When Negative Is Not "less than Zero": Electric Charge as a Signed Quantity

Electromagnetism (E&M) is often challenging for students enrolled in introductory college-level physics courses. Compared to mechanics, the mathematics of E&M is more sophisticated and the representations are more abstract. Furthermore, students may lack productive intuitions they had with force and motion. In this article, we explore the mathematization of electric charge. Specifically, we explore how difficulties with positive and negative signs can arise for learners who approach integers primarily as positions on a number line. We discuss the nuances of electric charge as a physical quantity and situate it in a body of work by mathematics and physics education researchers to characterize the uses and meanings of signs. We then describe preliminary research that illustrates the effect of wording differences on student reasoning about electric charge as a signed quantity. Finally, we discuss implications for instruction.