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M. Lynn Breyfogle

This department publishes brief news articles, announcements, and guest editorials on current mathematics education issues that stimulate the interest of TCM readers and cause them to think about an issue or consider a specific viewpoint about some aspect of mathematics education. This month, the chair of the TCM Editorial Panel welcomes readers to a new academic year; and the Coaches' Corner suggests ways for math specialists to intrinsically motivate teachers.

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M. Lynn Breyfogle and Barbara Spotts

What are you doing to grow professionally and improve instruction when no one is looking?

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Renee Parker and M. Lynn Breyfogle

This student-friendly rubric helped improve third graders' competencies when explaining solution strategies in writing.

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M. Lynn Breyfogle and Courtney M. Lynch

To analyze students' geometric thinking, use both formative and summative assessments and move students along the van Hiele model of thought.

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M. Lynn Breyfogle and Judith Quander

Share news about happenings in the field of elementary school mathematics education, views on matters pertaining to teaching and learning mathematics in the early childhood or elementary school years, and reactions to previously published opinion pieces or articles. Find detailed department submission guidelines at

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Brittany L. Hoffman, M. Lynn Breyfogle, and Jason A. Dressler

To bolster students' ability to prove as well as develop mathematical argumentation skills, create an environment in which students must regularly explain and justify their thinking.

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Jessica L. Schoffel and M. Lynn Breyfogle

How a first grade class is introduced ato the concept of symmetry. The lesson includes activities for classroom use on developing recognition of objects that have symmetry, as well as visualization of both horizontal and vertical lines of symmetry.

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Amy Roth McDuffie, Kay A. Wohlhuter, and M. Lynn Breyfogle

Thread small changes seamlessly into high-level reasoning tasks to reach all students.

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M. Lynn Breyfogle and Beth A. Herbel-Eisenmann

When viewing videotaped examples of his classroom teaching, Anthony, a veteran ninth-grade teacher, was surprised that he focused more on the students' responses than on the students' thinking. For example, he realized that he was not asking questions to understand what or how the students were thinking but rather to test their knowledge.

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Beth A. Herbel-Eisenmann and M. Lynn Breyfogle

Teachers pose a variety of questions to their students every day. As teachers, we recognize that some questions promote deeper mathematical thinking than others (for more information about levels of questions, see Martens 1999, Rowan and Robles 1998, and Vacc 1993). For example, when asking, “Is there another way to represent or explain what you are saying?” students are given the chance to justify their thinking in multiple ways. The question “What did you do next?” focuses only on the procedures that students followed to obtain an answer. Thinking about the questions we ask is important, but equally important is thinking about the patterns of questions that are asked.