How do we make sure our students are making the connections
between concepts that are necessary for them to have good number sense and a
solid understanding of the math they are doing?
My first year teaching I was worried that what I was teaching
might go over my students' heads. The way I dealt with this was to use tricks
and stories to help them understand things like solving one-step equations or
dividing by fractions. I had learned some math concepts this way as a student,
so I thought it made sense to teach it to my students. This made me feel like I
was continuing in the grand tradition of math teachers, so I didn't really stop
to examine what I was doing or why. It's just how it had been done. What I
found was these tricks not only muddied the waters while they were learning
with me, but very few of those tricks held up past my class.
"When we ask children to follow a procedure that holds no
meaning for them, they will conclude that math does not make sense. Go back to
the mantra “math makes sense” and make sure all students believe it..." -
Tina Cardone, "Nix the Tricks"
I was not setting them up for success down the road by telling
them to "keep, flip, change" when dividing by fractions. I was also
discounting my students' ability to understand what was really happening within
math; I was insulting their intelligence and dumbing things down.
Let's examine putting the bigger number on top when
subtracting as a simple example of why tricks are dangerous. Many of my
students would recoil in horror if I put a problem on the board like 7 - 10.
"You can't do that!" they would shriek at me, worried that the
time/space continuum was about to collapse before their very eyes. At first, I
couldn't understand their revulsion, until they explained to me that you must
put the bigger number on top when you subtract. Since most state curriculums do
not introduce negative numbers until 6th grade, I understand what their
elementary teachers were trying to accomplish by teaching them this
"rule." In all their experience, my students had started with a
number and taken an equal or smaller number away from it. This "rule"
worked for every situation they had encountered prior to meeting me.
A more concrete way to teach subtraction is to give students
manipulatives such as ten frames or unit cubes or base ten blocks. This way,
they can start with one amount and take some amount away. If they need to
regroup, they can break apart a ten or a hundred physically. Another method is
to have students model subtraction on a number line. This method also allows
students to explore negative numbers more easily and naturally. Once students
understand what is going on when they subtract, moving to the standard
algorithm becomes easier and makes more sense.
I came across Nix theTricks as a second year teacher, which helped me explore different
methods for teaching math which were simpler and more straightforward. I have
tried over the years to break my own bad habits of teaching math concepts in
unnecessarily complicated ways, and each time I am successful, my students
benefit greatly. Not only does it save time during the initial lessons, but
when we need to use previously learned math in order to problem solve and learn
something new, my students have a firmer foundation and a better understanding
that allows them to make new connections.
What are some tricks you have stopped using in your lessons? Share
in the comments!
