DirectInstructionAndTheRigorConundrum < Kitchen

27 Jan 2006 - 16:37

the rigor conundrum

There's all kinds of good stuff in the various comments threads — in particular, Rick Ballard, who is amazing with statistics and polling, is trying to figure out what the 'Boy Problem' numbers actually mean.

I'm all over the place on the Boy Problem, obviously.

I don't like what I see as anti-boy bias in textbook development, and I think schools are too female-dominated. Those observations are pretty much incontrovertible.

I also think schools over-reward clerical and organizational skills, while over-punishing the lack thereof. These perceptions are more debatable (especially seeing as how I don't know what middle school girls are experiencing).

What I'm not at all sure of is whether there's a 'real' boy problem in districts like mine, where divorce is rare and dads are present.

Here's what Rick's found so far:

I'm still working on the data sets but I'm not finding any clear distinctions - other than that men are more highly rewarded than women after college for the same level of performance in college. IOW - there is no economic payoff for any edge awarded to women during school. I'm beginning to wonder if the higher rate of matriculation and graduation might not be attributable to innate differences in the importance that each sex attaches to organizational skills. The "leveling of the playing field" back in the seventies may have just revealed women's superiority in completing tasks within an ordered environment.

This is exactly what I've been wondering.

Is college just more of a 'girl thing'? (I say 'girl thing' neutrally in this case.) I was talking to Ed about this yesterday. He doesn't know what to think about the whole thing, either, but he pointed out that when you look at Continuing Ed, it's all women.

It's true. I've tried to take a couple of continuing ed. courses (I always end up dropping out) and the ratio is 10 to 1, if that. For every 10 middle-aged women taking a continuing ed. course, there'll be 1 guy.

Women like school!

So I don't know. I think Rick's still looking into it.....I'm going to be interested to read what he comes up with.

There's lots of other good stuff, too, but I wanted to get this up front sooner rather than later.

Here's Ken, on acceleration of normal students through Direct Instruction:

Engelmann also claims that in a low mobility school with sufficient number of high performers, these high performers can be accelerated at 3-4 times the usual acceleration rate that DI achieves. To do this you'd need an affluent suburban school to become a DI immersion school and there's esentially zero probability of that happening in the absence of outright parental revolt.

At this point, I'd like to know exactly how fast a high-achieving child taught via Direct Instruction can move.

Toru Kumon, who wrote the KUMON worksheets and founded the company, had his own son doing calculus in 6th grade.

Even though I haven't taken calculus myself (yet), I'll go out on a limb and say I believe it. Now that I've worked with Singapore Math a bit, and spent so much time immersed in K-8 math, it makes sense.

Here in 6th grade, Christopher is being taught Algebra 1. That's what this course is. Algebra 1 and geometry (without the proofs). AND the kids have all started Algebra 1 without being anywhere near mastery of fractions, decimals, or percents.

He's having a heck of a time, but it's obvious to me, sitting and working with him, that if John Saxon or Siegfried Engelmann were running this course he'd be learning the material.

He'd be learning the material because it's not 'hard.' The fact that Christopher has apparently reached some kind of mastery on integers is evidence. He was utterly confused by integer operations at the beginning of the year; he's remained confused throughout the year (for 'the year' please substitute '3 months'); and now, all of a sudden, he can take a pop quiz on integer operations and score 20 out of 20 correct.

If integer operations were hard, he'd be scoring 0. Because he has sure as heck not been taught to mastery.

So how far and how fast can a high achiever go with Direct Instruction?

Do we know?

the rigor conundrum

For me, Direct Instruction and KUMON have solved the 'rigor conundrum.'

The rigor conundrum is this.

Many parents want their schools to provide a more rigorous curriculum.

At the same time, parents don't want their kids homeworked to death.

I'm not going to take the time now to pull all the evidence for this; you'll just have to trust me. There's plenty. Here's one: Tom Loveless, at Brookings, has some great stuff on the Homework Wars. All over the country you've got parents in open rebellion about how much homework their kids have to do — and when you look at it, it turns out nobody's doing any homework! We're doing less homework than other countries, and homework levels are the same as they always were. (This isn't strictly true; Loveless explains why parents believe homework demands have soared.)

