says our state standards are fuzzy, but our district doesn't want to look into it that deeply. -- RobynW - 26 Oct 2006
"But there can be drawbacks to their social "development." Our public schools are really big on this sort of thing. They carry it to an extreme and don't allow any separation, for any subject, through 8th grade. This is made worse with the wide ability, full-inclusion model they use. In the case of social development based on empathy or peer tutoring for lower ability kids, they're really pushing it. They use this as an excuse for not providing more for the more able kids. Quality curricula and high year-to-year expectations take second place behind social development and other fuzzy ideas of education. Considering what I have seen, I would rather a school stick with the academics. I can handle my son's social development, thank you very much. -- SteveH - 26 Oct 2006
You make excellent points, Robyn. But flexible ability grouping (I've also seen it referred to as "clustering") is not at all the same animal as tracking. Especially the rigid tracking of the 1960s and 70s. I think we've learned quite a bit about the way kids learn. Sometimes you find a strong student in math is also strong in other areas, but this is not true for many many students that have strengths and weaknesses all over the board. Personal anecdote, I have a math brain son with a particularly strong artistic side, but at writing he is well behind the curve. Thanks, Catherine for pointing out the Hirsch book again. I've got to get my copy back from my sister so I can finish reading it. -- LynnGuelzow - 26 Oct 2006
"I work with my son on Singapore Math, although it's not always easy to fit in with all the other things we're doing." Well, our 5th grade Singapore Math books haven't been opened yet this year. There is after-school sports/recreation, then come home to eat, then homework that can take forever (focus is a problem), then piano practice. There is something to be said about daily worksheets that take only 10 minutes to do. I get angry thinking that this would be so easy for them to do at school. -- SteveH - 26 Oct 2006
There is something to be said about daily worksheets that take only 10 minutes to do. I get angry thinking that this would be so easy for them to do at school. -- SteveH? - 26 Oct 2006 This kind of stuff drives me NUTS. Although I am a homeschooler, I occasionally have fantasies of sending my children to ps just for a semester (so I can recover). During this time, I would do the following: * Put a big, red "X" through any pieced of homework that I deem "busywork" OR that my child has not been taught OR my child has mastered. My child would be instructed to turn them in and have the teacher email/call me if he or she has a problem with it. * I would not care about threats that my child will get a failing grade for not completing these homework assignments. I know my child's capabilities and no grade from a teacher is going to affect that one way or another. Then, after my vacation from homeschooling was over, I'd be more convicted than ever to continue to homeschool. On days like today (when my kids seem hellbent on annoying each other), I REALLY want to do it! -- NicksMama - 26 Oct 2006
"But I think there are a lot of parents who look at standardized tests scores in math and assume their children are getting a fine education." I just tell parents to look at the tests and find out how many correct answers they have to get to meet the minimum proficiency cut-off. Our town is ranked "High Performing" with a Performance Index of something like 98. Sounds good, doesn't it? What this means ONLY is that a high percentage of kids get over a very minimum cut-off of expectations. It says absolutely nothing about anything else. Of course, this doesn't stop our schools from trumpeting our rating AS IF it means much, much more. they know darn well what they are doing. Parents don't look too deeply. If they do (and are able), they send their kids elsewhere and wash their hands of the problem. (Unfortunately, elsewhere can also mean Everyday Math.) I went to an open house a few years ago on our state testing. I was the only parent who wanted to see the actual math and English tests. I was horrified at what I saw. I remember one 4th grade math question. They showed a simple bar graph (they do love these kinds of problems) showing the results of a student election. The graph had four bars that showed how many voted for each child. Each of the bars was less than 20 votes. The first question was: "Who won the election?" The second question was: "How many students voted?" Time allowed for the problem? Fifteen or twenty minutes, I forgot which it was. The proficiency cut-off allowed students to get about half the problems wrong. "I know that's our district's defense of EM. Scores are up. The Fordham Foundation says our state standards are fuzzy, but our district doesn't want to look into it that deeply." Our schools do the same thing. This past year, they did an "analysis" of our math students when they got to high school (There have always been math complaints from parents when their kids get to high school.) and found that "our" kids "hold their own" compared to other towns. They blamed the problem kids were having in high school to the problem of not being placed in the proper level of math - NOT because they weren't prepared properly. Because some kids do well (they are math brains, or, more likely, got tutoring outside of school), they think that everything is OK. It's all really quite amazing! -- SteveH - 26 Oct 2006
