Education Reform

[TimG]

As far as math goes, I think a lot of the problem is rooted in failure to build foundation skills in the middle grades, something like 5th through 8th.

 

Like KenBerg pointed out, kids get to high school without being able to handle things like determining the measure of an angle in a triangle given the measure of the other two angles. High school teachers spend time reviewing (and teaching) material that kids should have down pat. This time drain prevents them from presenting the material they are supposed to and students fall further behind.

 

It is not a matter of throwing better educated and more skilled teachers at high school students. Their talents will be wasted on kids lacking a solid foundation.

[hrothgar]

I was also surprised by those figures, and wondering where all the money is going. I suspect a big chunk of it is health insurance (for both teachers and other staff), not teacher salaries or school equipment (textbooks and computers). So education reform is probably intimately tied with health care reform.

 

All I know is that every year my town newspaper reports on further cuts in our school budget. You hear about art and sports programs being cut back or dropped entirely. In my town, families have to pay extra for each sport their kids participate in (ranging from $408 to $720/season, but they recently compromised by adding a per-family cap and multi-sport discounts).

 

My understanding is that the US spends enormously more on "special needs" education than is typical in the rest of the world.

[nigel_k]

People who are good at maths can find jobs that pay better than high school teaching. Schools don't have the budget to pay enough to retain a full complement of knowledgable math teachers. I think there are three things that can reasonably be done:

 

1. Set salaries based on supply and demand so math teachers earn much more than others.

 

2. Accept that most students can graduate from high school without ever learning calculus, advanced algebra or maybe even trigonometry. Then you can spread the most capable teachers among the 10-20% of students who will benefit from learning this stuff.

 

3. Have larger class sizes for advanced maths or other subjects where teacher supply is low.

 

I suspect the reasons why these three things don't happen are, respectively: unions, some distorted notion of equality, and unions.

 

Of course, none of this will help the students who can't subtract a number from 180. For that, I think parents have to take at least half the blame. Partly for not making sure their kids know this stuff even if they have to teach it themselves, and also for failing to hound the responsible teacher until they either get better or give up teaching altogether.

[mike777]

"Total spending ratio. Based on 1999-2000 school year data, the total expenditure

to educate the average student with disabilities is an estimated 1.90 times that

expended to educate the typical regular education student with no special needs.

This ratio has actually declined since 1985, when it was estimated by Moore et al.

(1988) to be 2.28.

Total current spending ratio. Excluding expenditures on school facilities, the

ratio of current operating expenditures on the typical special education student is

2.08 times that expended on the typical regular education student with no special

needs."

 

 

 

 

 

http://csef.air.org/publications/seep/national/AdvRpt1.pdf

[hrothgar]

"Total spending ratio. Based on 1999-2000 school year data, the total expenditure

to educate the average student with disabilities is an estimated 1.90 times that

expended to educate the typical regular education student with no special needs.

This ratio has actually declined since 1985, when it was estimated by Moore et al.

(1988) to be 2.28.

• Total current spending ratio. Excluding expenditures on school facilities, the

ratio of current operating expenditures on the typical special education student is

2.08 times that expended on the typical regular education student with no special

needs."

 

 

Any figures about what percentage of students are classified as special needs compared to other parts of the world?

[mike777]

According to the Department of Education, approximately 6 million children (roughly 10 percent of all school-aged children) currently receive some type of special education services.[38]

 

 

 

http://en.wikipedia.org/wiki/Special_education

[hrothgar]

According to the Department of Education, approximately 6 million children (roughly 10 percent of all school-aged children) currently receive some type of special education services.[38]

 

http://en.wikipedia.org/wiki/Special_education

 

I suspect that this percentage explains a lot

[matmat]

A few things.

 

I very much enjoyed reading the essay linked through here.

 

 

As far as math goes, I think a lot of the problem is rooted in failure to build foundation skills in the middle grades, something like 5th through 8th.

I would actually back up further. I think when it comes to math and reasoning skills the system fails before the school even starts, or around kindergarten time. Ability to think about problems, whether algebraic, arithmetic, or geometric in nature does not require complicated expressions, just a touch of imagination an interested parent/guardian/teacher. I feel like too many parents think it is the schools' responsibility to teach their kids math, science, or languages. Some of this might stem from the parents' own math phobia, but come on... it's not like we expect 5 year olds to be doing calculus, but simple logical reasoning, why not?

