How students use mathematical resources in an electrostatics context

Abstract

We present evidence that although students' mathematical skills in introductory calculus-based physics classes may not be readily applied in physics contexts, these students have strong mathematical resources on which to build effective instruction. Our evidence is based on clinical interviews of problem solving in electrostatics, which are analyzed using the framework of Sherin's symbolic forms. We find that students use notions of "dependence" and "parts-of-a-whole" to successfully guide their work, even in novel situations. We also present evidence that students' naive conceptions of the limit may prevent them from viewing integrals as sums.

An Investigation of Incorporating Dialogical Argumentation into Peer Instruction (PI) for Pre-Service Teacher Learning of Current Electricity

“…The common misconceptions the students identified before the intervention were: how an insulator works, diodes, resistors and resistance, electrical circuits, capacitors and capacitance. Meredith and Marrongelle (2008) asserted that students had learning difficulty with capacitors. The outcome of Question 10 from Table 1 cannot be separated from this assertion.…”

Teaching integration with layers and representations: A case study

“…However, research by Meredith and Marrongelle has shown that students may rely on cues to decide when an integral is necessary, including recall, dependence (a quantity that varies with another quantity), and parts-of-a-whole cues [1]. When such cues are inadequate to decide how to solve a problem or answer a question, we might expect that students would not know what to do.…”

“…Amber had taken Advanced Placement Physics B in high school in the past, giving her a stronger than usual background relative to students who typically take our introductory mechanics class. 1 Her math background was similar to her classmates'. Her introductory mechanics course contained little or no material about integration.…”

Students’ use of symbolic forms when constructing differential length elements

“…Meredith and Marrongelle adapted the conceptual side of symbolic forms to describe what cues students to integrate in electrostatics [4]. They identified dependence, the reliance on a particular quantity, and parts-of-a-whole as major cues for integration.…”

“…While previous work has addressed student use and understanding of integration [2][3][4], applications of Gauss's and Ampère's Laws [1,[6][7][8], and vector differential equations in mathematics and physics settings [9][10], little work has been done to address student understanding of differential elements and how they are constructed or determined in the non-Cartesian coordinate systems typically employed in E&M. Pepper and colleagues identified an instance in a homework help session where students neglected to include the necessary scaling factors when writing spherical differential areas, using rather than [1]. Another group of students attempted a line integral in three dimensions using as a length element [1].…”