"Put a big, red "X" through any pieced of homework that I deem "busywork" OR that my child has not been taught OR my child has mastered. My child would be instructed to turn them in and have the teacher email/call me if he or she has a problem with it." I was surprised, a few years back, when I first heard a parent say that he and his wife did all of the dumb projects and busywork for their sons. I should do this, but I can't bring myself to do it. I would do his EM homework and he can do the Singapore Math workbook. This might be a problem, however, when he has an EM test that asks him to "Find the One", as they call it. -- SteveH - 26 Oct 2006
Wow, skip a day on one topic and you miss a lot of comments! Just popping in to comment on a couple of things. The fastest third has got two-digit addition after a median of 5 trials, so now they spend the next 10 trials investigating, solving real-world problems, and tutoring their slower peers. It's worse than that. If you're truly teaching everyone to mastery, then you've got to teach to mastery that one student that took 33 trials, so the one student who "got it" after 3 trials has to sit there while the teacher goes over it 30 more times. In the worst case it's 11:1, not 5:1. You're dredging up memories here. I'm now remembering how at times in elementary school math I was days ahead on my homework because I'd do it in class for lack of anything else to do. We were already grouped: we had the orange, green, yellow, red, and blue groups. I think I remember that some kids did move among the groups, so they weren't tracked permanently, and that some kids were in e.g. orange for math but green for language arts. This was in the 1970s. Sounds like it's worse now. the fast learners really, truly don't need as many resources I don't think this is either true or fair to those students. True, the fast learners don't need as many resources in order to learn the "standard" K-12 course material in the "standard" amount of time, but if you're going to teach them to mastery the material they're capable of learning in that same standard amount of time, then they need more resources, not fewer. More resources because, since they learn the material faster, they will be coming back for more instruction more often than the middle-of-the-pack students. As an example, the teacher teaches the three thirds of the class their three lessons and gives them 33 practice problems each to work out.
I haven't read everyone's comments yet, so if I'm parroting someone else, forgive me. Real-world teachers and schools do not "teach to mastery" for exactly the reason they give: teaching to mastery in a mixed-ability classroom, and the mixed-ability classroom is a given, would slow the entire class down to the pace of the slowest third of students. No wonder parents (and teachers) want smaller class size. All of this begs the question: why do parents and teachers want smaller mixed-ability classes? It's obvious to me that mixed-ability grouping is the problem. A smaller mixed-ability class will mitigate, not solve, the problem. But no one wants to do "tracking" because then we'd have to admit that some kids learn faster than others, and that would bruise someone's (usually parental) ego. And you know, it's soooo much easier to deny reality when it's staring you in the face and just go on trying to build a utopia. Here's a crazy thought: what if we did away with grade levels, for the most part, and had content-based classes? IOW, instead of taking 5th-grade math, you take "Fractions, Decimals, and Percents" class. Whenever you finish that class, you move onto the next group of concepts, in a new class. It may take the average student x number of weeks to get through the material, a fast learner x/3 weeks to get through it, and a slow learner x+10 weeks. -- BrendaM - 26 Oct 2006
the fast learners really, truly don't need as many resources I don't think this is either true or fair to those students. True, the fast learners don't need as many resources in order to learn the "standard" K-12 course material in the "standard" amount of time, but if you're going to teach them to mastery the material they're capable of learning in that same standard amount of time, then they need more resources, not fewer. I heard once that teaching a gifted math student at the same pace as the whole class is like feeding an elephant one blade of grass at a time. Faster learners do not benefit from the make work, fill up the extra time enrichment that they are typically given. They are ready to move ahead and experience great frustration when they are held back. -- LynnGuelzow - 26 Oct 2006
