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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)

#21

Post by yequalsx »

wortiz wrote: post #18
yequalsx wrote: post #16

Earlier quoted context omitted.

I strongly disagree with the notion that college algebra ought to be the place where one learns practical applications of mathematics. A valuable skill for any educated person is the ability to plod through minutia and make sense of it. Being able to be focused on the point at hand and not let distractions cloud judgment is a valuable skill. If one really understands the mechanics of logs then I think they will not f…

To answer your last question first I think traveling problems are taught in math because speed and time are easy for students to relate to, the same way that finding the height of a flagpole by its shadow problems are easy for students to visualize and relate to. As for average speed that is one of those concepts that really isn't that relatable and should probably require an introduction beforehand. As for the goal…

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.

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

#22

Post by olliesaunders »

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…

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.

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

#23

Post by yequalsx »

SlyShy wrote: post #8
yequalsx wrote: post #5

Earlier quoted context omitted.

A great deal of work. Some problems won't be easily changed to suit his paradigm. For instance, how does one go about redefining an equation like, sqrt(2x+1) = sqrt(x) + 1? I'd like to know what this guy does for these types of problems. I've been teaching community college mathematics for 10 years and we simply don't have the time to do what he says. Maybe I'm bad at motivating students but my anecdotal experience i…

Math major here: I think actually he is arguing for a cure to the apathy. The reason people are apathetic about mathematics is it is presented like a dry and idiotic subject. A common complaint about word problems is "this is contrived, why does the water tank have exactly that parabolic curve, pfft math sucks, I quit" whereas the common complaint about questions that are pure symbol manipulation is "this doesn't mat…

Using word problems is one likely to discover why sqrt(2x+1) = sqrt(x) + 1 is fundamentally different than cuberoot(2x+1) = cuberoot(x) + 1? Give this problem to calc one students and many will do both problems incorrectly. They'll incorrectly cube both sides in the second equation. They don't understand why we solve sqrt problems but not cube root problems but they know how to compute doubling time for bacteria growing in a petri dish.

Your fourth paragraph is an argument in favor of what I've been saying. The applications we teach ought to be applications to math; not to physics or biology.

But back to the apathy problem. People aren't going to be motivated by number theory or bacteria in a petri dish if they possess too great a disdain for knowledge.

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

#24

Post by wortiz »

yequalsx wrote: post #21
wortiz wrote: post #18

Earlier quoted context omitted.

To answer your last question first I think traveling problems are taught in math because speed and time are easy for students to relate to, the same way that finding the height of a flagpole by its shadow problems are easy for students to visualize and relate to. As for average speed that is one of those concepts that really isn't that relatable and should probably require an introduction beforehand. As for the goal…

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.

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

#25

Post by adamtj »

yequalsx wrote: post #16
wortiz wrote: post #15

Earlier quoted context omitted.

I'm going to chime in from experience and say that your college algebra students are the bottom of the barrel in regards to math students. With that respects there can be many reasons why they are there: they didn't care about math, they never really understood math, and/or they never really tried to get math. If you are judging the ability of finishing word problems in the textbook, I'm assuming for homework assignm…

I strongly disagree with the notion that college algebra ought to be the place where one learns practical applications of mathematics. A valuable skill for any educated person is the ability to plod through minutia and make sense of it. Being able to be focused on the point at hand and not let distractions cloud judgment is a valuable skill. If one really understands the mechanics of logs then I think they will not f…

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 reasons he's talking about. That problem is completely unlike anything they've ever solved in high school, because it doesn't give them the numbers to average. It's a two step problem where they need to use the given numbers in one formula, to get the resulting numbers for the second. HS students don't learn to solve problems: they learn to match paragraphs to formulas, then plug and chug.

Also, don't be such a purist. It's not useful. There is a great deal of overlap between math and physics. Physicists often invent new math to understand physics, and old math is often found to describe some newly discovered physical phenomenon.

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

#26

Post by yequalsx »

olliesaunders wrote: post #22
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…

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!

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

#27

Post by yequalsx »

adamtj wrote: post #19
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…

During training, soccer players often run around the field in a big group, but you'll never see them do that during a game. Running laps around the field isn't the goal, but it does help them achieve their goals. His basic argument is that the point of high school math education is to teach kids how to reason and understand the world quantitatively. I agree. The teaching of algebra to high school students is secondar…

Teaching so called practical word problems is not accomplishing this goal.

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

#28

Post by yequalsx »

adamtj wrote: post #25
yequalsx wrote: post #16

Earlier quoted context omitted.

I strongly disagree with the notion that college algebra ought to be the place where one learns practical applications of mathematics. A valuable skill for any educated person is the ability to plod through minutia and make sense of it. Being able to be focused on the point at hand and not let distractions cloud judgment is a valuable skill. If one really understands the mechanics of logs then I think they will not f…

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 goal and it's distracting from the learning of mathematics.

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

#29

Post by yequalsx »

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.

Perhaps you should watch the video and then you would realize that your characterization of this professor and me is wrong.

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

#30

Post by [deleted] »

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?

[deleted]
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