# Investigations Blog

## “This is Only Getting Better!…And Harder!”

Who knew a deck of +10/-10 cards could be so exciting? A group of 25 first graders, that’s who. As their teacher, Karla, introduced them to Plus or Minus 10, she explained that they would need numeral cards (10-90), cubes (assembled in sticks of ten), and a new deck of cards. When she displayed the +10/-10 cards, the students, many of them on their knees, some literally bouncing up and down and clapping, were clearly excited. Oooo… Whoa… Plus ten… Minus ten. I hear two students exclaim This is...

read more## The Hard Work of Counting by Groups, Part 2

Last week, I wrote about some first graders’ work on problems about how many fingers were on 4 or 8 hands. This week, I want to share an interaction I had with one child, as the class’s work turned to thinking about groups of 10. Students were working on two types of problems about cubes, organized in towers of 10. · Given the number of towers of 10, how many cubes? · Given the total number of cubes, how many towers of 10? When I joined Nik, he had already solved problem 1, about a...

read more## The Hard Work of Counting by Groups

The other day I visited a class that was at the very beginning of How Many Tens? How Many Ones?, the final unit of the grade 1 sequence on Addition, Subtraction and the Number System. The class began with a conversation in which they modeled, recorded, and discussed the previous day’s work, about the number of hands on different numbers of people, organized as a table. The teacher then explained that today they were going to be thinking about fingers instead of hands. With minimal...

read more## Reflections on NCSM, Part 2

Eight of our staff traveled to DC to attend the NCSM conference at the end of April. Below are four staff members’ reflections on a Session that stood out to them. (Also see Part 1.) Karen: “Teachers First. Everything Else Follows.” by Tracy Zager In this session, honoring the 50th anniversary of NCSM, Tracy Zager began by describing some of the important history of mathematics education, highlighting how, across the decades, classroom teachers were part of each new effort because it was they...

read more## Reflections on NCSM, Part 1

Eight of our staff traveled to DC to attend the NCSM conference at the end of April. Below are four staff members’ reflections on a Session that stood out to them. Four more to follow next week. Keith: “Transforming Teaching and Learning Through Number Talks” by Ruth Parker Ruth was my mentor when I was teaching 5th grade, and then a Math Coach, in the Clark County School District. Any time I get the opportunity to hear her speak, I take it, and she never disappoints. Ruth and her colleague,...

read more## Developing Mathematical Language is Hard Work

Using language to effectively communicate one’s mathematical thinking is an important skill—one that is a focus of Math Practice 6: Attend to Precision. Many of us know firsthand that clearly articulating mathematical ideas is challenging work, and that when students use ambiguous, imprecise terms in their explanations, their language can actually get in the way of understanding. Developing precise language is key if we want to students to engage in rich, collaborative discussions in which...

read more## Come see us at NCSM & NCTM in DC!

We’ll be away next week, at the NCSM and NCTM conferences in Washington DC. We’d love to see you at one of our Sessions, or at the TERC booth! Monday, April 23, 2018 Session 1317: But Why Does It Work?: Using Examples to Investigate Structure Many students appear to know how to compute, but what do they understand about the underlying structure of the operations? This talk will use evidence from our classroom-based research, including video clips, to show how, through reasoning about what...

read more## Q&A: The Definition of a Trapezoid

Question: Why did you decide to use the exclusive definition of a trapezoid? As the question suggests, there is more than one definition of a trapezoid. Mathematicians define trapezoids in one of two ways: Using the inclusive definition, all parallelograms (which include rectangles, squares, and rhombuses) are trapezoids. Using the exclusive definition, they are not. In determining which definition to use, we thought about a couple of things: Most elementary textbooks use the exclusive...

read more## And Then, She Waited

Have you ever been teaching (or leading professional development) and asked a really good question only to be met with silence? We all have teacher moves in our back pocket for situations like this—maybe do a turn and talk, ask the student if they’d like to call on someone to help them, or ask a different question. I recently observed a third grade lesson when I saw a teacher face this exact situation. The lesson (Unit 5, Session 3.4) focused on strategies for solving division problems. The...

read more## What Does It Mean to be a Math Person?

“I’m just not a math person.” I don’t know how many times I heard this sentiment over the course of a three-day workshop kicking off a new project focused on professional development for paraeducators. But, it surprised me that it was Tonya saying, “I’m good at it, but I’m just not a math person.” In the three days we spent looking at student work, solving problems together, discussing strategies, and playing games, Tonya was comfortable, active, and engaged. She shared her strategies for...

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