Larry's Take on Maths Education in the USA

Asian elephant
Asian elephant | Source

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.


Feeding time at the Melbourne Zoo.
Feeding time at the Melbourne Zoo. | Source

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.


Bronx Science students working on their school newspaper.
Bronx Science students working on their school newspaper. | Source
Maria Montessori
Maria Montessori | Source

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.


Martin Gardner
Martin Gardner | Source
Jaime Escalante
Jaime Escalante | Source

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


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Comments 15 comments

Davesworld profile image

Davesworld 4 years ago from Cottage Grove, MN 55016

My Jr High School daughter, I forgot the grade it's been a while, brought home here math books and wanted help from her Dad. I have a B.S. degree in mathematics and dozen graduate credits beyond. I couldn't make heads or tails out of what she was trying to do. I spent the evening reading the textbook(?) trying to figure it out.

The idea in the book was to simplify mathematics by having the student guess as opposed to determine the right answer. Why? I don't know. I went through the sample problems at the end of a chapter. I could work the arithmetic in my head and knew the solution but couldn't find it in the answers given in the book. Then it dawned on me that the kid was NOT supposed to find the right answer just supposed to get close.

When this is what passes for math education it's no wonder our children are mathematically illiterate.


Paul Kuehn profile image

Paul Kuehn 4 years ago from Udorn City, Thailand

Larry,

This is an interesting and useful hub. I do agree that math and science education has to be improved on the secondary level. A hands on approach with less talking from the instructor would certainly help. The Soviet approach you refer to does sound very interesting and worthwhile. My dad once said that if you can express your ideas in math, you really know what you are talking about. Voted up and sharing.


yoginijoy profile image

yoginijoy 4 years ago from Mid-Atlantic, USA

Hi! I am here thanks to Paul's sharing. As an educator at the college level, I see the fear in my students' eyes when I tell them they need courses in math and science for their bachelor's degree. They are so afraid! It is a direct result of a poor high school math/science education. I agree that something has to be done! I remember my favorite day in physics was very "hands on"--we learned about waves by using slinkies. I agree too that part of the issue is that we need a way to enforce discipline--from kindergarten all the way through. The self-esteem will happen when the student is confident in his/her learning, no?


Larry Fields profile image

Larry Fields 4 years ago from Northern California Author

Hi Davesworld. Great comment!

The idea that you mentioned is called Guess and Check. Here's how it came to pass.

In one of his autobiographical books, Nobel Laureate (physics) Richard Feynman mentioned that he got a head start on high school algebra by looking at the problems in his older brother's textbook.

At the time, Feynman didn't know how to solve the problems; so he guessed. If the guess was not correct, he guessed again. Whichever guess--A or B--was closer, he would continue in that direction, until he nailed the correct answer.

That approach--successive approximation--is used in computer programs that tackle mathematical problems for which there are no exact solutions in closed form.

Of course, Feynman's early experience had precious little to do with solving algebra problems in an efficient way. What he learned instead was that he could understand algebra without a teacher! That experience was one of many that shaped his lifelong habits of active learning and nonstandard thinking.

Some 'educator' read the autobiography, failed to grasp the big picture about active learning, and founded a secular religion about Guess and Check instead.


Larry Fields profile image

Larry Fields 4 years ago from Northern California Author

Hi Paul Kuehn. Thanks for stopping by.


MarleneB profile image

MarleneB 4 years ago from Northern California, USA

I hate to admit that math was not my strong talent in school. I struggled, but in the end, I got it. Ironically, the things I thought I would never use in real life, I'm using almost on a daily basis. Now, I am an advocate for developing a strong math environment in schools. This is an excellent hub on the subject.


Larry Fields profile image

Larry Fields 4 years ago from Northern California Author

Hi yoginijoy. You wrote:

"I agree too that part of the issue is that we need a way to enforce discipline--from kindergarten all the way through."

Good point. I'm reminded of a group hiking experience, in which I made the acquaintance of an animal behaviorist. She felt that the animal training part was fairly straightforward. However remedial training for the dog owners was equally important, and more challenging.

Similarly, disciplinary problems in school are usually traceable to ignorance on the part of the parents. Except for the rare cases in which there's an underlying medical problem, if you could somehow straighten out the parents, the classroom disruption would taper off quickly.

In our imperfect world, little Johnny needs to learn that his actions have natural consequences. Attempting to shield him from that important life lesson is a disservice to everyone in the long run.

I also agree with you about the self-esteem issue.


Larry Fields profile image

Larry Fields 4 years ago from Northern California Author

Hi MarleneB. Thanks for your comment.


Davesworld profile image

Davesworld 4 years ago from Cottage Grove, MN 55016

Larry,

Thanks for the explanation for Guess & Check - I never knew what prompted the whole mess before.


Nell Rose profile image

Nell Rose 4 years ago from England

Hi Larry, as I was reading I was nodding my head in agreement. Maths is my one achilles heel. And the reason why was because when I was at school the attitude of the teachers was frustrating, annoying and downright confusing! They did two main things that put a dampner on my learning, one was the fact that they presumed we should know it and spoke to us as though we were stupid, and two, they used to write everything in full on the blackboard and expect us to know what the heck they were talking about! if only they had taught us step by step then it would have been fine. Maths is one of those subjects that cannot be rushed, or bits left out. it just doesn't work. I helped teach maths to a small group of kids after school, it was called Kumon, maths and english, and we taught them by giving them a small booklet of sums, and then making them do it over and over again until they could do it really quickly, and guess what? it worked!


Larry Fields profile image

Larry Fields 4 years ago from Northern California Author

Hi Nell. Thanks for sharing your experiences.


ksinll 4 years ago

Larry, Great topic, I enjoyed reading it. I just read the book Outliers and it talked about the achievement gap in math when you compare American students with Asian students. Apparently the language simplifies the math concepts for them. From what I remember, very few of my teachers understood the reasons behind what they were teaching but just taught you to memorize steps. They showed us shortcuts withtout giving us the concepts. I think it is sad that so many people think that they are not good at math because the "math" taught in schools is really not math its just procedural compliance. Real math teaches problem-solving and critical thinking through the use of symbols.


Larry Fields profile image

Larry Fields 4 years ago from Northern California Author

Hi Ksinll. Thanks for stopping by.

I agree with you about "procedural compliance." Since I'm not as polite as you are, I'd call it animal training. You also wrote:

"Real math teaches problem-solving and critical thinking through the use of symbols."

Agreed. True maths education (together with physical science education) can be a liberating experience, provided that teachers and students approach it in the right way.


Karen 2 years ago

All the numbers you see reported in the media about the state of education in the USA and test scores are AVERAGES, and as anyone who actually lives in the USA can tell you, we have as much educational and wealth disparity as the third-world Latin American countries to the south. Average scores are driven down hard by the pockets of poverty. And let's not forget we allow parents to educate their kids at home in lieu of school, so all these home "schooled" (yeah right!) kids are also skewing the averages in the eyebrow-raising direction. One of the curiouser aspects of living in a country that has the word "freedom" tattooed on its forehead...

The education I received growing up in an affluent area is comparable to that any European or Asian country, better than their national averages I would say. It's a disgrace that the quality of education I received is not available to all students everywhere inside the country. Canada also has the same problem as the USA, lots of stellar school systems in rich areas, but also lots of mediocre school systems in impoverished areas, especially on First Nations lands.


Larry Fields profile image

Larry Fields 23 months ago from Northern California Author

Hi Karen,

Thanks for your thoughtful comment. Sorry for not responding sooner. Health issues and a computer problem.

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