 

There is too much meddling of politics in education (I think some touched on this already). Saw this article recently, and it nearly made me throw up.

A democratic society needs Republican scientists.

WTF?

No, a democratic society needs scientists who can leave their politics behind.

 

Frankly, we need more of this.

[kenberg]

 

Frankly, we need more of this.

 

It is stated humorously, but this is fundamental. I can't think of any mathematician I have ever met who would say that he chose his line of work to be of service to humanity. I explain to people that I became a mathematician because I enjoy mathematics and I can make a decent living at it. People pay us because it is useful, and the fact they pay us is important, but we didn't really think much about social utility when we signed on. There may be some exceptions, but I haven't met them.

[hrothgar]

 

Saw this article recently, and it nearly made me throw up. WTF?

 

 

I found it quite amusing that an article that professed to complain about the under-representation of Republicans amongst scientists could be so confused regarding cause and effect.

[matmat]

I found it quite amusing that an article that professed to complain about the under-representation of Republicans amongst scientists could be so confused regarding cause and effect.

That was one of my reactions as well. It reminded me a little bit of an article from a few years back when a journalist argued that mathematics was not important, since he managed to get through life without knowing it. Citing his lack of understanding of percentages as a badge of honour. let's see if i can dig that old piece out...

[han]

It is my opinion that any post graduate degree is an excess when it comes to teaching high school students. In math, for instance, things like Abstract Algebra, let alone Differential Equations, will be of little or no use when teaching Pre-Calculus.

 

Several people in this thread have complained that their math classes were lacking, mostly because they focused too much on memorization and that their teachers failed to enthuse them.

 

But how can a math teacher inspire you for mathematics if they have never seen the true beauty of mathematics themselves? And isn't abstract algebra for most math students a first glance at what mathematics is about? If a math teacher has never gone as far as abstract algebra, what then does that say about his or her love for the subject?

 

And how can a high school teacher be enthousiastic about calculus if they don't know the importance of differential equations? If they haven't seen how Newton derived Keplers laws using differential equations? If they can't understand why current day's scientists, engineers and bankers to a great extend depend on differential equations? I'd say that a mathematics teacher that doesn't know about differential equations is completely out of touch with modern science.

 

If we don't motivate math with practical, real world problems we're never going to convince kids to care.

[hrothgar]

 

I very much enjoyed reading the essay linked through here.

 

 

I read the essay last night and left it with mixed feelings:

 

I very much agree with the pedagogic approach that the author recommends.

I think that I would have loved to have him as a math teacher.

 

At the same time, he seemed to think that math could be treated as an elective.

Not everyone needs to take art or music.

In a similar vein, not everyone needs to take math.

 

I'm not sure that I agree with this. Most high paying jobs in the modern "knowledge" economy require strong math skills. I'm not sure whether kids are in a good position to make an informed decision about whether or not they need to take math. In a similar vein, I doubt that their parents are necessarily any better placed (especially if "math" is being taught in the manner described in this article).

 

The methods that the author is describing are very far removed from the standardized testing approach currently in vogue...

[hotShot]

The think the article the OP mentioned misses a main point if not the main point.

Some countries have a "competition" attitude about school, they are interested in the best and don't care much about those who fail.

They don't even care much about the fact that a lot of children with a high potential, don't make it to the top or even finish school.

Company's will hire top people from other countries if there are not enough.

 

My understanding is that Finland has a different attitude more like the armed forces "We don't leave our people behind" mantra.

Pupils that already understood what the teacher has explained, are immediately involved into teaching those who did not get it the first time.

To do this the teacher creates small groups who teach each other. This way the teacher can focus his efforts to those who need "special education".

The "Nerds" gain social competence and are better integrated into the class. With a little luck every child can be a tutor to his/her classmates somewhere between math and sports.

[kenberg]

A few random comments:

 

When I was in high school I took algebra and I took metal shop. I helped Lug Larson with his algebra, he helped me with the lathe.