So the question is: which is it?

Do parents want a more rigorous curriculum?

Or do they want a less rigorous, lower-work-loads curriculum?

Policy experts don't know; that's why you see Forums on the question of Will the American public support excellence in education & the like.

Meanwhile, I've had a paradigm shift.

More rigorous education versus Less homework is the wrong question.

'Rigor' doesn't mean '4 hours of homework' plus an Extended Response problem you have to know modular arithmetic to solve.

I think Ken's expression for this is fake rigor.

'Rigor' means material is taught to mastery so students can accelerate their progress through the curriculum.

and:

Material taught to mastery is far easier to learn than material taught through exposure.

What parents want is more rigor without more homework — without pointless, overwhelming, ditch-digging-in-San-Quentin levels of homework.

I'd put money on it that if parents saw their kids being assigned more homework that obviously increased their learning and mastery they'd support it.

But given what I've seen of KUMON, quantity shouldn't be the 'standard' in K-8 or perhaps even in K-12 (not sure about that).

KUMON's philosophy is slow and steady wins the race. Ten to twenty minutes a day, and don't over-do it.

They've shown that it works.

KUMON and 'responsibility'

KUMON talks about self-learning.

Kumon students study independently at both Kumon Centers and at home. The role of instructors within the Kumon Method is focused almost entirely on the development of a student's ability to learn on their own. Kumon refers to the ability to set goals and solve unfamiliar and challenging tasks independently as "self-learning" ability. Instructors foster this "self-learning" ability in students by using worksheets that allow students to learn at one's own pace, moving forward when they are ready. The students' enthusiasm for learning is aroused in this process, as the goals they set are their own goals. In addition, this process awakens a desire in the students to take on new challenges.
Instructors ensure that students can, without any hindrances, experience over and over a sense of accomplishment, thereby boosting confidence in their own abilities. Problem solving abilities are enhanced, and independent methods of solving problems are encouraged. Instructors must also observe the study behaviors of each student, get a sound idea of each student's particular learning situation and incorporate this into the method of instruction. Instructors routinely analyze the learning process. If problems become apparent, the instructors ask themselves pertinent questions about the problem before proceeding such as, "Is the student's pencil moving too slowly?" or "Is the student too lost in thought?" Through such careful observation of the student's learning, small obstacles are removed in a timely manner thus assisting the students in their self learning.
Consequently, it is a uniform approach, using the worksheets, the instruction method, the input and analyses of the instructors, and the abilities of the students, which make the method a great success.

That's a terrific description of KUMON, Ideal Type.

Around here, we're not experiencing KUMON, Ideal Type. Christopher isn't becoming a Self-learner via KUMON at this point; he'd quit today if I let him.

Nor are we having a lot of helpful analysis of pencil grip.

Doesn't matter. Christopher is practicing and learning every day.

KUMON draws a connection between correctly paced teaching to mastery and the child's eventual independence and self-motivation.

I believe it (and in fact I do see signs of it in Christopher at times).

Here's Ken again (yes, we're having an all-Ken-all-the-time day here at ktm):

The reason why DI and Kumon create more independent learners by the middle school years is because they start with a high degree of student support in the lower grades and gradually fade the support structure by the end of the program. Still, many low performers always need some level of support over the average student. With other kids, the support can be faded even faster.
Bear in mind that in any event the support is faded gradually and that the kids have been exposed to effective learning techniques over the course of many years off of which they can model their own learning. The rug just isn't pulled out from under them come sixth grade. There is no sink or swim, nor should there be at this age.

This is as good an explanation as I think I'm likely to see of how a 'passive,' 'spoon-feeding,' Directly-Instructing program like KUMON in fact leads to an active, independent, self-motivated and self-directed student over time.

