During a lesson on ratios involving percentages of paint, four research-based criteria are used to evaluate students' mistakes. The takeaway is that painting all mistakes with the same brush can also be a blunder.

Contributor Notes

James C. Willingham, willinjc@jmu.edu, is an assistant professor of mathematics education at James Madison University in Harrisonburg, Virginia. He is most interested in the development of mathematical knowledge for teaching and effective K–12 mathematics teaching practices.

Jeremy F. Strayer, jeremy.strayer@mtsu.edu, is an associate professor of mathematics education at Middle Tennessee State University in Murfreesboro, Tennessee. He is interested in creating professional Mathdevelopment opportunities to support K–16 teachers working to implement standards-based teaching practices.

Angela T. Barlow, abarlow5@uca.edu, is the dean of the graduate school and director of sponsored programs at the University of Central Arkansas in Conway, Arkansas. Her research interests focus on supporting the instructional change process in elementary mathematics classrooms.

Alyson E. Lischka, alyson.lischka@mtsu.edu, is an assistant professor of mathematics education at Middle Tennessee State University. She is interested in how beginning and practicing teachers learn to implement mathematical practices in their classrooms.

(Corresponding author is Willingham willinjc@jmu.edu)
(Corresponding author is Strayer jeremy.strayer@mtsu.edu)
(Corresponding author is Barlow abarlow5@uca.edu)
(Corresponding author is Lischka alyson.lischka@mtsu.edu)
Mathematics Teaching in the Middle School
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