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Larry's Take on Maths Education in the USA
The Elephant in the Room
Suppose that you are serving on a committee of some kind. Your group sits at a table in the middle of a very large, sparsely furnished room. You're a few minutes late for the meeting. Immediately after walking in, you see a real live elephant quietly standing in a far corner. What to do?
It's remotely possible that nobody else has noticed the elephant. If you mention it, the chairperson may announce a recess, call Animal Control, and then call the local zoo to see if any of their resident pachyderms are missing.
However it's much more likely that everyone else has seen the elephant, and that they are not the least bit concerned about it. Although the presence of the elephant may be more important than any small decisions the committee makes on that particular day, your most likely course of action would be to keep a stiff upper lip, and to remain silent about the elephant, as long as she is just standing there, not doing anything.
The failure of maths and physical science education is the elephant in the room for the teaching profession in the USA. How so?
A secondary effect of maths education here is to prepare gifted students for university-level courses in engineering, and in the physical sciences. However the primary effect is to make most students feel stupid. Essentially everyone is aware of that fact. Although some educators may speak in general terms about the need to promote self-esteem in their charges, few are willing to come to grips with the underlying issue. Why not? Educators are under enormous pressure that comes from multiple directions.
Abandoning maths education is not an option
We need to teach future engineers and physical scientists. At the moment, we are the beneficiaries of a Brain Drain. Asian scientists are all too happy to fill well-paying job vacancies, for which there are too few qualified American applicants.
When I was studying analytical chemistry in graduate school, one of the required courses was electrochemistry. I remember that the professor and I were the only American citizens in the classroom. There was one guy from Brazil. Everyone else was from China!
But in the near future, the rapidly developing Asian countries may shut off their Brain Drain valves. If and when that happens, the USA will be in a real pickle without homegrown maths and physical science education.
Classrooms are becoming Zoos
Some maths and physical science teachers spend 80% of their time riding herd on the 20% of students who have no interest in learning, and who create disturbances that spoil the learning atmosphere for everyone else. In conventional public schools, it would be impolitic to shunt off the Neanderthals to a warehouse classroom, where they could spend their days watching videos about American history, drivers' ed, etc.
The typical parental attitude is: What, my little Johnny? You must be mistaken.
One of my hiking acquaintances from several years ago is a high school teacher, who has a degree in physics. When he first started teaching in the early 1960's, all of his students had a "Yes Sir" attitude. But by the 1990s, he was very happy to have a teacher's aide, whose main job was to document each disruption. When the aide had accumulated sufficient evidence, 'Jack' would 'strongly encourage' the yahoos to transfer into non-physics courses. Then 'Jack' would have a belated start in teaching a normal physics course for the remainder of the term.
Self-esteem and the Talking Paradox
History teachers need to do a lot of talking. History students remember more when they hear the details from their teachers, and then read the same things in their textbooks, because two different senses are involved in the learning process. Maths and physical science education is a different ball of wax.
The almost universal fault of educators in these disciplines is that they talk too much. A certain amount of talking is necessary, and a talking optimum exists. Increasing the talking beyond that optimum will result in decreased learning.
I once observed a junior high school school maths class. When the teacher wasn't struggling to prevent the class from boiling over into total chaos, she spent her time trying to 'teach' the concepts of "greater than" and "less than." Judging by the blank stares, I inferred that very few profited from that day's lesson.
What gives? "Greater than" and "less than" are ordinary English expressions. Nobody needs to be 'taught' these things.
Her students sensed that something was wrong, and jumped to the conclusion that the concepts were more difficult than they thought. The lesson that was originally intended to be educational mutated into Stupidification.
There's another wrinkle on the Talking Paradox. Most elementary school teachers have Mathophobia. When presenting maths lessons to their classes, they communicate their attitudes without intending to do so. The students pick up on the body language and vocal inflections. Because they have minimal conscious awareness of what's going on, they can't fight against it.
The Talking Paradox is more pernicious for girls than for boys. Girls tend to have better communications skills than boys. And in maths classes, they internalize the insidious subliminal message more readily than boys do.
For the majority of American students in elementary schools and middle schools, 21st Century maths education is DUBAR (dumbed down beyond all recognition). Nevertheless the insidious effect on self-esteem is at least as great as in 'old school' maths education, before New Math was invented in the early 1960s. That's because of the Talking Paradox.