I want my school to adopt an educational philosophy and practice of teaching to mastery.

extended response problem from IL state test
extended response problem 1
extended response problem 2
extended response problem 6
extended response problems 7, 8, 9
direct instruction & the rigor conundrum
Dan's daughter reacts to extended response problem
defensive teaching of Singapore bar models
open-ended problems in math ed
problems that teach - "Action Math"
email to the principal

-- CatherineJohnson - 27 Jan 2006

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What you say about the homework wars is really true.

Our middle school has a no-homework-on-the-weekend-ever policy. I don't think the teachers and administrators are thrilled with it, but judging by the applause when the policy was announced at the beginning of the year, the parents love it.

At our meeting yesterday, I had to ask special permission for Ben to make up his literature logs over the weekends.

-- CarolynJohnston - 27 Jan 2006

The reason he has to do that is that there's no time during the week; he's doing homework nonstop. But that's mainly Ben -- his attention issues cause everything to take 5 times as long as they need to.

He has a lot LOT less homework in middle school than he had in elementary school!

-- CarolynJohnston - 27 Jan 2006

Re the homework/rigor paradox:

Homework is supposed to be an opportunity for more practice not idependent learning. Thus, homework should not be overly difficult; it should be at the student's instructional level (i.e, where he already knows 90%+ of the material and won't be making many mistakes). When homework is above the instructional level you're going to get lots of mistakes and frustration, lots of inefficiently used time, and learning lots of wrong rules (which are diffcult to correct, assuming they get corrected at all). A proper education is about efficient use of instructional time which means you don't waste time learning thigs the wrong way and having to unlearn misrules. A proper education is about controlling the learning environment to avoid this kind of inefficiency.

Kids should not be strugglingto complete their homework. This is not efficient. When the instructional level of the material is above the child's ability level, they don't learn as much or as quickly.

There is a very good reason why there is little homework assigned in a DI program: instruction needs to take place in a controlled environment that is closely monitored by the teacher who is assuring that all the children are learning what they are supposed to be and who is correcting mistakes immediately to prevent mislearning.

This is the stuff that needs to be taught in ed schools and every teacher needs to have mastered these principles. Clearly this is not the case or we'd have alot less Ms. Kahls doing it all wrong.

-- KDeRosa - 27 Jan 2006

At our meeting yesterday, I had to ask special permission for Ben to make up his literature logs over the weekends.

good grief

-- CatherineJohnson - 27 Jan 2006

Homework is supposed to be an opportunity for more practice not idependent learning

That's one I'll have to tattoo to my forehead

-- CatherineJohnson - 27 Jan 2006

although....what about high school?

At that point, students are supposed to be doing independent learning from their books....right?

-- CatherineJohnson - 27 Jan 2006

It doesn't matter, though.

The principal still holds: homework should be assigned rationally and with efficiency & motivation in mind.

Homework should have a point.

-- CatherineJohnson - 27 Jan 2006

When homework is above the instructional level you're going to get lots of mistakes and frustration, lots of inefficiently used time,

Christopher could be the poster child for this observation.

It's surreal, the time we're wasting here.

We're grabbing huge handfuls of time and just flinging them aside.

It's shocking.

Now, we can't even do our 5-KUMON-sheets-a-day. Mr. Liu said Christopher is stressed, and I should cut back (he was right).

So I'm now paying twice the money for KUMON (it's a flat fee) AND Christopher is moving forward at half the rate.

All so we can get through Phase 4 math.

-- CatherineJohnson - 27 Jan 2006

although....what about high school?

At that point, students are supposed to be doing independent learning from their books....right?

I think that's right. And, by that time most should be able to do this. Gradually, they should be able to attain the level where they are prelearning the next day's material beforehand so they bring something to the table during the classroom instruction.

-- KDeRosa - 27 Jan 2006

A proper education is about efficient use of instructional time which means you don't waste time learning thigs the wrong way and having to unlearn misrules. A proper education is about controlling the learning environment to avoid this kind of inefficiency.

It's exactly the opposite.

I hadn't thought of it in these terms until recently, but FOR YEARS I've been complaining that constructivists act as if there's 'no tomorrow'; they act as if a child's childhood lasts forever.

Which, for them, it does.

