Rules That Expire

Amy Wix

6th grade Math

Kasson-Mantorville Middle School

MCTM Region 1 Director

Having grown up sandwiched between two brothers, I have always had an interest in
how birth order influences adult life and careers. Katrin Schumann, in her book The
Secret Power of Middle Children, says that middle children are flexible, teambuilders,
independent, social, and think outside of the box. Some of these skills I developed
because I was in the middle. If I wanted to be more grown up I played school with my
older brother. If I wanted to just be a kid and have fun, I played with my younger
brother. When the 3 of us were together, plotting our next adventure, I was the
go-between. I could interpret what each of my brothers was meaning and translate it to
the other.

Teaching in a greater Minnesota school district, I often think the same ideas apply to the
middle school level. Our students are too old to require they have snow pants and
snow boots, but too young to not give them recess time outside. Our students have
important classes, but they aren’t always given the same resources as the primary
school reading classes or the high school you-need-this-to-graduate level classes.
Sometimes in our K-12 subject area meetings, it’s the middle level teachers
who are the go-between for the elementary and high school teacher.

This topic hit home for me when I was reading the NCTM Mathematics Teaching in the
Middle School article, “12 Math Rules That Expire in the Middle Grades.” The authors
(Karp, Bush and Dougherty) highlight rules and vocabulary that are sometimes taught to
younger children that end up no longer working in the middle grades. The article can be
found here.

Let me be clear, I think our elementary teachers are working hard to teach the grade
level standards. It is the innate trait of a teacher to try and make things easier for our
students; we don’t like to see them struggle. But in making things easier by providing
“tricks” to help students remember, we are cheating them out of sense making and
reasoning – the mathematical practices described in Principles to Actions . Discussions in
my classroom often have me asking students “Why? ”Why do we add a zero when we
multiply by 10? Is that always true?” “Why do we flip the divisor when we divide
fractions?” Let’s not even go into the discussions about “Fish” and “Butterfly.”

Of the 12 rules in the NCTM article, 6 expire in 6th grade, 4 in 7th, 1 in 8th and 1 in high
school. Middle school teachers walk a fine line with these rules. We can understand
where the rule makes tasks easier for the elementary students, but we also understand
the misconceptions or overgeneralizations the tricks have with the math in the upper
grades. As the authors say, “Using terminology and notation that are accurate and
precise (SMP 6) develops student understanding that withstands the growing
complexity of the secondary grades.” It’s our job, as the middle level educators to be
the go-between and start the dialog with our math departments K-12 to encourage the
reasoning and understanding with the use of precise language in our classrooms. Let’s
get rid of these rules that expire!

Additional Links on this topic:
nixthetricks.com has a free downloadable book appropriate for all math teachers
Learnzillion has a nice summary of the rules and other language to avoid here.