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Dan Meyer dissects the flaws of math textbooks (video)

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Re: Dan Meyer dissects the flaws of math textbooks (video)

#31

Post by zackattack »

anuleczka wrote: post #13
yequalsx wrote: post #6

I'm a teacher of mathematics at a community college. It appears to me that the crux of the problem is that people, including the guy in the video, confuse problem solving with mathematics. The utility of mathematics comes in the remarkable fact that a great deal of phenomena can be adequately modeled mathematically. The focus of an algebra class ought to be in learning the language of algebra. That is, in manipulatin…

In a world where Wolfram Alpha can do all the algebraic calculations for you, isn't learning to solve problems more relevant? I'd say that problem solving is the core of mathematics. Am I wrong?

Let me share a frustrating experience I recently had.

I hired some dude off Craigslist to install my TV wall mount because I don't have the proper tools. I tried to explain where I wanted the TV: I want it to be centered in the wall, but then moved a few inches to the right.

He simply couldn't understand what I was saying. It blew my mind, I had to just measure it out myself and mark the spot. If he had a solid of understanding of basic high school algebra, he would have been able to formulate the problem in his head.

Done.

Re: Dan Meyer dissects the flaws of math textbooks (video)

#32

Post by dustingetz »

yequalsx wrote: post #6

I'm a teacher of mathematics at a community college. It appears to me that the crux of the problem is that people, including the guy in the video, confuse problem solving with mathematics. The utility of mathematics comes in the remarkable fact that a great deal of phenomena can be adequately modeled mathematically. The focus of an algebra class ought to be in learning the language of algebra. That is, in manipulatin…

addressing this statement in a vaccuum: "The focus of an algebra class ought to be in learning the language of algebra"

i think learning the relevance of its applications goes hand-in-hand and is necessary for a deeper understanding.

Re: Dan Meyer dissects the flaws of math textbooks (video)

#33

Post by dhimes »

yequalsx wrote: post #28
adamtj wrote: post #25

Earlier quoted context omitted.

His argument is that current HS math doesn't provide enough distractions. Students don't learn to focus on the problem at hand, because the problem is already in sharp focus. All the variables are provided. The word problem is a slightly jumbled description of the formula to use. All you have to do is look up the formula, then plug in the variables. Your students can't solve the travelling problem for the very reason…

You wrote: "HS students don't learn to solve problems: they learn to match paragraphs to formulas, then plug and chug." I agree completely and this is why I advocate for an end to the focus on so called practical word problems in high school in algebra classes. It should be in physics where one learns about travelling problems not in algebra. The focus on so called practical word problems is not accomplishing the goa…

I taught physics in a community college as a full-time prof for 10 years, and had the occasion to teach math there a few times as well. After that stint, I started work with an ed software company developing math content for algebra students in the cc.

In my experience, the "word problems" can be used to motivate the students as to the interesting part of what they are studying. My focus wasn't on making them learn how to reason through complicated applications, it was on getting them to master the skills. So in that sense I agree with you. However, building a story around it (how do you determine which cell phone plan to buy?) helps keep their attention and shows them that they- yes THEY (the "bottom of the barrel" as was noted above- but I'll clarify this below)-- can apply math to their lives and live more intelligently. And getting students to that stage is my life's mission.

I think where math goes wrong is displayed beautifully in the rational expressions units (I didn't go to the original link, so forgive me if I'm entirely redundant here). When I was building the math content for the ed s/w company I was struck that nowhere in the chapter where students learn to simplify fractions involving a polynomial numerator and a polynomial denominator (tough stuff when you are first learning it) nowhere in the textbooks did they tell the student WHY. Why do all this hard work? What is the answer that we seek from all this?

[rant] About the idea of "stupid teachers teaching stupid students" in community college: Anyone who truly speaks from experience knows better. In a cosmopolitan setting you will have downright brilliant students in your classes- especially in your night classes. I've had many ivy-leaguers in my classes, top accountants for Exxon-Mobile and other high-power operators, sometimes from government agencies (I taught in Alexandria Virginia, about a mile from the Pentagon, where Mrs. Biden currently teaches). A common reason for them to be there? They've burned out in their careers and want to do something that "makes a difference." Going to med or vet school was common. They've got the degree, they've got the grades, they just need a couple of classes that they didn't take as undergrads, they're too smart to spend the money on a school that won't help them any more than a little ol' cc will. Keeping their job for an extra year and taking night classes is a smart move, so they come to the local cc. [/rant]

Re: Dan Meyer dissects the flaws of math textbooks (video)

#34

Post by yequalsx »

dhimes wrote: post #33
yequalsx wrote: post #28

Earlier quoted context omitted.

You wrote: "HS students don't learn to solve problems: they learn to match paragraphs to formulas, then plug and chug." I agree completely and this is why I advocate for an end to the focus on so called practical word problems in high school in algebra classes. It should be in physics where one learns about travelling problems not in algebra. The focus on so called practical word problems is not accomplishing the goa…

I taught physics in a community college as a full-time prof for 10 years, and had the occasion to teach math there a few times as well. After that stint, I started work with an ed software company developing math content for algebra students in the cc. In my experience, the "word problems" can be used to motivate the students as to the interesting part of what they are studying. My focus wasn't on making them learn h…

"I think where math goes wrong is displayed beautifully in the rational expressions units (I didn't go to the original link, so forgive me if I'm entirely redundant here). When I was building the math content for the ed s/w company I was struck that nowhere in the chapter where students learn to simplify fractions involving a polynomial numerator and a polynomial denominator (tough stuff when you are first learning it) nowhere in the textbooks did they tell the student WHY. Why do all this hard work? What is the answer that we seek from all this?"

