Tag Archives: precalculus

August 8, 2010, 12:47 pm

Calculus and conceptual frameworks

Image via http://www.flickr.com/photos/loopzilla/

I was having a conversation recently with a colleague who might be teaching a section of our intro programming course this fall. In sharing my experiences about teaching programming from the MATLAB course, I mentioned that the thing that is really hard about teaching programming is that students often lack a conceptual framework for what they’re learning. That is, they lack a mental structure into which they can place the topics and concepts they’re learning and then see those ideas in their proper place and relationship to each other.¬†Expert learners — like some students who are taking an intro programming course but have been coding since they were 6 years old — have this framework, and the course is a breeze. Others, possibly a large majority of…

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May 15, 2010, 11:41 am

The semester in review

Plot of the vector field f(x,y) = (-y,x).

Image via Wikipedia

I’ve made it to the end of another semester. Classes ended on Friday, and we have final exams this coming week. It’s been a long and full semester, as you can see by the relative lack of posting going on here since around October. How did things go?

Well, first of all I had a record course load this time around — four different courses, one of which was the MATLAB course that was brand new and outside my main discipline; plus an independent study that was more like an undergraduate research project, and so it required almost as much prep time from me as a regular course.

The Functions and Models class (formerly known as Pre-calculus) has been one of my favorites to teach here, and this class was no exception. We do precalculus a bit differently here, focusing on using functions as data modeling …

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April 11, 2010, 2:56 pm

MATLAB as a handout creator

One of the fringe benefits of having immersed myself in MATLAB for the last year (in preparation for teaching the Computer Tools for Problem Solving course) is that I’ve learned that MATLAB is an excellent all-purpose tool for preparing materials for my math classes. Here’s an example of something I just finished for a class tomorrow that I’m really pleased with.

I was needing to create a sequence of scatterplots of data for a handout in my Functions and Models class. The data are supposed to have varying degrees of linearity — some perfect/almost perfectly linear, some less so, some totally nonlinear — and having different directions, and the students are supposed to look at the data and rank the correlation coefficients in order of smallest to largest. (This is a standard activity in a statistics class as well.)

I could have just made up data with the right shape on Excel or…

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September 15, 2008, 11:14 am

Average velocity

Average velocity is another one of those basic calculus (really pre-calculus) topics that, like difference quotients, leave me at a loss for why students have such a hard time with them. There’s a very simple and common-sense definition, namely that the average velocity of an object with position s(t) from t = a to t = b is

\(\frac{s(b) – s(a)}{b-a}\)

(See? It’s just distance = rate * time solved for “rate”.) There are examples in the book and examples on the internet ad infinitum of how to calculate average velocities, and all of these are simple numerical calculations with absolutely no algebra involved. You have to know how to plug numbers into a function and then do basic arithmetic on your calculator. That’s all.

But students get so turned around. They calculate only the position at time t=b. They add up the positions at t=a and t=b and divide by 2 (“average”). They add in…

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October 17, 2007, 2:13 pm

Flowchart for data modeling

I just made this flowchart for the Calculus Preparation lesson coming up next Monday, which is on how to model nonlinear data. Click to enlarge:

flowchart-for-modeling-data.png

I <heart> OmniGraffle. It’s one of my top ten e-learning tools for good reason.
The PDF version of this is in my Box.net widget — go to the sidebar and scroll down. Feel free to download and use/share.

October 2, 2007, 9:15 am

Age-old questions about freshman math students

7176859_a1d302e4f3_m.jpgMidterms are coming up in a couple of weeks, and while most of the students in my precalculus class are doing reasonably well, some aren’t. Here are some questions I’ve struggled with every time I teach a freshman class, and maybe some of you out there have suggestions. If so, leave them in the comments.

  1. How do you impress upon students (freshmen) the importance of coming to office hours? I don’t think I’ve had more than six distinct students visit office hours for help all semester long, and I’d consider this an active semester in terms of office hours. The rest go to the Math Study Center, study tables for football or fraternities, etc. but it does no evident good for a lot of them. I think it would do them good to come see me; but how to convince them of this?
  2. How do you convince a student that their purpose for being here, their job, is to be a student? Some of the students don’t …

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