Investigations Blog
Are 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 moreCounting is More than 1, 2, 3: Engaging Adults in K-2 Mathematics
How do we engage adult learners in the seemingly simple yet complex mathematical ideas of the primary grades? While teachers can examine the mathematical focus of K-2 tasks, and think about what they might look for as they observe, what questions they might ask to assess understanding, or consider how they might support or extend the targeted math ideas, playing Counters in a Cup or solving a How Many of Each? problem is not exactly an engaging math task for adults. A few weeks ago, I...
read moreThe 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 moreThe 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 moreCounting is Serious Business
“One, two, three, four, five…” I was interested in how quickly Owen and Ravi figured out a way to count the set of 40 yellow hexagons in their Inventory Bag. The boys took turns saying a number as they placed the hexagons in a line which started to snake across the rug in the meeting area of their kindergarten classroom. “Twenty-eight, twenty-niiiinnnne…” Ravi pauses unsure about what number comes next. Owen whispers “30” and Ravi says “30” as he places the thirtieth block in the line....
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