From the general board: A Mathematician's Lament

[Jane in NC]

Rivendellmom posted this on the general board and am I glad I found it!

 

http://www.maa.org/devlin/LockhartsLament.pdf

 

While I am not in total agreement with every point made by the author, Paul Lockhart, it does give great food for thought on how mathematics is taught and, consequently, why most people in the culture have no clue what mathematics is. This article is not intended to help you choose the "best" curriculum. Rather, it raises questions on why we cram algorithm after algorithm down student's throats. Lockhart writes:

 

"By concentrating on what, and leaving out why, mathematics is reduced to an empty shell. The art is not in the “truth†but in the explanation, the argument. It is the argument itself which gives the truth its context, and determines what is really being said and meant. Mathematics is the art of explanation. If you deny students the opportunity to engage in this activity— to pose their own problems, make their own conjectures and discoveries, to be wrong, to be creatively frustrated, to have an inspiration, and to cobble together their own explanations and proofs— you deny them mathematics itself."

 

An excellent read.

[Myrtle]

If anyone finds that article moving and wants to dig into this a little more I highly recommend the mathematical novel, "A Certain Ambiguity" which is the mathematical equivalent of "Sophies World." It is intended for someone with little more than high school algebra who is interested in math for its own sake. It mixes up philosophy, math, and math history, into one story. Check out the reviews at the above link.

 

I haven't gotten to the end yet.

[MaryM]

Lovely!!

 

It is well worth taking the time to read this, I agree. Thanks for bringing it to my attention.

Mary

[Charon]

I don't agree with anything he says. He basically thinks that we need to take rigor out of math and that Euclidean Geometry is the worst course we teach in K-12 because it is so dogmatic and not "charming" enough. I bet if you read far enough he'll be calling for us all to sit in a circle and sing Kumbyah. Perhaps we should teach what an all inclusive and happy subject math is and not so ethnocentrically focus on western thought and start teaching about the mathematics of the aboriginal tribes of New Guinea. We should try to emphasize the role of women and minorities in math. We should ask students questions like "If math was a color, what color would it be??"

 

No. The reason no one knows what math is is because of turkeys like this that want to turn math class into the chess club. If he has his way, everyone will think that math=go in 10 years because playing games like go is "real math". We want people to know what math is? How about we cut the crap and start teaching some? The reason no one knows what math is is because we don't actually start teaching it until about your senior year in college if you happen to major in the subject. And, it is just this kind of nonsense that has led us to this point.

[Jane in NC]

 

No. The reason no one knows what math is is because of turkeys like this that want to turn math class into the chess club.

 

I would not go so far as to say he is a turkey. There are valid points in the article. For example, when Lockhart complains about the lack of interesting problems in a standard math text:

 

"How long is the diagonal of a cube? Do prime numbers keep going on forever? Is infinity a number? How many ways can I symmetrically tile a surface? The history of mathematics is the history of mankind’s engagement with questions like these, not the mindless regurgitation of formulas and algorithms (together with contrived exercises designed to make use of them)."

 

These are good questions to engage a young mind. Now the danger I see is that there is a good chance that self discovery could lead to great oversimplifications. But he also points out that the current system leads to the same. For example, how many people think that there are 180 degrees in a triangle? Every elementary school kid learns this "fact" (which is true in the plane, but not on a sphere, as Lockhart notes). High school geometry teachers do not teach about geometries which exclude Euclid's parallel postuate. Have most high school teachers ever learned about hyperbolic or spherical geometries?

 

There are some good discussion points within the article. I certainly would like to see some mathematics in math classes.

 

Jane

[Charon]

I would not go so far as to say he is a turkey. There are valid points in the article. For example, when Lockhart complains about the lack of interesting problems in a standard math text:

 

"How long is the diagonal of a cube? Do prime numbers keep going on forever? Is infinity a number? How many ways can I symmetrically tile a surface? The history of mathematics is the history of mankind’s engagement with questions like these, not the mindless regurgitation of formulas and algorithms (together with contrived exercises designed to make use of them)."