I just reread (with more care) Catherine's original post on "learned helplessness." I wonder if I am suffering from this having experienced helpless failure repeatedly at the hands of the board of ed. How many parents no longer try to save themselves and instead sink to the bottom and drown from learned helplessness? Maybe I'm taking this too far. OTOH, repeated failure makes it very hard to keep trying. 5 years into EM, I see no realistic hope of ridding it from our curriculum. -- LynnGuelzow - 26 Oct 2006
"It's obvious to me that mixed-ability grouping is the problem. A smaller mixed-ability class will mitigate, not solve, the problem. But no one wants to do "tracking" because then we'd have to admit that some kids learn faster than others, and that would bruise someone's (usually parental) ego. And you know, it's soooo much easier to deny reality when it's staring you in the face and just go on trying to build a utopia.' Ergo, differentiated instruction. That's the solution at our schools. It doesn't work because the spread of abilities is so great due to full-inclusion. They want it all and it can't work. They are struggling and they see the kids leaving to go to other schools. It's surprising to me that so many parents give up and go to other schools - 20 to 25 percent of the kids in our town. They wash their hands of the problems and remain quiet. Some (very few try it) who have written letters to the editor get trashed. Those who go off to private schools are called elitist. It's a very touchy subject. Constructivism is nothing compared to this. There are lots of parents who love full-inclusion. The idea of kids of all abilities working together has a very strong pull. The lower ability kids get more challenge and the higher ability kids get empathy and a chance at peer tutoring. Some parents have told me that they like this idea - for a while, but they start to get very nervous by 5th or 6th grade. I haven't figured out why this whole approach hasn't collapsed already. Part of the answer is that our town is known for its focus on LD kids. Families move to our town for this reason. The school committee wants to "tuition-in" these kids from other towns at a lower cost-per-student than our town budget requires. All-the-while, parents of more able kids are sending them to private schools - that only teach Everyday Math. How do I get out of this rabbit hole? -- SteveH - 26 Oct 2006
Let me know when you figure it out. We have not done an exception job on the LD kids here, so we aren't getting emigration. I guess we are no better and no worse than most neighboring towns. In 5th grade, teachers block off 1 1/2 hours each day for math, with a combination approach of state test prep, EM, and gap remediation. Some days it seems that EM is a small % of the math time, but usually it seems like a 60/40 split, EM v. supplementing. I wonder how they can draw any conclusions from this. How do you know what is working and what isn't when you mix so much? I think the answer is, something is working so let's keep doing this until we stop. We've only had 5 years of EM, so it's too soon to really see the effect in the HS. Kids who are freshmen this year started in EM in 5th grade (I have one of those, so I can keep track). It will be a couple more years before we can answer the ultimate question, are the kids from the EM/Supplement approach prepared for higher level math? -- LynnGuelzow - 26 Oct 2006
Maybe their middle school can bridge the gap between EM and the high school AP track, but it's not going to be easy. "Parents of the top kids quietly teach at home or hire tutors." "If your child isn't given a norm-referenced exam, you won't discover the gaps until its too late." I agree 100 percent with Lynn. Too late is usually the first year in high school when they get out of the fuzzy world of K-8 education. That's where the middle school kids are going to be.....I'm pretty sure. And these kids aren't constructivist kids. They are the products of what now looks to me like a dreadfully bad middle school math curriculum, which was not created by Ms. K. What we've had with Ms. K is brand-new-young-unmentored-teacher handed horrifically bad course to teach. -- CatherineJohnson - 26 Oct 2006
Here's a crazy thought: what if we did away with grade levels, for the most part, and had content-based classes? I'm slightly too tired to reason this through.....Wickelgren had a proposal like this, and Engelmann seems to say that when you start everyone at exactly the same level in the content, with the same degree of mastery of prior content, somehow slower learners move along at the same pace..... can that possibly be right? I don't see how there are too many unknowns here - I can certainly see the social benefit in "diversity" of any kind, but how much diversity does the dimension of learning speed introduce? I'm not sure Christopher has very close friends in the fast-thirds & in the slow-thirds (don't know how many friends I'd put in the middle...) I'm not sure how different these kids are -- CatherineJohnson - 27 Oct 2006
