Investigations Blog
Teaching and Learning, Remotely
Many people are or will be teaching online, for some or all of their school day, at some point this year. Like everyone else, we have been thinking hard about remote instruction. How do we hold on to what we value in the teaching and learning of mathematics, in an online environment? What needs to shift? Below are blogs that we have found interesting and useful as we think through these and other questions. Recommendations & Strategies David Wees reviewed what the research on online...
read moreStarting School, 2020
As teachers and students start – or get ready to start – the school year, people have been thinking about what’s important to focus on after the chaos and challenges of the emergency remote teaching and learning of last spring. How can teachers and students enter the school year in a way that best supports students’ continued learning and their development of a strong sense of mathematical identity and agency? How can teachers best find out about their students’ thinking and...
read moreRobot Fingers and Multiplicative Structure
In a blog post over a year ago, I wrote about the importance of using story contexts to support students in developing mental images of the operations. In that post, I concluded: “Along with pictures, drawings, diagrams, equations, and physical models, story contexts are critical parts of a student’s repertoire of representations. In fact, it is often the case that three kinds of representations are in play: a numerical representation, a picture or diagram, and a story. Moving among these to...
read more“Is 100 a Teen Number?” Part 2
What follows is a lightly edited version of the second part of an end-of-Kindergarten discussion about the teen numbers. In Part 1, students took up the question of whether 100 is a teen number. That conversation built on a previous one, about why there are so many 1s in the teen numbers. At a certain point in the conversation about whether 100 is a teen number, the discussion began circling around the same ideas, ones that had already been shared. At that point, the teacher made a decision to...
read more“Is 100 a Teen Number?” Part 1
Not long after I witnessed a Kindergarten conversation about why there are so many 1s in the teen numbers, I visited the same classroom. This time, it was Nicole who asked a question that knocked my socks off. “I wonder if 100 is a teen number?” When I asked why she thought it might be she said, “Because it starts with a 1.” Her partner nodded, nudged her to take her turn, and they returned to their game. Several days later, I returned, for their end-of-unit discussion about the teen numbers....
read moreWho Gets Challenged to Extend Their Thinking? A Conversation About Differentiation
In conversations about differentiation, strategies to scaffold learning for students who need more support, and strategies to extend the learning for students who are ready for more challenge often come up. One topic that is rarely considered however, is the importance of finding ways to offer students who typically need more support, opportunities to think about a task in ways that will extend their thinking about the mathematics. In the following conversation, excerpted from the Supporting...
read moreAre There Going to Be More Than 20? More Than 50?
Many of us were taught to “estimate” in elementary school. Maybe we were asked how many jellybeans there were in a jar. Or asked to round before finding the answer to a computation problem. But for many of us there was little connection between those activities and actually solving problems. I would argue that estimating — determining what an approximate and reasonable answer might be — should be a part of the process of solving problems. A visit I made to a 1st grade classroom at the end of...
read more“Why are there so much 1s in these numbers?”
Last spring, I visited a Kindergarten classroom near the end of the year. Students were participating in a Math Workshop focused on the teen numbers, choosing among activities that asked them to identify and recognize teen numbers; to represent them in several different ways (e.g. on Ten Frames, with cubes, with numerals); and, ultimately, to come to see them as being composed of ten ones and some numbers of ones. I wandered over to Stella, who was playing Race to the Top: Teen Numbers. In...
read moreReflections on NCSM/NCTM, Part 2
Six of our staff traveled to San Diego to attend the NCSM and NCTM conferences at the beginning of April. Below are four staff members’ reflections on a session that stood out to them. (Read the first three here.) Keith: “The Iris Carl Equity Address: Equity and Agency from Inside the Classroom” by José Luis Vilson (NCTM) José Vilson began his talk with an elegant, powerful statement — “Equity is belonging.” — and then challenged us with this question: “Do you believe your students belong?”...
read moreReflections on NCSM/NCTM, Part 1
Six of our staff traveled to San Diego to attend the NCSM and NCTM conferences at the beginning of April. Below are three staff members’ reflections on a session that stood out to them. Four more to follow next time. Keith: “From Oakland to Wakanda: Transforming Mathematics Classrooms to Become Empowering Spaces” by Imani Masters Goffney (NCTM) Imani Masters Goffney gave a fascinating talk about making math classrooms equitable spaces for learning. She used the movie Black Panther as a context...
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