'An Appalling Report'

[karlhenning]

It is a classic example of life not being fair.

As with most any Eric thread: Follow the Whinge.

Hardly any of us expects life to be completely fair; but for Eric, it's personal.

[Homo Aestheticus]

Karl,

As with most any Eric thread: Follow the Whinge.

Hardly any of us expects life to be completely fair; but for Eric, it's personal.

Those were Murray´s words (page 30), not mine.

[adamdavid80]

Hardly any of us expects life to be completely fair; but for Eric, it's personal.

Hellllllllooo, new siggie...  

[karlhenning]

Hellllllllooo, new siggie...  

(* chortle *)

[lisa needs braces]

The whole "below average" thing is blatant nonsense. It doesn't follow that a child who is below "average" in innate mathematical ability should never learn the type of algebra and geometry one comes across in high school, unless the child is severely handicapped. Just because something doesn't come easy to someone doesn't mean learning it is an insurmountable task. It's as if Eric wants other people to be identified as congenitally stupid just so he doesn't feel alone (he has essentially said as much upthread.)

[Florestan]

It doesn't follow that a child who is below "average" in innate mathematical ability should never learn the type of algebra and geometry one comes across in high school, unless the child is severely handicapped. Just because something doesn't come easy to someone doesn't mean learning it is an insurmountable task.

That's correct, in principle. If I understand Eric (or is it rather Murray?) correctly, though, he makes the point that, of all children "below average" in innate mathematical ability, few have the interest of learning high-school algebra, geometry or calculus, and the time they spend  struggling compulsory with them is lost for other subjects, presumably more suitable and interesting for them.

[karlhenning]

That's correct, in principle. If I understand Eric (or is it rather Murray?) correctly, though, he makes the point that, of all children "below average" in innate mathematical ability, few have the interest of learning high-school algebra, geometry or calculus, and the time they spend  struggling compulsory with them is lost for other subjects, presumably more suitable and interesting for them.

I think there's a balance.  I had no interest in (or subsequent use for) calculus.  But then again, I was not compelled to study calculus.  I had modest interest in geometry;  and I don't know how I can judge, at this point, "interest" in algebra (on the principle of, when I was in high school, I had no interest in Debussy;  how could I have, when I was almost completely unaware of him?).  I did study geometry and algebra in high school, to fulfill my math component;  and I found them both engaging.

I think it fairly obvious that there is value for the individual in being 'compelled' to learn more than he quite has an 'interest' in.  But then, I also think it obvious that a parent feeds a child more kinds of food than the child 'feels like' eating.  I don't think that the individual is being tyrannized in either case, just by virtue of considerations broader than his personal, momentary 'interest'.

And, in my own public school experience, again, I enjoyed both modes:  pursuing subjects which engaged me profoundly, and acquisition of the discipline of learning subjects 'in the abstract', apart from whether it was quite something I 'felt like' learning.  The latter, too (meseems), is a whetstone to sharpen the mind.

[Florestan]

I had no interest in (or subsequent use for) calculus.  But then again, I was not compelled to study calculus. 

Is calculus not required in US high-schools? Here in Romania it is studied  9th through 12th grade.

when I was in high school, I had no interest in Debussy;  how could I have, when I was almost completely unaware of him?). 

That's a very good point.

I think it fairly obvious that there is value for the individual in being 'compelled' to learn more than he quite has an 'interest' in.  But then, I also think it obvious that a parent feeds a child more kinds of food than the child 'feels like' eating.  I don't think that the individual is being tyrannized in either case, just by virtue of considerations broader than his personal, momentary 'interest'.

Agreed.

What I think is, though, that by the time of high-school graduation, a man knows, broady speaking, what his interests and abilities are, so he can choose what kind of education (if any) he'd like to pursue further.

[karlhenning]

Is calculus not required in US high-schools? Here in Romania it is studied  9th through 12th grade.

Argh! That would be hell.

In the US, the responsibility for public school curricula is largely local;  calculus was not required in my high school, at the time I attended (for all I know, it may be different now).  I remember that graduation requirements varied even for friends of mine in nearby towns.  There is a lot that is 'standard', I just don't know that much of that is specifically 'managed' from the Federal level.  To an extent, there's a free market ambience to education, too;  and some Fed attempts to regulate or 'improve' educate across-the-board have been more controversial than effective ("no child left behind," anyone?)