 

These are good questions to engage a young mind. Now the danger I see is that there is a good chance that self discovery could lead to great oversimplifications. But he also points out that the current system leads to the same. For example, how many people think that there are 180 degrees in a triangle? Every elementary school kid learns this "fact" (which is true in the plane, but not on a sphere, as Lockhart notes). High school geometry teachers do not teach about geometries which exclude Euclid's parallel postuate. Have most high school teachers ever learned about hyperbolic or spherical geometries?

 

There are some good discussion points within the article. I certainly would like to see some mathematics in math classes.

 

Jane

 

 

No -- his article is the standard student led discovery reform math BS. You don't need to be teaching alternative geometries to students, for that matter. Going "Aha! But, in non-Euclidean space....!" is about the most hackneyed pile of bull**** online. Yes, those problems are great and all, but he clearly has no intention of teaching his students any of that. He might bring those problems up, but he is clearly all in favor of just bull****ting the students like normal about them, playing a game of chess and calling it a day. He is a turkey because he is selling out his own field with a whole lot of bull**** rhetoric. He has earned his place on my list right beside Morris Kline.

 

He's just trying to sell his royal road to geometry. That's why he's a turkey. And everything he says in that article is almost entirely just a bunch of cheap, hackneyed, self-aggrandizing rhetoric. What's wrong with math ed has never been not disclosing "the beauty of math" or failing to foster a "students love of the subject". It has always been that people start spewing that crap right before they take out the rigor and the standards just like what Paul is doing in this article.

[Charon]

Math is not a science. But, it is intellectually repugnant to watch someone imagine that this must mean it is an "art" like painting or something. There is an art to mathematics as there is an art to painting -- just as there is an art to doing science. A physicist could come along and spew the same old hackneyed crap: "science is art!" "You must appreciate the beauty of physics!" (In fact, they do it all the time.)

 

He is also right that we don't do any math with people until they are seniors in college at the earliest. And, he is right that most people don't have a clue what math really is. He also does a great job of extracting the idea out of the imperfect empirical depiction of it, for that matter. He is half right that elegance, for instance, in a proof matters. Well, it is absolutely true that it does matter and someone can get published by proving an old result in a new way. But, the way he's talking, it is all about the poetry of the proof or something.

 

Now, you know that's BS. It is far more important to just come up with one no matter how ugly it might be. The theorem is going to be named after the guy that got the job done in the first place, not someone that had a more elegant proof a few decades later. And, anyway, if you think that calculus as it's taught at the university is more like real analysis and we need to actually dumb it down some more and get rid of all that "formalism", then you just need to be put down. That's all there is to it. Especially when that is what real math is -- the real analysis not the calculus. In fact, what he is saying there is such an obvious and outrageous lie that you cannot call it a difference of opinion or simply a mistake or even a misinterpretation. He is unequivocally trying to just gain popularity with a bunch of self-serving bull****. Everybody knows that the real subject is real analysis and that is precisely what is being refered to when we say that you don't start really learning math until you are a senior or a graduate student -- because you don't start doing math that way -- like real analysis -- until then.

[Jane in NC]

No -- his article is the standard student led discovery reform math BS. You don't need to be teaching alternative geometries to students, for that matter. Going "Aha! But, in non-Euclidean space....!" is about the most hackneyed pile of bull**** online. Yes, those problems are great and all, but he clearly has no intention of teaching his students any of that. He might bring those problems up, but he is clearly all in favor of just bull****ting the students like normal about them, playing a game of chess and calling it a day. He is a turkey because he is selling out his own field with a whole lot of bull**** rhetoric. He has earned his place on my list right beside Morris Kline.

 

 

 

Oh dearest Charon and Myrtle,

 

If you were not more than a thousand miles away, I would be inviting you to dinner. The conversation could be quite amazing. And entertaining.