If you teach 4th grade, and you always teach 4th grade, children are always 10 years old.

-- CatherineJohnson - 27 Jan 2006

In fact, this is a question of efficiency.

Efficiency is NEVER mentioned or discussed in the schools I've been involved with.

(Never say never, but you know what I mean.)

-- CatherineJohnson - 27 Jan 2006

Gradually, they should be able to attain the level where they are prelearning the next day's material beforehand so they bring something to the table during the classroom instruction.

Actually, another excellent point.

Boy, that is SURE never taught.

-- CatherineJohnson - 27 Jan 2006

I have to stop saying 'never.'

-- CatherineJohnson - 27 Jan 2006

Ken you've got to read HOW TO DOUBLE YOUR CHILD'S GRADES.

You'll love it.

It's really extraordinary, because it's Direct Instruction in metacognitive skills, to a degree.

He is directly instructing (and then practicing to mastery) a child in how to analyze and 'interrogate' a text.

This is a skill Ed doesn't see in his entry-level Masters candidates.

-- CatherineJohnson - 27 Jan 2006

Efficiency is never mentioned because because it is off the radar screen. You can't even begin to measure efficiency until you have a standard to measure it against. There are no standards or expectations in education today. Hyperbole aside, the very notion of the spiral curriculum itself does away with the need for efficientcy. No need to worry if the kids aren't learning, we'll spiral back around next year. Efficiency = 0 since the material has to be completely retaught from square one.

Imagine if your typical car factory were structured this way. Build the car and then test it to see if it works. If it doesn't, just send it back through again and rebuild it until it runs. And, if it doesn't run by the third time through it doesn't matter because then it's time to ship to the customers. They can fix it.

-- KDeRosa - 27 Jan 2006

Efficiency is never mentioned because because it is off the radar screen.

you can say that again

-- CatherineJohnson - 27 Jan 2006

the very notion of the spiral curriculum itself does away with the need for efficiency. No need to worry if the kids aren't learning, we'll spiral back around next year. Efficiency = 0 since teh material has to be completely retaught from square one.

wow

you're on a roll today

-- CatherineJohnson - 27 Jan 2006

One more book to buy.

-- KDeRosa - 27 Jan 2006

we need to start issuing white papers

(I'm serious)

at a minimum, I have to get THIS POST sent to the Carnival — and get the efficiency comments incorporated....

-- CatherineJohnson - 27 Jan 2006

I must be. My speed of thought is exceeding my ability to catch typos.

-- KDeRosa - 27 Jan 2006

seriously, though, it's true that to adopt a spiral curriculum you almost by definition have decided not to think about efficiency

not quite: you could argue that repeated exposure over several years' time is more efficient than massed practice

but the fact that you never see people make this case tells you efficiency is off the screen

-- CatherineJohnson - 27 Jan 2006

not quite: you could argue that repeated exposure over several years' time is more efficient than massed practice

This might be a good argument but for the shelf life of knowledge factoid. Once you know that fact you know that anyone making the argument h asnot only not thought about efficiency but is clueless as well.

-- KDeRosa - 27 Jan 2006

you're on a roll today

This is a good example of increased domain knowledge ans the Bayesnian approach to learning.

You can only learn stuff so fast in isolation. But when high quality ideas are bouncing around, you modify and expand your thinking, even when you disagree with something. This constant challenging of your thought processes and knowledge and looking at things from different perspectives sometimes results in additional insights that you wouldn't have had on your own.

Chalk another one up to Bayes.

-- KDeRosa - 27 Jan 2006

This might be a good argument but for the shelf life of knowledge factoid.

RIGHT!

of course

-- CatherineJohnson - 27 Jan 2006

Ken

It's absolutely true.

I find that, for me, what I need is a community of brainy people who agree on 'the fundamentals'.....and who have different ideas, including disagreements, on the details or implementation.

I also find that the words people use are critically important.

Almost every day, someone here will phrase a familiar idea in words that make it much more powerful and useful.

Even though I already 'have' the idea, I didn't have it in that form.

God is in the details.

