# Category Archives: Calculus

April 1, 2011, 5:20 am

# Speaking of the inverted classroom

On Wednesday, I gave a talk at Indiana University – Purdue Universty – Indianapolis (IUPUI, for short) to the teaching seminar for math graduate students on the inverted classroom. It was sort of a generalization of the talk I gave on the inverted linear algebra classroom back at the Joint Mathematics Meetings in January. Carl Cowen was in attendance at that talk and invited me to make the 20-minute drive from my house to IUPUI to do something like it, and I was happy to oblige.

Since putting the talk up on Slideshare yesterday morning, it’s gotten over 200 views, 2 favorites, a handful of retweets/Facebook likes, and is currently being highlighted on Slideshare’s Education page. So I thought I would share it here as well. Enjoy and ask questions!

[slideshare id=7467479&doc=iupuiseminartalk-110331131627-phpapp02]

December 21, 2010, 4:41 pm

# Coming up in January

Fall Semester 2010 is in the books, and I’m heading into an extended holiday break with the family. Rather than not blog at all for the next couple of weeks, I’ll be posting (possibly auto-posting) some short items that take a look back at the semester just ended — it was a very eventful one from a teaching standpoint — and a look ahead and what’s coming up in 2011.

I’ll start with the look head to January 2011. We have a January term at my school, and thanks to my membership on the Promotion and Tenure Committee — which does all its review work during January — I’ve been exempt from teaching during Winter Term since 2006 when I was elected to the committee. This year I am on a subcommittee with only three files to review, so I have a relatively luxurious amount of time before Spring semester gets cranked up in February. A time, that is, which is immediately gobbled up by the…

December 16, 2010, 2:30 pm

# A problem with "problems"

I have a bone to pick with problems like the following, which is taken from a major university-level calculus textbook. Read it, and see if you can figure out what I mean.

This is located in the latter one-fourth of a review set for the chapter on integration. Its position in the set suggests it is less routine, less rote than one of the early problems. But what’s wrong with this problem is that it’s not a problem at all. It’s an exercise. The difference between the two is enormous. To risk oversimplifying, in an exercise, the person doing the exercise knows exactly what to do at the very beginning to obtain the information being requested. In a problem, the person doesn’t. What makes an exercise an exercise is its familiarity and congruity with prior exercises. What makes a problem a problem is the lack of these things.

The above is not a problem, it is an exercise. Use the

November 29, 2010, 9:00 am

# What correlates with problem solving skill?

About a year ago, I started partitioning up my Calculus tests into three sections: Concepts, Mechanics, and Problem Solving. The point values for each are 25, 25, and 50 respectively. The Concepts items are intended to be ones where no calculations are to be performed; instead students answer questions, interpret meanings of results, and draw conclusions based only on graphs, tables, or verbal descriptions. The Mechanics items are just straight-up calculations with no context, like “take the derivative of $$y = \sqrt{x^2 + 1}$$”. The Problem-Solving items are a mix of conceptual and mechanical tasks and can be either instances of things the students have seen before (e.g. optimzation or related rates problems) or some novel situation that is related to, but not identical to, the things they’ve done on homework and so on.

I did this to stress to students that the main goal of taking …

November 12, 2010, 4:04 pm

# This week in screencasting: Optimization-palooza

My calculus class hit optimization problems this week — or it might be better to say the class got hit by optimization problems. These are tough problems because of all their many moving parts, especially the fact that one of those parts is to build the model you plan to optimize. Most of my students have had calculus in high school, but too many calculus courses in high school as well as college focus almost primarily on algorithms for computation and spend little to no time with how to create a model in the first place. Classes that are so structured are doing massive harm to students in a number of ways, but that’s for another post or two.

Careful study of worked-out examples is an essential part of understanding optimization problems (though not the only part, and this alone isn’t sufficient). The textbook has a few of these. The professor can provide more, but class time really …

October 21, 2010, 10:06 am

# This week in screencasting: The polar express

It’s been a little quiet on the screencasting front lately, but in the next couple of weeks my colleague teaching Calculus III will be hitting material for which I volunteered to provide some content: namely, using MATLAB to visualize some of the surfaces and solids used in multiple integration. Yesterday, I finished two of these. The first on is on polar coordinates and polar function plotting in MATLAB:

And the second one is on cylindrical coordinates and plotting two-variable functions in cylindrical coordinates:

MATLAB doesn’t provide a built-in function for plotting in cylindrical coordinates. Instead — and this is either ingenious or annoying depending on how you look at it — to plot something in cylindrical coordinates, you generate all the points you need in cylindrical coordinates and then use the pol2cart function to convert them en masse to cartesian coordinate…

September 5, 2010, 1:37 pm

# This week (and last) in screencasting: Functions!

So we started  back to classes this past week, and getting ready has demanded much of my time and blogging capabilities. But I did get some new screencasts done. I finished the series of screencasts I was making for our calculus students to prepare for Mastery Exams, a series of short untimed quizzes over precalculus material that students have to pass with a 100% score. But then I turned around and did some more for my two sections of calculus on functions. There were three of them. The first one covers what a function is, and how we can work with them as formulas:

The second one continues with functions as graphs, tables, and verbal descriptions:

And this third one is all on domain and range:

The reason I made these was because we were doing the first section of the Stewart calculus book in one day of class. If you know this book, you realize this is impossible be…

August 21, 2010, 6:50 pm

# This week in screencasting: Contour plots in MATLAB

By my count, this past week I produced and posted 22 different screencasts to YouTube! Almost all of those are short instructional videos for our calculus students taking Mastery Exams on precalculus material. But I did make two more MATLAB-oriented screencasts, like last week. These focus on creating contour plots in MATLAB.

Here’s Part 1:

And Part 2:

I found this topic really interesting and fun to screencast about. Contour plots are so useful and simple to understand — anybody who’s ever hiked or camped has probably used one, in the form of a topographical map — and it was fun to explore the eight (!) different commands that MATLAB has for producing them, each command producing a map that fits a different kind of need. There may be even more commands for contour maps that I’m missing.

I probably won’t match this week’s output next week, as I’ll be on the road in

August 17, 2010, 4:01 pm

# Why change how we teach?

Sometimes when I read or hear discussions of innovation or change in teaching mathematics or other STEM disciplines, whether it’s me or somebody else doing the discussing, inevitably there’s the following response:

What do we need all that change for? After all, calculus [or whatever] hasn’t changed that much in 400 years, has it?

I’m not a historian of mathematics, so I can’t say how much calculus has or hasn’t changed since the times of Newton and Leibniz or even Euler. But I can say that the context in which calculus is situated has changed – utterly. And it’s those changes that surround calculus that are forcing the teaching of calculus (any many other STEM subjects) to change –radically.

What are those changes?

First, the practical problems that…

August 13, 2010, 1:21 pm

# This week in screencasting: Making 3D plots in MATLAB

I’ve just started on a binge of screencast-making that will probably continue throughout the fall. Some of these screencasts will support one of my colleagues who is teaching Calculus III this semester; this is our first attempt at making the course MATLAB-centric, and most of the students are alums of the MATLAB course from the spring. So those screencasts will be on topics where MATLAB can be used in multivariable calculus. Other screencasts will be for my two sections of calculus and will focus both on technology training and on additional calculus examples that we don’t have time for in class. Still others will be just random topics that I would like to contribute for the greater good.

Here are the first two. It’s a two-part series on plotting two-variable functions in MATLAB. Each is about 10 minutes long.

Part of the reason I’m doing all this, too, is to force myself …

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