 

Colman McCarthy was an entertaining and sometimes aggravating columnist some years back. He wrote a column about how kids really didn't need algebra and argued that in the unlikely event that anyone actually did need it he could learn it then. Smart people often make this very wrong argument. Yes, Colman McCarthy could learn it if he needed it. He is smart, he knows how to learn new things, he has the resources to hire a tutor if needed, he has a job with flexible working hours, etc. A twenty-five year old bagging groceries who decides he would like to, say, study chemistry or economics or business or whatever at the community college and maybe get a better job will not find this "just learn it" so easily done.

 

 

Mrs. Swan, the woman who taught me math in my first two years of high school, probably knew nothing about differential equations. But we did geometric proofs and constructions, she knew these, and she was excellent. For the next two years I had Mr. Berger, who I am sure knew differential equations but probably was vague (very vague) on how to derive Kepler's Laws from the inverse square law of gravitation. He was also excellent. And he took an interest in me and got me a scholarship. Thanks, Dude, wherever you now are. If all teachers were like these two, we would not be fretting about our children's education. The gap, from there to where we are in some systems, is a chasm.

[TimG]

I very much enjoyed reading the [Lockhart's] essay linked through here.

I showed this paper to a friend who teaches music in a public elementary school. She lamented that Lockhart's opening scenario is not as far from reality as most readers would believe.

 

I do not think that Math students are unique in that they could benefit from more exploratory learning. Students in all disciplines are being taught to memorize rather than think. This is not a new phenomenon. 200-300 years ago, young men learned Greek and Latin, not through spoken exploration of those languages, but through translation of written works. The purpose of the translation was not to investigate the new ideas presented in the works -- there were existing translation that could be read for the ideas and the ideas in the works were rather old anyway. Thomas Paine did not write Common Sense in Greek. Everyone of us who took the SATs likely at one time or another worked through some vocabulary word lists. List of words that we've probably never used or heard used. We've likely all been required to memorize dates and names in History classes. I know my Earth Science class entailed a lot of memorization of things like rock and cloud types and characteristics.

 

From the paper:

 

I'm complaining about the complete absence of art and invention, history and philosophy, context and perspective from the mathematics curriculum. That doesn't mean that notation, technique, and the development of a knowledge base have no place. Of course they do. We should have both.

 

I imagine this little bit from the paper gets lost or overshadowed. Perhaps how students learn about notation and technique should be taught differently, but Lockhart is not arguing that students shouldn't come away from school with an understanding of these things. I don't see in the paper a claim that all students will want to explore all techniques that they should learn.

 

I think it should also be pointed out that the students which Lockhart encounters at St. Anne's quite likely tend toward the exceptional, or at the very least are not your average students; what works for him might not work for teachers in public schools, especially in non-affluent areas.

[TimG]

But how can a math teacher inspire you for mathematics if they have never seen the true beauty of mathematics themselves? And isn't abstract algebra for most math students a first glance at what mathematics is about? If a math teacher has never gone as far as abstract algebra, what then does that say about his or her love for the subject?

 

I think there is lots of beauty in numbers, shapes, and patterns that students and teachers alike can appreciate without either ever having encountered a course in Abstract Algebra.

[kenberg]

The Lockhart piece was interesting enough. Caution is recommended. Here is part of the Wiki description of St.Anne's:

 

Saint Ann's School was founded in 1965 with 63 students and seven teachers in the basement of the St. Ann's Episcopal Church under the aegis of the vestry of the church and several interested parents. In 1966, the Church purchased the former Crescent Athletic Club House, a building designed by noted Brooklyn architect Frank Freeman, for the sum of $365,000, which has since served as the school's main building.[1] Stanley Bosworth became its first headmaster. In 1982, Saint Ann's School formally disaffiliated from the church, having been granted a charter from the Board of Regents of the State of New York. When Bosworth retired in 2004, Larry Weiss, formerly the head of the upper school at The Horace Mann School, began his tenure as head of school at Saint Ann's. In September 2009, it was announced that Weiss would not return to Saint Ann's for the 2010–2011 academic year. In May 2010, Vincent J. Tompkins, Jr., the Deputy Provost at Brown University, was named Weiss's successor. He assumed leadership of Saint Ann's beginning with the 2010-2011 academic year.[2][/Quote]

 

The principal at my high school, St. Paul Monroe, was not a former Deputy Provost at Brown. One student that I know of from Monroe went to Stanford. He was a talented quaterback. We are speaking of a very, very, different environment. Lockhart's ideas are worthy of thought, but a grain or two of salt is advised.

