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# Math for Art Students

> boasts about having math skills far, far above what the course teaches

> cannot distinguish between first and last entries within a sequence

posted by Sticherbeast at 2:29 PM on September 11, 2011 [5 favorites]

Sticherbeast: where are you getting these from?

posted by madcaptenor at 2:42 PM on September 11, 2011

What if you were in college and that was the level of math you were ready for? Would you be insulted then? That's not a rhetorical question. And it's not an irrelevant question, because that really does happen, and not just at art school, that's for sure.

Another relevant point: K-8 math is not what it used to be. My son started kindergarten last week and on his second day they made a histogram of the number of letters in the names of the kids in the class. I think this is great! I also think it's substantially more sophisticated than the curriculum when I was in school. Lots of mathematicians and educators are working hard to get more math into all parts of the curriculum. Kindergarten histograms are part of this and so, in my view, is Worden's course. I truly don't think his students would be better off taking calculus (but I recognize that there is much room for disagreement on this point.)

posted by escabeche at 2:49 PM on September 11, 2011 [2 favorites]

Considering the number of engineering students in an Intro Calculus class that have an "8th grade" competency in mathematics (do they still even teach algebra in the 8th grade?) I'd say that sounds about reasonable for a class in an art school... in a sense I agree, as a physics major in college I had to take a distribution requirement and thinking it would be nice to take a drawing class i took one that happened to be "Drawing for Non-Art majors." After the first week it was clear that it was going to "Drawing Fun for College Students," I felt insulted.

The problem with these sorts of things is that raising your expectations means a large number of the students will drop out of the class... even if they are still showing up.

I firmly believe you could take a class of 30 art majors and by the end of the semester have them using actual mathematics... but it would probably only be 2 or 3 of them doing anything at that point. Personally, I think that's time better spent than having everyone make-believe: it's better to try something difficult and fail than never try. But, (and this gets into why grade inflation occurs) everyone seems to want a grade to seem meaningful (God knows why, they mostly aren't). We think "gentleman's C's" are an aristocratic privilege rather than a fact of life. So, in order to give a 'C' which is meaningful we create 'A' which isn't.

Most people can't do math, many engineers basically memorize what they need and do things by rote. It may be nice to get on your high moral horse and say "STANDARDS," but it's actually the demand for standards that creates these sorts of situations. You really can't fail everyone.

posted by ennui.bz at 3:48 PM on September 11, 2011 [3 favorites]

Seriously, if you're interested in network theory stuff, go read it. I took Kleinberg and Easley's course the first year they offered it using a very preliminary version of this textbook. It's been a lot of fun to see the text evolve over the past couple years.

posted by zachlipton at 4:48 PM on September 11, 2011

Exactly. And this sort of "STANDARDS" nonsense makes it extremely hard for the non-mathematically inclined to try puzzle it out voluntarily once we escape the pass-this-bar part of our education. I can happily float through my life with nothing more complicated than what I learned in middle school (interest, fractions, long division) but I want to learn more without fighting to get through some sort of arbitrary ability marker.

posted by Phalene at 5:07 PM on September 11, 2011 [2 favorites]

But that is exactly what they say, my art school professors were dismissive of science and math. I did a project in 1975, the first CG images ever shown at my art school. I wrote a BASIC program to display a stereoscopic replica of Spatial Construction no. 12 by Rodchenko, but I had no way to get a hardcopy so you had to go over to the Comp Sci building to see it live on the graphics terminal using my stereopticon. I showed it to the professor, he snorted dismissively, "oh that's just math" and walked away.

Computer graphics is one of the hot areas in modern art schools, everyone wants to do CG. If you want to do CG, you better study math.

posted by charlie don't surf at 5:10 PM on September 11, 2011 [1 favorite]

Oops, I sort of explained that poorly. What my art professors were saying was that studying math took valuable time away from honing your artistic abilities, so it was a waste of time.

posted by charlie don't surf at 5:14 PM on September 11, 2011

I really kind of disagree. As someone with a PhD in math I'll say that there are a lot of problems with standard math curriculum in the US but, this kind of course tends to be really shallow, not the least of which because it's really hard to teach.

I think if you have a background in combinatorics, for example, problems in "systems and networks" seem pretty intuitive because you've absorbed a ton of elementary concepts and elementary problems. Translating that intuition for students doesn't actually work, because they haven't spent to the time with those elementary problems... no matter how fast their computers are. And then you have the problem that this sort of "translation" is really hard to do and harder to do well. My experience has been that their tends to be a wide gap between how successful the course seemed to the prof. {Oh Hey, we talked about lots of cool problems!} and to the students {Ummm... I don't really understand but the Prof. is really enthusiastic and we can sometimes talk about tangents}

The whole "8th grade mathematics" idea is really a red herring: lots of "advanced" mathematics is really kind of simpler than what you might try to learn in the 8th grade. You can see this in the grave disconnect between the Math GRE and a typical 1st year grad. school math course. Part of the problem is that there tends to be a "all or nothing" approach to foundations in mathematics: either you learn all of the foundations for everything (sort of): grad school, or you don't get a boarding pass to get on the train. IMHO many subjects have a much narrower base, so you get can a student up to speed without sending them into years of remedial math. But, you still need *some* foundation and frankly, most students aren't interested enough to practice the basics of some (effectively) random discipline i.e. combinatorics.

