Investigations Blog

What Does It Mean To Be Smart?

“Wow, you’re so smart.” These words drew my attention to a pair of 5th grade girls in a class I was visiting, who I’ll call Cassie and Sophia. They were mid-way through a turn and talk, each sharing her strategy for solving 84 x 59. I casually moved closer, curious about what prompted the comment and trying hard to see each girl’s strategy, recorded in their math journals. Upon hearing Cassie’s comment, Sophia responded in an inviting tone, “No, no. Explain to me what you did.” She...

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What Happens When There Are More Than 10?

Imagine you are 6 years old. Or 7. You know you can use your fingers to model subtraction. For example, for a problem where there are 7 grapes and 2 get eaten, you can raise 7 fingers, put down 2, and count how many are left. But what do you do when the problem involves more than 10 things? Take a moment, before looking at the student work and video below. How would you use your fingers to solve a problem about having 12 scissors, and lending 5 to another class? A student I’ll call Miguel is a...

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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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Using Tools in Art and Math

Recently, I was chatting with a 7-year-old I know pretty well. I asked her about school, and she quickly started telling me about her current math work, complete with eye rolls and boredom. I decided to change the subject a little. “I know you like to tell me about math because I love math, but what’s your favorite subject?” I asked. She thought for a moment and then said, “Art.” Art was never my favorite subject. I’m not even sure I’ve passed stick figure drawing yet. “Why?” I asked. She...

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Puzzling Through Making Fraction Sets

Last year I volunteered in a third grade class. The school mainly uses Investigations 3. During a visit last spring, the class was working on the second session of the fractions unit. I was excited to find out about the students’ beginning understandings of fractions. I sat with a group of four students who were working on making fraction sets. Their task was to fold each of 5 sheets of paper into two, three, four, five, and six equal parts and then to label each piece. The students made 4...

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“What Was Thomas Thinking?”

I often think about a lesson, captured on video some years ago. Liz, a fifth-grade teacher, gave her students two-digit multiplication problems—12 × 29 and 36 × 17— and asked them to come up with strategies other than the conventional algorithm to perform the calculation. For 12 × 29, Jemea thought about twelve 30s and then subtracted 1 for each of 12 groups. 360 – 12 = 348. For 36 × 17, Duane thought of 36 bowls, each holding 17 cotton balls. Ten bowls hold 170 cotton balls, and there are...

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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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From “Uh Oh!” to “Aha!”

Over 20 years ago, just out of college, I applied for a job at TERC after seeing an ad in a newspaper. A project called Investigations in Number, Data, and Space was looking for a classroom observer. I had spent most of my college years volunteering in an elementary classroom once a week, so I sent a writing sample – from a course I’d taken with Ted Sizer – and got an interview. The last step? Meet Susan Jo Russell, the Principal Investigator of the project. We chatted and...

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It’s Not What’s New; It’s What’s Old

People often ask me, “What’s your favorite part of the new edition of Investigations?” My first inclination is to blurt out “That it’s finished!”, despite the fact that the development stage has been over for almost a year. While many aspects of the revision were engaging and rewarding, I’m sure that someday soon I will not cringe when I hear the word deadline! That said, I think I can honestly say that my favorite part of the 3rd edition is also my favorite part of the 1st and...

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