A Summary of Students' Mental Models and Their Applications in Contexts Pertaining to Newton's II law

Abstract

We investigated students’ use of Newton’s II law in mechanics and electricity and magnetism contexts. We interviewed 16 students in a two-semester calculus-based physics course. We found students’ answers are consistent with two principal mental models and a combination of these two. We explore whether the students who use Newton’s Second Law in mechanics contexts continue to do so in electricity and magnetism. Introduction Students use various knowledge structures (or mental models) to make sense of situations.[1] Students build these knowledge structures from information based on prior experience or through instruction. Researchers have been probing students’ mental models to better understand the origin of student difficulties.[2] In this paper we present a summary of our ongoing research on how students’ knowledge structures are consistent or not with Newton’s II Law in mechanics, electrostatics and magnetism contexts. Goal & Methodology We attempted to address the following research questions: • What knowledge structures (mental models) do students in calculus-based introductory physics courses use to describe motion? • How do these knowledge structures change with contexts as students progress through a twosemester course sequence in contexts in mechanics and electricity and magnetism? We interviewed 16 students in a calculus-based physics class six times over two semesters. The class operates with two 1-hour lectures and a two-hour lab integrated with the recitation (Studio). The interviews were conducted at the beginning, middle and toward the end of each semester. The first interview was conducted before Newton’s Laws were introduced in class. We present preliminary results from our interviews. We will discuss these and other results in a forthcoming paper. Instruments: Semester I Our first semester interview protocol is partly based on questions from the Force Concept Inventory (FCI).[3] Interview 1 addressed two contexts, which we label “vertical” and “horizontal.” The vertical context is based on FCI question # 17: An elevator is being lifted up an elevator shaft at constant speed by a steel cable. • What is the force in the cable when the elevator is at rest, moving up, or down at constant velocity? • What is the force if the velocity is doubled? • What is the force if the velocity is steadily increasing? • How does the velocity change if the force is doubled? • What force is needed to move an elevator, twice as massive at the same velocity? The horizontal context questions were based on FCI questions # 25 through 27: A woman exerts a constant horizontal force on a large box. As a result, the box moves across a horizontal floor at a constant speed. • How does her force compare with friction? • What force does she need to double the velocity? • What force is needed to steadily increase the velocity? • How will the velocity change if her force is doubled? • What force is needed for two boxes with the same velocity? • What happens if she stopped pushing? In Interview 2 we explored the same vertical and horizontal contexts with other physical features, i.e. changing from pushing to pulling and from lifting to hauling. We also changed from a person to a mechanical device performing these activities. In Interview 3 we explored contexts that included Atwood’s machines. Based on research by