Reaching the Unteachable – how to succeed using differentiation

How to Reach Your Lowest Student


Kwame was a level one student, meaning he was in the bottom 25% of students in the state. He was a behavioral issue in the classroom and was constantly absent. He was in my 8th grade, Pre-Algebra class, but was obviously years behind in abilities.


I thought about what it must be like for him to come to class everyday, and have NO IDEA what we were talking about; nor did he have the ability to do the work that we were working on.


Advanced Mandarin

I reflected on what it would be like if I were dropped in the middle of an advanced Mandarin class, where everyone was speaking in complete sentences, yet I barely knew five words. No matter how much the teacher yelled at me, or wrote me up, or called home; I would never be able to do the work.


What would I do all day in school while everyone was doing things I couldn’t understand? I’d probably be bored in class and misbehave, or become a distraction. I would also probably do things to hide my inabilities and insecurities.


Making Him Successful


So I decided that I was going to help Kwame, by making him successful.


I picked one standard for him to master; I chose graphing lines. I selected the simplest element of that standard: graphing points in the first quadrant. I had Kwame work on that using a laptop with tutorial videos and then practice on

As soon as he mastered the assignments, I gave him a test, which he Aced! I expressed to him how proud I was, and even called home to tell his parents the good news. The next day Kwame came to school and almost cried when he told me that he had never had a teacher call home and tell his mom anything positive about him (I almost cried too).


I then moved Kwame to the next skill in this sequence of skills leading up to graphing lines: graphing points in a quadrant plane. I again assigned activities to teach him, and had him practice the skill with immediate feedback. Eventually he learned it, and got another A on the test. Two A’s in 4 weeks earned him an A on his progress report. He again was excited, claiming that he had never earned an A on his report card, and wanted to continue to do well so that he could reach that goal.


Not Left Behind, Just Differentiated


While the class and I worked on other standards, like solving equations with variables on both sides, or the Pythagorean Theorem, Kwame kept chipping away at prerequisite skills to help him learn how to graph a line in the form of y = mx + b (which took 18 weeks!)



It wasn’t all Easy


I wish I could tell you it was all smooth sailing for me and Kwame, but it wasn’t. There were times he wanted to quit, because he couldn’t grasp something (like slope). There were times when he’d be absent or suspended, which further slowed the process. But when he was able to be successful, and work towards a goal, he was often able to motivate himself to press on.


It also helped him know that if he didn’t get it right away, I was going to give him all the time he needed, without penalizing his grade, reprimanding him, or leaving him behind.



A Surprising Success


In Florida, on the state diagnostic, students are given a score, which correlates to a level 1 through 5.

1 is the lowest, 3 is on grade level, and 5 is the highest.


Our school grade is earned through three different categories for mathematics. The first is the % of students who scored a level 3 or better. The second is the % of students who make a “Learning Gain” (show a year’s worth of growth by increasing their level on the diagnostic). And the third category is students who are in the bottom 25% of students (level 1) who earn a learning gain. Thus, Kwame could help our school in all three categories, since he started 8th grade as a level 1.


Kwame had been a level 1 his whole life. But this year, he earned a level 3!!!


Explaining the Madness


Most people don’t realize that a proficiency score is earned by comparing your raw score to the rest of the students in the state (like a bell curve). Normally, to earn a level 3, a student only needs to get between 33% and 50% of the questions correct.


There are 26 standards on the State Diagnostic for Pre-Algebra (we’re supposed to all be on Common Core, so it should be the same in your state as well). One of those standards is y=mx + b. Five standards deal with slope, graphing from a table, and determining if a line or equation is linear. And several more actually have some element of slope or linear equations in them (like triangles on a plane and scatterplots). Thus, by teaching this one skill, and a few more ways to make it relatable, I actually covered almost a third of the test! (remember some years, 33% is a level 3 – thus it’s not necessary to ‘expose’ him to all the standards at the expense of ‘mastering’ a few of them).





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