 

We read the Lockhart article differently, I think. I am a genuine Pollyanna while I dare suggest that you may have a bit of a cynical soul. Essentially I see his theme as "Let's ask different questions." I want to buy into it. The current methodology of teaching Mathematics as algorithm after algorithm with the end game being Calculus and Physics or business applications is disturbing. I would like students to see some of the beauty and sheer excitement that I find in mathematics. Even if they don't make it that far, I would like to see more students achieve a comfort level with abstraction, learn how to write a convincing argument. I am not assured that by tinkering on their own students would master these things. But again, as the author said, they are not really learning any mathematics now.

 

My poor head aches these days as I try to keep up with my son in sorting out the differences between "audiverunt nos discedere" vs. "audiverunt nos discessisse", that is, "They heard we were leaving" vs. "They heard we had left". Somebody heard something and somebody is going somewhere. These discussions on Math always lead me to think about Latin. Because I tend to use English imprecisely, I have to look twice at Latin endings or consult my grammar guide for the subtlety. This is not easy and it is no wonder that students want to throw in the towel. But to do Latin well one needs to memorize and practice.

 

Same for the piano.

 

Same for mathematics.

 

There is a certain element of formal practice that is quite different from play. Mixing baking soda and vinegar is not chemistry. On this we can probably agree.

 

Jane

[Myrtle]

 

But again, as the author said, they are not really learning any mathematics now.

 

Jane

 

I will grant that perhaps they are not learning "real" math, but to entirely convince me Lockhart needs to explain why the pursuit of real math is worth sacrificing SAT scores and AP Calculus and by what means could we evaluate students' knowledge of real math.

 

On the one hand, we've got an authority, Morris Klein, telling us that math is all about the applications and the real world. On the other hand, we've got Paul Lockhart, an authority, telling us that real math has nothing to do with the real world.:001_huh:

 

The traditionalists (drill and kill) say that students can't move on to higher math until they've mastered the basics. I don't see anything other than lip service being paid to "higher math" It seems under that program one never stop learning new algorithms. Why exactly is it that three semesters of engineering calculus and linear algebra is conceptually prequisite to abstract algebra? There's no answer.

 

I am equally suspicious of postponing formalism. Learning the formal logic and set theory that it takes to properly do these proofs has been no easy task and one that I am far from mastering. It is not because I lack desire, motivation, or interesting problems. It's because it's haaard. (And I say that with my best imitation of Britney Spears.)

 

I've taken a few cracks at problems that were interesting to me on the advice similar to what Lockhart is giving, "just pick a problem and work on it" but without the formalism the job just doesn't get done.

 

And if we can't figure out a way to get students to master "solve for x" in four years of high school, I don't think it's any more realistic to think that they are going to be able to prove set equalities in the same amount of time. Just as traditionalists never quite nail down when it is that we finally get around to learning "higher math" Lockhart avoids any specifics of when the students will master proving theorems...even basic ones.

[Storm Bay]

Jane, thanks for linking to this today, as I missed it last March.

[Janet in Toronto]

Thanks for this. He articulates very clearly the issues that I have been trying to raise with my middle schoolers math teacher. That the joy of mathematics is being sucked out of his head by her insistence on there being only one way to solve a problem, one way to write it down, and G*d forbid if you use a multiplication sign (x) in grade 8 rather than a dot. When he has attempted to discuss alternate solutions to problems (after class), he has been all but ridiculed. I am fed up. I was almost in tears trying to have a discussion with her about my right-brained, visual-spatial child who used Singapore Math for years and has a different way of thinking about and solving problems.

 

Both my husband and I have post-graduate math degrees. If I hear one more time that if a student doesn't show all their work (actually, NOT their work, but the steps the teacher wants to see), they will NEVER be able to do upper level math, I will scream. It's all CR*P and I am tired of it.

[fractalgal]

He's just trying to sell his royal road to geometry. ...

It has always been that people start spewing that crap right before they take out the rigor and the standards just like what Paul is doing in this article.

 

:iagree:with Charon. I did not find Lockhart's article convincing.

 

In addition, he offers no realistic alternative to the way mathematics is taught now.

 

One can find beauty and art in math without removing the rigor.

