Tricks Are NOT for Students!
March 2024
The
Butterfly Method. Keep Change Flip and Keep Flip. Change. There’s no doubt you’ve seen or heard these mathematics learning
tricks and several others. I’m sure you’ve also heard, “Yours is not to reason
why; just invert and multiply.” Or you’ve noticed a student who has learned to “cross
multiply and divide” and begins to apply it to multiplication of fractions or
division of fractions rather than to proportional relationships.
What
message do we send to our students when we present mathematics as a series of
tricks? Do we send the message that mathematics is understandable, or do we
send the message that mathematics is so difficult that they need to resort to
tricks to get the correct answers? It is our responsibility to ensure that
students see the relevance and usefulness of mathematics, and a steady stream
of tricks won’t help convince them of this. I want students to recognize that
mathematics was and is being developed to explain the world. Memorizing a set
of tricks does not promote this recognition.
We, as
educators, must develop a positive mathematical identity with our students. As
I have shared with you before, it is socially acceptable to say that we are not
adept at mathematics. We must help students see themselves as capable of
learning mathematics. Students successfully learn mathematics by understanding
the concepts rather than merely memorizing a series of procedures, which are
often accompanied by tricks that must be memorized to get the correct answer.
We know that successfully learning mathematics is more than merely finding the
correct answer; it also involves problem solving, applying learning to the real
world, effectively describing strategies, and demonstrating a deep
understanding of how different concepts are connected.
Learning
many tricks leads to confusion later on, and students often misapply a trick to
other concepts. Sometimes, they only remember a portion of it. Often, I have
students who remember that “two negatives make a positive” but forget that they
heard this while they were learning integer multiplication and division.
Sometimes several different classes in a grade level will learn different
tricks or sayings for the same topic, which can lead to significant confusion
for them in the next grade. We should recognize that students must have
consistency within a grade level or course and that this is vital in helping
them be successful in future grades and courses.
As we head
into the last few months of the school year, for those who teach with a
traditional calendar, let’s continue to focus on learning mathematics through
reasoning, understanding, and sense-making rather than memorizing tricks,
sayings, and rote procedures. All students deserve to see that mathematics is
understandable!
Kevin Dykema
NCTM President
@kdykema