I always come back to parent choice, ultimately I think we probably know that grouping is optimal for learning content; I think many of us probably agree/assume/know that diversity is good for social learning these two goals are in conflict, and what we neither know nor agree upon is how to resolve the conflict I would absolutely leave it up to parents as far as humanly possible this can be done for instance, down in the Village a school sent out notice to all the parents of typical parents telling them they wanted to put together a full inclusion class that would include severely disabled kids like Andrew or Jimmy they asked parents whether they'd like their children to join the class there are some documented benefits of such classes that are very cool, one being that a typical child in such a class experiences a rise in social status amongst the other typical kids in the school! I love that anyway, it worked great parents who were interested put their kids in the class and were very happy with the experience I have no i dea whether these learned less than kids who didn't join the class they may have, but their parents are the morally & legally responsible authorities; it's their call In special ed it's always said that the parent knows his child best; often it's said, by teachers as well as parents, that the parent knows what's best for his child when trying to resolve this conflict, I want the school to attempt to give parents a grouping option and a mixed-ability option & let them choose -- CatherineJohnson - 27 Oct 2006
Another possibility is to split the school day a bit differently. Hirsch recommends a national core curriculum that would take up 40% to 60% of the school day. His core curriculum isn't just something he made up, btw; he convened a big panel of professors, authors, etc. & figured out the background knowledge a person needs to have "cultural literacy" That's what his Core Knowledge curriculum is based on so say a school devotes 40% to 60% of its day to very seriously getting that knowledge inside students' heads you could do ability grouping for that part of the day, mixed-ability grouping for everything else you'd make the groups as flexible as possible, so kids could move up, down, or sideways as needed everyone would know exactly what the curriculum was and where a child was in the curriculum; there wouldn't be Top Secret decisions being taken and pushy parents elbowing their kids in I know for a fact that after our experience of having Christopher in a class taught to the two gifted kids in the room I would never put him in such a situation again -- CatherineJohnson - 27 Oct 2006
my tennis mom friend from last year talked to Ms. Kahl and told her "If you had a math 3.5 I'd pull my kid. But you don't." That's our dilemma. An accelerated class of 16 or 17 kids taught to the top 2 -- CatherineJohnson - 27 Oct 2006
Actually, I'm thinking about Engelmann again.... You could have a somewhat mixed-ability group with Engelmann because of the small amount of new content he introduces in each lesson - only 15% to 20% The rest is review of material previously mastered to 80 or 90% (I've forgotten which) The savings in relearning time for the slow-thirds is huge. A "slow learner" is actually a "slow first-time learner." That's what differentiates them. With real teaching to mastery you're probably going to end up created a "modified mixed ability" group if I'm making sense.... You wouldn't necessarily have to have 3 separate groups.... I wonder what you see in his schools? I can imagine an Engelmann school ending up with everyone moving at a speedy clip, and maybe only a couple of groups... Then the truly gifted kids - the "breathes it in" kids - have to have their own thing. -- CatherineJohnson - 27 Oct 2006
Engelmann seems to say that when you start everyone at exactly the same level in the content, with the same degree of mastery of prior content, somehow slower learners move along at the same pace..... That was an artifact of the priorities of project follow through. The slowest kids were given the best teachers and extra time as needed. The priority was not to super-accelerate the high achievers. In any event few kids fell into this group anyway because of the high mobility rate in the low ses areas effectively precluded a continuing high peforming group since not enough kids were available to sustain a class. They were sacrificed. Engelmann has said that he estimates that higher performers culd be accelerated by 3x to 4x the rate of average students. This seems about right to me with my sample size = 1 experiment. I do two math lessons every day with my son in half the normal class period. And, so far he's never gotten less than 90% correct on any mastery test. At most it takes five minutes of actual teaching time. The rest of the time I look over his shoulder as he works problems. -- KDeRosa - 27 Oct 2006