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Learning From Our Errors

Mathematics teachers and students differ with respect to feelings about the treatment of errors. My conversations with quality mathematics teachers suggest that the best perspective on errors is for students to learn from them.

But, the question is...how to best approach this learning experience? This decision flies in the face of the felt urgency to keep all students on the same pace...plus, time is passing, and all must move on if the class is going to "cover" the required material.

Thus, the too-common response is for students to look at a test, mentally note their score, observe the amount of red markings on their test (assuming they imply negative things), and then go on with their lives...rarely reflecting on their errors or trying to learn from them.

Patricia Dulac (East Greenwich High School, Providence, NJ) argues that teachers must help students learn from their errors. She has created a three-step process, which her students pass through for every mistake on a quiz or test:

  1. Box 1: Rewrite the problem that had the mistake
  2. Box 2: Self-assess to determine what they did wrong and describe their misunderstanding if relevant
  3. Box 3: If possible, redo the problem correctly with their new understanding
During this process in her class, students who did well on the exam complete their reflection sheets first and then help their peers.

Does it work? Dulac and other members of her mathematics faculty think so. In their school, every mathematics teacher in grades 7-12 now uses this approach.

Dulac claims there are two positive outcomes

  • Sudents move beyond thinking a mistake was "careless" and focus on what they do and don't know, causing them to be more "open to asking and listening."
  • Teachers use this feedback to inform their teaching, tracking performance trends and allowing them focus their reteaching on either a class as a whole or individuals.
A final note...on the state's yearly performance-based exam, their school scored at the 71% proficient level. This was the highest level in the state of New Jersey...and about three times the state average of 28%.


D.E. (Seattle) adds this caution: The main article’s conclusion gives me the statistical heebee-jeebies! Its suggestion is that the “improvement plan” is helpful, but I think the better conclusion would be, “Well, it appears that this method is only effective in schools that are already high-achieving.”

Source: Providence Journal, December 12, 2010