As we come into another testing season, I am reminded of my first
year teaching mathematics in the public school classroom. As a naïve new
teacher, I had every confidence that my 7th graders were going to knock the
socks off the state assessment. I had spent the entire year giving my math
students the tools they needed to be successful on the state exam; furthermore,
I felt I had prepared them for their future math classes. I thoroughly taught
them every math trick
I had picked up on in my teacher prep courses and from veteran
teachers willing to share them on my
campus.
Check.
The bat and ball
method for solving proportions.
Check.
The alligator eats the larger
number for comparing rational numbers.
Check.
Keep change flip to multiply fractions.
Check.
I quickly realized that there are so many tricks that it could be
quite confusing for the students. In short, I may have been doing more harm
than good. If I were a doctor I may have been cited for not living up to the Hippocratic Oath. But what if I teach my
students all the necessary rules and algorithms to solve math problems? Is that
any better? Although well intended, in
reality I felt that even following logical rules was more focused on teaching
students to follow instructions rather than providing a pathway to become
mathematicians.
Where did I lose my way? I
was turning my students into robots that have an operating system, able only to
do simple tasks like memorization of facts and tedious procedures. What about
critical thinking, applying prior learning to new experiences, and being able
clearly explain reasoning?
The argument is made that we don’t have enough time to do those
types of things, but a good friend of mine always responds, "We don't have
time not to do it." Initially, the time spent is greater, but the benefits
are also greater. Teaching students conceptually
allows them to retain more and learn more, thus allowing for fewer
misconceptions when introducing new content from year to year.
“But what about the yearly state assessment?” you ask. Having a
solid conceptual foundation, I believe, is far more useful than a bag of
tricks. If we have worked with our students on reasoning practices, explaining
their thinking, and problem solving tools, won’t our students at the very least
confidently eliminate unreasonable answer choices on any given assessment? Perhaps students will even reason all the way
through a given math problem.
I have recently started reading "What's Math Got to Do with
It?" by Jo Boaler. In the book she
tries to answer the exact question we have raised, saying, "It [math] has
a lot to do with children having low self esteem throughout their lives because
they are made to feel bad in math classes; it also has a lot to do with
children not enjoying school as they are made to sit through uninspiring
lessons, and it has a lot to do with the future of the country, given that we
urgently need more mathematical people to help with jobs in science, medicine,
technology, and other fields."
Let me end by challenging myself and other math teachers to reflect
on the lasting impact we have on our students when we reduce the beauty of math
to a collection of tricks. I believe this
quote from the Institute of Mathematics and Computer Science sums it up quite
nicely. "Show a child some tricks
and he will survive this week’s math lesson. Teach a child to think critically
and his mind will thrive for a lifetime."
Check out the book written collaboratively by math teachers online: Nix the Tricks! http://nixthetricks.com/
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