[Storm Bay]

Both my husband and I have post-graduate math degrees. If I hear one more time that if a student doesn't show all their work (actually, NOT their work, but the steps the teacher wants to see), they will NEVER be able to do upper level math, I will scream. It's all CR*P and I am tired of it.

 

I'm with you. I never had to show all my work, and didn't even use all those steps to process. But if it cost me grades, I showed work, even though I didn't do it their way (can't tell you how many times I screamed inwardly when I had the right answer and the teacher would show the class how I solved it via their steps and they were wrong?). I do have my 10 yo show work, though, but her way, only because, at 10, sometimes she gets lost and I can't see where she went wrong. She's not in Algebra yet.

 

I do think some dc do better if they show their work, but some of us have our brains wired differently, for better or for worse;).

[fractalgal]

That the joy of mathematics is being sucked out of his head by her insistence on there being only one way to solve a problem, one way to write it down, and G*d forbid if you use a multiplication sign (x) in grade 8 rather than a dot. When he has attempted to discuss alternate solutions to problems (after class), he has been all but ridiculed. I am fed up. I was almost in tears trying to have a discussion with her about my right-brained, visual-spatial child who used Singapore Math for years and has a different way of thinking about and solving problems.

 

 

I am sorry you are experiencing this with your son's teacher. Many math problems have multiple ways to solve them. Creativity is something that should be rewarded.

 

When I taught math (at University level), I told my students to show their work. If a student shows no work, I can give no partial credit if their answers are incorrect. I would be impressed if they could show me a different way to solve problems.

[Jane in NC]

I am sorry you are experiencing this with your son's teacher. Many math problems have multiple ways to solve them. Creativity is something that should be rewarded.

 

When I taught math (at University level), I told my students to show their work. If a student shows no work, I can give no partial credit if their answers are incorrect. I would be impressed if they could show me a different way to solve problems.

 

The unfortunate reality is that many middle and high school math teachers have not been exposed to much math and hence demand that students solve problems "their way". I am with Fractalgal on this one: when I taught math at the university level, I too loved seeing clever, alternate solutions to problems. In fact, I would often drive my own students crazy by solving problems two ways. Not everyone thinks the same way, so I always felt that one presentation of the solution may not resonate with all parties. Some students prefer "brute force" algebra. Others love elegant, abstract solutions or geometric arguments. I think that it is enlightening to see a problem attacked from a couple of angles.

 

Regarding showing work: yes, work must be shown, but it is the level of detail that we may not all agree on. Personally, I love seeing sketches of problems that lend themselves to sketches. Some students "see" more than others and hence can, say, factor a mononomial and difference of squares simultaneously. These students think it is a waste of time to write out two steps when one will do. The trick is for any student to show sufficient work that 1) demonstrates their argument, 2) allows the reader to follow their argument and 3) helps the student see the path to the next step of the process (since not all problems are clear from the get go--sometimes you just have to try something to get started). This can vary from student to student.

[Janet in Toronto]

Regarding showing work: yes, work must be shown, but it is the level of detail that we may not all agree on.

 

This is exactly the problem. Viz, in grade 7 last year, students were asked to "solve" x + 2 = 7.

 

My son (who had completed Singapore 6B and is right-brained) can see IMMEDIATELY, that the answer is 5. Just by looking at the problem. But he was still forced to write out

 

x + 2 = 7

x + 2 - 2 = 7 - 2

x + 0 = 5

x = 5.

 

For 35 homework problems in an evening. It was pure busy work for this child. And the teacher claimed that if he can't show his work here, he won't be able to handle high school math. Give me a break.

 

I am all about showing work, when the work is actually used to solve the problem. I have finally persuaded his current teacher to let him show less work than what she would normally require, as long as his solutions are orderly and logical. And to not assume that he is cheating if some steps are skipped because he adds in his head.

[Storm Bay]

The unfortunate reality is that many middle and high school math teachers have not been exposed to much math and hence demand that students solve problems "their way". I am with Fractalgal on this one: when I taught math at the university level, I too loved seeing clever, alternate solutions to problems. In fact, I would often drive my own students crazy by solving problems two ways. Not everyone thinks the same way, so I always felt that one presentation of the solution may not resonate with all parties. Some students prefer "brute force" algebra. Others love elegant, abstract solutions or geometric arguments. I think that it is enlightening to see a problem attacked from a couple of angles.

