This passage describes a teacher working with a defiant 17-year old student in her GED class who has faced many hardships. To help the student understand fractions, the teacher uses physical fraction chips she made to demonstrate that 1/7 is a larger fraction than 1/8. Though initially resistant, the student discovers through lining up the chips along the full unit piece that 1/7 is indeed larger than 1/8, showing a moment of genuine learning. The teacher is able to break through the student's tough exterior and facilitate independent learning using hands-on materials.

1. “So, what’s larger, 1/7th
or 1/8th
?” I ask casually at the start of her GED class.
“1/8th
, of course,” she smirks.
This was one loud angry young woman who had a lot to be angry about. She
remembered as young as four years old cleaning up after her mother’s drunken binges. As a
mother herself, she is a seventeen year old caring for a two year old.
And one of the last things she was interested in doing was spending her morning in
class with me. Doing math.
We had a rough road to get to the point where we were that morning. I had spent
weeks struggling to find a point of connection so that we could even begin learning the
content. Her energy focused on defiance. She would to do exactly the opposite of what she
thought I expected of her.
I refused to give up because I knew the value of her GED certification to her and her
daughter. I had the emotional support of a staff team to keep myself walking down those
stairs to class. The consequences for expectations not met were not fun. I couldn’t take all
her anger personally whenever I entered a room and she was there. She wasn’t shy about
reminding me she was pissed at me for trying to make her work and making her life hell when
she couldn’t use the phone because she just chatted during study hour and the math
problems weren’t done or she had to stay in her room all day because she arrived at class
late for the second time in one week, then cheated on her reading worksheet and got caught.
She didn’t know the real hell would come if she was chronically paid a non-livable
wage and repeating her mother’s life experiences.
Now after months of consequences from her defiance, she and I had been finally
getting down to learning some material. She needed to master working with fractions to pass
her GED test. More importantly could she master meaningful fraction skills for life? And I
knew that adding, subtracting, multiplying and dividing fractions on a piece of paper with no
context were meaningless exercises for her. I needed to create something meaningful. First,
can she intuitively understand what these odd-looking numbers stand for? Today: an
example of what do they mean in relation to one another.
“You think 1/8th
, eh? Let’s test it out. Here are the fraction chips.”
She rolls her eyes.
“Yeah, yeah I know. You lovvvve them.” I grin.
I made a collection of wooden chips with my husband’s table saw, all sized exactly, to
teach fractions actively with my GED students. I used a different color nail polish to label
each fraction size from ½ through 1/20th
. The “1” piece is about 18” long.
My student picks up one 1/7th
and one 1/8th
like I am asking her to pick up two
dishwashers full of dishes laced with HIV. She notices the 1/7th
piece was bigger.
“No, you’re WROONNG!” she shouts. “These things are f****ed up.”
“Well, try lining them up along the ‘1’,” I suggest nonchalantly.
My student lines up eight 1/8th
’s and seven 1/7th
’s along the “1” piece. By this time she
understands eight 1/8th
’s go into “1” and so forth.
“Wow! The 1/7th
really is bigger!” Her face reads genuine discovery.
I get through the tough exterior again. I let her independent learning processes take
over. She plays around manipulating the fraction chips for a while forgetting I am there.
She successfully earned her GED certificate before leaving our program.