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Keep your HIGH SCHOOL math students engaged with these techniques

BLOG
https://www.edutopia.org/blog/9-strategi...osamentier

Book
https://www.booktopia.com.au/effective-t...40948.html
The approach is still wrong. One of my beefs is that the necessary math for engineering is presented in such a theoretical and sterile way, and without real application, with the idea that it must be laid as a foundation ahead of the need. How will that generate interest? How does that help the student understand what's going on in his circuit on the workbench? It won't. How about teaching the circuits and letting the students run up against problems they don't have the math tools to solve yet, then pausing the electronics work to learn what now suddenly there's an interest and application for. That's how I got through a lot of stuff, teaching myself. I kind of have to learn things my own way anyway.
from the referenced BLOG:
Teachers of mathematics ...basic motives already present ... to maximize engagement ... Exploiting student motivations ... can lead to ... artificial mathematical problems and situations ... OR ... generate genuine interest ...

When I instruct in TECHNICAL MATHEMATICS the schwerpunkt is measurement. I recognize the many branches and diversity of mathematics with my students and wholeheartedly encourage them to develop mathematical reasoning omitted from my limited and constrained pedagogy. This accommodation is intrinsic rather than inimical to their edification and as a class, we return to measurement from these intellectual excursions. I am confident this phenom is not exclusive to me.

BEST!
SlideRule
(07-08-2017 02:39 AM)Garth Wilson Wrote: [ -> ]One of my beefs is that the necessary math for engineering is presented in such a theoretical and sterile way, and without real application...
Sounds like you have a beef with teaching pure mathermatics, as opposed to topics that are perhaps better described as arithmetic and/or engineering calculations, i.e. topics on the periphery of mathematics.

I actually have a beef with pretending that such topics are representative of, or perhaps even the definition of, mathematics. Perhaps the teaching of "mathematics" should be split into those two separate areas then: one for students who are looking for (presumably commercially rewarding) applications, and one for students trying to learn something that goes beyond that...?
Engineering is the application of math and science. What's the point in math without the application? I've known people who enjoy math as an end in itself, like a sport, which is fine; but it's not right to approach it that way in the schools and separate it from the application.
(07-09-2017 03:10 AM)Garth Wilson Wrote: [ -> ]What's the point in math without the application?
Thanks for proving my point. Stamping out the short-sighted idea that mathematics (and other intellectual activities) only deserve to exist to serve some other purpose is exactly what that might achieve.

E.g. rather than telling the (probably untrue) story of Gauss adding the numbers from 1 to 100, a much better illustration of how mathematics works and interacts with science is the proven fact that he did not publish his work on non-Euclidean geometry because, finding no application (apparently because he could not measure the curvature of space), he thought it was not worth it. We should know better nowadays.

Perhaps your idea of "math" is as a collection of applied (typically brain-dead, mechanical) calculations. And I agree that that needs to be taught as an important toolkit. But it is not mathematics as mathematicians see it, just as (most cases of) folding paper planes isn't engineering. And I think proper mathematics should be taught as well.
Quote:Perhaps your idea of "math" is as a collection of applied (typically brain-dead, mechanical) calculations.

Not at all. In fact, that's part of what's wrong with math education. It almost invariably teaches students to throw the numbers into the chute and turn the crank, and they don't have to understand what makes it work or what the real applications are as long as they can remember the crank long enough to pass the test.

There was an editorial about this in one of the electronics industry magazines years ago. It said the industry is telling academia, "You're not giving us the kind of engineers we need. We need ones who can do this, this, and this..." and academia responds, "Look, you know your field, and we know education. Leave the education to us, 'kay?", so the problem persists. It was a constant frustration for me in the years when I was hiring technicians and engineers. Some of them could throw around the matrices and Greek letters better than I, but there was a severe disconnect between that and understanding circuits. Arithmetic and calculations are meaningless without understanding.
I think we are actually getting somewhere with this.

So we have (1) the brain-dead calculations sitting in the middle, (2) the application of those calcculations to science and engineering on one side, and (3) mathematics on the other side.