 

 

There is indeed a problem about high school mathematics being boring. But consider Silas Marner. Now that's boring. Or Percy Byshe Shelley. What parent names his kid Percy Byshe? And then there was organic chemistry. Octel-methyl-bentyl tri-chloro-butane anyone? Math looks pretty good against some of the alternatives.

 

Anyway, some things in high school interested me in spite of everything and I learned some things. For many kids today, this rather low standard is not being met.

[TimG]

I very much enjoyed reading the essay linked through here.

I understand that this is somewhat counter to the spirit of Lockhart's approach, but I'm curious whether anyone knows of material that helps guide a teacher or parent through such a course of math or present situations that are likely to elicit interest and exploration.

[hrothgar]

I understand that this is somewhat counter to the spirit of Lockhart's approach, but I'm curious whether anyone knows of material that helps guide a teacher or parent through such a course of math or present situations that are likely to elicit interest and exploration.

 

I bought a book for my (young) niece titled "The Adventures of Penrose the Mathematical Cat"

 

One of the founder's of The MathWorks wrote the following:

http://www.mathworks.com/moler/chapters.html

 

I think that its still quite dry, however, it provides a great introduction to "practical" math...

(Please note, you get to download a MATLAB variant with the free text)

 

One tactics that I've often found useful is to try to look back to the origins of different branches of math.

You often find a wealth of interesting and intuitive problems.

 

For example probability and statistics were primarily developed to analyze games of chance.

There's all sorts of useful examples that involve cards, dices, and the like.

 

From there, you can move on to slightly more complicated concepts like Buffon's needle.

[PassedOut]

Aside from own schooling (I was a math major, as was Constance), I only have the tiny sample of my sons to think about in their approaches toward learning math. My oldest son was always into history, politics, law, and literature, and never truly got into math (in my opinion), even though he was a top student in all his college courses.

 

My middle son is our artist, and I found it interesting that he got into both biology and math by way of improving his skills at the visual arts. 3-D computer modeling was one of his primary interests, and he learned programming and quite a bit of practical math in building specialized software tools for his art projects. So it was the usefulness of math to him that got him eventually hooked on the sheer beauty of it.

 

Our youngest son has always been keen on math, science, and programming, and was co-author of a book on programming when he was fourteen years old. I was hoping that he would use his college years to round out his education in the liberal arts, but he was heavily recruited and only completed one semester of college before the offers became irresistable to him. Naturally I keep encouraging him to enroll part-time, but he hasn't done that so far. Alas.

 

I got hooked on math when I took Geometry as a high school sophomore. Somehow the logic of the proofs combined with the visual elements really struck a chord with me.

 

I do believe that it is easier for people to get into math if they either find it fun to begin with or see its usefulness. Once you get past the basics, you begin to see the beauty.

[kenberg]

 

 

I was hoping that he would use his college years to round out his education in the liberal arts, but he was heavily recruited and only completed one semester of college before the offers became irresistable to him. Naturally I keep encouraging him to enroll part-time, but he hasn't done that so far. Alas.

 

 

 

Reminds me of a story. When Google was first making a splash Sergei Brin was interviewed. The interviewer asked him if he thought he would someday go back to Stanford to complete his Ph.D. His answer: I think my mother will be seeing this so yes, I will be going back to complete my degree.

[PassedOut]

Reminds me of a story. When Google was first making a splash Sergei Brin was interviewed. The interviewer asked him if he thought he would someday go back to Stanford to complete his Ph.D. His answer: I think my mother will be seeing this so yes, I will be going back to complete my degree.

And Zac talks the same way...

<_<

[helene_t]

Saw this article recently, and it nearly made me throw up. WTF?

No, a democratic society needs scientists who can leave their politics behind.

So a democratic society needs more anti-intellectual scientists. Right. We also need more surgeons with Parkinson's disease and more dyslectic literature critics. It's new to me that republicans favor affirmative action.

[luke warm]

So a democratic society needs more anti-intellectual scientists. Right. We also need more surgeons with Parkinson's disease and more dyslectic literature critics. It's new to me that republicans favor affirmative action.

republicans have favored affirmative action for at least 150 years, far longer than democrats...