How can I incorporate calculus into high school teaching?

[Arden1528]

I have been on this post for quit some time. I really do not post all that much, but there are a lot of people that know their stuff. My question, to those willing, are to apply calc. in terms for high schoolers. I am going to start student teaching, and I want to apply math in as many ways as I can. Math is everywhere, but I need some help to come up with ideas. If there is one thing I learned in high school it's that teachers never really applied it. Physics is an applied form of math, I want more. Like I was thinking music and beats or computer imagining. Ideas where the students would see the best sides of math.

 

[Sting]

What caught my attention to Calculus was the story of a wedding (perhaps an urban legend).

This one mathematician a long time ago was sitting at his wedding feast observing the servants pour wine from these barrels that are wider in the middle. Instead of thinking about the wedding night (like anybody would), he was thinking of how to calculate the volume of this irregularly shaped wine barrel.

He then concluded about dividing the barrel into little slabs and then adding the slabs to get an approximate volume.

The rest I need not tell you

But let's see...

How about a related rates problem dealing with a guitarist and an audience? For instance, sound is traveling in a circular pattern around the guitarist at a rate of <fill in here>...?

What about finding the surface area of a guitar or skateboard? Or working the physics of a famous car chase in a movie (like Ronin)?

Okay, I'm probably not helping but I'll brainstorm and see if I can come up with something reasonable.

 

[Arden1528]

No, all those are really good ideas. It's those ideas that may not seem like a good idea, that I would like to introduce to my class. If a apllication to skate boards or music is great. What about turn tables, any ideas about that. I was thinking about the beats per minute, or something. I want more ideas, thanks for the reply.

 

[phoenixthoth]

you might like this:
http://math.sfsu.edu/goetz/Teaching/math226f03/multimedia.html

 

[quantumdude]

Originally posted by Arden1528
If there is one thing I learned in high school it's that teachers never really applied it.

Perhaps the teacher didn't, but the book almost certainly did. Check the problems that the teacher skipped, and I'm sure you'll find a ton of applications. Right now, I am teaching Calculus II out of a book called Calculus, 7ed, by Larson, Hostetler and Edwards, Houghton Mifflin Co., 2002. Just flipping through it, I see applications to statics, kinematics, dynamics, chemistry, fluid flow, thermodynamics, mechanical engineering, economics, radioactive decay, population growth, air pressure, and fractal geometry. Furthermore, it has special Problem Solving sections that contain applied problems that are a bit more involved (they have several steps), but can be done with the methods learned in the chapter.

What book are you using? Does it have applications at the end of the exercise sets? I'd be really surprised if it doesn't.

 

[Arden1528]

Actually I am not a teacher yet. I am going to be done with classes in less then a year, then I start student teaching. I am using the 5th. ed. of Stewart books for my class. There are a lot of applications in this book. How is you class going Tom? I have a lot of questions when it comes to teaching math.

 

[JKLM]

Have you read Calculus for cats, that has some good references for the derivative but not much else. It's only about a hundred pages.

 

[quantumdude]

Originally posted by Arden1528
How is you class going Tom?

My Calculus II class is going great. My College Algebra and Trigonometry class on the other hand...

A lot of it has to do with the attitude of the students. My Calc class is full of engineering majors who want to be there, and my Algebra class is full of business majors who would rather be in Marketing class.

I have a lot of questions when it comes to teaching math.

Me too! This is my first semester doing it (I taught physics for 4 years prior to this). But ask away, and if I can be of any help, I'll do what i can.

 

[Arden1528]

Well I am doing observations right now, and I know the stuff being covered. It just seems so over whelming to teach kids. I guess I am just a little nervous.
My plan is to keep every student interested, is this impossible? I would like to introduce ways in which math is applied and show them math in work. Physics would be the best way, but is there more?

 

[chroot]

I teach astronomy classes for a local adult education system, and they have been very successful at helping just about anyone become a competent amateur astronomer.

I have considered for some time teaching a "calculus without the math" class, just teaching people about the concepts of calculus through real world examples. The class wouldn't include any of the drugery of learning the rules of integration and differentiation, or notation, which is a stumbling block for many.

It would only serve to educate people on the beauty of mathematics, and how a grasp on basic logic are all that is necessary to follow the thoughts of geniuses like Newton and Liebniz.

Any comments?

- Warren

 

[Arden1528]

Your class sounds like a really great idea. I believe that many students lose interest in math for just that reason, the computing. If students could see the applications of all this solving then maybe they would feel inclined to study longer and harder. I mean I have to be truthful here, math is not really all that easy for me. I have chosen to become a teacher because our society needs more people getting into math. Not even math, just the sciences. I know this is a broad question, but how do you apply math in your astronomy class? Do you talk about distance's in space or patterns? What would be a good way to get high school math students involved?

 

[mathwonk]

a nice application of integral calculus I think is magnetic resonance imaging, or MRI used in medicine. This evolved over many years as a method for creating a coherent image of a person's body from snaphots of successive slices viewed as he slides through a chamber.

by the way i have taught with as much enthusiasm as I could muster for over 40 years and have never succeeded in interesting every student or even in having a class where no one seriously disliked my teaching.

It is not your fault if some people refuse to get involved, but you can do your best.

the most important thing these days may be to defuse your disappointment in some students poor performance. encourage everyone. everyone learns at a different pace, and not everyone loves the subject. be thankful for those who do, as found on this website. try to help as much as possible but accept that each student limits his own learning by his interest and commitment.

even a student who disappoints you may be trying up to what he thinks is his maximum. most of them are trying to please you even if you are amazed at how little they do compared to what you would do in their place. try to appreciate it, but do not do their work for them.

even if most students prefer computation to reasoning, do not give up trying to teach reasoning, as it is more important for their intellectual growth.

even if your school district wants you mainly to increase standardized test scores keep trying to teach thinking.

take an interest in the students and they will respond by trying to take an interest in what you are trying to teach them.

good luck. you are one of the newest representatives of an ancient and honorable profession.

 

[zeronem]

How do you become a student teacher? Is it like being the teacher's assistant? For instance, I would like to help out the Math Faculty at my two year college, and would like to teach or tutor for that matter. I don't know if all comunity colleges are the same or not, but it's worth the question. I am a Student and would definatly like to teach too. Any helpful advice would be great.

 

[phoenixthoth]

Visit the math department chair and the head of the tutoring center at that college and ask them for assistance in becoming a student teacher or at least a tutor.

 

[zeronem]

Amazingly and coincedently, today I got a letter in the mail from the Dean of Mathematics of the Community College, and the dean offered me to do some tutoring and teaching. So I'm definatly not going to pass up this offer.