kitchen table math, the sequel: the middle 95%

Friday, August 1, 2008

the middle 95%

While we're on the subject of college-for-all.... I found all kinds of interesting books while trawling Amazon today:

“After forty years of intensive research on school learning in the United States as well as abroad, my major conclusion is: What any person in the world can learn, almost all persons can learn if provided with appropriate prior and current conditions of learning. This generalization does not appear to apply to the 2% or 3% of individuals who have severe emotional and physical difficulties that impair their learning. At the other extreme there are about 1% or 2% of individuals who appear to learn in such unusually capable ways that they may be exceptions to the theory. At this stage of the research it applies most clearly to the middle 95% of a school population.

The middle 95% of school students become very similar in terms of their measured achievement, learning ability, rate of learning, and motivation for further learning when provided with favorable learning conditions. One example of such favorable learning conditions is mastery learning where the students are helped to master each learning unit before proceeding to a more advanced learning task. In general, the average student taught under mastery-learning procedures achieves at a level above 85% of students taught under conventional instructional conditions. An even more extreme result has been obtained when tutoring was used as the primary method of instruction. Under tutoring, the average student performs better than 98% of students taught by conventional group instruction, even though both groups of students performed at similar levels in terms of relevant aptitude and achievement before the instruction began.

The central thesis of Human Characteristics and School Learning (Bloom, 1976) is the potential equality of most human beings for school learning. We believe that the same thesis is likely to apply to all learning, whether in schools or outside of schools. At least, it leads us to speculate that there must be an enormous potential pool of talent available in the United States. It is likely that some combinations of the home, the teachers, the schools, and the society may in large part determine what portions of this potential pool of talent become developed. It is also likely that these same forces ma, in part, be responsible for much of the great wastage of human potentiality.

Developing Talent in Young People
by Benjamin Bloom
pp. 4-5

Just to mix things up a bit!

And see: how to build a fast learner.

5 comments:

ElizabethB said...

Tutoring is a very effective way of teaching.

I sometimes call myself a "homeschool tutor" instead of a teacher or some other term, I think it more aptly describes what I'm doing.

Clickers should work like masterly learning, making a large classroom more like tutoring.

I think a one-room school could be set up for effective tutoring as well. Once you trained students to learn at a certain noise level, you could have periods of the day where productive tutoring occurred with older students teaching the younger ones and the teacher monitoring the situation.

I also think of all those people in assisted living and/or nursing homes that are there for physical reasons and wonder if there shouldn't be more efforts to employ them as tutors. I also read somewhere that having an older person just sitting in class decreased poor behavior, they could be productive by just being there! (I think that there is also a "wastage of human potentiality" for many of the elderly in our culture today.)

A 94 year old woman that I met in a nursing home used to teach in a one-room school, she had a broken hip and no family, she's a perfect candidate to be taken to a school to help out. Her mind was still sharp.

SteveH said...

When schools are caught up with statistics and small, relative changes, they cannot possibly see or understand fundamental or absolute problems. Our schools had a big meeting a few years ago to develop a 5+ year strategic plan for our schools. I was supposed to be on the panel until I found out that no questions about basic assumptions were on the table. They hired a facilitator to make sure of that.

It's all about relative, not absolute.

Linda Seebach said...

Bloom says:

"The middle 95% of school students become very similar in terms of their measured achievement, learning ability, rate of learning, and motivation for further learning when provided with favorable learning conditions."

On the contrary. Given favorable learning conditions, that is, adequate and appropriate instruction that allows each individual child to learn at close to his or her own natural rate of learning, the gap in measured achievement between smart children and less smart children will grow with each passing year. (Higher slopes for brighter kids.)

Zig Engelmann has a section on this in his book.

Catherine Johnson said...

I think Linda's right about this (though I haven't checked the passage).

The Mastery Learning book I quoted in the older post says (and I believe Engelmann found the same thing) that once students have reached a certain level of mastery or familiarity with the field the difference created by IQ "almost" disappears, or narrows significantly (words to that effect).

"Almost" isn't "all the way." Not by a long shot.

My understanding of the situation is that you can very significantly accelerate the learning of slow students; my opinion on this is that accelerating the learning of slow & slower students absolutely MUST be the goal (which is why I oppose inclusive settings & differentiated instruction as these concepts are currently implemented --- you're not just slowing down the fast kids, you're slowing down the slow kids).

If everyone is learning at full speed, the gap should grow larger, not smaller.

Catherine Johnson said...

I feel I have personal expertise in gaps & the closing of gaps.

Back when Jimmy was little, and we still had hope he would prove to be high-functioning, I saw over and over again how impossible it is to catch up.

I used to complain (partly as a joke) that every time I got him even close to the other kids his age they ruined all my hard work by roaring ahead.

My experience trying to close the gap C. had in math has been very interesting in light of all this.

C. had the ability to learn algebra in 8th grade. Easily. (I know that now from the two standardized tests he's had over the past two years, and from the fact that his new school has placed him in Honors Algebra 2 -- they have a regular Algebra 2 as well.)

But in 3rd grade he was placed in the regular algebra-in-9th grade track AND had a very ineffective teacher in 4th grade math. (I always need to add this: she was a lovely person, just not an effective math teacher, and she wasn't given tenure.)

So: when I began writing ktm, C was not only behind his peers in Europe and Asia, he was behind his accelerated peers here --- and he may have been behind his non-accelerated peers, too, because by the end of the school year he had failed 2 of 5 unit tests.

My job was to close that gap.

Well....number one: closing a gap is hard as he**.

The two of us working together definitely closed whatever gap there was between C and his regular-tracked peers; he closed the gap and raced ahead.

Did we close the gap between him and his accelerated peers?

I think the answer to that is that we probably managed to close, or at least very substantially narrow, the gap between him and all but the top 10 students in the track (10 out of around 45 students).

He's nowhere near his peers in Europe and Asia.

This took HUGE amounts of effort. Huge. Extra work during each school year, extra work every summer.