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In his article for Mathworlds dated November 29, 2023, Dan Meyer introduces a transformative approach to math education that emphasizes the proactive use of incorrect answers in the learning process. This method, inspired by recent research from psychologist Sarah Shi Hui Wong, suggests that deliberately asking students for wrong answers, a technique referred to as "derring," can significantly enhance recall and understanding of concepts.
Illustration by Michael Keany/AI
Traditionally, the math education community has fostered an environment where mistakes are not merely tolerated but are seen as valuable steps in the learning process. Expressions like "Mistakes are expected, inspected, and corrected" are common in classrooms, highlighting an understanding that the fear of being wrong can severely restrict mathematical exploration and comprehension. However, Meyer argues that this reactive stance towards mistakes should evolve into a more proactive strategy, as indicated by Wong's research findings.
Wong's study divided students into three groups to study neuroscience terms and their definitions. The first group was instructed to copy the definitions and underline key elements, the second to introduce and then strike out a conceptual error in the definition, and the third to correct the error they introduced. The outcomes showed that students who engaged in making deliberate errors (the latter two groups) had significantly better recall performance than those who merely copied the definitions.
Further experiments by Wong dispelled the notion that the improved performance was due to increased effort in the "error" conditions. Additional studies even demonstrated that these students could transfer their learning more efficiently to new contexts. This suggests that understanding what an answer is not can be as valuable as knowing what it is.
Meyer highlights practical applications of this research in the classroom. He suggests that even if students cannot identify the correct answer, they are often capable of recognizing an incorrect one. For instance, asking students to design a car that doesn't meet specific constraints or to propose an obviously wrong number of gummy bears to create a "super bear" can stimulate deeper engagement and understanding.
This innovative approach underlines a broader perspective where wrong answers are not just mistakes to be corrected but are valuable resources for teaching and learning. By integrating "derring" into classroom practices, educators can leverage the full spectrum of student responses as tools for exploration, understanding, and growth in mathematical thought.
Source: "Help Students Remember the Right Answers by Asking for the Wrong Answers First," by Dan Meyer, Mathworlds, November 29, 2023. Original URL
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