Numbers and Operations
Wolfram|Alpha can of course be used for simple calculations but it will go far beyond that, trying to give everything to you that you could be looking for.
Here, a relatively simple calculation results in the numeric answer (7), its verbal representation (seven), as well as a manipulatives representation and number line representation of the addition process. It also includes speed for computation at different ages which is fun to think about.
Wolfram|Alpha will attempt to guess what the user wants but will tell you what it’s assuming. For example, in this case it said “Assuming trigonometric arguments in degrees” and offered to use radians instead. It also provides links to “Related Queries” on bottom of the results page.
If we up the ante a bit, and try a quadratic equation:
It gives us the type of geometric figure (parabola) as well as a graph:
You can see that on the “geometric figure” field there is a button for “Properties”. Pressing this will yield additional information including the focus, vertex, semi-axis length, focal parameter, eccentricity, and directrix.
The graphs each have buttons to “enable interactivity” (although apparently that is now a WolframAlpha Pro feature).
But wait! That’s not all…
It also shows an alternate form, derivatives and the global minimum.
Typing different forms will result in different attempts to answer the user’s question. Try entering just “x^2 – 2” or “solve x^2 – 2 = 0”.
Notice that for solutions, it will offer the option of “Show Steps” which will walk you step by step through the solution process (although it looks like this feature is also now part of Wolfram|Alpha Pro).
An advantage is that many examples can be shown quickly (or explored), so students might make conjectures and look for patterns, as they experiment with values of parameters.
Data and Analysis
For example, you can search your name and see how popular it was when you were born. I found that my parents were almost 15 years ahead of the times – very few girls my age are named Eryn.
It also states that, with my name, it is most likely that I was born in 2000. Thus, my name will be helpful when I start pretending to be 25 years younger than I really am someday.
You can also compare two names (or really two of anything!) by typing “compare ___ and ____” or just “___ | ____”.
For example, I can type “compare provo and east lansing” or just “provo | east lansing”. Or I can ask to compare a specific characteristic like population or weather:
Wolfram|Alpha uses the most up-to-date data that is available online. In this case, it tells the user that Provo’s weather was last updated 31 minutes ago and East Lansing’s was last updated 33 minutes ago.
To sum up, Wolfram|Alpha can be useful in a number of ways and can add relevance to mathematics application questions. It can also provide some useful information to students, but care should be taken to ensure that they are thinking about the information provided rather than accepting it at face value.
To find more information or participate in an online mathematics educators community centered around teaching math with Wolfram|Alpha, visit Wolfram|Alpha for Educators (some lesson plans) or the Wolfram Demonstrations Project (interactive activities) or even Wolfram MathWorld (definitions).