 

Regarding showing work: yes, work must be shown, but it is the level of detail that we may not all agree on. Personally, I love seeing sketches of problems that lend themselves to sketches. Some students "see" more than others and hence can, say, factor a mononomial and difference of squares simultaneously. These students think it is a waste of time to write out two steps when one will do. The trick is for any student to show sufficient work that 1) demonstrates their argument, 2) allows the reader to follow their argument and 3) helps the student see the path to the next step of the process (since not all problems are clear from the get go--sometimes you just have to try something to get started). This can vary from student to student.

 

 

Now had I a math teacher like you or fractalgal, my academic career could have been much different. If, of course, you taught in high school, would take time from sitting at your desk watching everyone do their work and answer the once or twice a semester question I had when I worked ahead on my own. (I have no idea why that was so hard, and why they'd only let me work ahead if I never had a question. It's not as if there was anyone else doing that or as if it would start a trend;). Not in Algebra)

 

Of course, I was the student no one knew what to do with since school was so boring and I was one of those kids who couldn't be bothered to work hard if I couldn't see an immediate reward (like getting skipped, or moving up a level or two in a subject--marks didn't seem important in and of themselves). Or attend class, for that matter if there was no challenge and I could do all the work only attending half of the classes (happened to me once. I got a P for pass because I went to half the classes even though I'm the only one who finished the entire math course and I had an A average in it.) You can see why homeschooling appealed to me from the first moment I heard the word...

[IsabelC]

Bump.

 

Any more opinions on this?

 

I'd be particularly interested to hear from anyone who is a mathematician, or who has done college math, and/or taught math.

 

I've read the article several times and I'm not sure what to think. On the one hand, the points he makes about school math stopping kids from enjoying it or being interested resonate with me, since I was one of those kids who was put off and convinced I couldn't do math. But on the other hand, he appears to be taking some cheap shots, and doesn't really offer a serious alternative, apart from scrapping math curricula and playing games instead :confused:

 

There has got to be a middle way, hasn't there? To take art, which is one of Lockhart's examples, he points out that it would be silly if we didn't let kids paint until college level. But on the other hand, isn't it equally useless to give a baby a full studio worth of art materials and expect her to magically become an artist? The middle path would be to introduce the paints and other materials within a controlled environment, along with showing your child some techniques as she goes along. The child still gets to be express herself creatively, but she doesn't waste time drinking the paint before discovering what it's for. So I guess I really want to know how to find the mathematical equivalent. I know I spent most of high school hating math, and if I had to sit exams now I wouldn't come anywhere near being able to pass anything past about basic algebra. I don't want my kids to have that experience, but I'm not going to just play Blokus etc and call that math (we do play those kinds of games, but they are in addition to teaching number skills).

Edited December 14, 2010 by Hotdrink

[regentrude]

I think one of the underlying problems is that math teachers themselves have no idea what math is and are often just barely able to teach the required curriculum for their grade. And they are probably not having fun - with a few exceptions.

I have read the article a while ago and it really struck a cord. Math in school is painful and gives the students the impression that computing and arithmetic are math. It is no wonder students are not excited.

There are, however, actually math curricula written by people who themselves are excited about math and that joy radiates form every page. Art of Problem Solving is one of those. Students get to discover properties themselves instead of just begin handed a formula to plug and chug. Puzzles are posed which present a challenge to the thinker. And the "math is important and good for you"-seriousness is absent.

 

It amazes me that public school curricula take three years to teach the students arithmetic with fractions - assuming arithmetic with integers is done by the end of 4th grade and algebra, for the more advanced students, begins in 8th grade. During all those years, no math is being taught, just boring computations. There is not possibly enough material to stretch through middle school. Even the interested students must be bored to tears after that time.