I think the music analogy is useful: this kind of class is sort of expecting the students to be able to improvise and "jam" when they can barely hold their instruments... and math really isn't punk rock as much as if it were cool if it were.... or, I guess I could summarize by saying: students who want to do punk mathematics still need to practice and this course is actually too busy to give them time to practice.

posted by ennui.bz at 6:35 PM on September 11, 2011 [1 favorite]

I would love to give this as a midterm. Obviously it would be easy for me to write. Grading would be challenging, more so than an ordinary midterm, but hopefully at least interesting. But I'm afraid it would be impossible to defend my grades against complaining students...

posted by madcaptenor at 6:45 PM on September 11, 2011

I think much of what is done for grading in university math classes (what students actually pay attention to) is driven by the filter problem and the "convince the student the grade means something" problem. The whole process gets a mind of it's own so that the content and structure of the curriculum becomes more about this than anyone's ideas about math.

And, of course, graduate level "grading" is really binary: do you get it or not...

posted by ennui.bz at 7:55 PM on September 11, 2011

This is easy to say but it really isn't true. The status quo is a mish mash of canned exercises, "real life problems", black boxes, archaic calculator explorations.

The funny thing is that students in the US (especially Calc I students) are actually *terrible* at drills. The best they can do is memorize one, maybe two steps. Ask them to memorize problems/techniques that contain multiple steps and it all falls apart. There are definite problems (and advantages) with "drill" based learning: the strengths and weaknesses of chinese grad students is a testament to this, but it's not generally what happens in the US.

The problem with teaching based on "understanding" or "problem solving" is that both of these are end points, things you want students to be able to do after class is dismissed and, naturally, hard to do. There's something appealing to the 'learning by doing' but as 'pedagogy' it turns into an ideology. The problem with things that are hard to do well is that and you end up with things done badly and by pushing an ideology you end up violating the freedom of the teacher to teach as they see fit.

You mention the "Prussian" system, which really has more to do with the relationship between the university and the state. Teaching in the German system traditionally involves the professor lecturing on whatever the hell they want and the students teaching themselves the basic steps in problem/private sessions. This is how Weierstrass was able to create 'Modern Analysis' as a academic discipline practically out of whole-cloth in Berlin by giving a course of lectures. I've taught in Germany and the academic culture is really different, especially for undegrads.

I could go on but I don't think the problems with math education in the US have anything to do with ideology (much like the problems with US government) but sociology, politics, and economics.

posted by ennui.bz at 8:51 PM on September 11, 2011

Wait, didn't you say you're unemployed? Have you considered looking into these fields?

If only deeply ironic condescension was considered a marketable skill...you'd have a mansion and a yacht!

posted by chronkite at 11:14 AM on September 13, 2011

Post

# Math for Art Students

September 11, 2011 1:20 PM Subscribe

Systems, networks, and strategies is a math course being developed and taught this semester at the San Francisco Art Institute, by Lee Worden. The course-outline-in-progress is online at the linked wiki, including links to course materials like "the two-in-one-out game," "Places to intervene in a system," on-line flocking simulations, and "street math in graffiti art."

As a BFA grad who passed Calculus I and II, I came into this FPP feeling vaguely insulted. Then I saw the college level course linking to 8th grade math materials as the course's last and toughest unit, and I most definitely felt insulted.

I wonder what would happen if I was an undergrad at SFAI and wanted to take a

posted by charlie don't surf at 2:09 PM on September 11, 2011 [1 favorite]

I wonder what would happen if I was an undergrad at SFAI and wanted to take a

*real*math course.posted by charlie don't surf at 2:09 PM on September 11, 2011 [1 favorite]

charlie don't surf, I think the document you linked to is for the first week of class, not the last.

posted by escabeche at 2:17 PM on September 11, 2011

posted by escabeche at 2:17 PM on September 11, 2011

Charlie Dont Surf: One of the reasons I went into the arts (I have an MFA in directing and work as a designer and writer) is because I have a kind of math learning disability. I know I am not the only one who took this path. We all know you are special, but there are larger reasons for things.

posted by MrChowWow at 2:23 PM on September 11, 2011 [1 favorite]

posted by MrChowWow at 2:23 PM on September 11, 2011 [1 favorite]

*I wonder what would happen if I was an undergrad at SFAI and wanted to take a real math course.*

> boasts about having math skills far, far above what the course teaches

> cannot distinguish between first and last entries within a sequence

posted by Sticherbeast at 2:29 PM on September 11, 2011 [5 favorites]

Kleinberg and Easley's Networks, Crowds, and Markets is an excellent book, available online for free (legitimately!), that covers some of the same ground.

posted by madcaptenor at 2:35 PM on September 11, 2011 [3 favorites]

posted by madcaptenor at 2:35 PM on September 11, 2011 [3 favorites]

OK, so it's the last and toughest math lesson on the wiki

When I was in college, "math disability" was not recognized and if you couldn't pass the required Quantitative Reasoning courses, no degree. And this was true for art majors too.

posted by charlie don't surf at 2:36 PM on September 11, 2011 [2 favorites]

*so far*. My mistake. But I'd still be pretty damn insulted if I took a college level course and was given 8th grade materials.When I was in college, "math disability" was not recognized and if you couldn't pass the required Quantitative Reasoning courses, no degree. And this was true for art majors too.

posted by charlie don't surf at 2:36 PM on September 11, 2011 [2 favorites]

