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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)

#11

Post by chrjozefharibo »

bshep wrote: post #7
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…

This doesnt make any sense: sqrt(2x+1) = sqrt(x) + 1 EDIT: Ahh I thought he was saying that he had factorized/simplified the left side into the right and it wasnt making any sense.

I solved it numerically. x=4 or x=0

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

#12

Post by XFrequentist »

bshep wrote: post #7
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…

This doesnt make any sense: sqrt(2x+1) = sqrt(x) + 1 EDIT: Ahh I thought he was saying that he had factorized/simplified the left side into the right and it wasnt making any sense.

Yes it does: x=4,0

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

#13

Post by anuleczka »

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?

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

#14

Post by flatline »

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?

The conceptual understanding is certainly essential, but if you want to use a computer to do symbolic/algebraic manipulation, how could you be sure to understand the results or even properly phrase the question without a thorough understanding of the symbols and the rules for their manipulation? The best I think that something like Alpha could do is to help elucidate the underlying principles or give you a quick answer for guesswork or estimation, like a calculator.

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

#15

Post by wortiz »

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…

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 assignments, and they really don't understand the actual math I think your problem is probably that most are using a solutions manual or spending what would seem too much time solving the homework problems.

As for solving word problems or practical problems I believe that this is exactly what math should be for especially at the college algebra level. To be serious most students entering college who want or are going to pursue a degree in mathematics are going to start off closer to the calculus level and maybe trigonometry depending on underlying circumstances. What people in college algebra are going for is a degree where math has to be practical and the more diverse applications they see the better. To give a simple example take logarithms: if you were to teach logarithms on the sole basis of algebraic symbols and expressions when it comes time that these students need to apply logarithms to real world problems (like say compound interest) there is going to be a good chance that they didn't really comprehend logs when they were taught them and won't be able to use them properly.

Which brings me to another point for word problems: word problems exist because they make students think and relate math to the real world it is fundamental to learning for many students to apply mathematical concepts in a multitude of ways in order to actual grasp a concept and one of the easiest ways to do this is to place that concept into word problems.

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

#16

Post by yequalsx »

wortiz wrote: post #15
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…

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 freak out when presented with a formula involving logs. I'm all in favor of applications but isn't this the job of other subjects? The applications should be taught in the subjects that apply it. The goal of a mathematics class ought to be to understand mathematics.

This lecture,

http://www.youtube.com/watch?v=WwslBPj8GgI

is long but well worth watching. He provides strong evidence that students learn to solve word problems but haven't the slightest idea of what is really going on. They are memorizing steps. This happens at Harvard and the community college.

I've given my students the standard word problems on travelling problems. They get the problems right. Then I ask them this simple problem and they universally get is wrong:

You drive 1 mile at 40 mph and then the next mile drive 60 mph. What is your average speed? (Almost everyone says 50 mph.) We aren't teaching thinking skills. We are teaching memorization of problem types. Almost none of them is actually practical, correct, or useful.

But why are we teaching travelling problems in a math class? I think it should be taught in physics.

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

#17

Post by yequalsx »

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?

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 equations to solve. All of them can be manipulated to yield the solution (or be reduced to showing all numbers are solutions or have no solutions). Linear equations are really 1st degree polynomials. What about second degree polynomials? After a clever bit of insight and some work we get that all 2nd degree polynomials can be solved. The quadratic equation is a solution to a problem in mathematics. It's useful as it leads to a greater understanding of mathematics.

I believe that this is what mathematics courses ought to focus on. Not on problems that involve throwing a ball in the air and predicting how long it takes to hit the ground.

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

#18

Post by wortiz »

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…

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 of a math class being that students should come out understanding math I completely agree but the beauty of math is that it is applicable everywhere and the goal of teaching a math class should be that students understand mathematics and where to apply it.

I couldn't imagine being taught vector calculus without some mention of applications and examples, my professor catered more towards mathematics majors with an abundance of Tensor notation and proofs but he never failed to understand that many in his class learned well by physical and other practical examples such as magnetism or fluids and so on.

Although I failed to watch your video I believe there is most likely a counterargument to word problems and what effect they have on students because if students really are solving word problems with the math they are learning the issue isn't that they don't understand what is going on but rather how to apply it to an actual math problem. Either that or the word problems do not incorporate well enough with the math that a student can grasp it quickly without knowing underlying ideas.

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

#19

Post by adamtj »

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 secondary to the real goal. Without a good education, most people are sloppy thinkers -- and they vote more frequently than they solve equations.

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

#20

Post by yequalsx »

kscaldef wrote: post #9
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…

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 can't be solved by algebraic methods and anyone who really needs to solve an equation and trust the answer is better off having a computer do the computation.

In solving the 30 problems one might get to a point in understanding why sqrt(2x+1) = sqrt(x) + 1 is slightly harder than solving sqrt(x+1) = sqrt(x) + 1. In solving 30 problems one might get to a point to discover why sqrt equations can be solved but why we don't solve cube root equations. Or why sqrt(2x+3) = x is fundamentally easier than sqrt(2x+3) = x + 1. You won't get this from solving word problems.

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