Math Errors Personified
Perhaps last week's review did not satisfy your appetite for mathematical errors. So, let me suggest two more web sites.
The first web site innumeracy.com is Steve Head's collection of links to articles and web sites pertaining to lapses in numeracy and critical thinking. His catogorizes items by basic innumeracy, the law of large numbers, probability and statistics, and critical thinking (reasoning and logic). As a side personal interest, Editor Head tosses in materials on urban hoaxes, media watch, net safety, and food for skeptics.
Though the previous site does overlap the area of mathematics education, mathematics teachers will feel at home (unfortunately) with Eric Schechter's The Most Common Errors in Undergraduate Mathematics. As you browse it, you might even be able to attach past student names to the specific errors. One nice feature is that with each error type, Eric includes a discussion of both the likely causes of the error and and its remedy. Eric discusses these error types:
The discussion is helpful to mathematics teachers in grades 6-14, as much of the content and error types span those grade ranges.
- Errors in Communication (including teacher hostility or arrogance, student shyness, unclear wording, bad handwriting, not reading directions, loss of invisible parentheses, terms lost inside an ellipsis)
- Algebra Errors (sign errors, everything is additive, everything is commutative, undistributed cancellations, dimensional errors)
- Confusion in Notation (idiosyncratic inverses, square roots, order of operations, ambiguously written fractions, stream-of-consciousness notations)
- Errors in Reasoning (going over your work, overlooking irreversibility, not checking for extraneous roots, confusing a statement with its converse, working backward, difficulties with quantifiers, erroneous methods that work, unquestioning faith in calculators)
- Unwarranted Generalizations (Euler's square root error, xx.)
- Other Common Calculus Errors (jumping to conclusions about infinity, loss or misuse of constants of integration, loss of differentials)