Math (and more) with WolframAlpha

First, WolframAlpha 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 visual representation (the seven dots) and number line representation.

WolframAlpha 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 the left side 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 couple of graphs from different perspectives.

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".  There are some limitations, especially when working with lower math skills.  For example, for quadratics it does not seem to recognize "vertex form" or "complete the square".

Notice that for solutions, it will offer the option of "Show Steps" which will walk you step by step through the solution process:

One drawback to this is that some steps are not fully explained, so a student could use it and write each correct step down without understanding why it works or why it is important.  For example, in the third step "Add 1 to both sides" it is not explained why 1 works or how it is chosen.

An advantage is that many examples can be shown quickly, so possibly patterns could be seen. Also, the computer never gets lazy so the steps reflect "proper" mathematics. For example, in the fifth step "Take the square root of both sides" it is shown that the square root of the LHS yields an absolute value instead of skipping straight to the next step.  (Again, it might be even better if there was an option to choose additional information explaining where the absolute value came from.)

For non-mathematical tasks - there is an incredible amount of additional searches that can be made.

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 am ten years old.  This 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:

WolframAlpha uses the most up-to-date information that is available online.

In this case, it tells the user that Provo's weather was last updated 23 minutes ago and East Lansing's was last updated 45 minutes ago.



To sum up, WolframAlpha 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 WolframAlpha, visit WolframAlpha for Educators (some lesson plans) or the Wolfram Demonstrations Project (interactive activities) or even Wolfram MathWorld (definitions).