RUME 28
2026
Alexandria, Virginia
Exploring Aspects of Student Facility With Taylor Series in the Context of the Electric Dipole
Page: 763
Using a mixed methods approach, we investigate students’ facility using Taylor series expansions in the context of the electric dipole. Eight students participated in one-on-one teaching-learning interviews, during which audio and video data were recorded while they completed a written activity. We show that while physics students at this level are very familiar with the procedural aspects of Taylor series expansions, they may not recognize several common cues to use them to simplify functions. We find that sketching out the exact function and an approximation of it can help students learn to associate these common cues with Taylor series. In addition, we probe students’ conceptions of the meaning of the expansion point and find that one difficulty in choosing an expansion point in a physics context is associating that ‘point’ with a spatial location. We conclude with recommendations for physics and calculus instructors.