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Edutopia: Critical Thinking
Using Calculators to Deepen Students’ Engagement With Math
Calculators can be vital tools for encouraging students’ mathematical curiosity and conceptual understanding.
By Kelly Baum-Sehon
February 18, 2020
Whether we love them or hate them, calculators are here to stay—gone
are the days when we could tell students, “You won’t always have a
calculator.” We have to rethink what it means to teach kids how to do
basic math in the calculator age.
I’ve spent years figuring out how to incorporate calculators into my
teaching in ways that teach my middle school students important skills
like number sense, estimation, and problem-solving. Through trial and
error, I have created and taught lessons that integrate calculators as
a central tool in developing students’ mathematical curiosity,
conceptual understanding, and procedural fluency. Two of my favorite
lessons cover what many consider basic middle school concepts:
percentages and fraction operations.
PERCENTAGE
In this lesson, I always begin by telling students that I’m going to
give them several percentage problems as well as the answers. The first
thing students wonder is why I would give them the answers. Aren’t they
supposed to figure those out?
Not in this case, I tell them: The goal is not to get the answer, but
to figure out how the answer was gotten. The first problem we tackle is
pretty simple: What is 50% of 24? The students can usually shout out
“12!” before I finish writing the problem on the board.
“Excellent!” I respond. “Now, how could you figure that out on a calculator?”
At that moment, students grab a basic four-function calculator. I walk
around and have students show me their methods, and I tell them that
dividing 24 by 2 is not what I wanted.
“But 50% is half,” they protest. “So you divide by 2.”
“Certainly,” I say. “But we’re not always going to have something as nice as 50%, so we have to find a different way.”
Exasperated, my students try to figure out what I want. After letting
them engage in productive struggle, I guide them toward the idea that
we can use the numbers 50 and 24 to reach 12. Soon, they’re getting
ideas like multiplying the numbers, resulting in 1,200.
“That’s kind of like 12,” someone will say. “But I have to get rid of these zeroes.”
My students start figuring out that to reach the answer, we can
multiply the percent by the whole number and then divide by 100. Some
students even propose that you just turn one of the numbers into a
decimal before multiplying (50 times 0.24 or 0.50 times 24). Others say
that you put a decimal point into both numbers, but only one digit in
each (5.0 times 2.4). Some suggest using the % button on the
calculator, which would also turn their number on the screen into a
decimal. I then have students provide conjectures about why all of
these strategies work and what they have in common.
Soon, my students are engaging in a mathematical discussion about
relationships between decimals and percents, how the number 100 is
inherent to all of the calculations, and how 50%, 0.50, and ½ are all
the same thing.
I continue the lesson with more complicated problems. Trying to solve
something like 17.35% of 8.4 using paper and pencil is overwhelming—but
with calculators, my students approach even seemingly scary problems
like this with confidence, armed with the knowledge that the
relationships remain constant regardless of the complexity of the
numbers. Using ideas like percent-decimal equivalence—as well as
efficient algorithms like “% × n ÷ 100”—my students develop, with the
help of calculators, conceptual understanding and procedural fluency.
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