September 13, 2011, 7:30 am

By Robert Talbert

*To all the new readers: Ready for some math? We love math here at Casting Out Nines, and I’ll be taking at least one day a week to talk about a math topic specifically. If you have a math post you’d like to see, email me (robert [dot] talbert [at] gmail [dot] com) or leave a comment. *

The Fundamental Theorem of Calculus is central to an understanding of how differential and integral calculus connect. It says that if f is a continuous function on a closed interval [a,b] and x is in the interval, then the function

is an antiderivative for f. That is, F’(x) = f(x). The FTC (technically, this is just one part of that theorem) shows you how to construct antiderivatives for any continuous function. Possibly more importantly, it connects two concepts about change — the rate of change and the amount of accumulated change in a function. It’s a big deal.

I use a lot of technology in my…

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July 27, 2010, 8:10 pm

By Robert Talbert

Wolfram, Inc. has just rolled out its newest creation: Wolfram|Alpha Widgets. These are small “apps” that execute a single W|A query using user input, without actually loading the W|A website. In just the last few days since W|A widgets have been around, hundreds of them have been made, from widgets that find anagrams to widgets that calculate comparative economic data between two states to widgets that take derivatives. Each widget also comes with the option to customize, share among social media applications (21 different services are represented), or embedded in popular blogging and wiki services such as WordPress and Mediawiki. (Sadly, there’s no WordPress.com embedding yet.) Take a look through the gallery at what’s been done.

What’s really exciting here is that you don’t need any programming knowledge to create a widget. You start with a basic W|A query, then highlight the…

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March 12, 2010, 7:38 am

By Robert Talbert

It’s a beautiful day here on the shores of Lake Michigan as the ICTCM gets underway. It’s a busy day and — to my never-ending annoyance — there is no wireless internet in the hotel. So I won’t be blogging/tweeting as much as I’d like. But here’s my schedule for the day.

- 8:30 – Keynote address.
- 9:30 – Exhibits and final preparations for my 11:30 talk.
- 10:30 – “Developing Online Video Lectures for Online and Hybrid Algebra Courses”, talk by Scott Franklin of Natural Blogarithms.
- 11:10 – “Conjecturing with GeoGebra Animations”, talk by Garry Johns and Tom Zerger.
- 11:30 – My talk on using spreadsheets, Winplot, and Wolfram|Alpha|Alpha in a liberal arts calculus class, with my colleague Justin Gash.
- 12:30 – My “solo” talk on teaching MATLAB to a general audience.
- 12:50 – “Programming for Understanding: A Case Study in Linear Algebra”, talk by Daniel Jordan.
- 1:30 – “Over a Decade of…

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March 1, 2010, 9:21 pm

By Robert Talbert

My apologies for being a little behind the curve on the MATLAB-course-blogging. It’s been a very interesting last couple of weeks in the class, and there’s a lot to catch up on. The issues being brought up in this course that have to do with general thinking and learning are fascinating, deep, and complicated. It’s almost as if the course is becoming only secondarily a course on MATLAB and primarily a course on critical thinking and lifelong learning in a technological context.

This past week’s lab really brought that to the forefront. The lab was all about working with external data sets, and it involved students going to this web site and looking at this data set (XLS, 33 Kb) about electoral vote counts of the various states in the US (and the District of Columbia). One of the tasks asked students to make a scatterplot of the land area of the states versus their electoral vote count…

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January 15, 2010, 9:00 am

By Robert Talbert

Last night I received this email from my colleague Dan Callon, who is at the Joint Mathematics Meetings in San Francisco:

Robert,

I went to a session at the national joint meetings tonight on Wolfram|Alpha, sponsored by the MAA Special Interest Group on Mathematics Instruction Using the Web, with speaker Bruce Yoshiwara of Los Angeles’ Pierce College. He cited the blog of the best-known expert (outside of Wolfram itself) in the country on using Wolfram|Alpha in education: Robert Talbert. Congratulations!
Dan

I would have to rank Maria Andersen way above myself both in terms of her expertise with W|A and in terms of how well-known she is, but still, I’m honored by Prof. Yoshiwara’s mention. And I’ll keep trying to crank out relevant posts about Wolfram|Alpha in the future.

January 4, 2010, 7:00 am

By Robert Talbert

Last week, I wrote about structuring class time to get students to self-verify their work. This means using tools, experiences, other people, and their own intelligence to gauge the validity of a solution or answer without uncritical reference an external authority — and being deliberate about it while teaching, resisting the urge to answer the many “Is this right?” questions that students will ask.

Among the many tools available to students for this purpose is Wolfram|Alpha, which has been blogged about extensively. (See also my YouTube video, “Wolfram|Alpha for Calculus Students”.) W|A’s ability to accept natural-language queries for calculations and other information and produce multiple representations of all information it has that is related to the query — and the fact that it’s free and readily accessible on the web — makes it perhaps the most powerful self-verification tool…

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June 3, 2009, 12:06 pm

By Robert Talbert

By now, you’ve probably heard about Wolfram|Alpha, the “computational knowledge engine” that was recently rolled out by the makers of Mathematica. If you haven’t, here’s a good place to start. There is considerable debate among ed-tech people as to exactly what kind of impact Wolfram|Alpha, abbreviated W|A, is going to have in education. For me, W|A is still a little raw and gives back too many “*Wolfram|Alpha isn’t sure what to do with your input*” responses when given mathematically legitimate (at least they seem so to me) queries. But the potential is there for W|A to be a game-changing technological advance, doing for quantitative information what Google did for text and web-based information back in the 90′s. (W|A is already its own verb.)

One thing that seems clear is that, with technology available that is free and powerful and hardware-agnostic, technology …

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