Yesterday I got an email from a reader who had read this post called What should math majors know about computing? from 2007. In the original article, I gave a list of what computing skills mathematics majors should learn and when they should learn them. The person emailing me was wondering if I had any updates on that list or any new ideas, seven years on from writing the article.

If anything, over the past seven years, my feelings about the centrality of computing in the mathematics major have gotten even more entrenched. Mostly this is because of two things.

First, I know more computer science and computer programming now than I did in 1997. I’ve learned Python over the last three years along with some of its related systems like NumPy and SciPy, and I’ve successfully used Python as a tool in my research. I’ve taken a MOOC on algorithms and read, in whole or in part, books…

I’m at the American Society for Engineering Education Annual Conference right now through Thursday, not presenting this time but keeping the plates spinning as Mathematics Division program chair. This morning’s technical session featured a very interesting talk from Kathy Harper of the Ohio State University. Kathy’s talk, “First Steps in Strengthening the Connections Between Mathematics and Engineering”, was representative of all the talks in this session, but hers focused on a particular set of interesting data: What engineering faculty perceive as the most important mathematics topics for their areas, and the level of competence at which they perceive students to be functioning in those topics.

In Kathy’s study, 77 engineering faculty at OSU responded to a survey that asked them to rate the importance of various mathematical topics on a 5-point scale, with 5 being the…

Screencasting is an integral part of the inverted classroom movement, and you can find screencasting even among courses that aren’t truly flipped. Using cheap, accessible tools for making and sharing video to clear out time for more student-active work during class make screencasting very appealing. But does it work? Do screencasts actually help students learn?

We have lots of anecdotal evidence that suggests it does, but it turns out there are actually data as well that point in this direction. I’ve been reading an article by Katie Green, Tershia Pinder-Grover, and Joanna Mirecki Millunchick (of Michigan State University and the University of Michigan) from the October 2012 issue of the Journal of Engineering Education in which they studied 262 students enrolled in an engineering survey course that was augmented with screencasts. Here’s the PDF. This paper is full of interesting…

We’re about to start working with gradient vectors in Calculus 3, and this topic uses a curious mathematical symbol: the nabla, which looks like: \(\nabla\). This symbol has several mathematical uses, one of which is for gradients; if \( f \) is a function of two or more variables then \( \nabla f \) is its gradient. But there does not appear to be a use for the symbol outside mathematics (and mathematical physics).

One of my students asked me about the origin of this symbol, and I had to confess I didn’t know. I always figured it was somehow related to the much more common capital Greek delta, \( \Delta \), but the real story is a lot more colorful than that.

The nabla is so-called because it looks like a harp; the Greek word for the Hebrew or Egyptian form of a harp is “nabla” . What does a harp have to do with mathematics? The image came up in relation to mathematics…

Many indicators are pointing to a critical shortage of engineers among the current high school generation. What’s the cause of all that? A study (PDF) by the nonprofit organization Change the Equation (with backing from Intel), focusing on 1004 students between the ages of 13 and 18 with computer access, suggests two things: a perception of difficulty coupled with an overall lack of knowledge about what engineering really is in the first place.

The Intel survey showed 63 percent of the students ages 13 to 18 have never considered the career despite having “generally positive opinions of engineers and engineering.” The perception that engineering is difficult also played a part in the lack of job consideration.

But the teens were especially interested when they learned about the potential for engineering to help others, such as saving the Chilean miners who were trapped in 2010,…

The title of this NY Times article making the rounds in the blogosphere is titled “Why Science Majors Change Their Minds (It’s Just So Darn Hard)”. But it seems like the real reason that 40% of university students today who plan on careers in the STEM disciplines end up changing into other fields or dropping out is only partly about the hardness of the subjects. What are the other parts? Read this:

But, it turns out, middle and high school students are having most of the fun, building their erector sets and dropping eggs into water to test the first law of motion. The excitement quickly fades as students brush up against the reality of what David E. Goldberg, an emeritus engineering professor, calls “the math-science death march.” Freshmen in college wade through a blizzard of calculus, physics and chemistry in lecture halls with hundreds of other students. And then many wash …

Through a smoldering brush fire, past wind-shearing road trains, across the Australian continent, the University of Michigan’s Quantum was the first American car to finish the World Solar Challenge today. The Solar Car Team placed third overall in the international competition.[...]

After driving for 35 hours and 33 minutes over five days, the U-M team crossed the end-of-timing line in Angle Vale, South Australia at 3:55 p.m. race time (2:25 a.m. U.S. ET). They are spending the night there. In the morning they will drive the remaining 20 miles to the ceremonial finish line in Adelaide’s Victoria Square.

“It was an incredibly close race, especially due to the unexpected elements such as the brush fire which delayed the race, dust storms, major cloud cover at the end of the race, and the ultra reliable cars of …

In the latest issue of the Journal of Engineering Education, there’s a guest editorial by Rick Stephens and Michael Richey, both from The Boeing Company, that describes Boeing’s internal efforts to educate its engineers. Here’s the video abstract:

You’re more likely to associate the name “Boeing” with airplanes than with education, but in fact it turns out that Boeing’s educational portfolio is massive: 7 million hours of instruction to more than 150,000 employees across 45 countries — in 2009 alone! That comes out to about 28,000 hours of instruction per week, which would put Boeing in the league of a mid-sized university in terms of contact hours in the classroom.

But comparing Boeing to traditional educational structures is decidedly not the point of the article. The Boeing people ask: Why is it, after so much has been invested in STEM education research and practice, that…

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…

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.

I am a mathematician and educator with interests in cryptology, computer science, and STEM education. I am affiliated with the Mathematics Department at Grand Valley State University in Allendale, Michigan. The views here are my own and are not necessarily shared by GVSU.

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