Investigations Blog

Asked and Answered: Why Ask the Same Question When You’ve Already Gotten a Perfectly Good Answer?

I was watching one of those legal shows on TV the other night. The prosecutor was asking the defendant a version of the same question for the third time. The defendant’s lawyer, getting annoyed, objected: “Asked and answered!” I’ve heard this phrase a hundred times in the (made-up TV) legal context, but this was the first time it struck me how pervasive this idea was in my own mathematics education, and how powerful it still is: If a student has given a perfectly good answer to a math...

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The Lesson? Students Never Cease to Surprise Me

On a recent visit to a school in a small city in the Midwest, Karen and I joined a class of 5th graders as they learned a game in Unit 3 called Roll Around the Clock. In the previous session, students used a clock to find and name fractions and equivalent fractions. For example, if the minute or hour hand moves from the 12 to 3, it has rotated 3/12 or 1/4 or 15/60 around the clock. Students would use these ideas in this lesson. In this game, players take turns choosing which of two dice to...

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Incomplete, inarticulate, ill-formed, incorrect: Brilliant!

Over the last decade, much of my work has been focused on mathematical argument in the elementary classroom. Observing in our collaborating classrooms, I was struck again and again by how teachers supported students to build on each other’s incomplete ideas. Constructing a mathematical argument is difficult and challenging for elementary students and, therefore, necessarily collaborative. When students are learning what it means to make an argument, not just about the solution to a single...

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