-- CatherineJohnson - 27 Jan 2006

"To do this you'd need an affluent suburban school to become a DI immersion school and there's esentially zero probability of that happening in the absence of outright parental revolt."

This list of Colorado Charter Schools shows two schools advertising that they use a Direct Instruction curriculum. Unless I'm mistaken, both are in solidly middle-class neighborhoods.

Littleton Prep has overall grades of High and Excellent (middle school and high school, respectively). James Irwin Charter Elementary doesn't seem to be doing as well, but it seems to have only two years of data, indicating a new school.

I don't know what that means, but thought it might be useful to mention in case someone else cares to examine it further.

-- DougSundseth - 27 Jan 2006

oh that's very interesting.....

hmmm

middle-class neighborhoods

I'd LOVE to know how that happened

Doug, can you keep your eyes open for any media/press about these schools?

The poor scores of James Irwin don't raise a flag for me yet given that it's a new school.

Interesting.

What are people's politics like there?

Direct instruction would be a very tough sell here, I assume.

Partly because it's associated with low achievers, and partly because liberal Democrats lean towards progressive ed without realizing what 'progressive' means inside ed school.

-- CatherineJohnson - 27 Jan 2006

I must be. My speed of thought is exceeding my ability to catch typos.

you've got a few more than usual!

That could probably serve as a symptom on a list somewhere.

-- CatherineJohnson - 27 Jan 2006

key words:

direct instruction schools in Colorado

-- CatherineJohnson - 27 Jan 2006

Catherine,

You are too kind in your assessment of my skills in statistics. I do know how to deconstruct a poll but I tiptoed away from actual statistical work at the point where the sigmas had to lie down to take a rest. I'm a fair hand at finding anomalies or unremarked trends in a data set, though, and there is no lack of data to mine.

That said, the strongest statement that I can come up with is that, using college matriculation and graduation as determinative outcomes, boys are rewarded less than girls at the median in relationship to what is known about IQ distribution. A girl with a 100 IQ is more likely to 'perform' well than a boy, according to educational standards. At the upper level of the IQ distribution (using acceptance to graduate school as a rough measure) even though women are taking a proportionate number of masters degrees, men still have a slight edge in doctorates. And as I mentioned earlier, using post graduation income levels as a surrogate for "success", men still do much better than women. The primary reason for that difference is probably field of study and employment sector.

Returning to organization for a moment, I trained 9 estimators (quantity surveyors) over a period of ten years (training took about a year). Three of them were women who did excellent work with a very low 'oops' rate on errors that I classified as "leave outs". I finally made the six men use a signed check list on every bid that had to be completely filled out before I would conduct an estimate review prior to signing off on a bid. The guys were good estimators and their projects had a higher rate of return than did the gals (risk assessment ability, I believe) but they blew projects at an unacceptable rate until I instituted the check list.

Maybe the boys would perform better if they were tasked to a checklist at the moment they returned from school? Tell them that pilots do one before every takeoff (I hope).

-- RickBallard - 27 Jan 2006

[I apologize in advance that currently my only area of "expertise," such as it is, is in the toddler-realm, but hey, that's where we're at.]

The notion of "How do they move from being handheld to independence?" in Kumon is interesting to me because it's so similar to a lot of the independence transitions that happen at this age.

There's a school of thought that claims that if you provide a super-secure, hand-holding environment for a wee little one, they end up being more secure and more independent when they mature and move on.

In our own experience we found that to be true for Audrey and I wonder if there's a similar sort of dynamic going on, albeit in a more mature form. If you pull away the support and security of the elementary-style educational environment too early, some kids will regress rather than immediately develop the independence that this move was supposed to foster in the first place.

-- TerriWheeler - 27 Jan 2006

Tell them that pilots do one before every takeoff

Hey, that might actually work!

For a couple of days.

-- CarolynJohnston - 27 Jan 2006

"What are people's politics like there?"

Colorado tilts libertarian (small 'l'), which expresses differently in different areas. Colorado Springs tends strongly Republican (and parts are fundamentalist), Littleton is probably weakly business Republican, Denver is union Democratic, Boulder is granola Democratic.

