Wolfram|Alpha: Recalculating Teaching & Learning
October 23rd, 2009
My talk today at the 2009 International Mathematica User Conference:
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 the higher levels? Answering this question will require us to recalculate how we teach and learn mathematics.
There are two videos embedded in the slideshow. You should be able to click on the slide to open the videos in a anew web browser. However, if you’d just like to watch the video demos, here are direct links:
- Complexity and Relative Advantage: Comparing the use of Mathematica to Wolfram|Alpha (for educational purposes, 2 minutes)
- Trialability and Observability: Demonstration of how the use of W|A is likely to spread via direct online contact (sounds like a virus, doesn’t it? 5 minutes)
Note that I’ve turned ON commenting for these two video demonstrations and I will try to load them into YouTube later this weekend.
There are several other posts about Wolfram|Alpha that you may want to check out:
- What we’re doing with Wolfram|Alpha
- Don’t get Wolfram|Alpha? Try these examples
- Shaking Up Math Education
- Impact of Wolfram|Alpha on Math Ed
- Chemistry Takes a Hit Too
- Implications for Math Instructors
If you were at the live version of this talk, and you would like to rate the presentation, you can do so here at SpeakerRate.
Possibly Related Posts:
- Collection of Math Games
- What does the classroom say?
- Signed Numbers: Colored Counters in a “Sea of Zeros”
- Register for the 2012 MCC Math & Tech Workshop
- See you at AMATYC 2011
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“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.” A very good point, but the CAS Sage (http://www.sagemath.org) can also be used online, through any browser (http://www.sagenb.org), and whereas Sage does not have the breadth of W|A, it certainly equals it in depth. W|A really only allows you to answer single questions – you can’t for example, create your own function and play with it. Nor is it easy to use the result of one question as the input to another question. As well, W|A, being not open source, is not extendable – you can’t add your own functionality to it. I am entirely ambivalent about W|A, especially for teaching. It may have its uses as a sort of “super-calculator”, but to me that’s very limiting. Maybe I should blog about this myself…
Anyway, that being said, I always enjoy your posts about technology in mathematics education – keep up the good and inspiring work you do!
Actually, I think I posted too soon! It is possible to evaluate your own function, although you can’t save a function for future use. And it does have a cut-and-paste facility. But my main concern – its lack of extensibility, still holds. (It also doesn’t do much advanced stuff – computations with finite fields, elliptic curves etc).
Although I do stress WA some faculty at my college have high praise for the free Sage program. Maria, how do you compare the two?
I also agree that W|A is limited in the sense that you’re limited to just one line of input. More complex problems in a junior/senior applied math course will need more functionality than W|A offers.
However, if you’re interested in illustrating concepts quickly and easily, W|A is the way to go. I had W|A factor a fifth degree polynomial very easily and then had the students analyze the results in the context of the Fundamental Theorem of Algebra. This was in a proofs course for math majors. Graph the same polynomial in W|A and you can talk about end behavior and tie in the meaning of real/complex roots etc.
(As an aside, conceptual ideas of precalc seem to alien to my math majors, so I have to do this in my proofs course. )
Maria,
First: I enjoy your blog tremendously, it is always informative, comprehensive and interesting.
Second: I have a question that you touched upon in your Prezi presentation (but I couldn’t get the audio): do we have any studies, that have a statistically rigorous analysis of the benefits of using technology in mathematics? We all intuitively feel that a CAS, W!A or even a TI-Nspire would help the kids, but it seems to be just that … an intuition. (Of course how we define learning math is another conundrum.) I would be grateful for any citations. For the record I have a Ph.D. in engineering and after many years of doing engineering research I am now teaching HS math. I do not think that we are putting out a very good product and some of the reasons are cultural and political, but still I would like to know how to do better. Thanks in advance
Dean