I wish my senior high students had been taught math during primary school or junior high. I wish that they had not been taught that you can pass math class by showing up occasionally, copying your friend’s homework, then cheating on the test (which everyone fails), and then copying your friend’s take-home make-up test. I did not know that was the legacy I was about to inherit when I started teaching, but some informal quizzing of my school’s “mathematicians” showed me that arithmetic skills were lacking in the senior class. Opening week, I conducted a pre-test of arithmetic and learned that, at best, half of my senior high students could add two decimal numbers, and fewer than one tenth of my students could add signed numbers or do anything with fractions. For weeks, I could not find a student who knew to multiply before adding. “That’s OK,” I thought, “They have seen it before, I can review arithmetic in the first grading period (6 weeks) and move on.”
For the first two weeks I taught place values, adding, subtracting, multiplying, and dividing decimal numbers, and combining, multiplying, and dividing signed numbers. I used visual aids, stories, notes, in-class assignments, and homework. Homework every day, which was a shock to my students. They were used to getting a homework assignment maybe once a week (and with only 4-6 problems, not 20-40). After two weeks, I gave a quiz and compared the results to the pre-test. The numbers had not moved. There were more students in class now, and the quiz was more rigorous than the pretest. So, certainly some students had learned the material. But still, only half of my students could add, and it got worse from there. Grading the quizzes was as depressing as it was enlightening.
I had refrained from announcing a grading system at the beginning of the school year because I did not have one. Mostly, because I am interested in student learning, and grades are not for students. Grades are for the system. Grades tell administrators and institutions how to rank and compare students. Give a student an 80% or a 32%. It tells them nothing useful about what they learned or did not learn, and how to improve. As I wrote a detailed solution to a multiplication problem on a student’s quiz paper (for the 153rd time), I wondered how I could motivate students to actually learn something by the end of the grading period. I also wondered how I could give them more meaningful feedback than a percentage (show a percentage to a student who cannot divide and see how sell they respond). I also realized that my quiz was testing ten distinct skills, and with that my system (v1.0) packed up its things and moved from my sub-conscious to conscious mind.
The next Monday, I entered class ready to return the quiz papers. I explained that I would cover ten skills during the period. Each skill was worth 10 points toward a student’s period grade. I told them that I did not care if they learned the skill before or after quiz, I just needed them to learn it. I said, “This is how it works. I teach a skill, you practice the skill, you demonstrate that you have the skill, and I give you ten points.” Along with the quiz, I handed out a checklist to each student with an ‘X’ next to every skill they demonstrated on the quiz. Finally, I introduced the small-small tests.
I needed students to start developing and proving there skills, and I needed them to start right away, not the night before the period test. So, I took one copy book and wrote one test per page, one test per skill. I bought more copy books and labeled them “workbooks.” I told my students that anywhere they could find me (at school, at my house, on the road) they could take a small-small test, prove they had that skill, and earn 10 points toward their period grade. Within a week, students were lined up on my porch and at school to take tests.
Take the test and earn ten points, or get tutoring and practice problems. That is how it works. Bring nothing but your brain. I supply the test, the workbook, and the pen or pencil. If you get the test completely correct, you earn ten points. There is no partial credit on small-small tests. Miss any part of any one problem and you receive tutoring. You then get practice problems that target any weakness in your skill, which you work until you are completing them all on your own. Finally, I say, “I You can’t earn points for a skill on the day I teach you. You must fall asleep and wake up and still have the idea in your head. So, come back tomorrow and get these points.” It is not uncommon for me to be administering these tests and tutoring students from the time I wake up in the morning (as they knock on my door) until dark, when there is no more light on the school campus. But, in my town, you need to be carful after dark; because, you might get mathbushed.
Administrators at my school like to complain that students are not serious. “The students are always on the road at night,” they lament. “The road” is the 50 yard stretch of pavement where there are enough generators running that you do not need a flashlight to scope out members of the opposite sex, which means it is where the high school students spend their evenings. Well, Mr. Kemokai (aka Mr. Bruey) also likes to hang out on the road (because that is where his friend’s diesel shop is located) and he has a piece of paper in his bag with every student’s name and a check for every skill that the student has demonstrated. His magic bag of tricks also includes the the skills tests, workbooks, and various writing implements. Students walking by get called over to take tests; and, if you are failing, Mr. Kemokai will send someone to your house to bring you to the road to earn points. First period this worked pretty well. Second period, Mr. Kemokai got reverse-mathbushed as students tracked him down on the road to study and take tests, trying to “cover-up” before the period test.
A test at the end of the grading period gives students a chance to prove their skills. On this test, I give partial credit for skills if only some of the conditions for mastery are met. A passing grade is 70 points. First grading period, I added up to ten bonus points for homework. Second period, I added up to ten bonus points for completing a times-table quiz (36 problems in 3 minutes). At the end of the first grading period, my pass rates for 10th, 11th, and 12th grades were 60%, 75%, and 83%. Second period, more rigorous testing, harder material (fractions), interruptions in the school schedule, and a few other factors, dropped those numbers to 50%, 60%, and 80%. To me, these numbers still indicate failure on my part to adequately motivate students, but at least there is no curve. Every point a student earns is a direct result of demonstrating math skills. I give no points for attendance or participation, and there is no curve. We were taught in our pre-service training that it is typical in Liberia to take all your grades, add 100 and divide by 2. That effectively takes 40 and makes it a passing grade. Consider that up to 25 points could be attributed to attendance or participation and you do not need much math to pass math class. I am glad that my students are proving that most of them (not just the top 10% of students) are able to succeed based on their own merit. In fact, I believe that lesson is the most valuable one I am teaching, and the real value of my system.
Junior High Classrooms
Some Senior High Classrooms
The Administration’s Offices
More classrooms, the library (with no librarian), and the laboratory (with no equipment, benches or sinks).
Outside the library.