Investigations Blog

The Bad Rep of Word Problems: “Two trains leave the station…”

When people want to make a joke about how difficult, convoluted, or inaccessible word problems are, they often cite some version of the “two trains” problem. You can see an example of this problem here: Maybe you want to try solving this problem yourself before reading on. (Maybe not!) The “two trains” problem has become an emblem in popular culture. Saying the opening phrase, “Two trains leave different stations at the same time …,” invariably results in uncomfortable laughter. It surfaces...

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“That Seems Way Too Big”

On a recent visit to a small district in the Midwest, I got the chance to visit a third grade class that was working on division (3U5, Session 3.4). When I joined Nicole, she was in the middle of working on the following problem: Gil loves toy cars. He saved enough money to buy 32 toy cars. How many 4-packs of toy cars did he get? (SAB p. 333) Below the problem, Nicole had written I asked her to tell me about her thinking. She said she wanted to start with something she knew, which I agreed...

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Watch, Notice, and Learn

Classroom video is a powerful tool for studying and reflecting on mathematics teaching and learning. Unlike in-the-moment interactions with students, watching video enables us to slow down and more closely examine student-to-student exchanges. This affords us a unique opportunity to learn about students’ mathematical thinking. Several months ago, I began watching and discussing video footage of elementary mathematics classrooms with a group of colleagues. We were using the footage to study...

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