Comments on: Polar Graphing Introduction

By: Michael Fenton

Michael Fenton — Fri, 07 Aug 2015 03:14:07 +0000

Cinda,

Thanks for the comment, and the two great applications!

Take care,

By: Cinda Walker

Cinda Walker — Thu, 06 Aug 2015 14:43:21 +0000

My husband was in the Marine Corps. In his early training, he was dropped off in the middle of a forest and had to find his way out. He was given a map and a compass. He used the heading and paces to get from one point to another. (polar coordinates). When he was a pilot, polar coordinates again in a sense because he had to fly from one point to the next knowing heading and distance.

By: Michael Fenton

Michael Fenton — Thu, 07 May 2015 16:01:43 +0000

Dan, I know the standard answer for this and other questions is usually to point to applications (http://en.wikipedia.org/wiki/Polar_coordinate_system#Applications). And I know this is relevant to some people, either personally (interest) or professionally. But I don’t teach polar coordinates to scratch the applications itch, and none of my students have ever seemed particularly inspired by my references to applications (which I do make).

For me, this is simply another mathematical playground for developing the things I care most about. I want my students to make connections and develop habits-of-mind/SMP-style things. I can’t tell if this is the world’s most epic motivational cop-out, or if it’s a healthy standard measure of whether something is worth teaching: “Does this give students an opportunity to grow in (fill-in-the-blank-meaningful-way)?”

Regarding why we invented so many different notations, I’d offer: Someone at some point found it more efficient/effective/powerful/simple to represent something in another way. So he/she did. End of (that) story.

The next story (and the one I’m more interested in) is how we decide which notations/representations (whether of points in space, or some other topic) are worth bringing before our students. There are plenty of “useful” things (from an applications standpoint) that we leave out of the classroom. What makes the canon? What doesn’t? And why?

P.S. If I took my response-rant in another direction, I’d be all over Kaleb’s rotation angle. And probably would have mentioned a few things Michael Pershan has said about complex numbers and transformations. But to me, some of that is a means to an end, and the end is not navigating an airplane more effectively. I think. 🙂

By: kaleb40

kaleb40 — Thu, 07 May 2015 13:41:49 +0000

Just a quick thought… Maybe because they are functions this way… Also lots of things rotate.

By: danmeyer55351818

danmeyer55351818 — Thu, 07 May 2015 13:27:51 +0000

Question I’ve never thought to ask. Why polar coordinates? What itch does that scratch? Best I have is that some of these polar functions which are quite simple to write in polar notation would be a pain in the ass in their Cartesian form. Is there something else I’m missing, though?

In general: I’m curious why we invented so many different notations to represent a point in space.

By: Polar Graphing Exploration | Reason and Wonder

Polar Graphing Exploration | Reason and Wonder — Mon, 20 Apr 2015 14:00:41 +0000

[…] the weekend I wrote about an alternative launch to my Precalculus polar graphing unit. After that first lesson, I decided to throw out my usual […]