Category: Future of Math

Wolfram Alpha for Inquiry Based Learning in Calculus

Now that all my Calculus II students know about Wolfram Alpha (I showed them), I have to make sure that the assignments I ask them to turn in can’t just be “walphaed” with no thought.  In Calc II, our topics list includes a lot of “techniques-oriented” topics (integration by partial fractions, integration by parts, etc.) and because of the need to keep this course transferable to 4-year schools, I can’t really get around this.  So now I’m in the position of having to reconcile the use of technology that easily evaluates the integrals with making sure that students actually understand the techniques of integration.  There are two ways I’m tackling this: 1. CCC (Concept Compare Contrast) Problems: I’m writing problems that focus on understanding the mathematical process and the compare/contrast nature of math problems.  While Wolfram Alpha can evaluate the integrals for them, the questions I’ve asked require (I hope) a deeper level of understanding about what happens when the techniques are used.  Here’s an example from my recent problem set: There are two pairs of problems below that are exactly the same. You won’t see why until you do the integration, showing all the steps. Find the pairs and then explain how the matched integrals are fundamentally the same. 2. Inquiry Based Learning: One appropriate use for any CAS (computer algebra system) is to use it as a...

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What we’re doing with WolframAlpha

Originally, I started this post with the title “What I’m doing with Wolfram|Alpha” and then I revised it, because it’s not just me using Wolfram|Alpha. My students are using it too. Here are some of the things we’re doing: Discussion Boards: Wolfram|Alpha + Jing = Awesome Before Wolfram|Alpha, it could take several steps to get a graph or the solution to solving an equation to the discussion board in an online class. You had to use some program to generate the graph or the equations, then make a screenshot of the work, then get that hyperlink, image, or embed code to the discussion board. With Wolfram|Alpha, sometimes a simple link suffices. Suppose, for example, I needed to explain the last step in a calculus problem where the students have to find where there is a horizontal tangent line. After finding the derivative, they have to set it equal to zero and solve the equation (and calculus students notoriously struggle with their algebra skills). Rather than writing out all the steps to help a student on the discussion board, I could just provide the link to the solution and tell them to click on “Show Steps.” Sometimes, a bit more explanation may be required, and in these circumstances, Jing + Wolfram|Alpha really comes in handy. For instance, I needed to show how to reflect a function over the line y=1....

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Moving Math from Analog to Digital

Arthur Benjamin has been on TED in the past (see Mathemagics) and has done a really phenomenal job. Here’s his latest 3-minute appearance, called “A Formula for Changing Math Education.” The problem is that the very short talk does not present a “formula” for changing education, just Benjamin’s idea that the pinnacle at the top of the math pyramid should be statistics instead of calculus. There is nothing in the the short talk that suggests any kind of coherent plan for how it could be done, or even a suggestion that he has a plan. That’s what I would want to know about. Of course, it’s only a 3-minute talk and it’s certainly possible that he had nothing to do with the name of the talk. I did agree with these two statements, but want to add my own two cents: 1. “very few people actually use calculus in a conscious meaningful way in their day to day lives” … but I’m not sure we teach people how to use calculus in a “conscious meaningful way” nor are many of us required to use calculus for the simple reason that our superiors don’t understand it at all. Calculus could be used in a “conscious meaningful way” but our society chooses not to engage. As a matter of fact, very few people actually use statistics in a conscious meaningful way...

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Shaking Up Math Education

In case you missed this, there’s a great Wall Street Journal article and blog post about Wolfram Alpha … Sum Help: New Search Engine for Mathletes (The Wall Street Journal, 6/16/09) Wolfram Alpha, A New Online Computation Engine Shakes Up Math (The Numbers Guy Blog, 6/16/09) Of course, I could just think they are great because I was quoted in them. 🙂 Possibly Related Posts: Reimagining Calculus Keynote Group Exploration in Math Elaborations for Creative Thinking in STEM Learning Math is Not a Spectator Sport Recorded Webinar: Teaching Math in...

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Don’t get WolframAlpha Implications? Try these examples.

Wolfram|Alpha is a “computational search engine” built by Wolfram Research (the developers of Mathematica). W|A (pronounce this as “walpha” if you’d like) is similar in appearance to the search engines that we are used to and easy to use. It’s not that W|A will replace other search engines, because it won’t. It’s more of a missing piece in the search engine puzzle. W|A provides a collection of data, formulas, computations, and interpretations that are different from other search engines. Although the media has stressed data-driven examples (for example, type your first name to see a graph of the frequency of that name over time), the ability of W|A to function as a combination of CAS and natural language computational system is stunning. Let me illustrate with a couple of examples for you to try yourself.  Simply follow the links below to see how W|A handles these search requests: • 126 (make sure to click on “other historical numerals”) • convert 125 m^3 to gallons • sphere r=7 cm • Line (2,7) and (3,1/2) • Solve x^2-6x=16 (make sure to click on “show steps”) • 4 – x^2 • Triangle 7,8,9 • x^2-y^2=9 • limit x->3 (x-3)/(x^2-9) (again, make sure to click on “show steps”) • integral (x^2)sin(x^3) (“show steps”) • sum 1/n^2 • New York City, Chicago • convert 78 to base 5 There are several differences between W|A...

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