Let's Make Sense
December 2022
The
thought of going to IKEA is incredibly stress inducing for me. It’s not really
the actual shopping, but rather knowing any purchase will have to be assembled
when I get home. When our children were younger, I always tried to avoid buying
anything that required assembly. I found no joy in following a seemingly
endless series of steps and always had a moment of panic when there were parts
left over!
I wonder how often this is true for
our students with mathematics. How often do they find no joy with the content
when they view it as a series of steps to memorize and follow? Do they see
themselves as capable of learning mathematics? For the past few years, when
assembly has been required with one of my purchases, I have tried to make sense
of what needs to be done. I look at the pieces and begin to figure out how they
might all connect together. Although not always initially successful, I dread
the required assembly less than when I try to merely follow a series of steps.
As mathematics educators, we must
continually work to have our students make sense of the mathematics rather than
just memorize a series of steps. Not only will they truly understand the
concepts being learned, but they will see themselves as capable of learning
mathematics. Consider how you would find a solution to 245 + 98. Perhaps you
calculated 245 + 100 – 2, or perhaps you did 243 + 100 or maybe 250 + 100 – 5 –
2. I suspect that most of us did not use the traditional algorithm to do a
series of steps. Most of us reasoned through the problem to find a solution.
Our students should be allowed to do the same and to think and have it make sense
to them rather than memorize a set of steps to find solutions.
This sense making must occur for
all of our students, not just for those who are deemed to be “good” at mathematics.
Too often, we use results of assessments to sort our students into different
groups. Those students who score well are placed in an “advanced” group where
they are allowed and encouraged to make sense of the mathematics. But for those
students who do not score well, we assume, often incorrectly, that they are incapable
of learning mathematics in this way. Their instruction focuses on following
rote procedures and memorizing those procedures by doing repeated practice
problems that are very similar. Every single student of ours deserves
instruction that allows them to think and make sense of the mathematics being
learned. We must continually work to help our students learn mathematics by
understanding rather than by memorizing.
As
we approach some time away from our normal routines with our students at the
end of this month, I hope each of you is able to find some time to rest, relax,
and rejuvenate before resuming the important work we do in helping students make
sense of mathematics.
Kevin Dykema
NCTM President
@kdykema