kitchen table math, the sequel: Gilbert Highet on competition

Sunday, March 8, 2009

Gilbert Highet on competition

Amy P pointed me to Gilbert Highet's The Art of Teaching, which has a number of passages on Jesuit education:
The Jesuits, who worked out in the sixteenth and seventeenth centuries one of the most successful educational techniques the Western world has seen, used the spirit of competition very strongly and variously. They treated it not as a method of making the boys learn, but as a way of helping them to learn by bringing out their own hidden energies. As well as pitting the best individual pupils against each other, they used the technique familiar to modern leaders of mass meetings, and balanced groups against groups, half the class against the other half, teams of six against each other, and finally the whole class against another class slightly more or less advanced. They got the best boys to challenge each other to feats of brainwork which would astonish us nowadays. A top-notch pupil would volunteer to repeat a page of poetry after reading it only once; another would offer to repeat two pages. (The Jesuit teachers paid the greatest attention to the development of memory. Even their punishments were often designed to strengthen the memorizing powers, making a late or lazy pupil learn a hundred lines of poetry by heart, and the like.) A group of specially gifted boys would challenge another—always under the smiling, flexible, encouraging, but canny Jesuit supervision—to meet them in debate on a series of important problems, and would spend weeks preparing the logic, the phrases, and the delivery of their speeches. Perhaps the fathers overdid it, although we do not seem to hear of nervous breakdowns among their pupils. Certainly they made more of the spirit of competition than we could possibly do nowadays. Yet that was part of the technique which produced Corneille and Moliere, Descartes and Voltaire, Bourdaloue and Tasso. No bad educational system ever produced geniuses.

It is, then, the teacher’s duty to use the competitive spirit as variously as possible to bring out the energies of his pupils. The simple carrot-and-stick principle does not work, except for donkeys. Really interesting challenges are required to elicit the hidden strengths of really complex mind. They are sometimes difficult to devise. But when established, they are invaluable. It is sad, sometimes, to see a potentially brilliant pupil slouching through his work, sulky and willful, wasting his time and thought on trifles, because he has no real equals in his own class; and it is heartening to see how quickly, when a rival is transferred from another section or enters from another school, the first boy will find a fierce joy in learning and a real purpose in life. In this situation—and in all situations involving keen emulation—the teacher must watch carefully for the time when competition becomes obsessive and the legitimate wish to excel turns into self-torture and hatred. Long before that, the competition must be resolved into a kindlier co-operation.

The Art of Teaching by Gilbert Highet
p. 131-132

This reminds me of something I once read about race horses.


Barry Garelick said...

And in ed school we are told that competition is bad. Posting the five highest test scores on the blackboard (or white board, or SmartBoard) is a no-no. Test scores are kept secret. People who do well, it is thought, can discourage others and result in people not trying. They practice this in ed school. No one knows what anyone else gets on a paper or test. Then again, there are no wrong answers in ed school, so maybe that's moot.

Kinda hard to foster that kind of competition with "portfolios".

xantippe said...

Speaking of educational innovators, I think you should have a look at the book Cheaper by the Dozen. Frank Gilbreth, the efficiency expert father of the family, did very interesting educational work with his children. I'm just watching the old movie version, and he teaches the kids Morse code by having it painted on the inside of the lavatory door. I believe in the book he has riddles and the locations of prizes painted all over the house in Morse code, and eventually the kids were tapping out messages to each other at the dinner table.

xantippe said...

Wow--that is terrible cover art. (For anybody who doesn't know, Amy P and Xantippe are the same person.)

Catherine Johnson said...

Kinda hard to foster that kind of competition with "portfolios".


oh, gosh

my high school has announced that we are now to have differentiated instruction, which means, among many other things, different assessments for different kids in the same class

Catherine Johnson said...

OH I've read Cheaper by the Dozen at least twice -- I read it out loud to C. when he was little.

Catherine Johnson said...

What I like in this passage is the idea that competition is a way of "bringing out energies."

This is a striking difference between a great school and a sloggy, not-great school: the energy level of the kids.

I almost think you may be able to choose a high school on the basis of the kids' posture walking out of the building after school.

(Not sure about that, but I think it's possible.)

Amy P said...

When I taught high school English in Russia, I had several classes of just boys (because it was a group headed toward the Marine Academy in Vladivostok) and it was very noticeable how different they were from the one class I had that was nearly entirely female. The boys were a rough crowd, but competitive games worked like magic.

Amy P said...

"And in ed school we are told that competition is bad. Posting the five highest test scores on the blackboard (or white board, or SmartBoard) is a no-no."

