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A Step Backwards Can Make a Big Difference!

Weekly, for the past nine months, web sites have been reviewed on this web site.....selected because (in my opinion) they are web sites that can enrich either students' learning of mathematics or enhance teachers' teaching of mathematics.

Those who are regular readers/uses have perhaps noticed that my reviews tend to be positive. That is, I avoid reviewing/identifying a web site that is a step backwards in how students can learn mathematics in an exciting way. Do such web sites exist?

Yes, they do.......many of them. Often they are called "interactive lessons," but in reality they are little more than drill-and-kill. No helpful diagrams. No explanations that get at meaning. No challenges to a student's intellect. Basically, no mathematics!

Furthermore, some of these sites often make bothersome mathematics errors. For example, consider this site (unnamed here but often included on "Recommended Lists for Teachers")and its "lesson" on how to find the missing number in a sequence: (the following is copied verbatium)

  • Determine if the order of numbers is ascending (getting larger in value) or descending (becoming smaller in value).
  • Find the difference between numbers that are next to each other.
  • Use the difference between numbers to find the missing number.
And then the site continues with an example: "Find the missing number: 15, 13, ?, 9. The order of numbers is going down or descending. The difference between numbers is 15 - 13 = 2. Since the order is descending subtract 2 from 13. The missing number may be 11. The missing number is 11 since it is 2 more than the last number 9."

Why is this bothersome? First, it creates a false confidence in a stated rule, suggesting that it works for all sequences (which it does not...e.g. try 3, 4, 6, 9, ...). Second, this "nugget" was found under the Pattern lesson plan section. No attempt to explain what a pattern is....no attempt to encourage students to look at a sequence of numbers and make observations about what they notice. In sum, this is not good mathematics, as patterning is both very rich and a primary foundation to mathematyical thinking.

And, what bothers me the most? That the above site is the first site listed as part of the recommended Great Web Sites for Kids....put out by the American Library Association. Thus, as mathematics teachers, it is important that we educate not only our students but our parents and colleagues (including librarians) as to what makes a good mathematics website.