2024 ASEE Annual Conference & Exposition

We conducted research 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 the process of our research, eleven experienced college algebra graders of a large state university were asked to grade graphs of linear equations generated by students in their classes, and interviewed to clarify what features of the graphs were important to them in grading. When grading each graph on a scale of 10 points, the graders generally agreed on the relative worth of particular features: a correct slope was worth 4 points, y-intercept was worth 4 points, labeling is worth 1 point. After that, and everything else was a matter of one point. Furthermore, the graders judged slope and intercept from two points (the y-intercept and the first point to the right). The relative number of current or incorrect points did not impact grades. Graders did not attempt to deduce the causes of student errors, and graders were reluctant to change their grade in one case where the interviewer suggested a sign error as a cause for a student’s graph. Returning to the students’ work, the researchers saw that the students also placed extra importance on points to the right of the y-axis.

This grading style may reinforce students' thinking about only about two points in a line. Students understand graphing a line as just plotting two points and then connecting them. Beginning at the y intercept, students then go "over one and up m" to graph a line with slope m, or decomposing a fraction into "rise over run." In both cases, a slope is thought of as being composed of two discrete points. This method is good enough to generate graphs of lines but begins to fail as students begin dealing with any type of non-linear function or discontinuous function. As mathematics becomes more complex, a strong foundation of continuous reasoning becomes even more necessary. We conclude that use of this grading style may have implications for student learning of more advanced mathematics. If a machine is doing the grading style, it can look at just those two points without making more work for the teacher. However, based on our research, it shows that replicating human grading may not be the best use of machine grading.