Manipulating Math
Using blocks to make numbers make sense.
Numbers on a page—plus signs, minus signs, equals signs—don’t mean much to a young learner on their own. Children need something they can see, and preferably hold, before those symbols start to make sense.
Second-graders in Ms. Kathy Thompsen’s class began the year using hands-on manipulatives to solve addition and subtraction problems.
"This provides students with a concrete way to represent numbers, to model their thinking, and to develop a deeper understanding of the strategies we're learning," said Ms. Thompsen. "Students can visualize place value and understand what is happening when we add and subtract, rather than solely relying on memorization."
"This provides students with a concrete way to represent numbers, to model their thinking, and to develop a deeper understanding of the strategies we're learning," said Ms. Thompsen. "Students can visualize place value and understand what is happening when we add and subtract, rather than solely relying on memorization."
One of those strategies is making ten. Ms. Thompsen had students rearrange blocks into stacks of ten to make addition easier. Take 8 + 8. Students build two stacks of eight blocks. Then they move two blocks from one stack to the other. Now they have a stack of 10 and a stack of 6—and 16 is much easier to see, and to hold in their heads.
That is concrete learning, and it is the bridge to abstract learning later on. Once students have felt what it means to regroup, the written problem 8 + 8 = 16 is no longer a string of marks on paper. It is a picture they already know.
"The use of manipulatives support students in becoming more independent problem solvers as they try a variety of ways to solve the same problem," said Ms. Thompsen.
Blocks today. Mental math tomorrow. The goal is the same either way: numbers that make sense.
Jacksonville Country Day School
Located in Jacksonville, FL, Jacksonville Country Day School is a private school for Pre-K 3 through 5th grade. JCDS prepares students for a healthy and productive lifetime of intellectual exploration, character development, and social responsibility.
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