I have an idea--how about extending that approach to high school athletics.

Catherine Johnson said...

I have an idea--how about extending that approach to high school athletics.

Been there, done that!

“Sports to me is not about winning or losing, it’s about giving kids opportunities to exercise and expand their development in all ways.”

That's our athletic director, quoted in the local newspaper.

Anonymous said...

It might be that this is a chemical phenomenon. I read a study (probably linked from here) that people learn better when physically active. Researchers hypothesis that this is a holdover from our days as predator and prey. They've discovered chemicals that get released during action that heighten learning. Kind of like the brain's answer to adrenalin for the muscles.

It makes a lot of sense, doesn't it? You'd definitely want to be at your all around best if something was lusting after you for (their) lunch!

SteveH said...

"my high school has announced that we are now to have differentiated instruction, which means, among many other things, different assessments for different kids in the same class"

Is this for honors or AP classes? Do they give any examples of how this works? Are they reverting to rubrics, or can someone get an 'A' doing easier work?

Perhaps you can get away with this in K-6, but beyond that, I'm sure that students will not put up with a "differentiated" grading scheme. In my son's middle school, the honor roll is all about an effort rubric, and the academic grade (rubric) is hidden away in the report card. However, kids know who got what on the tests. They aren't fooling anyone.

Speaking of differentiation, what happens when you use a rubric that talks about exceeding expectations. As you improve your work, the expectation increases, making it harder to get the same ranking. I could come up with a "differential" equation that described this effect. This also defines our rubric system.

What the teachers do is compress the grades. Those at the low end are given encouraging rubric grades, and those at the upper end have to work their asses off to just get a grade of 4 out of 5. Actually, they added the 5 (really an A+) a few years ago because many students didn't want to do the work to get a 4. The '5' grade allowed the teachers to uncompress the grading and offer more 4's. They realized that many students would still try to get the 5.

Rubrics allow teachers much more flexibility with judgment-based grading. It's easier to manipulate students.

It's more difficult to do this in math, but last year, I tried to calibrate the rubric with percent correct scores on tests. A 5 was a grade above 95%. A 4 was a grade above about 87%, and a 3 started ataround 75%. Definitely non-linear.

Low end students don't flunk out and there is room at the top to put the screws to the best students. The work is not differentiated. The grading is.

Anonymous said...

I remember an elementary-school field day, with the whole school divided into two teams, grade by grade. The PE teacher tried to balance the teams and I have no problem with that. However, each event was graded individually and students could enter all they wanted - soccer dribble for accuracy and time, baseball throw for distance, timed push-ups, sit-ups etc. - a wide variety. Individual awards were also given, but no kid could have more than one, no matter how many events he REALLY won. As if all of the kids didn't know. One of the very few elite athletes in the school won more than 10 events - one ribbon. The next year they had no individual awards.

Even worse, I know of a new high-school(~1500 kids) principal who told all of the coaches that there would be no cuts. Since state or county rules prohibited seniors on JV teams, there were seniors on the varsity who had never been able to make the JV. Of course, they didn't play and the situation was often pretty ugly. I'm not sure that policy lasted beyond the fall season; I suspect there was a coaches' revolt.

Anonymous said...


That grade spread sounds perfect. 95+ gets distinction. 87 to 95 get mastery. 75-87 get competence. One could extrapolate that 67-75 get some sort of basic rating and <65 fails.

What is the issue with non linear grading?


SteveH said...

"That grade spread sounds perfect."

Perfect for what?

" ...87 to 95 get mastery."

Mastery is 87 to 95?

"...75-87 get competence..."

Competence is non-mastery? Actually, this a about a '3' on our rubric scale.

"One could extrapolate that 67-75 get some sort of basic rating ...

This is a '2'. Our school likes to think of this as a 'C', but everyone knows it's worse than that.

"... and <65 fails."

With full-inclusion at our schools, almost nobody fails.

So, few get a 2 and few get a 5. The grades are compressed into 3's and 4's.

Grades are supposed to provide feedback to students and parents. A non-linear rubric that depends on teacher judgment does not provide that feedback. In math, those are ranges I determined, not the school. The school pretty much leaves the breakdown to the teacher.

Although rubrics break into many different sections, there is a real loss of information. As a parent, I want to see the raw percent correct on the test or homework, not some subjective rubric number. I want to see the work and see the teacher's comments. If there is a judgment to be made, I want it made on a problem by problem basis, not on a full test or assignment basis. I also want to see it in a timely fashion and not kept hidden at school in a portfolio. Then, when it comes to determining a final rubric grade, the process of averaging the numbers is magic. How do you average rubric numbers that are non-linear?

