Student interpretation of the signs of definite integrals using graphical representations

Physics students are expected to apply the mathematics learned in their mathematics courses to physics concepts and problems. Few PER studies have distinguished between difficulties students have with physics concepts and those with either mathematics concepts and their application or the representations used to connect the math and the physics. We are conducting empirical studies of student responses to mathematics questions dealing with graphical representations of (single-variable) integration. Reasoning in written responses could roughly be put into three major categories related to particular features of the graphs: area under the curve, position of the function, and shape of the curve. In subsequent individual interviews, we varied representational features to explore the depth and breadth of the contextual nature of student reasoning, with an emphasis on negative integrals. Results suggest an incomplete understanding of the criteria that determine the sign of a definite integral.