This is an interesting blog I wrote in 2013. I'm not going to make huge changes, but in the intervening years, I did teach some basic college math courses. As I look over this blog, I'm still in complete agreement in terms of why college students struggle with math.
Having taught both basic writing and basic math classes, I can say for certainty that teaching writing is exponentially harder. If you're a math instructor and find that a bitter pill to swallow, sorry, but that's my experience. With writing it's important to teach creativity. There is a multitude of ways to write a story, essay, or research paper. With math, I found there was always some sort of step-by-step process to find the right answer. There was far less ambiguity. And, the grading end of things for math is far more objective than writing.
Now, realize I'm am talking teaching basic math—the type of math that would be found in a general education requirement. And, I'm comparing it to a basic, general education writing or composition class. I do realize a great deal of creativity and critical thinking is needed when teaching upper level math and delving into topics like geometric proofs and the type of math that theoretical physicists are involved with. Growing up I was a math whiz until I hit Calculus. I then hit a wall. So, those that have mastered upper level mathematics are smarter than I in that arena. But, what I'm dealing with in this essay is why people struggle with foundational math skills. So, let's look at my blog...
I’ve
been teaching college for about a decade and I can tell you—college students
can’t do math. I don’t even teach math. But, I do give out grades and when it
comes time to update students on their progress, I’ll have the following
conversation innumerable times:
“Mr.
Tipton, why am I failing your class?”
“Well,
you didn’t turn in this assignment and this assignment.”
“Yeah,
but I got hundreds on these five assignments.”
“Yes,
but your grade is weighted.”
“Weighted?
Look, if I add up all these grades I have five hundred points. Divide that by
seven and I’m getting an eighty-three percent.”
“Actually,
five hundred divided by seven is more like a seventy-one.”
“Okay, but that’s still a C!”
“Okay, but that’s still a C!”
“But,
you don’t just add them up and divide. Your grade is weighted.”
“I don’t get it?”
“I don’t get it?”
“Look,
those five hundreds are worth three percent each. The two assignments you’re
missing are worth ten and twenty percent.”
“So, what’s your point?”
“So, what’s your point?”
“That
zero on the twenty percent assignment is worth more than those five hundreds
combined.”
“Nuh-huh?”
“What
is five times three?”
“Fifteen!”
“Good,
now put away your calculator. Is fifteen more than twenty or less?”
“So,
why am I failing your class?”
At
this point I just want to grab the nearest math instructor and choke him to
death!
When
I first started teaching, I thought this was an isolated incident. I felt sorry
for the poor student. “Well, she’ll never be an engineer. Tough break she’s
also failing my writing class.” After having this discussion thousands of times
and killing a few math instructors, I came to realize—college students can’t do
math.
So,
I’ve identified the problem, but what’s the cause? Talking to students (or
anyone that hates math) it becomes quite apparent there’s a huge mental block
when dealing with math. I’ve met bright, articulate people whose heads fill
with cement as soon as the word “math” is uttered. “MATH! I HATE MATH!” The
eyeballs cross and steam begins pouring out the ears. When students have a
mental block it’s so often math. Why?
Imagine
you’re back in school. The Arithmetic Nazi has you at the board. She has that
scowl across her face. In her right hand is a pneumatically loaded chalk
holder. In her left hand is a book of evil spells (also sometimes called an
Algebra textbook). You’re scribbling on the blackboard, while your mind furiously
tries to form an answer: x=4.
“No,
no, no! What are you doing? X does not equal four. X equals eleven!”
You
stare at the blackboard in bewilderment. “How does X equal eleven?” you think
to yourself.
Math—it’s
so black and white, cut and dry, right or wrong. There is no discussion. There
is no wiggle room for a difference of opinion. You’re either right or
wrong—and, quite frequently you’re WRONG! Good thing that pneumatic chalk
holder doesn’t have pepper spray!
Imagine
for a moment a child learning to walk. If you’re thinking, “What does this have
to do with math?” then quit thinking that. Just shut up and allow yourself to
take a vacation from math. Can you see the child?
The
first time the poor kid stands up, he wobbles and falls. The second
time—wobbles and falls. He wobbles and falls many times. Then, he begins to
fall forward and puts out his right foot to catch himself. Yes, he still does a
face plant, but not before taking his first step. There’s a great deal of
wobbling and toddling before he can finally stand and walk as well as you or I.
Now,
think about his parents for a moment. As he wobbles and toddles, what are they
doing? They are encouraging his every attempt. Think about his brain. It’s not
just his body that’s wobbling and toddling. His brain is doing the same
thing—trying to make connections to control his steps and gain his balance.
Let’s
suppose rather than being supportive, his parents were to smack him across the
forehead every time he stood up and didn’t walk perfectly? What do you think
would happen? Well, he would stand up and then SMACK! Stand up and SMACK! Stand
up and SMACK! Then, he would just crawl around too afraid to try to walk. He
has now developed a mental block to walking.
So,
there are two different approaches being illustrated in terms of walking. One
is a positive approach that encourages the wobbling, toddling process of
learning to walk. The other is a negative approach that punishes an attempt to
walk that does not produce the perfect gait.
Which
approach seems closer to the Arithmetic Nazi? It seems she is taking the
negative approach. Should she? Or, is learning math just like learning
walking—where the brain goes through a wobbling, toddling stage? Doesn’t the
brain go through a wobbling, toddling phase anytime it’s learning something
new?
X
equals thirteen—SMACK! X equals two—SMACK! X equals forty-seven—SMACK! And, the
brain develops a cement block anytime math is brought up. When someone is
learning math (or any subject) their brain will come up with wrong answers when
the brain is in that wobbling, toddling stage of learning. However, the brain
must go through that wobbling, toddling stage. Keep whacking a brain when it’s
going through the process of learning and the learning factory shuts down.
That’s the mental block that happens with math.
I
know someone is out there thinking, “Well, we can’t just accept wobbly,
toddling answers. Two plus two cannot equal five. X must equal eleven. The
square root of two-hundred-fifty-six is sixteen, not seventeen or twenty-nine!”
Let’s consider the parents of that toddler. They certainly embrace the
wobbling, toddling phase. But, would they find it acceptable if their child was
six and had a gimpy gait? Certainly not! If the wobbly, toddling phase didn’t
work as it should, they would take corrective actions—but, even then it
wouldn’t be done with a SMACK! It would be done in a nurturing way.
The
reason college students can’t do math is quite simple—the education system kept
smacking their brain as it went through the wobbling, toddling phase of
learning. Once someone has a mental block, they can still learn—but, the block
must first be removed! Removing a block that is the result of hundreds or
thousands of mental smacks is a laborious task. Perhaps we need to evaluate our
education system so we don’t put that block there in the first place.