Sitting in the back of Ms. Corey's sixthgrade mathematics class, I enjoyed seeing students enthusiastically demonstrate their understanding of absolute value. On the giant number line on the classroom floor, they counted the steps that they needed to take to get back to zero. The old definition of absolute value of a number as its distance from zero—learned by students and teachers of the previous generation—has long ago been replaced with this algebraic statement: |x| = x if x ≤ 0 or − x if x < 0. The absolute value learning objective in high school mathematics requires students to solve far more complex absolute value equations and inequalities. However, I cannot remember students attacking the task with enthusiasm or having any understanding beyond “make the inside positive.”

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Contributor Notes

Mark W. Ellis,, a National Board Certified Teacher in early adolescence mathematics, has taught middle school and high school mathematics in California public schools. He is an associate professor and chair of the secondary education department at California State University, Fullerton.

Janet L. Bryson,, a former high school mathematics teacher and mathematics coach, provides professional development training by sharing her expertise and passion for mathematics content and pedagogy done differently.

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