My Struggle with Math: Understanding Real-World Applications

[zoobyshoe]

Interesting. I agree that the system failed you when you were most receptive. But let's analyze this situation a little further, because it is very interesting.

1) Let's first assume that he did actually know what problems an engineer might be confronted with. I personally don't know specific problems, but I can certainly justify to you that high school algebra is useful. Nevertheless, I would have given the same reply as your teacher? Why, because you were most likely not mathematically mature enough to grasp the application. Furthermore, if you're a teacher, then you don't teach to one person, but rather to an entire class. And the class has weak and strong students. So while giving a discourse on applications is fun for the strong (maybe!), it will be very useless for the weak. Furthermore, you have a series of topics to cover in a limited time, so it is unwise to give a very long application that might prevent other topics from being seen.
I do sympathize with you and with the students asking for applications, but things are just not that easy sadly.

2) What if he didn't know any applications. That still doesn't mean he's a bad teacher. Class management and connection with the student is more important than knowing advanced mathematics (although the teacher should know the basics of his field). It is still unwise to say that "he personally failed you". Rather, it would be better to think of solutions to this problem. You can't blame the teacher for not knowing this, and you can't blame the student for asking this. On the other hand, I feel some cultural shift must happen so that both parties are more satisfied. For example: textbooks and courses that are better and cover some applications (I mean really, most textbooks these days are horrible), or additional schooling for teachers, or additional classes for the interested students, etc.
I know of some program in scandinavia where university students are able to eliminate their student debt by teaching for 2 years. This is an excellent idea, but only privded that they are properly guided and get the audience they deserve.

I didn't give the full context, which would modify your understanding. This was at a college prep school. That's one of the reasons class management wasn't such an issue: most of the students were above average and 100% were intending to go on to college. To that end, I was struggling very hard this particular year to pull my math grade up so it would look better on college applications. This school was a boarding school; students and teachers all lived on campus, and this particular math teacher made himself available for off hours homework help. I availed myself of that frequently, and it was during one of these one-on-one homework help sessions that I asked about practical applications. The point being, no other student's time was being infringed on, it wasn't cutting into class time. He was already giving me three or more hours extra per week, so his patience was just about limitless. Time was definitely not the issue.

Rather, it would be better to think of solutions to this problem.

The solution is spread throughout my 'complaint,' and it obviously is: to prevent math from becoming abstracted from practical applications. Math is a requirement because it is a powerful and universally used tool in a huge variety of careers and occupations. It's not there in the curriculum for it's aesthetic properties (as mentioned by WWGD). Keeping it grounded in practical reality in the student's mind is such an obvious necessity it is migraine-inducing to contemplate that all teachers, and all members of all educational systems, don't automatically understand this and take pains to do it. As I mentioned in an earlier post, in the years after school, whenever I've encountered a real life use for math, it is suddenly clearer than it ever was in high school, and I feel absolutely enthusiastic about it's power as a tool. That taught me I wasn't born missing the math lobe. I feel I was failed: it was laid on me as an abstract, disembodied burden when it could have been a source of enthusiasm.

As for expert teachers; I don't think it's at all desirable to have math experts teaching (except at very high levels). I wouldn't want Gauss teaching me because Gauss had some kind of preternatural grasp of math that I'm sure he didn't understand and couldn't possible communicate. The average high school math teacher should be someone who once matched the average student he's going to be teaching, not the genius who could have picked it up himself in his spare time from a book. You can't teach if you're suffering from "the curse of knowledge." A teacher has to be able to psychologically put him/her self in the mind of the ignorant to understand what they need to be taught next, or to understand what miasma of confusion and cognitive dissonance is preventing them from understanding what's being taught. It's not expertise in the subject matter that's missing in teachers.

 

[WWGD]

But, Zooby, what is it that you found attractive: the potential applications or the fact that Math is a tool in so many areas (which is kind of amazing)? I found attractive the fact that so many different pieces of Math fit together coherently. That is a rare find.

