# Tag Archives: Wolfram Alpha

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 specific search terms you want to turn into user-defined variables, and the graphical tools on the website do the work. In other words, if you can perform a W|A query, you can make a widget out of it in short order and then share it with the world via social media or embedding on a blog or wiki.

There’s a lot of potential here for use in teaching and learning:

• The ability for anybody, with or without programming skill, to create widgets from simple W|A queries opens the door for creative technology projects for students at almost any level. An instructor could assign a project in which students simply have to create a widget that does something useful for the class, for example to generate a comparison of two stocks in an economics class (though that’s already been done) or generate a contour map of a two-variable function in a multivariable calculus class. Students work in teams to create the widget and then post on a class blog or wiki.
• Instructors can easily add a W|A widget to a homework or writing assignment for easy generation of data from user-defined sources. For example, a standard exercise in precalculus and science is to determine when a sample of a radioactive substance is reaches a certain mass, given its half-life. In textbooks, we have to stick with one element and its half-life. But an instructor could now create a widget where the student enters in the name of an element or selects it from the list, and the widget spits out the half-life of that element. The instructor can alter the problem to say, “Pick your favorite radioactive element and use the widget to find its half-life. How long until 10mg of that element decays to 8mg?”

I’m very excited about the shallow learning curve of these widgets and the consequent potential for students to make and play with these things as creative components of a class. Here’s a screencast on how to make a widget, in which I do a complete walk-through of the creation process.

What are some other ways you could see Wolfram|Alpha widgets being used effectively in a course?

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## ICTCM underway

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.

• 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 of WeBWorK Use in Calculus and Precalculus in a Mathematics Department”, session by Mako Haruta.
• 2:30 – Exhibit time.
• 3:00 – “Student Projects that Assess Mathematical Critical-Thinking Skills”, session by David Graser.
• 5:00 – “Visualizing Mathematics Concepts with User Interfaces in Maple and MATLAB”, session by David Szurley and William Richardson.

But first, breakfast and (especially) coffee.

## MATLAB and critical thinking

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 counts. Once you make that scatterplot, it looks like this:

The reaction of most students to this plot was really surprising. Almost unanimously and without consulting each other, the reaction was: “That can’t be right.” When I’d ask them why not, they would say something like: It looks strange; or, it’s not like scatter plots I’ve done before; or, it just doesn’t look right.

The first instinct of those who felt like they had made a critical error in their plot was to ask me to verify whether or not they had gotten it right. That’s understandable, but it doesn’t go very far because I have a rule that I don’t answer “Is this right?” questions in the lab. (See the instructions in the lab assignment.) Student teams are responsible in the labs for determining by themselves the rightness or wrongness of their work. So it’s time for critical thinking to take center stage — which in this context would refer to using your brain and all available tools and information to self-verify your work. (I wrote about the idea of self-verification here using Wolfram|Alpha.)

Some of the suggestions I gave these teams were:

• Have you checked your plot against the actual data? For example, look at the outliers. Can you find them in the data set itself? And look at the main cluster of data; given a cursory glance through the data set, does it look like most states have a land area less than $10^6$ square miles and an electoral vote count of between 5 and 15?
• Have you tried to create the same scatterplot using different tools? For example, everybody in the class knows Excel (because we teach it in Calculus I); the data are in Excel already, so it would be virtually no work to make a scatterplot in Excel. Have you tried that? If so, does it look like what MATLAB is creating?
• Have you taken a moment just to think about the possible relationship between the variables, and does the shape of the data match your expectations? Probably we don’t really expect much of a relationship at all between the land area of a state and its electoral vote count, even with the outliers trimmed out, so a diffuse cloud of data markers is exactly what we want. If we got some sort of perfectly lined-up string of data points, we should be suspicious this time.

Once you phrase it like this, students pretty quickly gain confidence in their results. But, importantly, most of them have never been put into situations — at least in the classroom — where this sort of thing has been necessary. If critical thinking means anything, it means training yourself to ask questions like this and pursue their answers in an attempt to be your own judge of your work.

I was particularly surprised by the rejection of any scatter plot that doesn’t look like points on the graph of a function. “Authentic instruction” is a term without an operational definition, a lot like the term “critical thinking”, but here I think we may have a clue to what that term means. Students said their scatterplots didn’t “look right”, meaning they didn’t look like what their textbook examples had looked like, i.e. the points didn’t have an overwhelmingly strong correlation despite the existence of a few token outliers. In other words, students are trained by the use of made-up data that “right” means “strong correlation”. So when they encounter data that are very much not correlated, the scatter plot “looks wrong” rather than “looks like there’s not much correlation”. Students are somehow trained to place value judgements on scatter plots, with strong correlation = good and weak correlation = bad. I’m not sure where that perception comes from, but I bet if we gave students real data to work with, it would never take root.

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## Courses and “something extra”

Some of the most valuable courses I took while I was in school were so because, in addition to learning a specific body of content (and having it taught well), I picked up something extra along the way that turned out to be just as cool or valuable as the course material itself. Examples:

• I was a psychology major at the beginning of my undergraduate years and made it into the senior-level experiment design course as a sophomore. In that course I learned how to use SPSS (on an Apple IIe!). That was an “extra” that I really enjoyed, perhaps moreso than the experiment I designed. (I wish I still knew how to use it.)
• In my graduate school differential geometry class (I think that was in 1995), we used Mathematica to plot torus knots and study their curvature and torsion. Learning Mathematica and how to use it for mathematical investigations were the “something extra” that I took from the course. Sadly, the extras have outlived my knowledge of differential geometry. (Sorry, Dr. Ratcliffe.)
• In the second semester of my graduate school intro abstract algebra class, my prof gave us an assignment to write a computer program to calculate information about certain kinds of rings. This was a small assignment in a class full of big ideas, but I had to go back and re-learn my Pascal in order to write the program, and the idea of writing computer programs to do algebra was a great “extra” that again has stuck with me.

Today I really like to build in an “extra”, usually having something to do with technology, into every course I teach. In calculus, my students learn Winplot, Excel, and Wolfram|Alpha as part of the course. In linear algebra this year I am introducing just enough MATLAB to be dangerous. I use Geometers Sketchpad in my upper-level geometry class, and one former student became so enamored with the software that he started using it for everything, and is now considered the go-to technology person in the school where he teaches. In an independent study I am doing with one of my students on finite fields, I’m having him learn SAGE and do some programming with it. These “extras” often provide an element of fun and applicability to the material, which might be considered dry or monotonous if it’s the only thing you do in the class.

What kinds of “extras” were standouts for you in your coursework? If you’re a teacher, what kinds of “extras” are you using, or would you like to use, in your classes?