Investigations Blog

From “Defective” Fractions to Infinite Equivalents

On a recent site visit, I was observing in a fourth grade classroom. The teacher started the lesson (Unit 6, Session 2.1) by writing “3/2” on the board and asking students to name the fraction. Most said “three halves” although one or two said “two thirds.” The teacher then displayed two blank 4 x 6 rectangles. She established that one rectangle was the whole, and asked students to use their copy of the rectangles to draw a representation that showed 3/2. The math coach called me...

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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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