Grading criteria of college algebra teachers.

Abstract

The purpose of my research is to identify what features of a graph are important for college teachers with the intention of eventually developing a system by which a machine can recognize those features. In particular, I identify the features that college algebra teachers look at when grading graphs of lines and how much disagreement there is in the relative importance graders assign to each feature. In the process, eleven students from college algebra classes were interviewed and asked to graph six linear functions of varying difficulty. Eleven experienced college algebra graders were asked to grade the selected graphs, and interviewed to clarify what features of the graphs were important to them in grading. Altogether, a general grading rule appears to be: slope is worth 4 points, y-intercept is worth 4 points, labeling of intercepts, points and graph is worth 1 point. After that, add 1 point if everything is correct. All graders considered slope and y-intercept to be very important. Only some of them considered labeling to be important. Anything else was a matter of a single point adjustment. Furthermore, the graders judged slope and intercept from two points(the y-intercept and the first point to the right). Returning to the students’ work, I saw that the students also placed extra importance on points to the right of the y-axis. I conclude that this grading style may have a role in students’ learning to think only about two points in a line (but nothing else), and that replicating human grading may not be the best use of machine grading.