Navigating WolframAlpha Pro Features

Last week I had to do a workshop about WolframAlpha, and I noticed that there are three different feature sets: not logged in, logged in, logged in to Pro.

I needed to know which login settings provided which features (especially for giving workshops and working with students), so I decided to be thorough about it.  You can download the PDF of this document, Guide to Wolfram Alpha Features, as well.

Hope this makes the decision-making a little easier for you!

 

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Abandoning Ship on Wolfram Alpha?

I am really getting fed up tired of having to explain Wolfram Alpha graphs to students.  For some reason, the default in Wolfram Alpha is to graph everything with imaginary numbers.  This results in bizarre-looking graphs and makes it near-impossible to use Wolfram Alpha as a teaching tool for undergraduate mathematics, a real shame.  Now that Google has entered the online graphing fray, I have a wary hope that the programmers at Wolfram Alpha might finally (after two years of waiting) fix the problem.

Here are a few examples.  I’ll show you the graph in Wolfram Alpha, on a TI-84 Plus emulator (TI-SmartView), from Google Search, and from Desmos Graphing Calculator.  These are all the “default” looks.  Wolfram Alpha consistently shows this confusing imaginary view as the default whenever working with graphs involving variables in radicals.

Example 1:

Example 2:

Example 3:

I was hoping to really teach my College Algebra students to use Wolfram Alpha next semester.  But, between the Logarithm Issues and this graphing issue, I’m afraid I’m going to have to abandon ship on using Wolfram Alpha as a teaching tool for students. Students simply don’t have enough mathematical sophistication to look at the graphs and realize that they aren’t seeing what they are supposed to be seeing and I’m seeing far too much confusion on assessments that are caused by the oddities in graphs and logarithms on Wolfram Alpha.  What a shame that we can’t work this out, huh?

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Wolfram Alpha in a Nutshell

This little video is reminiscent of the “in Plain English” videos that we all love.  If you’re trying to explain Wolfram Alpha to a non-math person, try Wolfram Alpha in a Nutshell.

Thanks to the Tech the Plunge blog for pointing this one out.

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Shifting Assessment in a World with WolframAlpha

I let my students use Wolfram Alpha when they are in class and when they are doing their homework (um, how would I stop them?).  Because of this, I’ve had to shift how I assess on more formal assignments.  For the record, it’s the same adjustment you might make if you were using ANY kind of Computer Algebra System (CAS).

The simplest shift is to stop asking for the answers to problems, and just give the students the answers.  After all, they live in a world where they CAN easily get the answers, so why pretend that it’s the answers that are important?  It’s the mathematical thinking that’s important, right?  Giving the students the answers turns problems into “proofs” where the evaluation (grade) is based on the thought-process to get from start to finish. It also eliminates the debate about whether to award points for a correct answer with no correct process.

Here are two examples of problems from a recent Calculus exam (old and new wording).

I wish I had thought to do this years ago, because students who insist on just doing the “shortcut” (and not learning what limits are all about) now have nothing to show for themselves (the answer, after all, is right THERE).

Again, a student that knows the derivative rules might get the right answer, but the right answer is now worth zero points.  The assessment is now clearly focused on the mathematical thinking using limits.

Another reason that I really like this is that it allows students to find mistakes that they are capable of finding “in the real world” where they can quickly use technology to get an answer.  They are now graded solely on their ability to explain, mathematically, the insides of a mathematical process.

Wolfram Alpha also allows me to pull real-world data into my tests much faster.  Here’s a question about curve shape (the graph is just a copy/paste from W|A):

If you haven’t begun to think about how assessment should change in a world with ubiquitous and free CAS, you should.  You don’t have to change all your problems, but I think some of them should change.  Otherwise, we’re just testing students on the same thing that a computer does, and that doesn’t sit well with me.  If you can be replaced by a computer, you’re likely to be replaced by a computer.  Let’s make sure we’re teaching students how to think mathematically, not how to compute mathematically.

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Math Technology to Engage, Delight, and Excite

This is the Plenary Address from MAA Michigan last week.

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