Self-esteem and Maths Tutoring
If you're a maths tutor, you can instill self-esteem in your student. Here's how. Organize the big problem into manageable steps. For each step, ask a question. If you've asked the right question in the right way, the student will struggle with it for a few seconds or a few minutes, and then figure out the answer himself. He'll feel good about himself, because:
A. He was successful.
B. The question was not a trivial one.
Guided self-discovery can be a power self-esteem booster. Some caveats. You need to understand where your student is coming from, intellectually. Although the question that you just asked was appropriate for the individual student whom you are tutoring, it would probably be too difficult for some other students, and two easy for others. For this reason, the questioning technique is less efficacious in a classroom of students with different learning styles, and with different ability levels, than with an individual student.
You've struck a reasonable balance between talking and listening. It's possible to achieve a communication balance in the classroom too. Simple example: Have your students work out some of last night's homework problems on the blackboard.
Creative Administrative Alternatives
Magnet Schools and Charter Schools are two fairly well-known venues for students who are serious about learning. The Bronx High School of Science is arguably the best-known example of the former.
As the Charter Schools link points out, there are a few public Montessori Schools in the USA. The Montessori approach to maths education is to emphasize hands-on learning. There's also an outstanding Montessori spin-off, called Mortensen Math. In terms of maths, Montessori kids are typically two years ahead of their counterparts in conventional public schools.
We don't hear very much about this, but there's another alternative in the Sacramento area: Fundamental Schools. A Fundamental School is similar to a Magnet School, but with a broader base. The 'magnet' for a Fundamental School is simply an environment that's conducive to learning. Parents and students sign contracts, agreeing to regular attendance, to doing one's homework, and to being well-behaved.
If some particular student does not live up to the agreement, he is automatically transferred to a rowdier conventional school.
Here's a LINK to the web page for Arcade Fundamental Middle School, in Sacramento County. It includes clickable short articles about The Fundamental School Concept.
If the parents in a community truly value learning environments in their children's schools, they can make it so, without spending big bucks on private school tuition.
What About Educational Innovation?
No Child Left Behind is bureaucratic approach to education reform that's worse than doing nothing. Too many teachers are under pressure to teach for the test, rather than being educators. Here's a LINK to an article by Greg Palast, who tells you everything that you're not supposed to know about NCLB. That is a disturbing example of what's going on in the name of educational 'reform'.
To a large extent, maths education at the elementary and secondary levels stopped being child-oriented a long time ago. From the perspectives of most administrators and textbook authors, it's mostly about egos, money, and power. My slightly jaded opinion is that we won't get meaningful educational reform--especially in maths and the physical sciences--until we really hit bottom.
How can the teaching profession get it so wrong? Dietrich Dörner's book, The Logic of Failure, looks at the general phenomenon of disastrous decisions made by educated people who should know better. The tacit assumption is that there are no hidden agendas at play. Dörner's book does not mention maths education.
In contrast, one of the best approaches to maths and physical science education comes from the old Soviet Union. An acquaintance of mine is a leading mathematical physicist from Armenia. His description (or at least my recollection of it) of historical events may be exaggerated slightly for dramatic effect.
Stalin locked the very best maths and physics educators in a building, gave them all of the resources that they needed, put a gun to their heads, and ordered them to create the very best maths and physics curriculum in the world. Surprise, surprise! They succeeded.
The system was highly integrated. One day you learn a maths concept; the next day you apply it to a physics problem.
The system also emphasized mathematical games and puzzles as educational enrichment. Translations of the works of the late Martin Gardner (who had a column in Scientific American) were extremely popular. Ironically, this Totalitarian state actively encouraged nonstandard thinking in maths and physics! The single most innovative thing that we could do would be to adopt the old Soviet maths and physical science curriculum.
Of course, the success or failure of a maths and physical science education system depends on several factors: teachers, student motivation, administrators, and the availability of first-rate educational materials. It would be unfair to place all of the blame on teachers. Given the degree of local control over school districts in our fair country, parental attitude and informed participation by parents are the most important forces that shape the educational process.
Small university towns--like Corvallis, Oregon--tend to have high performing students. My explanation: University professors are very serious about the education of their children. And the professors have political clout at the local level.
Nationwide, most parental complaints are about the wrong things. For example, many of their gripes are about teaching the theory of Natural Selection in high school biology classes. Unfortunately, Fundamentalist parents in the USA outnumber parents who are concerned about all aspects of secular education, including science.
Although I like what I've heard so far about the old Soviet model of maths and physical science teaching, there would be some serious obstacles to adopting it here. First, there's the NIH (not invented here) Syndrome. Moreover American parents would be another wild card.
The late Jaime Escalante needed to network with parents in order to make his modest innovations successful. He also took a lot of flack from administrators, and from fellow teachers, who were jealous of his abilities and successes. Escalante's story was made into a reasonably accurate film, Stand and Deliver. The process of cloning the Soviet maths and physical science education model would make Escalante's tribulations look like a walk in the park!
Copyright 2012 and 2013 by Larry Fields