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Algebra for All: Educators Challenge Idea That Math Skills Must Come Naturally

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Re: Algebra for All: Educators Challenge Idea That Math Skills Must Come Naturally

#11

Post by kklein »

I now do a lot of stats for my work (I'm a psychometrician), and as such, people see me as being good at math, but in school, I was a mess.

Here is the problem with math education: The way we teach it guarantees that only those with a cognitive predisposition to it will develop an interest. Math is just a tool. You can use it to do all sorts of really cool things, but you never even get to see those things in school. What you see is an entire evening shot solving quadratic equations for no reason whatsoever.

I actually enjoyed geometry and trig, and the former is still useful many times a year. I also enjoyed physics, which just just math.

Basically, we approach teaching math the way people used to approach teaching language (full disclosure: I teach foreign language--I develop standardized language tests, which is where I use a lot of math): memorizing conjugations, etc., rather than focusing on tasks that one can complete using what you know already, but which will stretch you and make you develop new skills. Language teaching has realized that the way to keep people who may not be predisposed to language (another very difficult, largely-left-brain activity that I actually did like in school) interested is to keep the application of skills front and center at all times. Not everyone will be a great mathematician or become highly proficient in a foreign language, but many more people than do now could do very, very well if classes were more focused on application than "here are 100 problems; they're due tomorrow."

Re: Algebra for All: Educators Challenge Idea That Math Skills Must Come Naturally

#12

Post by ahoyhere »

In many countries, math has long been recognized as a tough subject that can be mastered through hard work, said Tom Loveless, a scholar at the Brookings Institution who analyzes international math test results and cultural differences. Efforts to make math more fun or dress up textbooks are not the answer, he said.

OK, yes, but the state of American textbooks is TERRIBLE. They don't need shiny graphics or examples using social cliques. They don't need personality quizzies. (Ex-Winnie Cooper, I am pissed at you.)

In the lower grades, some schools are subsidizing textbooks by purchasing ones from companies that use brand names in the problems. E.g. "If Tommy has 3 Oreos..." That is not the kind of dressing up they need, no.

But if you compare your basic Silver Burdett piece of shit to a book like "Mathematics: A Human Endeavor" or Geometry by the same author (Harold Jacobs), you'll see the difference.

I have the Geometry book. It uses Escher, Alice in Wonderland, and other great and useful devices for explaining math. (Hofstadter uses the same devices - not a coincidence, I am sure.) It uncovers math in everyday life and unexpected places. It reveals. It pulls back the curtain. That is the magic of learning.

It does not pander, which is what all the other textbooks do. And, in fact, the entire school system does.

Re: Algebra for All: Educators Challenge Idea That Math Skills Must Come Naturally

#13

Post by telegraph »

Shooter wrote: post #5
telegraph wrote: post #2

This was somewhat buried in the article, and it deserves repetition: "In many countries, math has long been recognized as a tough subject that can be mastered through hard work, said Tom Loveless, a scholar at the Brookings Institution who analyzes international math test results and cultural differences. Efforts to make math more fun or dress up textbooks are not the answer, he said." It's absolutely shocking to me…

RE: "Well, I was never good at math either!" Even more upsetting to me (as a horrible math student in K-12) was: "Well, you'll never really use this in the real world anyway. But you should learn it. Now stop asking 'Why?'" It is almost impossible to learn something if you have no interest in it, and it's difficult to develop an interest in something very complicated without at least a basic understanding of WHY you…

I have to respectfully disagree with you. It's true that there is a large group of kids who would be better served if their teachers focused more on applications; however, I think that there's an equally large (if not bigger) group of students for whom learning about applications is not helpful. When I was in public school, my teachers always made an effort to highlight how the math we were learning could be applied to real world problem -- the end result was that often the struggling students would say "You use this to build rocket ships? Well I'm NEVER going to do that... I give up."

The most important thing we can do is change our attitude. It's hard to develop an interest in something that you find difficult when you're receiving mixed messages from all of the adults in your life; when adults will demand you get better grades all while telling you it's okay because "math is for nerds" or "not everyone can do math."

I did well (good grades, but it's not like I was Terence Tao or anything) in math in school, and my teachers in other subjects, my coaches, my friends' parents, etc, acted like I was a freak because of it. You can't give a high five with one hand while you're pointing and laughing with the other. This is the attitude that must change before we can raise a generation who take pride in developing math skills.

Re: Algebra for All: Educators Challenge Idea That Math Skills Must Come Naturally

#14

Post by lutorm »

telegraph wrote: post #2

This was somewhat buried in the article, and it deserves repetition: "In many countries, math has long been recognized as a tough subject that can be mastered through hard work, said Tom Loveless, a scholar at the Brookings Institution who analyzes international math test results and cultural differences. Efforts to make math more fun or dress up textbooks are not the answer, he said." It's absolutely shocking to me…

There is a strong mindset about math that "you're either good at it or not". It's a nice application of the research by Carol Dweck about people's views of intelligence, popularized in this article: http://www.scientificamerican.com/article.cfm?id=the-secret-...