 

I think including topics like number theory, geometry (at a much earlier age than 10th grade!) and probabilities would lend themselves to many exciting discoveries by children. It just would take a lot of courage of a teacher to let kids explore instead of filling out worksheets.

Obviously, the state of the math education in public schools can hardly get worse. Maybe it does take a complete overhaul and crazy ideas such as doing geometry before arithmetic to get children excited about math. I don't know, I am not a school teacher.

I just see that, despite all those years in school, my college student's math skills are woefully inadequate (and these are the science and engineering majors who presumably are more mathematically inclined). They can manipulate equations (while making quite a few mistakes), often are at the mercy of their calculators - and they have not learned to think.

[Guest]

I'm not a mathematician, but I really got a lot out of Out of the Labyrinth: Setting Mathematics Free, by Robert and Ellen Kaplan. They were the creators of the original Math Circle at Harvard, before most math circles went the way of the math olympiad. Their discussion is quite detailed, offers lots of specific examples, and aligns closely with Lockhart's Lament.

 

So does the story of In Code, from a young woman who won an international mathematics prize in her early twenties. She talks about how her father, a mathematics professor in the UK, gave his kids mathematical puzzles and riddles, always was drawing ideas out on a blackboard in the dining room, and made math a central conversation piece in their home.

 

Jane, I think you'd be interested in the Kaplan book. If you do get hold of it, please tell me what you think.

[justamouse]

Thanks for this. He articulates very clearly the issues that I have been trying to raise with my middle schoolers math teacher. That the joy of mathematics is being sucked out of his head by her insistence on there being only one way to solve a problem, one way to write it down, and G*d forbid if you use a multiplication sign (x) in grade 8 rather than a dot. When he has attempted to discuss alternate solutions to problems (after class), he has been all but ridiculed. I am fed up. I was almost in tears trying to have a discussion with her about my right-brained, visual-spatial child who used Singapore Math for years and has a different way of thinking about and solving problems.

 

Both my husband and I have post-graduate math degrees. If I hear one more time that if a student doesn't show all their work (actually, NOT their work, but the steps the teacher wants to see), they will NEVER be able to do upper level math, I will scream. It's all CR*P and I am tired of it.

 

When my oldest went back to PS in 10th I would get calls from his Alg teacher almost every night.

 

He's not showing the problems, I'm marking all of his papers wrong-

But he got all of the answers right!

I need to see the work the way I teach it

He has ADHD, he can't show you all of his work, and we used a different curric-

it doens't matter.

But he got them all right! And there are different ways to do algebra!

You can only DO Algebra one way.

 

At that point I gave up because it was an exercise in futility.

 

He failed, of course. And before he had her class, he loved math. It was very, very sad.

[regentrude]

But he got them all right! And there are different ways to do algebra!

You can only DO Algebra one way.

 

At that point I gave up because it was an exercise in futility.

 

 

 

Ouch. I suspect the teacher probably could only do algebra one way and never understood it well enough to see that there may be different ways to solve a problem.

[justamouse]

Ouch. I suspect the teacher probably could only do algebra one way and never understood it well enough to see that there may be different ways to solve a problem.

 

Exactly. Which is sad not only for her, but for the hundreds of children who sat in her classes.

[LoriM]

And ihave the opposite problem...students who are successfully learning to build an argument, and parents who call me complaining that I am not requiring the work to be "neat" enough, or that they show "enough" work. One mom is frustrated because her son doesn't show work "the way she would work the problem"...even when he is consistently right and is quite brilliant in math. She is sucking the joy out of it for him.

 

Personally, we spent yesterday contemplating volume and surface area...and calculating how many Barnes and Noble boxes would fit in our classroom, why boxes are rectangular prisms, and how cardboard is made. :)

 

I don't think every math teacher is the problem...but I do know a lot of students who are not in class to learn math. Or even arithmetic.