Are there other subjects X for which it would seem reasonable to include some time at the beginning of the class on "X anxiety"? Or is math unique in this respect? I've seen references to "math anxiety" in course materials for a lot of math-for-non-math-people classes; I haven't really looked at X-for-non-X-people materials for other values of X, so I don't know.

posted by madcaptenor at 2:40 PM on September 11, 2011

posted by madcaptenor at 2:40 PM on September 11, 2011

*> boasts about having math skills far, far above what the course teaches*

> cannot distinguish between first and last entries within a sequence

> cannot distinguish between first and last entries within a sequence

Sticherbeast: where are you getting these from?

posted by madcaptenor at 2:42 PM on September 11, 2011

Wow, if he can come even close to doing all that with those prereqs, I really want to take that class!

posted by jamjam at 2:44 PM on September 11, 2011

posted by jamjam at 2:44 PM on September 11, 2011

*I'd still be pretty damn insulted if I took a college level course and was given 8th grade materials*.

What if you were in college and that was the level of math you were ready for? Would you be insulted then? That's not a rhetorical question. And it's not an irrelevant question, because that really does happen, and not just at art school, that's for sure.

Another relevant point: K-8 math is not what it used to be. My son started kindergarten last week and on his second day they made a histogram of the number of letters in the names of the kids in the class. I think this is great! I also think it's substantially more sophisticated than the curriculum when I was in school. Lots of mathematicians and educators are working hard to get more math into all parts of the curriculum. Kindergarten histograms are part of this and so, in my view, is Worden's course. I truly don't think his students would be better off taking calculus (but I recognize that there is much room for disagreement on this point.)

posted by escabeche at 2:49 PM on September 11, 2011 [2 favorites]

I got my MFA from SFAI and for fun took the single math course offered one semester because it was being taught by a philosophy teacher with whom I had studied Marx and the Frankfurt School years before. The course was entitled "Space, Time and Number." The course consisted of reading some fascinating stuff on the use of statistics as a means of racial profiling in education, and then watching movies with the theme of Frankenstein (technology out of control) - Blade Runner, The Conversation, Blowup and Zelig. No math was involved in any part of the course.

As I said, this was the sole math course offered at the Institute that year, normally taken only by the BFA students. Math was a joke at the school (early 90s). It had the word "Number" in the title, and therefor was a math class.

posted by johngumbo at 2:54 PM on September 11, 2011

As I said, this was the sole math course offered at the Institute that year, normally taken only by the BFA students. Math was a joke at the school (early 90s). It had the word "Number" in the title, and therefor was a math class.

posted by johngumbo at 2:54 PM on September 11, 2011

I notice that the next course, MATH-106, "Math in Design" is taught by an architect and uses algebra and trig. I suspect we could all agree that professional architects should know calculus.

My university still offers remedial math courses if you can't pass your quant credits. Students who can't pass quant are politely encouraged to seek a degree elsewhere (unless they're football players and part of the "scholar athlete" program, which has looser standards).

I am sorry, I just don't like the stereotype of the artist who is unable to do math.

posted by charlie don't surf at 3:06 PM on September 11, 2011 [1 favorite]

*What if you were in college and that was the level of math you were ready for?*My university still offers remedial math courses if you can't pass your quant credits. Students who can't pass quant are politely encouraged to seek a degree elsewhere (unless they're football players and part of the "scholar athlete" program, which has looser standards).

I am sorry, I just don't like the stereotype of the artist who is unable to do math.

posted by charlie don't surf at 3:06 PM on September 11, 2011 [1 favorite]

It's one thing to say "artists can't do math" and another thing to say "time and effort you spend honing your artistic abilities is time and effort you don't spend learning to do math"

posted by LogicalDash at 3:47 PM on September 11, 2011 [1 favorite]

posted by LogicalDash at 3:47 PM on September 11, 2011 [1 favorite]

*As a BFA grad who passed Calculus I and II, I came into this FPP feeling vaguely insulted. Then I saw the college level course linking to 8th grade math materials as the course's last and toughest unit, and I most definitely felt insulted.*

Considering the number of engineering students in an Intro Calculus class that have an "8th grade" competency in mathematics (do they still even teach algebra in the 8th grade?) I'd say that sounds about reasonable for a class in an art school... in a sense I agree, as a physics major in college I had to take a distribution requirement and thinking it would be nice to take a drawing class i took one that happened to be "Drawing for Non-Art majors." After the first week it was clear that it was going to "Drawing Fun for College Students," I felt insulted.

The problem with these sorts of things is that raising your expectations means a large number of the students will drop out of the class... even if they are still showing up.

I firmly believe you could take a class of 30 art majors and by the end of the semester have them using actual mathematics... but it would probably only be 2 or 3 of them doing anything at that point. Personally, I think that's time better spent than having everyone make-believe: it's better to try something difficult and fail than never try. But, (and this gets into why grade inflation occurs) everyone seems to want a grade to seem meaningful (God knows why, they mostly aren't). We think "gentleman's C's" are an aristocratic privilege rather than a fact of life. So, in order to give a 'C' which is meaningful we create 'A' which isn't.

