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**Contents:**

Title and Synopsis

Basics

Try It!

Elementary School

Middle and High School

Calculus

Combinatorics

Linear Algebra

Differential Equations

Other Advanced Topics

It's Not (Only) About Math!

More Examples (and Data!)

Less Is More

So Is It Perfect Yet?

What About Google?

Possible Implications

A Threat?

Resources

[Note: This article appears best using the Firefox browser.]

Wolfram|Alpha can be viewed as a threat to mathematics education because students can get answers to (some) questions without any understanding of how that answer was computed. But it might also be a useful tool, because its computational power can free up student time for thinking about mathematical ideas rather than simply carrying out algorithms that can be performed without understanding.

When there are concepts we want students to master, we can still ask conceptual questions. But if a machine can provide the answer to a question, then the question probably does not test understanding (unless we are willing to grant that machines display understanding).

Before hand-held calculators became common, algebra students would master linear interpolation when using log tables. To get accurate numerical answers to standard questions, the use of tables was the only means available. Today log tables are mostly viewed as relics of the past. However we still require our students to memorize the multiplication table when they are young and we still teach them long division and the Euclidean algorithm a few years later.

Will Wolfram|Alpha cause us to alter what we require of our students? This is a difficult and multifaceted question, and just as in the case of the calculator, mathematics instructors will eventually have to come to terms with this issue on their own. We will need to ask ourselves several more specific questions: Do students need to master the skill of integration by parts or partial fraction decomposition in a calculus class just because we want them to find antiderivatives? Do algebra students need to master factoring polynomials simply for solving equations and rewriting expressions? Do any students need synthetic division?

Some of your colleagues who teach courses prerequisite to your class may encourage their students to use Wolfram|Alpha, and students may come to your class with different skills sets than your previous students. What will you do to accommodate the weaknesses and to take advantage of the strengths of these new students?

It is not obvious how best to answer these questions. One place where the discussion has already begun is the Wolfram|Alpha wiki (link opens in new window or tab).