 

[wabbit]

The solution is spread throughout my 'complaint,' and it obviously is: to prevent math from becoming abstracted from practical applications. Math is a requirement because it is a powerful and universally used tool in a huge variety of careers and occupations. It's not there in the curriculum for it's aesthetic properties (as mentioned by WWGD). Keeping it grounded in practical reality in the student's mind (...)

Applications are important both in math in general and in its pedagogy, and you make a good case for that. This depends on the student tough, it is essential for some, not so much for others.
But there is also another reason for teaching math, and for doing it right : it expands the mind. Math, like philosophy, history and other disciplines is highly formative and provides us tools to expand our thinking, as well as sharpen our deductive ang general logic abilities and capacity for abstract thought. As such it is highly valuable - if done right - in a curriculum, separately from its applications.

As for expert teachers; I don't think it's at all desirable to have math experts teaching (except at very high levels).

Agreed. That would be unnecessary and I wouldn't necessarily expect Perelman for instance to do well as a high school math teacher. Doing math research and teaching math, especially at introductory level, are different jobs requiring different qualifications (some excel at both, but one could almost say this is akin to the fact that a good ice skater can also be a great cook. : ) )

 

[zoobyshoe]

But, Zooby, what is it that you found attractive: the potential applications or the fact that Math is a tool in so many areas (which is kind of amazing)? I found attractive the fact that so many different pieces of Math fit together coherently. That is a rare find.

It is attractive to me when I, myself, have a specific use for it. Barring that, there has to be the clear prospect I could possibly have a use for it in the future. Despite the fact arithmetic was taught in a dry, unenthusiastic manner to me, it's future potential use became apparent at each step, and it was reasonable to pay attention. Likewise, the uses of geometry seemed always apparent to me. Somewhere into algebra, however, things departed from any practical application, and it became increasingly abstracted from there on. I went to a liberal arts college that was so heavily weighted in favor of the liberal arts that there was no math or science requirements for a degree, and high school algebra was the last math I ever had to study. It bothers me now that it was taught such that it was the last math I wanted to study. After those last two years of algebraic miasma, I was elated to be rid of it.

 

[zoobyshoe]

Applications are important both in math in general and in its pedagogy, and you make a good case for that. This depends on the student tough, it is essential for some, not so much for others.
But there is also another reason for teaching math, and for doing it right : it expands the mind. Math, like philosophy, history and other disciplines is highly formative and provides us tools to expand our thinking, as well as sharpen our deductive ang general logic abilities and capacity for abstract thought. As such it is highly valuable - if done right - in a curriculum, separately from its applications.

I agree, and it is in this spirit that I've gone back and taken a look at it all these years later, and found it to be, as you say, mind expanding. This is the spirit in which Archimedes and the other ancients pursued it: contemplatively, with breathing space, for it's benefits to the mind.

I think the modern student who somehow manages to consciously grasp that aspect of math does it on his own. I would say, too, that students exhibiting this bent of mind, or who see math as "aesthetic" might be in some danger of becoming mathematicians, and should be closely monitored. ;)

 

[wabbit]

There is one silver lining here, a benefit from a poor early experience with math - something I've experienced not in maths but for other things I hated at school : it leaves untouched the joy of discovery for when you later become interested.

 

[Tyrion101]

I would like to report that when I pass my current mathematics class it will be the end of math for me in college (at least as far as taking math specific courses!) Yay me. I had one plan and stuck with it., and so far it has worked.

 

[symbolipoint]

I would like to report that when I pass my current mathematics class it will be the end of math for me in college (at least as far as taking math specific courses!) Yay me. I had one plan and stuck with it., and so far it has worked.

Beware of the future need for more Mathematical skill and knowledge. Your current, formal terminal required course may not be enough for you to be competitive enough for what you want to accomplish; and you do not yet know what you wish to accomplish ten years from now.

 

[Tyrion101]

Well I simply meant the requirements for my degree, I don't need any extra math at this point, and I never thought I'd make it.

 

[symbolipoint]

Well I simply meant the requirements for my degree, I don't need any extra math at this point, and I never thought I'd make it.

As I said, BEWARE!

 

[Tyrion101]

I will keep that in mind, though I think I will concentrate on actual course load.