*I am sorry, I just don't like the stereotype of the artist who is unable to do math.*

Most people can't do math, many engineers basically memorize what they need and do things by rote. It may be nice to get on your high moral horse and say "STANDARDS," but it's actually the demand for standards that creates these sorts of situations. You really can't fail everyone.

posted by ennui.bz at 3:48 PM on September 11, 2011 [3 favorites]

Even in my arts papers, about half of the courses I have taken have devoted at least a lecture to what many people would consider "kindergarten" or, at best, "high school" coverage or introductions to certain subjects, such as grammar, geography, or maths. This is a practical way for the lecturer to at least ensure that everyone is working from the same very basic assumptions. There's no value in having half the class be completely on to it while the other half sit there confused because someone thought it was beneath them to explain what a part of speech was - and coming from a place where they don't teach English grammar at any level of school, I appreciated the "refreshers".

posted by doublehappy at 4:21 PM on September 11, 2011

posted by doublehappy at 4:21 PM on September 11, 2011

In my course on American Politics there was actually a 25 minute argument between the lecturer and a significant minority faction of the class who insisted there were 52 states in the USA.

posted by doublehappy at 4:24 PM on September 11, 2011

posted by doublehappy at 4:24 PM on September 11, 2011

52 states? Seriously? Getting out a map should have disproved that. Unless they thought that, say, the Upper Peninsula of Michigan and Baja California were states.

posted by madcaptenor at 4:30 PM on September 11, 2011

posted by madcaptenor at 4:30 PM on September 11, 2011

Those of us in the international "insert math into everything" conspiracy would like to remind you that we take broadening mathematics education very seriously.

posted by jeffburdges at 4:37 PM on September 11, 2011

posted by jeffburdges at 4:37 PM on September 11, 2011

*Kleinberg and Easley's Networks, Crowds, and Markets is an excellent book, available online for free (legitimately!), that covers some of the same ground.*

Seriously, if you're interested in network theory stuff, go read it. I took Kleinberg and Easley's course the first year they offered it using a very preliminary version of this textbook. It's been a lot of fun to see the text evolve over the past couple years.

posted by zachlipton at 4:48 PM on September 11, 2011

*It may be nice to get on your high moral horse and say "STANDARDS," but it's actually the demand for standards that creates these sorts of situations. You really can't fail everyone.*

Exactly. And this sort of "STANDARDS" nonsense makes it extremely hard for the non-mathematically inclined to try puzzle it out voluntarily once we escape the pass-this-bar part of our education. I can happily float through my life with nothing more complicated than what I learned in middle school (interest, fractions, long division) but I want to learn more without fighting to get through some sort of arbitrary ability marker.

posted by Phalene at 5:07 PM on September 11, 2011 [2 favorites]

I dropped out of art school (SMFA represent!) and ended up getting a phd in math.

So there.

(true story!)

posted by kaibutsu at 5:07 PM on September 11, 2011 [1 favorite]

So there.

(true story!)

posted by kaibutsu at 5:07 PM on September 11, 2011 [1 favorite]

*It's one thing to say "artists can't do math" and another thing to say "time and effort you spend honing your artistic abilities is time and effort you don't spend learning to do math"*

But that is exactly what they say, my art school professors were dismissive of science and math. I did a project in 1975, the first CG images ever shown at my art school. I wrote a BASIC program to display a stereoscopic replica of Spatial Construction no. 12 by Rodchenko, but I had no way to get a hardcopy so you had to go over to the Comp Sci building to see it live on the graphics terminal using my stereopticon. I showed it to the professor, he snorted dismissively, "oh that's just math" and walked away.

Computer graphics is one of the hot areas in modern art schools, everyone wants to do CG. If you want to do CG, you better study math.

posted by charlie don't surf at 5:10 PM on September 11, 2011 [1 favorite]

Also, there are piles of low-hanging fruit in mathematics that don't necessarily depend on being Really Good at Trigonometry Drills, which is mainly what high school math is set up to get you. You can turn the curriculum upside down a bit and develop skills in algebraic techniques in response to more interesting problems. And given that computers are way better than humans at computation, I believe this is the way courses - especially for the non-specialist - should be set up. Attack interesting problems, and learn a bit about techniques and how to throw computers at the crunchy bits along the way.

posted by kaibutsu at 5:11 PM on September 11, 2011

posted by kaibutsu at 5:11 PM on September 11, 2011

*time and effort you spend honing your artistic abilities is time and effort you don't spend learning to do math*

Oops, I sort of explained that poorly. What my art professors were saying was that studying math took valuable time away from honing your artistic abilities, so it was a waste of time.

posted by charlie don't surf at 5:14 PM on September 11, 2011

I was a design student once, and I would have been very interested in a foundational math course that focused on systems, networks, and strategies-- arguably all buzzwords for the design field. Thing is, many design problems touch on these core concepts, but none of us (designers) are trained to approach problems with an awareness of fundamental principles that other fields of study have already established. Statistics (in relation to design research) was as close as it got.

posted by amusebuche at 5:25 PM on September 11, 2011

posted by amusebuche at 5:25 PM on September 11, 2011

*And given that computers are way better than humans at computation, I believe this is the way courses - especially for the non-specialist - should be set up. Attack interesting problems, and learn a bit about techniques and how to throw computers at the crunchy bits along the way.*

I really kind of disagree. As someone with a PhD in math I'll say that there are a lot of problems with standard math curriculum in the US but, this kind of course tends to be really shallow, not the least of which because it's really hard to teach.

