Learning Mathematics
June 2023
During the
past few months, social media has experienced a growing debate on how to best teach
mathematics. I believe the answer is based largely on how one defines
mathematics, which we examined last month. Because mathematics must be about
reasoning and sense making, it should be taught and learned differently than if
mathematics were only about getting answers.
As a
student learning mathematics, I saw mathematics almost entirely as finding the
correct answer and doing so quickly. I enjoyed mathematics because it was easy
for me to memorize the procedures and I could usually find the correct answer
very quickly; but I’m not sure I understood why any of the procedures worked. Many
other mathematics educators likely had similar experiences. Many of my
classmates, however, did not have that same experience, and they grew to dread
mathematics, seeing themselves as incapable of learning it.
During my
first few years as a middle school teacher, I taught mathematics as most
importantly finding the correct answer. I often used “tricks” that students needed
to memorize because I thought they would be helpful, but I quickly realized
students either only partially applied the trick or applied the trick to a
wrong type of problem. This led to frustration on their part and on mine. I
began to appreciate that mathematics must be taught differently than I had been
teaching it, and since then I have consistently worked to develop better
instructional tools and strategies.
The
National Research Council released Adding It Up: Helping Children
Learn Mathematics
in 2001. This landmark publication identified five strands of mathematical
proficiency: conceptual understanding, procedural fluency, strategic
competence, adaptive reasoning, and productive disposition. These five strands
helped me realize that I had focused almost exclusively on procedural fluency but
that mathematical proficiency entails much more. Mathematics is not only
about getting the correct answer. It must also be about reasoning and sense
making and helping students build a positive mathematics identity.
As I
consider why procedural fluency is often heavily emphasized over the other four
strands, I wonder if it is partially because it is easier to assess.
Determining if a student has calculated the correct answer is often easier than
assessing if that same student is capable of adaptive reasoning or has a
productive disposition. We must not teach mathematics as answer-getting just
because it is easier to measure. Instead, we must continue to integrate all
five strands of mathematical proficiency into our instruction and assessment.
As your school
year concludes, I hope you enjoy the summer and then look forward to the next
school year. Let’s all find time during these next few months to consider how
to best teach mathematics to benefit all our students!
Kevin Dykema
NCTM President
@kdykema