Feeling a bit better after two months of recovering from the flu while juggling three preps, BTSA, and other teaching tasks, I took a moment to pen the kernel of the following for my Facebook friends. Sharing an expanded version now with those who follow my blog.
The two charts below depict my AP Calculus AB students’ performance (N=35) on a cumulative test covering second semester topics: 1) integration techniques; 2) applications of integration; and 3) separable, first order, ordinary differential equations.
The first chart depicts scores as a histogram using 10% bins. The second chart shows scores using my rating scale spanning categories from far below basic to advanced. These correspond to letter grades of F through A, respectively. My cut scores break at 15% intervals from 40% to 85% corresponding to far below basic to advanced, or F to A.
The results include distributions of the total score as well as sub-scores for Integrals, Applications of Integration, and Differential Equations. The overall average was 47%. High score was a 95%; low score was an 8%. I am not pleased with the results; however, I am not surprised. I do wish I knew how best to motivate these advanced students to invest more time in their studies; it seems the majority of them are so accustomed to minimal effort out of class based on earlier successes in mathematics that they simply do not know how to do so in an advanced course like calculus. A few have simply given up, which takes more time and energy from me to get them to re-engage.
It took 12 hours to score this test, as I needed to read the written work from 700 problems for maximal partial credit. As you might imagine, that is a considerable investment on a teacher’s part for one course (aka prep); I have two other preps. It is very worthwhile if students are investing significantly in their preparation for a test, and their learning, but not so much otherwise. I’ve asked my students to please consider this as they progress in their education.
BTW, the overall score is the only score that counts towards their grade at present. At some point, I will compare each of their sub-score percentages to earlier test scores to replace those that are higher, which helps late bloomers. I’ve also suggested that students look at their sub-scores and use them to guide subsequent studying for the course and AP Exam.
Let’s hope they do so!