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
• 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 and traditional CAS systems. The first, which you should have noticed after those examples, is that the less you ask for, the more you get. W|A just assumes you want all relevant computations and information that it can generate: graphs, solutions, alternate forms, derivatives, integrals, area under the curve (if bounded), and steps (if they are available). W|A provides quick and painless access to all sorts of data that has been organized so that it can be cross-referenced. In this sense, W|A could be a valuable tool for us in helping students to see the connections between concepts within mathematics and in relating mathematics to the real world.
On the other hand, you’re probably also seeing that there could be implications with academic dishonesty, especially in online and hybrid courses. We will all have to individually decide whether W|A is off limits, and if so, how we can possibly enforce it. Ready or not, W|A is now available on any computer with Internet access and on most SmartPhones.
It is up to us to think about (with as much advanced notice as possible) how we want to embrace, adopt, accommodate, or regulate the use of W|A in our courses. This is a conversation we should have in every department at every level of mathematics, including both full-time and part-time instructors. It is a conversation that we should have with our colleagues in the partner disciplines and with our colleagues at our transfer institutions.
Note: There are additional resources you may wish to view. A longer analysis regarding the rate of adoption and the impact of large-scale change in mathematics on the higher education system can be found here. A wiki (WalphaWiki) documenting some of the capabilities of W|A for math courses and the implications for teaching has also been started by Derek Bruff.
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