 

Right now, I have sixth graders at three separate levels of math learning...several already in beginning algebra. It's exhausting to manage but necessary since some have amazing grasp of arithmetic and number theory, and others still cannot master fractions, decimals and percents. I miss homeschooling and the luxury of my one (mathematically talented) child. :)

[flyingiguana]

When this thread was first started, someone's comment on the SAT seemed to suggest that the SAT math test was a rote test. That if we kept our students only doing "imaginative" math then they wouldn't do too well on the SAT.

 

Actually my take on the SAT is that it does encourage more out of the box thinking. The problems are that 1. they only allow one right answer and 2. there's an extreme time limit. The second point means that kids who think creatively tend to be discriminated against. The irony is that those are the kids who would do well in math down the road.

[4wildberrys]

This is exactly the problem. Viz, in grade 7 last year, students were asked to "solve" x + 2 = 7.

 

My son (who had completed Singapore 6B and is right-brained) can see IMMEDIATELY, that the answer is 5. Just by looking at the problem. But he was still forced to write out

 

x + 2 = 7

x + 2 - 2 = 7 - 2

x + 0 = 5

x = 5.

 

For 35 homework problems in an evening. It was pure busy work for this child. And the teacher claimed that if he can't show his work here, he won't be able to handle high school math. Give me a break.

 

I am all about showing work, when the work is actually used to solve the problem. I have finally persuaded his current teacher to let him show less work than what she would normally require, as long as his solutions are orderly and logical. And to not assume that he is cheating if some steps are skipped because he adds in his head.

 

Ridiculous! When I realized my son was one who did a lot of math mentally and how frazzled it caused him to be to write out steps when he already knew the answer---I too let my dogmatic training of "Show your work or you get NO credit" go down the drain.

[4wildberrys]

I don't agree with anything he says. He basically thinks that we need to take rigor out of math and that Euclidean Geometry is the worst course we teach in K-12 because it is so dogmatic and not "charming" enough. I bet if you read far enough he'll be calling for us all to sit in a circle and sing Kumbyah. Perhaps we should teach what an all inclusive and happy subject math is and not so ethnocentrically focus on western thought and start teaching about the mathematics of the aboriginal tribes of New Guinea. We should try to emphasize the role of women and minorities in math. We should ask students questions like "If math was a color, what color would it be??"

 

No. The reason no one knows what math is is because of turkeys like this that want to turn math class into the chess club. If he has his way, everyone will think that math=go in 10 years because playing games like go is "real math". We want people to know what math is? How about we cut the crap and start teaching some? The reason no one knows what math is is because we don't actually start teaching it until about your senior year in college if you happen to major in the subject. And, it is just this kind of nonsense that has led us to this point.

:iagree: LOL!

[Jane in NC]

This thread from '08 reminds me how much I miss reading posts from Charon and Myrtle. Anyone have any news about them?

[Lovin Learnin]

When my oldest went back to PS in 10th I would get calls from his Alg teacher almost every night.

 

He's not showing the problems, I'm marking all of his papers wrong-

But he got all of the answers right!

I need to see the work the way I teach it

He has ADHD, he can't show you all of his work, and we used a different curric-

it doens't matter.

But he got them all right! And there are different ways to do algebra!

You can only DO Algebra one way.

 

At that point I gave up because it was an exercise in futility.

 

He failed, of course. And before he had her class, he loved math. It was very, very sad.

 

 

Sometimes schools just suck all the love out of a subject, don't they. We have dealt with this kind of thing for years with my ds. He frequently and easily comes up with alternate solutions to problems and answers them correctly, yet he's had teachers that have actually told us that they have marked them wrong because either 1) it is not the method/algorithm they taught to the class, or 2) they themselves could not follow his solution (even though ds frequently explained his method, or at least offered to). His current calc teacher told us at pt conferences that at times ds’s math logic can be absolutely brilliant, yet at other times he's not sure what he is talking about. I quickly told the teacher that just because he didn't understand my son's logic does not make it wrong. In other words, that's your problem, buddy. Ds plans to major in math next year. I've always told him that his unconventional thinking will be an asset in college.

[regentrude]

His current calc teacher told us at pt conferences that at times ds’s math logic can be absolutely brilliant, yet at other times he's not sure what he is talking about. I quickly told the teacher that just because he didn't understand my son's logic does not make it wrong. In other words, that's your problem, buddy. .

