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ERIC Number: EJ1174854
Record Type: Journal
Publication Date: 2018-Apr
Pages: 9
Abstractor: ERIC
ISSN: ISSN-1072-0839
Examining Mistakes to Shift Student Thinking
Willingham, James C.; Strayer, Jeremy F.; Barlow, Angela T.; Lischka, Alyson E.
Mathematics Teaching in the Middle School, v23 n6 p324-332 Apr 2018
Middle-grades teachers and students can have different perspectives on the value of discussing students' mathematical mistakes, despite various classroom evidence that such discussions can help foster strong conceptual understanding. Some teachers consider student mistakes to be an opportunity to correct errors in individual student thinking. Others view the public inspection of mistakes as an opportunity for all students in the classroom to learn. Although both of these perspectives take students' learning into account students often regard their own mistakes in a very personal manner. They see mistakes as flaws for which their teachers will judge them. Helping students to learn from their mathematical mistakes can give teachers insight into their misconceptions and, depending on instructional reactions, can enable them to develop deeper understanding of the mathematics they are learning. A number of classroom tools are available that take advantage of this powerful idea, including setting up classroom norms that value mistakes; planning and selecting tasks to elicit mistakes; helping students focus on and discuss mistakes in meaningful ways; and assessing and designing responsive instruction based on student mistakes. The purpose of this article is to add to this set of tools a list of criteria for determining which student mistakes are worthy of class examination. As they authors discuss the criteria, they offer insight into why certain mistakes are worthy of inspection and how teachers might leverage their examination to shift students' mathematical thinking forward within the context of a specific mathematics lesson. This criteria is aimed at supporting the learning of each and every student, not just those who made the initial mistake.
National Council of Teachers of Mathematics. 1906 Association Drive, Reston, VA 20191. Tel: 800-235-7566; Tel: 703-620-9840; Fax: 703-476-2570; e-mail:; Web site:
Publication Type: Journal Articles; Reports - Descriptive
Education Level: Middle Schools
Audience: Teachers
Language: English
Sponsor: N/A
Authoring Institution: N/A
Grant or Contract Numbers: N/A