I think if you have a background in combinatorics, for example, problems in "systems and networks" seem pretty intuitive because you've absorbed a ton of elementary concepts and elementary problems. Translating that intuition for students doesn't actually work, because they haven't spent to the time with those elementary problems... no matter how fast their computers are. And then you have the problem that this sort of "translation" is really hard to do and harder to do well. My experience has been that their tends to be a wide gap between how successful the course seemed to the prof. {Oh Hey, we talked about lots of cool problems!} and to the students {Ummm... I don't really understand but the Prof. is really enthusiastic and we can sometimes talk about tangents}

The whole "8th grade mathematics" idea is really a red herring: lots of "advanced" mathematics is really kind of simpler than what you might try to learn in the 8th grade. You can see this in the grave disconnect between the Math GRE and a typical 1st year grad. school math course. Part of the problem is that there tends to be a "all or nothing" approach to foundations in mathematics: either you learn all of the foundations for everything (sort of): grad school, or you don't get a boarding pass to get on the train. IMHO many subjects have a much narrower base, so you get can a student up to speed without sending them into years of remedial math. But, you still need *some* foundation and frankly, most students aren't interested enough to practice the basics of some (effectively) random discipline i.e. combinatorics.

I think the music analogy is useful: this kind of class is sort of expecting the students to be able to improvise and "jam" when they can barely hold their instruments... and math really isn't punk rock as much as if it were cool if it were.... or, I guess I could summarize by saying: students who want to do punk mathematics still need to practice and this course is actually too busy to give them time to practice.

posted by ennui.bz at 6:35 PM on September 11, 2011 [1 favorite]

My interesting college math experience:

I took an Advanced Calculus class while at Temple in Philly. The professor told us it was the weeding course that was used to weed out those that shouldn't major in math. We started with about 25 at the beginning of the semester, ended with about 8 or 9, and only 3 or 4 of us passed.

There was only one question on the mid term for Advanced Calc 2: "Describe in as much detail as you can everything we've covered so far."

posted by Bort at 6:36 PM on September 11, 2011

I took an Advanced Calculus class while at Temple in Philly. The professor told us it was the weeding course that was used to weed out those that shouldn't major in math. We started with about 25 at the beginning of the semester, ended with about 8 or 9, and only 3 or 4 of us passed.

There was only one question on the mid term for Advanced Calc 2: "Describe in as much detail as you can everything we've covered so far."

posted by Bort at 6:36 PM on September 11, 2011

*There was only one question on the mid term for Advanced Calc 2: "Describe in as much detail as you can everything we've covered so far."*

I would love to give this as a midterm. Obviously it would be easy for me to write. Grading would be challenging, more so than an ordinary midterm, but hopefully at least interesting. But I'm afraid it would be impossible to defend my grades against complaining students...

posted by madcaptenor at 6:45 PM on September 11, 2011

There was only one question on the mid term for Advanced Calc 2: "Describe in as much detail as you can everything we've covered so far.

*Grading would be challenging, more so than an ordinary midterm, but hopefully at least interesting. But I'm afraid it would be impossible to defend my grades against complaining students...*

I think much of what is done for grading in university math classes (what students actually pay attention to) is driven by the filter problem and the "convince the student the grade means something" problem. The whole process gets a mind of it's own so that the content and structure of the curriculum becomes more about this than anyone's ideas about math.

And, of course, graduate level "grading" is really binary: do you get it or not...

posted by ennui.bz at 7:55 PM on September 11, 2011

ennui.bz:

I'll agree it's hard to do well, and one of the reasons it's hard to do well is that there's a huge expectation of the status quo. And unfortunately, people who do well in math at this point are, I believe, doing it in spite of the status quo, not because of it. This status quo consists of umpteen years of drill training; I personally checked out of math completely because of how tedious and dreadfully boring the system was, before getting into math through self-study. The System is an application of the Prussian model of teaching, big in the mid-19th century, and picked up full-force in the US for teaching math when there was a national need to churn out piles of people who could do rote computation in the absence of computers. These human computers were then employed in solving scientific and engineering problems up through WWII. But then computers started hitting the scene heavily by the seventies, and the need for human computers dropped through the floor.

It's a very different context, but I present for your consideration: The Five Colleges Calculus Project, also known as Calculus in Context. Which was a result of students (and teachers) at Hampshire college realizing that the calculus curriculum wasn't cutting it in the 1970's.

The approach is to attack a

For art students, one should absolutely think about the audience and what one intends for them to take away from the course. I would absolutely argue that teaching them exclusively remedial math would be worse than useless, since you'll have one half the class subjected to the same kind of traumatic experience they had in 8th grade the first time around, and the other half of the class will be bored to tears...

posted by kaibutsu at 8:05 PM on September 11, 2011 [3 favorites]

I'll agree it's hard to do well, and one of the reasons it's hard to do well is that there's a huge expectation of the status quo. And unfortunately, people who do well in math at this point are, I believe, doing it in spite of the status quo, not because of it. This status quo consists of umpteen years of drill training; I personally checked out of math completely because of how tedious and dreadfully boring the system was, before getting into math through self-study. The System is an application of the Prussian model of teaching, big in the mid-19th century, and picked up full-force in the US for teaching math when there was a national need to churn out piles of people who could do rote computation in the absence of computers. These human computers were then employed in solving scientific and engineering problems up through WWII. But then computers started hitting the scene heavily by the seventies, and the need for human computers dropped through the floor.

It's a very different context, but I present for your consideration: The Five Colleges Calculus Project, also known as Calculus in Context. Which was a result of students (and teachers) at Hampshire college realizing that the calculus curriculum wasn't cutting it in the 1970's.