The goal of rubrics and non-linear grading is to make it seem like all kids in a full-inclusion environment are fairly equal. Actually, we also have a separate 6 - 10 rubric scale for effort. This is what's used for the 3 (!) levels of honor roll. Few people in town know that the honor roll is not based on tests.

Instead of a resolution of 10+ (linear) letter grades (A+ down to D or lower), we have 2, 3, 4, and 5 rubric grades with some vague non-linear correlation to the raw % correct score.

VickyS said...

I just returned from our high school math league state tournament. After a grueling 3 month season, only a handful of the 170 member schools made it that far.

Competition. Excellence. High spirits, perserverence and fun.

It was all there and no less exciting than a sports event (to me, at least, and definitely to the kids).

The scores were posted for all to see. If your rival scored higher, the vow was to beat them next year. No hard feelings, plenty of handshaking & backslapping, and a determination to do better.

Gosh...isn't that how they do it in the football games? Imagine if the score wasn't displayed, so as to not hurt someone's feelngs!

SteveH said...

"Competition. Excellence. High spirits, perserverence and fun."

Is this a national contest? Our middle school wanted me to start an after-school group for MathCounts. It looked good, but I didn't have the time. I was already committed to helping the Science Olympiad group. This is for a school that is defined by full-inclusion. All I can say is that by 7th grade, reality, common sense, and parent pressure starts to seep in.

Many see no problem with competition in sports, but get all funny when it comes to academics. They think that some psychic damage will take place. Apparently, things like team work, effort, and passion don't apply to academics. I never wanted to compete in math, but I distinctly remember at the end of 8th grade, when others got awards, that I was going to show them in high school. Perhaps not the best of motivations, but I became a better student.

This is also true for mastery of the basics. Nobody gives it a second thought for sports or music, but when it comes to academics, it's drill and kill. There must be some sort of magical and delicate process that's going on.

vlorbik said...

anybody seen _the_hobart_shakespeareans_?
that guy is amazing. ordinarily language
like "a culture of excellence" has me running
for the exit so everybody won't have to watch
me throwing up all over the management hoo-hah.
but this SOB has the true faith and knows how
to pass it forward (a life of selfless dedication
to the art of teaching, alas... no royal road...).

VickyS said...

Steve, this is a purely Minnesota senior high school league. Here is the newspaper story about yesterday's event, and here is the Minnesota State High School Mathematics League website. We're pretty lucky to have this opportunity. 173 schools, 3500 kids. The trophies brought home by our little school really meant something and were proudly displayed in the school's front office this morning, giving the kids the recognition they earned and deserved for their preparation and hard work.

MathCounts for grades 6-8 is available for the younger kids and like Steve I tried to start up a MathCounts program at my younger child's middle school earlier this year. There was never enough interest (not one kid besides my own agreed to be on the team) and the school let the kids work on the qualifying test IN GROUPS so I had no idea as to who the top math students were anyway...well that was just sort of the last straw for me.

Not every athlete, musician or academic kid wants to compete...but some do, and math competitions are really a lot of fun for those who do. The scores are an integral part of the competition (obviously) and you win by (simply) getting the most points. What a concept! Hey it reminds me of the swimmer who wins the event by touching the wall first! We don't judge them on their swim suit style or their pretty strokes. And I repeat--those who didn't score as well as they hoped or who made "dumb" mistakes were simply driven to do better next time...shouldn't we as a society consider that a positive? When our basketball team met a rival for the third time this season, having lost twice already, they were supercharged, motivated, focused...and they won by two points. It brought out the best in them. Why not in math?

Btw the math tournament included a 10 question math bowl with the top 10 students in front of an audience. Everyone had fun trying to solve the questions during the alloted time. I got two. The kids on the stage got almost all of them...those kids are good!

SteveH said...

Thanks Vicky!

I may try to get the MathCounts going next year. The problem is that few students feel confident in math. Why do something that feels like torture? At least there are some fun tasks to do in the Science Olympiad.

You would think that six years of Everyday Math would turn them all into confident problem solvers itching to show their stuff. Ha!

Catherine Johnson said...

V - thanks for the link -- I'd never even heard of this movie!

I'm a sucker for this stuff.

I wept when I watched Stand and Deliver again a few years ago.

C. said, "Why are you crying?"

Catherine Johnson said...

Speaking of Jaime Escalante -- here are his students today:

Jaime Escalante Students: Where Are They Now?