Re: Algebra for All: Educators Challenge Idea That Math Skills Must Come Naturally

#15

Post by tokenadult »

ahoyhere wrote: post #12

In many countries, math has long been recognized as a tough subject that can be mastered through hard work, said Tom Loveless, a scholar at the Brookings Institution who analyzes international math test results and cultural differences. Efforts to make math more fun or dress up textbooks are not the answer, he said. OK, yes, but the state of American textbooks is TERRIBLE. They don't need shiny graphics or examples u…

the state of American textbooks is TERRIBLE.

Fully agreed. And most textbook evaluation processes used in American schools ensure that they will remain terrible. A favorite author of a favorite series of math textbooks once commented, "I would like to make one comment here. Some of my American colleagues have explained to me that American students are not really accustomed to thinking and working hard, and for this reason we must make the material as attractive as possible. Permit me to not completely agree with this opinion. From my long experience with young students all over the world, I know that they are curious and inquisitive and I believe that if they have some clear material presented in a simple form, they will prefer this to all artificial means of attracting their attention--much as one buys books for their content and not for their dazzling jacket designs that engage only for the moment. The most important thing a student can get from the study of mathematics is the attainment of a higher intellectual level."

http://math.berkeley.edu/~wu/Gelfand.pdf

Re: Algebra for All: Educators Challenge Idea That Math Skills Must Come Naturally

#16

Post by Shooter »

telegraph wrote: post #13
Shooter wrote: post #5

Earlier quoted context omitted.

RE: "Well, I was never good at math either!" Even more upsetting to me (as a horrible math student in K-12) was: "Well, you'll never really use this in the real world anyway. But you should learn it. Now stop asking 'Why?'" It is almost impossible to learn something if you have no interest in it, and it's difficult to develop an interest in something very complicated without at least a basic understanding of WHY you…

I have to respectfully disagree with you. It's true that there is a large group of kids who would be better served if their teachers focused more on applications; however, I think that there's an equally large (if not bigger) group of students for whom learning about applications is not helpful. When I was in public school, my teachers always made an effort to highlight how the math we were learning could be applied…

I agree with you wholeheartedly about the mixed signals thing. I definitely experienced that phenomena because of my science pursuits. I can also understand your point about how certain students would develop a "Well I'm NEVER going to do that..." attitude when shown certain specific examples of math. But a more practical applications approach - no matter how poor the examples - should still interest more students than a "I don't know why you have to do it, but just do it" approach.

I think your disagreement with me comes about in part because you are thinking in more concrete, specific terms than I am. You're correct that "You can use this math to build rocket ships" would probably not have helped me if I didn't have an interest in rocket ships. But a teacher wouldn't necessarily use just a single type of example. Beyond that, I'm saying that my teachers never explained the overarching concepts of math and how they were related or explained - in GENERAL terms - what it could be used to do. Each math 'concept' was presented as a discrete type of chore that you completed in order to satisfy some perverse deity for no apparent reason. Math was not presented as a language of logic and reason that could be used to solve practical problems, but as a completely made up busywork exercise. I might as well have spent my time memorizing Klingon grammar rules. I literally didn't realize calculus was the study of change until college, even after having passed a course in it! Maybe you had a better experience with math instructors, and it is just difficult for you to understand how woefully bad some practicing math instructors actually are?

Re: Algebra for All: Educators Challenge Idea That Math Skills Must Come Naturally

#17

Post by telegraph »

Shooter wrote: post #16
telegraph wrote: post #13

Earlier quoted context omitted.

I have to respectfully disagree with you. It's true that there is a large group of kids who would be better served if their teachers focused more on applications; however, I think that there's an equally large (if not bigger) group of students for whom learning about applications is not helpful. When I was in public school, my teachers always made an effort to highlight how the math we were learning could be applied…

I agree with you wholeheartedly about the mixed signals thing. I definitely experienced that phenomena because of my science pursuits. I can also understand your point about how certain students would develop a "Well I'm NEVER going to do that..." attitude when shown certain specific examples of math. But a more practical applications approach - no matter how poor the examples - should still interest more students th…

Re: my experience with math instructors, you're probably right. I do think that there's a certain sort of base level of application information that should be imparted with any given mathematical topic (for instance, that calculus is about change! Wow, I'm sorry you had such awful teachers), I just think that focus on applications is a method that's been tried already and just hasn't seemed to improve math education enough.
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