Interestingly, the very college system against which the OP rages is one of the 'free-market' forces for standardization.  Most colleges require that applicants have taken a test such as the SAT (Scholastic Aptitude Test), which has an English and a math component.  It was decades ago, and I may be misremembering, but what was strange in my case was that while by inclination I am more a language person than a numbers guy, I scored higher in the math component than in the English (though I did well in both, and had a strong score).

What I think is, though, that by the time of high-school graduation, a man knows, broady speaking, what his interests and abilities are, so he can choose what kind of education (if any) he'd like to pursue further.

Aye.

[Florestan]

Argh! That would be hell.

Well, I mistyped 9th for 11th, but even so, it is hell. I remeber scoring so bad in calculus in my 12th grade, that I began to fear I would never pass the admission test for college. (Eventually, I did pass it all right.)

To an extent, there's a free market ambience to education, too;  and some Fed attempts to regulate or 'improve' educate across-the-board have been more controversial than effective

Speaking of which, is it possible for someone to choose freely his elementary, secondary or high school, or are the choices limited to the area in which one lives?

[karlhenning]

In general, there's always some degree of choice.  In most places, anyway.

[karlhenning]

Well, I mistyped 9th for 11th, but even so, it is hell. I remeber scoring so bad in calculus in my 12th grade, that I began to fear I would never pass the admission test for college. (Eventually, I did pass it all right.)

I remember a passel of friends who had 'the math talent' in my class, and they always sounded like the calculus class was putting them through the wringer.  It was their choice, though (as I say, I didn't have to do it).  My old mate John made it pretty easily into MIT, so he did enjoy the fruit of all that labor.

[Florestan]

In general, there's always some degree of choice.  In most places, anyway.

I ask this question because recently, in two Romanian cities, the choice has been curtailed. Someone living in neigbourhhod A cannot got to a school in neighbourhood B. The rationale behind it was that schools downtown had too many pupils, while schools at the periphery were all but closed from lacking pupils.

I strongly disagree with this measure. In Romania, downtown schools are full of pupils because of their teachers' quality, while peripheral schools are not an option because they lack that quality. Forcing children to attend bad schools just for the sake of rescueing those schools from perish is plain stupid. Besides, this measure is going to discriminate against poor people, who generally live in cheap, peripheral neighbourhoods and whose children will attend disfunctional schools, while the children of rich people, who can afford living in expensive downtown quarters, will continue going to the best schools.

Whoever took the abovementioned decision has big problems with logic and common-sense.

[Homo Aestheticus]

That's correct, in principle. Though he makes the point that, of all children "below average" in innate mathematical ability, few have the interest of learning high-school algebra, geometry or calculus, and the time they spend  struggling compulsory with them is lost for other subjects, presumably more suitable and interesting for them.

That´s exactly right, Andrei.

Murray makes this point in Chapter 3:
_____________

Before you conclude that the schools just didn't do a good enough job of presenting the material, talk to elementary and middle school teachers about their experiences trying to teach children who are well below average in logical-mathematical ability. Yes, given time, you may be able to get such a child to understand percentages, right angles, cubes and decimal notation but a few days later you have to explain it anew, and a few days after the same thing; the understanding is lost again. The concept of a right angle will not stick. Similarly, the concept of decimal notation may be grasped for the duration of the tutoring, but it does not stick. A few days later, given a fresh exercise using decimal notation, the student will miss every question because the concept of decimal notation is beyond the capacity of that child  to absorb and retain.

Could such a child absorb and retain the concept of decimal notation if the teacher is given unlimited time and resources ? Sometimes yes, sometimes no, but the investment of time must be so large that it cannot possibly be generalized to the whole curriculum.

Limits on logical-mathematical ability translate into limits on how much math a large number of children can learn no matter what the school system does.

[Homo Aestheticus]

Abe,

It's as if Eric wants other people to be identified as congenitally stupid just so he doesn't feel alone (he has essentially said as much upthread.)

Not at all... I simply want to better understand why ´educational romanticism´ pervades the American school system.

The whole "below average" thing is blatant nonsense. It doesn't follow that a child who is below "average" in innate mathematical ability should never learn the type of algebra and geometry one comes across in high school, unless the child is severely handicapped.

Just because something doesn't come easy to someone doesn't mean learning it is an insurmountable task.

