Category: Find and Use Data

Teaching Math with Technology (Discussion Panel)

While I was at Wolfram Alpha Homework Day, I participated in a Panel Discussion about the Myths about Teaching with Technology. The panel ran 30 minutes and was mediated by Elizabeth Corcoran. There were three of us (all women, weirdly enough), Debra Woods, a mathematics professor at the University of Illinois at Urbana-Champaign; Abby Brown, a math teacher at Torrey Pines High School; and myself. I no longer remembered anything that I said in this panel, so it was fun to watch the discussion from an outside point-of-view. I am glad to see that I talked about the value of play during the discussion, because I am finding more and more that introducing play (and exploration) back into learning makes a big difference in engagement and in retention of the subject. Possibly Related Posts: Contemporary Algebra Collection (new resources 2/4/2019) Teaching in Higher Ed Podcast about ESIL Lens Add Graphs In The World to Courses Taking the Algebra Out of College Algebra Group Exploration in...

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WolframAlpha: Recalculating Teaching and Learning

For at least a decade, we have had the ability to let CAS software perform computational mathematics, yet computational skills are still a large portion of the mathematics curriculum. Enter Wolfram|Alpha. Unlike traditional CAS systems, Wolfram|Alpha has trialability: Anyone with Internet access can try it and there is no cost. It has high observability: Share anything you find with your peers using a hyperlink. It has low complexity: You can use natural language input and, in general, the less you ask for in the search, the more information Wolfram|Alpha tends to give you. Diffusion of innovation theories predict that these features of Wolfram|Alpha make it likely that there will be wide-spread adoption by students. What does this mean for math instructors? This could be the time for us to reach out and embrace a tool that might allow us to jettison some of the computational knowledge from the curriculum, and give math instructors greater flexibility in supplemental topics in the classroom. Wolfram|Alpha could help our students to make connections between a variety of mathematical concepts. The curated data sets can be easily incorporated into classroom examples to bring in real-world data. On the other hand, instructors have valid concerns about appropriate use of Wolfram|Alpha. Higher-level mathematics is laid on a foundation of symbology, logic, and algebraic manipulation. How much of this “foundation” is necessary to retain quantitative savvy at...

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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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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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Implications for Math Instructors

They say a picture is worth 1000 words.  Then here are about 15,000. I’ve taken screenshots of several examples of the algebra through calculus that WolframAlpha will do. You can see the album of screenshots here. I’ll let you see the implications for yourself. Possibly Related Posts: Contemporary Algebra Collection (new resources 2/4/2019) Teaching in Higher Ed Podcast about ESIL Lens Add Graphs In The World to Courses Bringing the Real World to Your Math Class Every Day Taking the Algebra Out of College...

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