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Wednesday, July 23, 2014

Misconceptions in Mathematics and Diagnostic Teaching

With the adoption of new standards for learning mathematics that place an emphasis on building students' conceptual understanding and using that to inform their development of procedural knowledge, there is a need for teachers to develop skills in uncovering students' thinking and providing opportunities to address misconceptions.  This article by Elizabeth Green in the New York Times offers a thorough look at the changes being called for: "Why Do Americans Stink at Math?

The following set of resources offer some good ideas to start approaching mathematics teaching conceptually by eliciting and building from students' thinking:

Diagnostic Teaching for Grades 6 and 7 (set of 12 problems and accompanying teacher materials)

How Do My Students Think? Diagnosing Student Thinking (research-based guide for teachers)

Learning from Mistakes and Misconceptions PD (slides and guide)

Gaps and Misconceptions in Maths (focuses on subtraction, division, and fractions)

Mathematics Assessment Probes (first chapter of Uncovering Student Thinking in Mathematics, Grades K-5)

Uncovering Student Thinking About Mathematics in the Common Core, Grades 6-12 (free sample chapters)

Chelsea Diagnostic Mathematics Tests (scanned versions of a book of diagnostic assessment from 1984)

Eliciting Mathematics Misconceptions (blog with two videos about fraction misconceptions)