Focus on the Question
By Timon Piccini, posted November 20, 2017 —
“What is the solution for x,
if three x plus five equals nine?” I
hope that sentence is difficult for you to read. I hope that reading those
words in that form makes you cringe and squirm. I know something within me
feels icky just writing it. It is math, it should be written in math: “3x + 5 =
9, Timon! That is how you write it!” This is because we are used to the
language of math. We are used to how it is expressed, and when we see it done
any other way, it seems off. Our students speak their own language, so to hear
math is just as cringe-inducing for them. Many of their hackles go up, or they
are simply oblivious to the question you are asking.
As mentioned in my previous post, algebra was my moment of
reckoning. After that first year of teaching, I desperately came back to asking
the question, “How can I make this demonstrable to students in a way that they
can jump in feet first?” I always get students to try math before I teach math.
I thought of balances, but realized that all our weights were too expensive or
were only in sizes of 50 g, 100 g, etc. I went to the bank, purchased hundreds
of pennies, and made many question-and-reveal videos, all so that I could begin
my class with the question, “How many pennies are in each cup?” When I showed the
video below, students had it solved before I even filled the second cup.
Yet, if you ask them to isolate and solve for x in the equation x/4 + 6
= 10, they can’t handle it. It is because we don’t naturally think in math.
Some of us have been taught to, and some of us pick up on thinking in math very
intuitively, but most of us think in the language that we originally speak. This
is why my first goal is to take a concept and reframe the question in a way
that does not involve any technical terms. Introducing students to the
technical terms will come at a later time. This is why I love manipulatives. It
puts the students in a state of relaxation. It gives them success early on, and
most important it allows them to experiment. Counting pennies is much less
daunting than solving equations. Messing around with toy army men is way more
chill than operations with integers. The fight or flight response comes down,
and the engagement goes up.
I remember the first experience I had with professional development using
manipulatives; the teacher leading the activity allowed us to take 5 minutes to
play with the manipulatives. She said that by the time students had a chance to
mess around with the manipulatives, many had taught themselves the concept.
Changing the question likewise gives students the chance to mess around with
the math. If the question is well formed, then you have the chance to get out
of the way and let the math happen itself. The students have something concrete
to wrestle with, which gives them the chance to build strong conceptual
Timon Piccini is an
elementary school teacher who has a strong love of getting students to see that
mathematics is more than just numbers. His favorite sound is
when an entire grade 7 class cheers because they are starting to understand a
base five number system (a true story). Piccini considers himself a jack of all
trades, and when he is not teaching, he can be seen running, hiking, playing
guitar, playing video games, and attending concerts, and pursuing just about
anything to do with good food. He especially loves doing all this alongside his
better half, Kelli.