Fighting the “good fight” can be a rewarding thing. To know you are a part of molding thinkers and mathematicians brings great feelings of a job well done. You’re fighting for all the little guys and gals that others may have been unequipped to do so.

When you are a middle school math teacher you have two options as I see it. You can carry on the tradition of rules and tricks minus the understanding. Or you can provide bricks for a shaky foundation put in place by the most well meaning teachers. I chose the latter. And so far this year, my students have not been resistant to the remodeling of their math thinking. Until today…

After conducting a number talk yesterday to discuss changing a fraction to a decimal, we as a class identified two strategies we could apply for this. One being, find an equivalent fraction with a denominator of 10 or 100 and the other divide the numerator by the denominator. We attempted to apply those strategies today bringing to light the old issue of being fluent with a procedure but not understanding why the procedure works.

Student: to change 5/6 to a decimal, you…well you can’t divide 5 by 6 so you put a decimal and zero. And 50 divided by 6 is…
Me: actually, you can divide 5 by 6 and we are getting ready to do it.
Student: well just add a decimal and zero
Me: Let’s think about what number we can multiply 6 by to 5.
Random students: 1. 0. -1

I inquired why do we need to add a decimal and zero and the only response given was, “Because you can’t divide 5 by 6.” Twenty minutes we spend on looking at numbers that would give us less than or just about 5. Many students lack the concept of fractions and decimals being part of a whole. Some wouldn’t budge from their add a decimal and zero rule and in turn decided not to make sense of the quantities. I could tell there were many that had just checked out. Those bricks I was trying to help lay sat squarely on my chest. I put my hand on the white flag, grasped it tightly and had a private conversation with myself.

Was it worth the struggle the students were facing as their rules of old were challenged? Was it worth the terrible feeling of knowing your students, a large majority of them, just weren’t getting it? I wanted to say, “yes, we just add the decimal and zero” and follow the steps of long division as I waved my white flag.

I left work feeling defeated, conflicted, and lost on what to do. In deciding to go for a walk after having such a tough day, a song came to mind. “Started From the Bottom” by Drake which discussed his struggles coming up before making it big as a rapper. Then it hit me, start from the bottom, the basics and strategically work my way up to what number I could multiply 6 by to get 5. I’m working a bottom up lesson to implement tomorrow. I’m hoping this bottom up remediation approach will help students make the connection between the procedure and why it works.

Started from the bottom now we’re here
Started from the bottom now my whole team ________here
Started from the bottom now we’re here
Started from the bottom now the whole team here, _______
Started from the bottom now we’re here
Started from the bottom now my whole team here, _______
Started from the bottom now we’re here
Started from the bottom now the whole team ______ here

– Drake, “Started From the Bottom” lyrics