Pretty much everybody outside of the union strongholds thinks that the government should mind its own business. (Well, and other people's business, too, but not their business.)

For example, even before the charter schools movement got rolling, Boulder had strong support for alternative school choices. (Not the sort of alternative choices I would make, but any extra choice puts pressure on the public schools.) There's still a fair amount of resistance to charter schools as "elitist" in some areas. And the teachers' unions hate them, of course.

-- DougSundseth - 27 Jan 2006

Isn't that where "management responsibility" comes in, Carolyn? It would provide a parent with an effective tool for the evening round of negotiations.

-- RickBallard - 27 Jan 2006

"What are people's politics like there?"

Doug, you are forgetting that Promise Keepers started in Boulder and the Dobson empire and related are in the Springs. And don't forget the fundies at the Air Force Academy. Plus Highland Ranch and Castle Rock are full of rich Republican fundies.

(Have to leave this one anonymous. Sorry.)

-- KtmGuest - 27 Jan 2006

That's very interesting.

I'd love to know more of this 'fine-tuned' sex difference stuff.....

-- CatherineJohnson - 28 Jan 2006

Interesting.

I wouldn't be surprised....AND, having had two autistic kids, BOY HAVE I SEEN REGRESSION.

You see it in typical kids, too.

Actually, that's probably a good word for what I've been seeing (or had been seeing) with Christopher: regression.

-- CatherineJohnson - 28 Jan 2006

No Geographical Knowledge Alert:

are these areas close to the two DI schools?

-- CatherineJohnson - 28 Jan 2006

I don't know how a DI school got off the ground.

I've never seen anyone 'spark' to the idea......

It took me awhile, and I'm an early adopter plus my kids had been in ABA schools for years, so the concept isn't new to me.

-- CatherineJohnson - 28 Jan 2006

"Doug, you are forgetting that Promise Keepers started in Boulder and the Dobson empire and related are in the Springs. And don't forget the fundies at the Air Force Academy. Plus Highland Ranch and Castle Rock are full of rich Republican fundies."

No, I'm not forgetting about them (and you certainly overstate the case for the Academy, Highlands Ranch, and Castle Rock). And an argument that Boulder is in any way conservative is an argument unloosed from its factual moorings. You might wish to know that I'm sitting in Boulder as I type this (and haved lived here in the past) and I've lived in Colorado Springs.

Colorado Springs has a combination of military (USAFA, Peterson AFB, Falcon AFB, Ft. Carson, Cheyenne Mountain) and religious influences, and is strongly conservative, but in a variety of competing ways. Pueblo (40 minutes down the road) is a union bastion.

I stand by my claim that Colorado trends libertarian. And while I'm not religious, and certainly not a fundamentalist, "fundies" is normally a marker of a very specific (and usually politically motivated) bigotry. You might wish to avoid that term in the future, as it's generally offensive.

"are these areas close to the two DI schools?"

One is in Colorado Springs, near the airport. The other is near none of the mentioned cities.

-- DougSundseth - 28 Jan 2006

Doug you are very correct that I should avoid terms that could be offensive. They were inappropriate, especially on this site.

I'm may be over-sensitive because I've been the object of very painful reverse bigotry from people who are associated with the places mentioned.

-- KtmGuest - 28 Jan 2006

Hello all,

Just a word of caution -- Catherine and I made a decision early on not to admit politics as a topic of conversation on the blog. The reason for this is that we wanted all people of all political stripes to feel comfortable coming here, and getting suggestions about how to teach their children and their students. The 'traditionalist' point of view cuts across political lines (and the phrase traditionalist doesn't even quite cut it, since as I've said many times, procedural knowledge to automaticity is only the beginning of our demands).

Thanks for respecting this unwritten 'rule', y'all.

-- CarolynJohnston - 28 Jan 2006

WebLogForm
Title:	the rigor conundrum
TopicType:	WebLog
SubjectArea:	CognitiveScience, DirectInstruction, EducationResearch, IrvingtonMath, IrvingtonSchools, KumonProgram
LogDate:	200601271136

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