What do you think are the answers to your questions?

Re: Dan Meyer dissects the flaws of math textbooks (video)

#35

Post by kscaldef »

yequalsx wrote: post #20
kscaldef wrote: post #9

Earlier quoted context omitted.

Step 1 is figuring out why someone would want, or need, to solve that equation. He's by no means saying that students don't have to learn how to do algebraic manipulations. He's saying that without motivating the process and letting students understand the process that leads to the algorithm, they aren't really going to learn how to use math in a way that will be helpful to them. I suspect that he'd also argue that a…

Do they really learn such motivation from solving word problems? Especially when many word problems are not practical or even correct? How about this for motivation, we solve such equations because we can. Solving equations is useful and the more equations we can solve the better. It's not really motivating when we give a word problem whose model is a radical equation and then say solve the equation. Most equations c…

Your second paragraph contradicts itself. You say solving equations is useful. So, why not show your students the use?

Re: Dan Meyer dissects the flaws of math textbooks (video)

#36

Post by yaks_hairbrush »

dhimes wrote: post #33
yequalsx wrote: post #28

Earlier quoted context omitted.

You wrote: "HS students don't learn to solve problems: they learn to match paragraphs to formulas, then plug and chug." I agree completely and this is why I advocate for an end to the focus on so called practical word problems in high school in algebra classes. It should be in physics where one learns about travelling problems not in algebra. The focus on so called practical word problems is not accomplishing the goa…

I taught physics in a community college as a full-time prof for 10 years, and had the occasion to teach math there a few times as well. After that stint, I started work with an ed software company developing math content for algebra students in the cc. In my experience, the "word problems" can be used to motivate the students as to the interesting part of what they are studying. My focus wasn't on making them learn h…

In response to yequalsx:

I see 2 applications of rational expressions off the top of my head: 1) From an abstract viewpoint, the message is "We can do the same stuff with polynomials that we do with integers. The only issue is that factoring is harder." This message gets very garbled 2) Solving ratio problems A/B = C/D come up very often. For example: I've won 43/87 freecell games. How many in a row do I have to win to get to 70%?

Re: Dan Meyer dissects the flaws of math textbooks (video)

#37

Post by argv_empty »

wortiz wrote: post #24
yequalsx wrote: post #21

Earlier quoted context omitted.

The experience of the professor at Harvard in the video contradicts your last paragraph. They know how to apply the math but they don't understand the problem. And the traveling problem I gave underscores this point. It's a very simple problem and almost no one gets it correct.

Then perhaps you and him are assigning the wrong word problems or not giving proper introductions to said word problems.

If all students are taught to do is "memorization of problem types" (to borrow GP's term), then they will only be able to handle actual problems that match one of the necessarily finite set of types of problems they have memorized. A different selection of problem types to memorize will not provide general coverage -- that requires learning to construct a solution to a new type of problem.

Re: Dan Meyer dissects the flaws of math textbooks (video)

#38

Post by jimbokun »

yequalsx wrote: post #17
anuleczka wrote: post #13

Earlier quoted context omitted.

In a world where Wolfram Alpha can do all the algebraic calculations for you, isn't learning to solve problems more relevant? I'd say that problem solving is the core of mathematics. Am I wrong?

Yeah, Wolframalpha is a disruptive technology. Is it still relevant to learn algebraic manipulations? I don't know. There are compelling arguments for both points of view. When you say problem solving do you really mean so called practical applications? If so then I disagree. If you mean solving problems to understand the essence of mathematical ideas then I agree. For instance, linear equations are the easiest equat…

"Yeah, Wolframalpha is a disruptive technology. Is it still relevant to learn algebraic manipulations?"

We've had calculators for decades now, and my kids are still learning how to do arithmetic.

Re: Dan Meyer dissects the flaws of math textbooks (video)

#39

Post by glyn »

yequalsx wrote: post #6

I'm a teacher of mathematics at a community college. It appears to me that the crux of the problem is that people, including the guy in the video, confuse problem solving with mathematics. The utility of mathematics comes in the remarkable fact that a great deal of phenomena can be adequately modeled mathematically. The focus of an algebra class ought to be in learning the language of algebra. That is, in manipulatin…

While I'd agree that students often approach word problems by basically memorizing mappings between a problem class and a small set of equations, I'm not sure that merely teaching them the mechanics of mathematics in the abstract is sufficient for imparting a thorough, practical understanding of the subject.

My experience with math-related courses was that I had the greatest difficulty generalizing the word-problem aspects into being able to reason about novel problems. A lot of the lectures and texts kind of paid lip service to the idea of problem solving in a general manner, but I think there's a lot of room for improvement in terms of capturing and teaching the underlying requisite types of mental activity, in a way that's explicitly procedural.

Re: Dan Meyer dissects the flaws of math textbooks (video)

#40

Post by olliesaunders »

yequalsx wrote: post #26
olliesaunders wrote: post #22

Earlier quoted context omitted.

You can give yours students an incredibly useful skill that has inordinate practical application, exciting their minds with possibilities, intrigue, and a sense of empowerment. Or you can engage them in rote mechanics, fail to impart the usefulness of mathematics, and send them all to sleep.

Great generalization and oversimplification. How about this oversimplification? Or you can teach a generation of students that if isn't 'practical' then it shouldn't be done and certainly isn't worth any effort or struggle. Hopefully then, we can eliminate poetry, music, art, literature, and p.e. We have practical problems to solve!

I consider engaging and consuming forms of art akin to play. At first sight to spend lots of time playing might be seen as a waste of time but the fact that a child prevented from playing would fail to develop properly says something about its purpose. Basically I don't agree that those subjects are purposeless.
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