February 20, 2012, 7:32 pm

The origin of the “nabla” symbol

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…

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February 18, 2012, 12:00 pm

Random reality

By Robert Talbert

In this month’s online issue of Books & Culture magazine, I have a short article called Random Reality, Part 3. This is (wait for it…) the third part of a series of articles written by science people focusing on the book The Matchbox that Ate a Forty-Ton Truck by Marcus Chown. This series itself is part of a larger series that B&C magazine is running called “Science in Focus” where a single book on science is examined from different points of view by people in the sciences. The first article in my series was written by a geologist, the second by a neuroscientist.

Here’s an excerpt:

The Bible describes the early universe as “without form and void” (Genesis 1:2). This is certainly true, according to Marcus Chown, in terms of how much information was in the universe then. Expanding on the ideas of physicist Stephen Hsu, Chown argues that, just after the Big Bang, the universe…

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February 17, 2012, 11:40 am

When are students teaching themselves?

By Robert Talbert

Over the last 24 hours I have run into at least three situations where I’ve heard either peer instruction or the inverted classroom model as being pedagogical frameworks in which — according to others — “students teach themselves”. I don’t think this is accurate, and I’m trying to understand where this idea comes from.

Certainly in the inverted classroom model and in many instances of peer instruction, it’s simply not the case that “there is no lecture”. There can be a lot of lecture in either of these models. It’s just that the lectures are not given in class. They are broken up into rewindable, pause-able, digestible chunks and posted online where people can view them on their own schedules and according to their own listening practices. For my inverted MATLAB class, I recorded 41 screencasts’ worth of lectures, amounting to about 332 minutes of lecture, which is not very far off…

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February 13, 2012, 9:33 pm

Four things lecture is good for

By Robert Talbert

A lot of my posts here are about alternatives to the traditional lecture-oriented classroom. Based on that, and on somewhat testy comments like these that I leave lying around the internet, you might get the idea that I am firmly anti-lecture. But that’s not entirely true. There are times and places where lecture works quite well, even better than the alternatives. Here are a few purposes for which I think lecture is well-suited:

Modeling thought processes. The benefit of hearing an expert learner lecture on a subject is that, if the lecture is clearly given, the audience can gain some insights into what makes the expert an expert. A good lecture does more than convey facts or put problems on the board — it lays bare the cognitive processes that an expert uses to assimilate those facts or think his or her way through those problems.
Sharing cognitive structures. Lectures provide…

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February 9, 2012, 8:48 pm

Starting off in SoTL

By Robert Talbert

Today I was excited to attend the startup meeting for a faculty learning community on the scholarship of teaching and learning (“SoTL”) here at GVSU. This group is sponsored and facilitated by our Faculty Teaching and Learning Center; it consists of the FTLC director and fellow faculty members from philosophy, history, computer science, and movement sciences. (And me.) Together over the next calendar year, we’re going to be working together to help each other develop research questions and projects in SoTL and serve as a sounding board for each others’ ideas.

I’ve been an end-user of SoTL for a long time and have done a lot of you might call “scholarship” in SoTL — for example all the writing and speaking I’ve done about the inverted classroom and clickers — but I’ve not done what I consider actual research in SoTL. One of the reasons I came to GVSU was to have the time, space, and …

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February 8, 2012, 11:00 am

Covey on education: Are we superficial?

By Robert Talbert

Here’s a quote from Stephen Covey’s classic The Seven Habits of Highly Effective People, which I am reading right now. Covey here is talking about the difference between improving one’s life through the “Character Ethic” (think: Ben Franklin’s autobiography) versus simply changing how you interact with other people without a corresponding shift in your worldview, which he refers to as “technique” or the “Personality Ethic”. All emphases are my own:

To focus on technique is like cramming your way through school. You sometimes get by, perhaps even get good grades, but if you don’t pay the price day in and day out, you never achieve true mastery of the subjects you study or develop an educated mind.

Did you ever consider how ridiculous it would be to try to cram on a farm—to forget to plant in the spring, play all summer and then cram in the fall to bring in the harvest? The farm is…

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February 6, 2012, 2:52 pm

Resistance to the inverted classroom can show up anywhere

By Robert Talbert

This past Saturday I was paired with one of our faculty from the College of Nursing to interview several prospective students for academic scholarships. In between interviews, we had a great conversation about the inverted classroom. It turns out that the College of Nursing is implementing an inverted model in some of their classes, although they don’t know it by that name and are not trying to jump on an educational bandwagon. They are taking some of their courses, putting the “theory” (as it was called) online as audio files accompanied by sets of notes, and then using the class time for practica, labs, and discussion. When I described what I’ve written about here on the inverted classroom, my colleague readily agreed it was the same idea.

This makes a lot of sense in the health sciences because as a practitioner, theory and raw information are important, but it’s the practice…

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February 1, 2012, 7:55 am

Why I believe in technology

By Robert Talbert

Saturday was the fifth anniversary of the day when we received our middle child, Penelope, in China. My wife and mother-in-law traveled to China to receive her and complete the adoption process, while I stayed home with our then-2-year old (who was also adopted from China). Celebrating “Gotcha Day” for our two daughters is always a fun and meaningful time for us. But there’s another anniversary that shares the same date as Penny’s Gotcha Day: It’s the day that I mark as the precise moment in time when I became 100% sold on the power of technology, both in my personal life and in my teaching.

Here’s why:

At about 2:00 PM local time in Nanchang, China on January 27 — a Sunday — Penny was brought into the room where my wife and mother-in-law were waiting, and they met for the first time. Lots of pictures were taken with our Canon PowerShot digital camera. This was 2:00 AM local…

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January 30, 2012, 7:55 am

The Owner and the Renter in Education

By Robert Talbert

Since moving to west Michigan in July, my family and I have been living in an apartment while our house in Indiana ~~sells~~ sits on the market. This is the first time since 2001 that we’ve spent longer than six months in a rental property. Sunday morning, as we woke up to find that we’d been buried in snow overnight (as per usual in west Michigan), I realized that the home ownership habit runs pretty deep with me.

When I looked out the door and saw the image you see in the photo, I naturally grabbed the snow shovel, walked out the door, and started clearing off the walkway and the van. I got some curious looks from my neighbors, as if to say: What are you doing? We are paying rent not to have to do stuff like this. And it’s true: The apartment manager usually comes through shortly after a snowfall and clears off the walkways. Usually. But who knows? Maybe he won’t come today. And anyhow,…

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January 18, 2012, 7:12 am

What I learned in 2011: There is always a backstory

By Robert Talbert

Here’s a previous article in an ongoing series of What I Learned in 2011.

While it was still on TV, the show LOST was a favorite of mine. No, that’s not strong enough — it was an obsession. I discovered the show about halfway through its fourth season when I downloaded the series pilot from iTunes on a whim. I was hooked. I proceeded to watch the episodes online at a rate of about one per day — sometimes two or even three — until I caught up. I read the blogs, edited the wiki, listened to the podcasts. I was completely and totally absorbed. And this is coming from a person who otherwise watches TV maybe about an hour a week (modulo football and kids’ shows).

What was it about that show that I found so engaging? For me, the main thing was the deep humanity of the characters. In the first few episodes, it was very easy to pigeonhole them all. Sawyer was the criminal you had to…