"Confronted with a clear need, those students asked for help. By the mid-1970s, Michael Sutherland and Kenneth Hoffman were teaching a course for those students. The core of the course was calculus, but calculus as it is used in contemporary science. Mathematical ideas and techniques grew out of scientific questions. Given a process, students had to recast it as a model; most often, the model was a set of differential equations. To solve the differential equations, they used numerical methods implemented on a computer."In short, the problem is far from new, and solutions needn't focus purely on combinatorics!

The approach is to attack a

*problem*, develop*techniques*to solve it, and feed it to a*computer*to get the actual solution. There are three phases here: traditional math classes focus on exactly one of them to the near-total exclusion of the other two. Worse, techniques tend to be very problem-specific; if you have the wrong set of techniques, and techniques are all you know, then you're useless. And if the computer already knows all your techniques, you're doubly-useless. Note that I'm not advocating the abandonment of teaching techniques, just a realignment of some very skewed priorities. (It's kind of like fighting the steady right-ward clip of American politics... I say 'health-care' and someone shouts 'communist!')For art students, one should absolutely think about the audience and what one intends for them to take away from the course. I would absolutely argue that teaching them exclusively remedial math would be worse than useless, since you'll have one half the class subjected to the same kind of traumatic experience they had in 8th grade the first time around, and the other half of the class will be bored to tears...

posted by kaibutsu at 8:05 PM on September 11, 2011 [3 favorites]

kaibutsu, your link is broken. Here's a working link.

Oh my god yes.

posted by madcaptenor at 8:15 PM on September 11, 2011 [1 favorite]

*I'll agree it's hard to do well, and one of the reasons it's hard to do well is that there's a huge expectation of the status quo*Oh my god yes.

posted by madcaptenor at 8:15 PM on September 11, 2011 [1 favorite]

From the first link I thought the trading activity was informative.

Reading that first link I thought that outline would make a fantastic middle school curriculum. I wish I had attended schools where math and science were integrated with other subjects.

Most skills start in childhood and formative distinctions about what you are good at and what you are not good at start here. Aaand then people go and have fundamentally different childhoods with varying degrees of support and reinforcement. Aaand then they start to silo students aaand it gets even worse from there.

posted by vicx at 8:29 PM on September 11, 2011

*one person saw that profit from cows was falling, so decided to sell them off to other players*-> Day Traders*several players wanted to sell cows back to me, but I wasn't buying*-> Investment Bankers*some people kept buying large numbers of cows, one "to see what would happen" and others for reasons I don't know*-> Hedgefund Managers*some people stopped buying*-> Economists*nobody tried to negotiate collective behavior with the other players*-> Umm that's cause the regulator was watching what happened when you turned your back?Reading that first link I thought that outline would make a fantastic middle school curriculum. I wish I had attended schools where math and science were integrated with other subjects.

Most skills start in childhood and formative distinctions about what you are good at and what you are not good at start here. Aaand then people go and have fundamentally different childhoods with varying degrees of support and reinforcement. Aaand then they start to silo students aaand it gets even worse from there.

posted by vicx at 8:29 PM on September 11, 2011

*This status quo consists of umpteen years of drill training...*

This is easy to say but it really isn't true. The status quo is a mish mash of canned exercises, "real life problems", black boxes, archaic calculator explorations.

The funny thing is that students in the US (especially Calc I students) are actually *terrible* at drills. The best they can do is memorize one, maybe two steps. Ask them to memorize problems/techniques that contain multiple steps and it all falls apart. There are definite problems (and advantages) with "drill" based learning: the strengths and weaknesses of chinese grad students is a testament to this, but it's not generally what happens in the US.

The problem with teaching based on "understanding" or "problem solving" is that both of these are end points, things you want students to be able to do after class is dismissed and, naturally, hard to do. There's something appealing to the 'learning by doing' but as 'pedagogy' it turns into an ideology. The problem with things that are hard to do well is that and you end up with things done badly and by pushing an ideology you end up violating the freedom of the teacher to teach as they see fit.

You mention the "Prussian" system, which really has more to do with the relationship between the university and the state. Teaching in the German system traditionally involves the professor lecturing on whatever the hell they want and the students teaching themselves the basic steps in problem/private sessions. This is how Weierstrass was able to create 'Modern Analysis' as a academic discipline practically out of whole-cloth in Berlin by giving a course of lectures. I've taught in Germany and the academic culture is really different, especially for undegrads.

I could go on but I don't think the problems with math education in the US have anything to do with ideology (much like the problems with US government) but sociology, politics, and economics.

posted by ennui.bz at 8:51 PM on September 11, 2011

My point about "drills" is that doing canned exercises is not *drilling.* Drills break down complex techniques into digestible parts and are then integrated so that the student is able to perform complex tasks.

Our students get a total mish-mash of things that don't make sense to either the student or even the professor (not many mathematicians do anything which resembles calculus) and are rarely integrated.

Trying to learn by understanding involves reinventing the wheel over and over again. To a certain extent you have to do this in mathematics anyway but, without really skillful "Socratic" guidance it's not going to happen for many.

posted by ennui.bz at 8:57 PM on September 11, 2011

Our students get a total mish-mash of things that don't make sense to either the student or even the professor (not many mathematicians do anything which resembles calculus) and are rarely integrated.