Murray addresses this in more detail in Chapter 2:

The first task is to understand what below average means when it comes to academic ability. The best way is to show the kinds of test questions that people with below average mathematical ability have trouble answering. I take them from items that have been used on the National Assessment of Educational Progress (NAEP). It is administered periodically to nationally representative samples of students in the fourth, eighth and twelfth grades. It is a test designed to test what has been learned, not academic ability, and is regarded as the gold standard for measuring academic achievement at the elementary and secondary levels. The examples I will use are from the test for eighth graders. I begin with a simple mathematics problem:

Example 1. There were 90 employees in a company last year. This year the number of employees increased by 10 percent. How many employees are in the company this year ?

(A) 9 (B) 81 (C) 91 (D) 99 (E) 100

By eight grade, it would seem that almost everyone should be able to handle a question like this. Children are taught to divide and to calculate percentages in elementary school. Dividing by ten is the easiest form of division. Dividing a whole number by ten is easier yet. Adding a one-digit number (9) to a two-digit number (90) is elementary. It is a problem based on a simple mathematical concept, using simple arithmetic, requiring a simple logical interpolation to get the right answer. It is an excellent example for starting to think about what below average means in mathematics -- because 62 percent of eight graders got this item wrong. It does not represent an item that below-average students could not do, but one that many above-avergae students could not do. Actually, more than 62 percent did not know the answer, because some of them got the right answer by guessing.

Example 2. Amanda wants to paint each face of a cube a different color. How many colors will she need ?

(A) Three (B) Four (C) Six (D) Eight

Twenty percent of eight graders did not choose C. Approximately 27 percent did not know the right answer.

Example 3. How many of the angles in the triangle next to letter e (bottom left) are smaller than a right angle ?



(A) None (B) One (C) Two (D) Three

Thirty-one percent of eighth graders did not choose C. Approximately 41 percent did not know the right answer.

Example 4.  What is 4 hunderdths written in decimal notation ?

(A) 0.004 (B) 0.04 (C) 0.400 (D) 4.00 (E) 400.0

Thirty-two percent of eight graders did not choose B. Approximately 40 percent did not know the right answer.
_________

The schools are the usual scapegoats for results like these. But how much can they be blamed that three-quarters of eighth graders did not know the answer to the question about percentages ? Ask those same children what 10 percent of 90 is, and you will find that many if not most of them learned enough multiplication and percentages to give you the answer. Ask them what 90 plus 9 is, and you will find that almost all of them can add those numbers. What they failed to do was  put everything together -- to realize that first they had to take 10 percent of 90, and then add the result to 90. This logical step does not lend itself to being taught in the same way that the rules for addition and multiplication can be taught. A teacher can explain the logical step for this particular example. That's why teaching to the test can work: If teachers know that the state competency test will include one item of this particular type, they can drill the students and raise the proportion that answer it correctly. But if the test uses a new context and puts a different twist on the problem (for example, asking students to calculate a percentage reduction instead of a percentage increase), it is up to the students to  generalize their knowledge, and that calls upon logical-mathematical ability.

It is even harder to blame the schools for mistakes in the other three math examples about cubes, right angles and decimal notation. All eight graders have encountered cubes, right angles, and decimal notation in the classroom before eight grade. Before you conclude that the schools just didn't do a good enough job of presenting the material, talk to elementary and middle school teachers about their experiences trying to teach children who are well below average in logical-mathematical ability. Yes, given time, you may be able to get such a child to understand percentages, right angles, cubes and decimal notation but a few days later you have to explain it anew, and a few days after the same thing; the understanding is lost again. The concept of a right angle will not stick. Similarly, the concept of decimal notation may be grasped for the duration of the tutoring, but it does not stick. A few days later, given a fresh exercise using decimal notation, the student will miss every question because the concept of decimal notation is beyond the capacity of that child  to absorb and retain.

Could such a child absorb and retain the concept of decimal notation if the teacher is given unlimited time and resources ? Sometimes yes, sometimes no, but the investment of time must be so large that it cannot possibly be generalized to the whole curriculum. Limits on logical-mathematical ability translate into limite on how much math a large number of children can learn no matter what the school system does.

[Homo Aestheticus]

Karl,

I think there's a balance.  I had no interest in (or subsequent use for) calculus.  But then again, I was not compelled to study calculus.  I had modest interest in geometry;  and I don't know how I can judge, at this point, "interest" in algebra (on the principle of, when I was in high school, I had no interest in Debussy;  how could I have, when I was almost completely unaware of him?).

I´m not sure that aesthetic experiences and scholastic work is a valid comparison.

I did study geometry and algebra in high school, to fulfill my math component;  and I found them both engaging.

