Investigations Blog
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 moreReflections 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 moreDeveloping 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 moreCome 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 moreQ&A: The Definition of a Trapezoid
Question: Why did you decide to use the exclusive definition of a trapezoid?Answer: 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 moreAnd 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 moreWhat 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...
read moreFrom “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...
read more“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...
read moreA Division Solution: Amazing or Perplexing?
At a recent professional development session on multiplication and division, my colleague and I asked participants to examine some student solutions to the problem: 1564 ÷ 36. Before looking at the student work below, think about how you would solve the problem. The following solution from a fifth grade student seemed to either amaze participants or they had a hard time making sense of it. I’ve been thinking a lot about their reactions. Take a moment to look at this work. What do you notice?...
read more