Trying to learn by understanding involves reinventing the wheel over and over again. To a certain extent you have to do this in mathematics anyway but, without really skillful "Socratic" guidance it's not going to happen for many.

posted by ennui.bz at 8:57 PM on September 11, 2011

I think you math guys are missing my point. This SFAI course is sort of a Montessori Kindergarten approach to college math. You're supposed to "feel" math and "develop a relationship" with the subject rather than learn it.

But you who actually learned higher math know it's about developing methods of abstract reasoning with precision and specificity. College courses are not necessarily intended to turn you into a mathematician. But they are intended to teach you how to think mathematically, and how to analyze problems from angles that cannot be solved except mathematically.

Let me give you an analogy. Undergraduate education almost always has a foreign language requirement. You have to take 2 years, and that is not enough to attain any serious level of fluency. But that's not the point. High school English education sucks. So by teaching you how to grapple with the structures of a foreign language forces you to deal with your native language structures. For example, I never learned what the difference between a transitive and an intransitive verb was until I studied foreign language, and hell, my city is UNESCO designated "City of Literature" with some of the best English education in the world. Of course I could use those verb structures, but I never understood how they worked until I studied them in a foreign language.

So you'll have to excuse me if I think that teaching pud math to art students is a terrible insult. It assumes they are incapable of higher reasoning. It seems to stem from the belief that art is a soft subject, with no hard facts or technical skills behind it. I disagree. I still remember using my slide rule in my freshman Mechanical Drafting and Perspective classes. Projective geometry is the mathematical basis of many visual arts, but those are considered "realistic" and art schools often ridicule that as "illustration" and too rigid to be capable of the murky realms of "fine art." Art isn't just a thing you do to emote and express feelings, something you can do if you can't do math and science. It is a system of communication, and has its own advanced methods of abstract thinking that are not innate skills, they must be learned. If you aren't capable of learning a fundamental like math, perhaps you're not cut out for a career that requires abstract reasoning. The world needs truck drivers and cement masons too.

posted by charlie don't surf at 9:26 PM on September 11, 2011 [1 favorite]

But you who actually learned higher math know it's about developing methods of abstract reasoning with precision and specificity. College courses are not necessarily intended to turn you into a mathematician. But they are intended to teach you how to think mathematically, and how to analyze problems from angles that cannot be solved except mathematically.

Let me give you an analogy. Undergraduate education almost always has a foreign language requirement. You have to take 2 years, and that is not enough to attain any serious level of fluency. But that's not the point. High school English education sucks. So by teaching you how to grapple with the structures of a foreign language forces you to deal with your native language structures. For example, I never learned what the difference between a transitive and an intransitive verb was until I studied foreign language, and hell, my city is UNESCO designated "City of Literature" with some of the best English education in the world. Of course I could use those verb structures, but I never understood how they worked until I studied them in a foreign language.

So you'll have to excuse me if I think that teaching pud math to art students is a terrible insult. It assumes they are incapable of higher reasoning. It seems to stem from the belief that art is a soft subject, with no hard facts or technical skills behind it. I disagree. I still remember using my slide rule in my freshman Mechanical Drafting and Perspective classes. Projective geometry is the mathematical basis of many visual arts, but those are considered "realistic" and art schools often ridicule that as "illustration" and too rigid to be capable of the murky realms of "fine art." Art isn't just a thing you do to emote and express feelings, something you can do if you can't do math and science. It is a system of communication, and has its own advanced methods of abstract thinking that are not innate skills, they must be learned. If you aren't capable of learning a fundamental like math, perhaps you're not cut out for a career that requires abstract reasoning. The world needs truck drivers and cement masons too.

posted by charlie don't surf at 9:26 PM on September 11, 2011 [1 favorite]

also from the "street math" link:

posted by ennui.bz at 10:02 PM on September 11, 2011

The community of graffiti writers exhibit particularly rich, sophisticated, efficient, application-specific forms of street mathematics, from which educators can learn much. Nunes et al. consider the significance of studying street mathematics to be in understanding the conditions under which it arises, how educators can use outside math understandings in teaching of formal math, and how these knowledges are developed, used, and transmitted through communities and to novice members.... The community of graffiti writers exhibit particularly rich, sophisticated, efficient, application-specific forms of street mathematics, from which educators can learn much. Nunes et al. consider the significance of studying street mathematics to be in understanding the conditions under which it arises, how educators can use outside math understandings in teaching of formal math, and how these knowledges are developed, used, and transmitted through communities and to novice members...."street" math... really? there's an ugly kernel of "racial knowledge" embedded in this essay. street math is the last thing i'd bring into a classroom of black students, if for no other reason than it would make the parents really mad.

Giant has talked of his use of “axonometric architectural renderings” 3 and the pyramidal form he uses to construct his pieces; there is “inherent balance, strength, and power associated with pyramids”, he says. Delux and Eskae and members of their crew, the Aerosol Syndicate, study sacred geometry and incorporate the “natural” proportions, symmetries, and patterns prescribed by it to create their artwork.

posted by ennui.bz at 10:02 PM on September 11, 2011

As an art school B.F.A. and M.F.A. grad who got up through multivariable calculus and whose sister is a graduate math student, I'm with charlie don't surf, here. This class is kind of insulting, and panders to stereotypes and math anxiety. There are interesting applications of mathematics and hard science to art, and I hope the students who can find them make it past the bullshit.

