Category: Calculus (MV)

Teaching Math with Clickers

Today’s guest blogger is Derek Bruff, Assistant Director for the Center for Teaching at Vanderbilt University. Derek writes a blog you may have stumbled across called Teaching with Classroom Response Systems. Here’s a question I ask the students in my probability and statistics course: Your sister-in-law calls to say that she’s having twins. Which of the following is more likely? (Assume that she’s not having identical twins.) A. Twin boysB. Twin girlsC. One boy and one girlD. All are equally likely Since I ask this question using a classroom response system, each of my students is able to submit his or her response to the question using a handheld device called a clicker. The clickers beam the students’ responses via radio frequencies to a receiver attached to my classroom computer. Software on the computer generates a histogram that shows the distribution of student responses. I first ask my students to respond to the question individually, without discussing it. Usually, the histogram shows me that most of the students answered incorrectly, which tells me that the question is one worth asking. I then ask my students to discuss the question in pairs or small groups, then submit their (possibly different) answers again using their clickers. This generates a buzz in the classroom as students discuss and debate the answer choices with their peers. After the second “vote,” the histogram usually...

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3-D Function Machine

Last spring break, I traveled to NKU and ICTCM. Andy Long, a mathematician at NKU, generously gave me a home for a few days while at NKU, and on the last night he confessed that he had a “Function Machine” in his basement. A what? A function machine. You type a 3-D function into MatLab, and it builds the function on this machine he created. No kidding. Although this would be a fantastic device to have for visually impaired students, it would also be great for students who just have difficulty envisioning curves in 3-D. Here’s the inside of the machine: The machine is based on metal pins with rounded tops. Each pin is pushed upwards to the correct height. Creating the 3-D surface on the top of the machine. Possibly Related Posts: Elaborations for Creative Thinking in STEM Learning Math is Not a Spectator Sport Recorded Webinar: Teaching Math in 2020 AMATYC Keynote Notes: Challenge and Curiosity AMATYC Keynote Notes: Interaction and...

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Math Provides Beauty and Truth in Physics

Murray Gell-Mann gives a TED Talk entitled Beauty and Truth in Physics. The second part of his presentation is subtitled “Math Matters” (you can forward to this one) Quote from Math Matters: “We express these things mathematically, and when the mathematics is very simple… when, in terms of some mathematical notation you can write the theory in a very brief space, without a lot of complication, that’s essentially what we mean by beauty or elegance.“ The third part of his presentation is subtitled “Symmetry Matters” (again, you can forward to this) As our notation improves and we are able to incorporate symmetry into equations, the equations become simpler and more elegant. Here is an example (from the talk) showing the progression in the equations for Relativity – I think that a multivariable calculus class would probably be able to appreciate it best: This was a great little tidbit – a quote from Newton on why he was not mentioning his theory of gravity in one of his books: Newton was worried that he would be labeled an “extravagant freak” and that readers would thus dismiss the rest of the book. Best quip of the talk – Newton could have really written a great essay on “What I did on my Summer Vacation” (referring to the time that Newton spent away from school during the plague years – some of...

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Mathematical Visualizations for Multivariable Calculus

Jonathan Rogness (UMN) has a great collection of mathematical visualizations for multivariable calculus that run on Java. I don’t teach multivariable calculus (and hope never to have this experience), but I always love looking at the 3-D surfaces. You may remember Rogness from the Mobius Transformations video I blogged about a while ago. Possibly Related Posts: Teaching Math with Clickers 3-D Function Machine Math Provides Beauty and Truth in Physics Flash and...

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Flash and Math

Barbara Kaskosz and Doug Ensley have put together a new site for learning to use Flash & Math with all their tutorials (beginning, intermediate, and advanced. To see some of the Flash applications that have been built, go to the Math DL site and search for Flash/Shockwave resources (as shown in the image below). Amongst other things, there is a nice collection of tools for multivariable calculus developed by Barbara. Possibly Related Posts: Teaching Math with Clickers 3-D Function Machine Math Provides Beauty and Truth in Physics Mathematical Visualizations for Multivariable...

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