Same here, but I found those subjects extremely difficult. It would have been impossible for me to pass those courses without the MAJOR HELP of private tutors, three hour sessions, twice weekly.

I think it fairly obvious that there is value for the individual in being 'compelled' to learn more than he quite has an 'interest' in.  But then, I also think it obvious that a parent feeds a child more kinds of food than the child 'feels like' eating.  I don't think that the individual is being tyrannized in either case, just by virtue of considerations broader than his personal, momentary 'interest'.

And, in my own public school experience, again, I enjoyed both modes:  pursuing subjects which engaged me profoundly, and acquisition of the discipline of learning subjects 'in the abstract', apart from whether it was quite something I 'felt like' learning.  The latter, too (meseems), is a whetstone to sharpen the mind.

But Murray makes a very important point here and I don´t see how anyone can disagree with him on this:

"It is a good thing for parents and teachers to encourage children to try hard. It is a good thing to teach children that they should not give up easily. It is better to push a child farther than he can go (occasionally) than not to push at all. But one of the responsibilities of parents and teachers is to  appraise  the abilities that a child brings to a task. One of the most irresponsible trends in modern education has been the reduction in rigorous, systematic assessment of the abilities of all the students in their care. To demand that students meet standards that have been set without regard to their academic ability is wrong and cruel to the children who are unable to meet those standards..."   

[karlhenning]

I´m not sure that aesthetic experiences and scholastic work is a valid comparison.

Your thinking's gone woolly there, Eric. That statement is not a "comparison of aesthetic experience and scholastic work."  It's a simple observation that much that is worthwhile studying, is outside one's awareness;  and that education is partly a process of extending the individual's field of awareness.

I think it fairly obvious that there is value for the individual in being 'compelled' to learn more than he quite has an 'interest' in.  But then, I also think it obvious that a parent feeds a child more kinds of food than the child 'feels like' eating.  I don't think that the individual is being tyrannized in either case, just by virtue of considerations broader than his personal, momentary 'interest'.

And, in my own public school experience, again, I enjoyed both modes:  pursuing subjects which engaged me profoundly, and acquisition of the discipline of learning subjects 'in the abstract', apart from whether it was quite something I 'felt like' learning.  The latter, too (meseems), is a whetstone to sharpen the mind.

But Murray makes a very important point here and I don´t see how anyone can disagree with him on this:

"It is a good thing for parents and teachers to encourage children to try hard. It is a good thing to teach children that they should not give up easily. It is better to push a child farther than he can go (occasionally) than not to push at all. But one of the responsibilities of parents and teachers is to  appraise  the abilities that a child brings to a task. One of the most irresponsible trends in modern education has been the reduction in rigorous, systematic assessment of the abilities of all the students in their care. To demand that students meet standards that have been set without regard to their academic ability is wrong and cruel to the children who are unable to meet those standards..."

First of all, Murray essentially agrees with me in the first two sentences there, although he reserves a complaint with the parenthetical "occasionally."

Second, he adds (what I did not trouble to) that a teacher appraises the child's abilities in the task.  This is something I did not bother to spell out, as fairly obvious.  And again, in no classroom in which I took part, was any pupil 'tyrannized'.  Nothing in the school curriculum made "wrong and cruel" demands (what a fondness for whingely quotes you have in this thread, Eric!) of any of my schoolmates;  not a single one.

Third, as to the 'demand' sentence closing your quote (which I must imagine is what you feel is the "very important point") you appear to want to take this one assertion as somehow 'damning' the whole system, Eric;  but so far as I can tell (again, going back to my own school experience) the school made accomodation for those students whose abilities did not match the (not in the least 'wrong' or 'cruel') demands of the standard curriculum, in Special Ed sections.

Far from a "very important point," Murray's statement does not (from the only experiemnce with which I can judge) have much purchase on reality.

[karlhenning]

[ A tangent. ]

[Florestan]

[ A tangent. ]

And you just have to love a book — O.K., I just have to love a book — that declares that while faculty must "respect students as persons," they are under no obligation to respect the "ideas held by students." Way to go!

A very strange assertion for an intellectual, to say that ideas held by someone else than you or your peers are not worth respecting.

Does this apply the other way around as well?

[karlhenning]

A very strange assertion for an intellectual, to say that ideas held by someone else than you or your peers are not worth respecting.

If we change "are not" to the modal "may not be," is your objection answered, Andrei? 

I think the idea is that challenging someone's ideas is not offering injury to his person.