Then again, I don't claim to remember or be good at math any more. I certainly don't think about it theoretically the way my sister does. I sure do wish I did.

posted by limnrix at 12:40 AM on September 12, 2011 [1 favorite]

Then again, I don't claim to remember or be good at math any more. I certainly don't think about it theoretically the way my sister does. I sure do wish I did.

posted by limnrix at 12:40 AM on September 12, 2011 [1 favorite]

I honestly wonder if you could design a math course for beginners starting with Peano and building your way up. It would probably take fucking forever before you get to stuff like quadratic reciprocity or the Mean Value Theorem, but I think it would be pretty awesome. Or maybe start from somewhere in the middle (basic arithmetic) and build down and up.

posted by kmz at 9:45 AM on September 12, 2011

posted by kmz at 9:45 AM on September 12, 2011

kmz, I think that was the "New Math" curriculum of the 1960s. I remember being taught Peano Postulates in elementary school, then Base 6 math, and then lessons in just enough Set Theory to prove why 1+1=2. I don't know why they don't teach this method any more, I think it was considered a failure.

I used to teach a BASIC programming course back around 1980 and I think I spent the first 3 or 4 weeks covering Peano so they would understand transitive operations, equalities and inequalities, and the precedence of operators. These were random adults with no particular math background, a lot of them told me this was the best math material they ever learned.

posted by charlie don't surf at 12:16 PM on September 12, 2011

I used to teach a BASIC programming course back around 1980 and I think I spent the first 3 or 4 weeks covering Peano so they would understand transitive operations, equalities and inequalities, and the precedence of operators. These were random adults with no particular math background, a lot of them told me this was the best math material they ever learned.

posted by charlie don't surf at 12:16 PM on September 12, 2011

As far as "math anxiety" is concerned, I'm waiting for someone to do a survey of the HLA types of working mathematicians as part of a case that adult mathematical talent is associated (not exclusively, of course) with a kind of 'defect' in the immune system which interferes with the developmentally scheduled decimation of certain populations of neurons in the brain around the time of middle school, as well as in infancy.

posted by jamjam at 5:41 PM on September 12, 2011

posted by jamjam at 5:41 PM on September 12, 2011

jamjam, I'm kind of curious, is there any reason to expect that? For example, are there studies that show that other types of talent are correlated with HLA type?

posted by madcaptenor at 5:53 PM on September 12, 2011

posted by madcaptenor at 5:53 PM on September 12, 2011

*~The world needs truck drivers and cement masons too.~*

Wait, didn't you say you're unemployed? Have you considered looking into these fields?

If only deeply ironic condescension was considered a marketable skill...you'd have a mansion and a yacht!

posted by chronkite at 11:14 AM on September 13, 2011

Ideally, basic computer programming and elementary proof oriented mathematics and should be taught at a very young age, maybe six. Spanish even earlier, obviously.

Artists will happen, which keeps us entertained, but maybe we should heed Banksy's lesson in Exit Through The Gift Shop.

Btw, a friend recently mentioned that Terence Tao's parents were both psychologists who studied child protégées. We apparently understand something after all.

posted by jeffburdges at 9:31 PM on September 13, 2011

Artists will happen, which keeps us entertained, but maybe we should heed Banksy's lesson in Exit Through The Gift Shop.

Btw, a friend recently mentioned that Terence Tao's parents were both psychologists who studied child protégées. We apparently understand something after all.

posted by jeffburdges at 9:31 PM on September 13, 2011

chronkite, you were specifically directed by cortex to stop harassing me. I am writing with cortex's explicit permission to tell you to stop defaming me and spreading lies that I am unemployed. You are not helping your position to defy moderators by threadshitting.

posted by charlie don't surf at 10:36 PM on September 13, 2011

posted by charlie don't surf at 10:36 PM on September 13, 2011

Jeff, I was one of the early advocates of "computer literacy," I used to lug around an Apple II in a big case and give big demos to PTAs and the like. But now I am opposed to the whole concept. IMHO it is preferable to focus on math early, that gives you a better foundation for programming, and everything else. It is often said that it is easier to teach an artist how to use computers, than to teach a computer expert to be an artist. Same with almost any application of computers.

Computers are becoming a blue collar trade, rather than a profession. Even in my day, the Comp Sci department at my university had the lowest graduation rate of any department. Anyone with 2 years of CS classes could drop out, get hired and begin their career, that's what I did. The way I think of computer literacy now, it's as if schools expected to everyone learn to repair engines starting in elementary school, because society depends on motor vehicles. Sure, some of them might become mechanics, some might even design cars and do automotive research. But you don't need to know how to design a Ferrari just to drive a car. And you don't want to set your curriculum based on an expectation that everyone is going to be a mechanic.

posted by charlie don't surf at 10:57 PM on September 13, 2011

Computers are becoming a blue collar trade, rather than a profession. Even in my day, the Comp Sci department at my university had the lowest graduation rate of any department. Anyone with 2 years of CS classes could drop out, get hired and begin their career, that's what I did. The way I think of computer literacy now, it's as if schools expected to everyone learn to repair engines starting in elementary school, because society depends on motor vehicles. Sure, some of them might become mechanics, some might even design cars and do automotive research. But you don't need to know how to design a Ferrari just to drive a car. And you don't want to set your curriculum based on an expectation that everyone is going to be a mechanic.

posted by charlie don't surf at 10:57 PM on September 13, 2011

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posted by Foci for Analysis at 1:34 PM on September 11, 2011