 

Although the bolded is true, part of studying mathematics is documenting one's thought process in a way that somebody else can understand it. A brilliant idea alone is not sufficient of you are unable to communicate your thoughts. And the responsibility to do this is on the one solving the problem - in this case, the student.

I encounter this a lot in my physics classes. Part of the learning objective is not just getting the physics right, but also developing effective ways (through diagrams and formulas) of communicating - because the biggest discovery is useless if you can't share it with the world.

So, I believe the teacher does have a point. (It still may be that the teacher is incompetent - but brushing off the demand for a well dopcumented slution is not the way to go, IMO.)

[Lovin Learnin]

Although the bolded is true, part of studying mathematics is documenting one's thought process in a way that somebody else can understand it. A brilliant idea alone is not sufficient of you are unable to communicate your thoughts. And the responsibility to do this is on the one solving the problem - in this case, the student.

I encounter this a lot in my physics classes. Part of the learning objective is not just getting the physics right, but also developing effective ways (through diagrams and formulas) of communicating - because the biggest discovery is useless if you can't share it with the world.

So, I believe the teacher does have a point. (It still may be that the teacher is incompetent - but brushing off the demand for a well dopcumented slution is not the way to go, IMO.)

 

I agree, which is what I have always stressed to my son. It's also the reason why I have never argued against any point reduction he has suffered. But I stand by the fact that just because he can't effectively explain it so YOU can understand it does not make his thought process wrong. And the truth is that most times the teachers don't even want to hear his thought process. The attitude is that it's not the way I do it so it's just wrong. This son has both ADD and minor language-based learning disabilities so he struggles a bit with communication, but his math is remarkable and I would love to see him find his voice.

 

K-12 schools don't seem to want to nurture the thought process of an unconventional thinker. What he needs is a true math mentor. I'm hopeful he will find that in college.

[mom31257]

Well...I LOVE math and am very excited by it's nature...and I was taught by these "methods from the Devil". I do see it as an art and am intrigued by mathematical relationships in nature, etc.

 

I skimmed through the article. No where did I see a true solution to this rant he has about a huge problem. If he wants change he needs to put practical ways out there for people to actually apply in real life.

 

Has he read Life of Fred? I would like to hear his opinion on it.

[Nan in Mass]

I didn't read the dates and thought they were back : (

[8filltheheart]

I didn't read the dates and thought they were back : (

 

I did at first, too. Then I read a few more replies and I thought some of the things sounded vaguely familiar.

 

I was excited at first b/c they did provoke some very interesting conversations!

[Melora in NC]

 

I didn't read the dates and thought they were back : (

:glare: I miss Myrtle's posts particularly.

[Storm Bay]

Ouch. I suspect the teacher probably could only do algebra one way and never understood it well enough to see that there may be different ways to solve a problem.

 

So do I. I had a teacher like that at least once; I once gave a restated equation and he went on and on about how mathematicians would have to prove it. My eldest, OTOH, knows there is more than one way to solve things, but hates any way that isn't the one she does. This led to clashes when I tried to help her.

 

I wish I'd known more about teaching math when I started homechooling, because dd loathed arithmetic with a passion, and didn't start turning around until sometime after starting Algebra. After reading a chapter about Calculus in a LOF book, she's eager to get to AP Calculus, so I'm planning to get her LOF Calculus as a gift sometime. Why wait? If it's too much math for her, she'll enjoy the story in the meantime.

 

This thread from '08 reminds me how much I miss reading posts from Charon and Myrtle. Anyone have any news about them?

 

Not since July 2009 when Myrtle asked me for the PDF file of the Gelfand's answers Charon had put up. The last post on her blog was earlier in 2009. http://myrtlehocklemeier.blogspot.com/

 

Someone on the forums knew or knows Myrtle IRL, but I can't remember who that was.

[mcconnellboys]

Is this why Russian math circles are not overly concerned with the low percentages of problems students get correct?