# Literature on learning from errors in mathematics

In teaching undergraduate mathematics, I implemented some strategies to encourage the students to look at errors they made or at "typical errors" in the current topic. One attempt was to compile a commented list of errors which appeared in the course.

At the moment I am looking for literature on learning by analysing errors in undergraduate mathematics education. I found a lot of literature focused on mathematics education at school but very few on undergraduates. I would be especially interested in evaluations of teaching strategies.

• Asking for literature on learning from errors in mathematics is a good question. The more general question is a different one, so you should rather ask that separately. Maybe wait and see what answers you get here, and then ask a follow-up question. – Joonas Ilmavirta Apr 16 '16 at 12:19
• @JoonasIlmavirta I removed the more general question. – Christian Apr 16 '16 at 12:20
• @JonBannonn The idea of my question is not only about avoiding errors. It is about how students can learn from errors they made themselves or "typical" errors. And whether if it is is effective to ask the students to analyse their errors and what they can learn from them. So I think that your links are "on topic" for my question. – Christian Apr 16 '16 at 13:40
• Some related questions: Test Correction Analysis, Teaching students to find and correct their own errors. A related answer: Check by substitution – Jasper Apr 16 '16 at 16:30
• Neither is an answer (hence this comment) but you may find something of use in a couple of earlier answers I supplied: One for a Lexicon of Math Mistakes and the other with a book on "error case studies" (although not generally at the undergraduate level). – Benjamin Dickman Apr 17 '16 at 6:00

You might be interested in systematic errors. From page 14 of Kurt VanLehn's "Mind Bugs: The Origins of Procedural Misconceptions" (MIT Press, 1990):

Systematic errors appear to stem from consistent application of a faulty method, algorithm, or rule. Slips are unsystematic "careless" errors (for example, fact errors, such as 7-3=5). Because slips occur in expert performance as well as student behavior, the common view is that they are due to inherent "noise" in the human information processor. Systematic errors on the other hand are taken as stemming from mistaken or missing knowledge, the product of incomplete or misguided learning.

(An example of a systematic error is writing the remainder of a division of two integers as a decimal fraction, such as saying that $17\div 5=3.2$.)

Many researchers have studied these. A few are John Seely Brown, Richard R. Burton, and Kurt VanLehn.

• More examples of systematic errors in arithmetic of college students can be found here. – Joel Reyes Noche Apr 16 '16 at 14:05

A colleague of mine did his dissertation on such matters. His book, Mathematical Misconceptions of College-Age Algebra Students might be of interest.

• Wow, as a TA I taught from his calculus text in the 90's. Still keep that book close at hand. – Daniel R. Collins Aug 22 '16 at 5:41