[TimG]

matmat, on 2010-December-28, 15:25, said:

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:

Quote

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]

han, on 2010-December-29, 07:08, said:

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:

Quote

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]

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]

matmat, on 2010-December-28, 15:25, said:

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]

TimG, on 2010-December-30, 11:11, said:

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...r/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]

PassedOut, on 2010-December-30, 13:21, said:

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]

kenberg, on 2010-December-30, 14:43, said:

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]

matmat, on 2010-December-28, 15:25, said:

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]

helene_t, on 2010-December-30, 15:51, said:

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...

[PassedOut]

Having mentioned in this thread that my son Daniel got hooked on math and physics through his art, I thought I'd post this link: Perfecting Animation, via Science

Quote

Mr. Grinspun enjoys working with studios, but he is not tempted to work for one full time, he said. At heart he is an academic. He does like contributing to the artistic enterprise, however.

As he sees it, his work frees the artists from worrying about a puffed sleeve so they can focus on what they do best, like capturing expressive emotion. His reward is different: “As long as you make pretty pictures, you get to keep learning all this math and physics.”

My son looks at this from the artist's side, but expresses the same opinion. He likes making his own tools, as he believes artists have often done through the ages. Now many of those tools are software-based, but the principle is the same.

[mike777]

Passedout:

I hope you realize how rare, very rare and very special the phrase "that my son got hooked on math and physics through his art, ..." is.


This has nothing to do with education reform.
----------

On the one hand the vast majority of people have no idea how many degrees are in a triangle( 1?,10?, 100?)...on the other hand your special son got hooked on math and physics through his art.
--

JUst for fun ask your date tonight how many degrees in a triangle. I dont mean this as a trick question for PHd students.


http://www.mathsisfu...roof180deg.html

[kenberg]

Your son is clearly choosing his own direction and that is always the right route.

Somehow the most creative minds manage to escape the potentially deadening effects of lesson plans. And the best teachers appreciate the youngster who says "I think about this a little differently". Best wishes to him, and I am sure he appreciates the pleasure that you take in him.

[mgoetze]

mike777, on 2010-December-31, 19:01, said:

On the one hand the vast majority of people have no idea how many degrees are in a triangle( 1?,10?, 100?)...on the other hand your special son got hooked on math and physics through his art.

I have no idea what this "degrees" stuff is. If you mean the sum of the interior angles, it's pi, obviously.

[kenberg]

mike777, on 2010-December-31, 19:01, said:

Passedout:
JUst for fun ask your date tonight how many degrees in a triangle. I dont mean this as a trick question for PHd students.

She knows the answer.

But addressing your point: Some years ago I started with a new barber. As barbers are inclined to do, he asked my profession and I confessed to being a mathematician. He responded that he really loves math!!! After some thought he continued "Not the hard stuff like algebra. I like...[pause for thought]... addition".

[mike777]

mgoetze, on 2010-December-31, 19:38, said:

I have no idea what this "degrees" stuff is. If you mean the sum of the interior angles, it's pi, obviously.

q=
what can I say you teachers, academics are so out of touch.

[blackshoe]

mgoetze, on 2010-December-31, 19:38, said:

I have no idea what this "degrees" stuff is. If you mean the sum of the interior angles, it's pi, obviously.

Apple or cherry?

[Cascade]

pumpkin is my favourite

[hrothgar]

luke warm, on 2010-December-30, 16:10, said:

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

There is virtually no relationship between the Republican party today and that of 150 years ago.

150 years, the Democratic Party the party of the slaveholding South.
Today, the Republican Party is the party of the racist/ignorant/religious South.

The political realignment has been immense.

Anyone who tries to use the accomplishments of the Republicans 150 years ago to prop up the party today just looks like a buffoon.

In a similar fashion, you really can't tar the Democrats with the fact that they were the party of "slavery and secession",
because all those good old boys started quitting the party back when Johnson signed the Civil Rights act.

[PassedOut]

mike777, on 2010-December-31, 19:01, said:

Passedout:

I hope you realize how rare, very rare and very special the phrase "that my son got hooked on math and physics through his art, ..." is.

Everyone is different.

mike777, on 2010-December-31, 19:01, said:

JUst for fun ask your date tonight how many degrees in a triangle. I dont mean this as a trick question for PHd students.

What Ken said.

BTW, Happy New Year everyone!