Unlike you (I think), I do not think that a mathematics class should focus on (2) but instead on (3) and use (1) for illustration purposes (and to make it more digestable) only. In my opinion (2) should be left mainly to science and engineering classes. Or perhaps, as I tried to suggest in my first post, separate (1) out as a topic on its own.

EDIT: E.g. throwing around matrices isn't mathematics (3) for me, my HP Prime can do that...
Oops. I just realised that you started by referring to "math for engineering". I actually totally agree with you in that context, but that's not what the link in the first post is about...
(07-09-2017 03:10 AM)Garth Wilson Wrote: [ -> ]Engineering is the application of math and science.
A suggested redaction - Engineering is {the} an application of math & science.

I am an Engineer (BS Civil) & Scientist (BS in Physical Science) undergraduate as well as a Business (MBA scl) graduate; my frame of reference is anchored in diverse academia. I value the nuances provided by each of these disciplines as well as the overlap they share.
Perhaps a perusal of the many publications containing the phrase understanding mathematics in their respective title will ameliorate your somewhat harsh and frankly limiting perspective on the diverse and encompassing discipline of mathematics.
I understand your thesis, I am trying to tell you it is viewed as narrowly focused and overly constrained. You are, however, free to retain your view.

BEST!
SlideRule
(07-08-2017 02:39 AM)Garth Wilson Wrote: [ -> ]The approach is still wrong. One of my beefs is that the necessary math for engineering is presented in such a theoretical and sterile way, and without real application, with the idea that it must be laid as a foundation ahead of the need. How will that generate interest? How does that help the student understand what's going on in his circuit on the workbench? It won't. How about teaching the circuits and letting the students run up against problems they don't have the math tools to solve yet, then pausing the electronics work to learn what now suddenly there's an interest and application for. That's how I got through a lot of stuff, teaching myself. I kind of have to learn things my own way anyway.

Although I love the euclidean-like way (from foundations to more complex topics}. I totally agree with your points
so, What are the strategies for Motivating (university) Students in Mathematics ?
Math in engineering college was frustrating - Wronskians, matrices, partial differentials, conformal mapping - all were taught as magical incantations that one had to do in a particular and seemingly randomly chosen way to get the correct answer. Then the next semester that same math was used to analyze electrostatic fields, Maxwell's equations, stress and strain in structures, etc. Then the math acquired a mental image of what it "really meant" rather than the somewhat mindless manipulation of symbols in accordance with seemingly arbitrary rules.

So, yes, math for its own sake is excellent. But understanding why the rules are what they are and having examples of applications can make a huge difference in learning, at least for me. Perhaps I'm weird that way...
(07-13-2017 07:56 PM)Jim Horn Wrote: [ -> ]Perhaps I'm weird that way...

Me too
1 +
(07-13-2017 07:56 PM)Jim Horn Wrote: [ -> ]Math in engineering college was frustrating - Wronskians, matrices, partial differentials, conformal mapping - all were taught as magical incantations that one had to do in a particular and seemingly randomly chosen way to get the correct answer. Then the next semester that same math was used to analyze electrostatic fields, Maxwell's equations, stress and strain in structures, etc. Then the math acquired a mental image of what it "really meant" rather than the somewhat mindless manipulation of symbols in accordance with seemingly arbitrary rules.

This is how I've always approached learning math. Focus on what it does, not what it is. What it is will just come after a lot of doing. That self discovery of something that had previously been discovered 100s a years ago is still just as rewarding. For me it has always started with patterns of use and application.

Now my wish for high school students, esp. in the US, would be statistics and probability first. Esp. statistics. IMHO, many in the US do a very poor job of interpreting everyday stats and data. I'd just be happy if a class on stats just got students questioning reported facts, esp. when backed with "data".

Re: calculus, et al for high school students. I wish something like this existed when I was a kid. The visuals are incredible. https://www.youtube.com/channel/UCYO_jab...V4b17AJtAw
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