Extending the Inquiry of Newton’s Second Law by Using Limiting Case Analysis

Abstract

This study proposes an instructional unit on extending the inquiry of investigating the motion of a system of two objects called a half-Atwood machine by applying limiting case analysis. While inducing algebraic operations such as multiplication or division to solve a physics problem is dictated by the engagement of the parameter of interest within the formula, applying the limits’ techniques is not explicit. Students who have precalculus or calculus backgrounds can handle reasonably well the process of evaluating limits. However, they usually are uncertain when limits can be applied to support inquiries in physics and how to interpret the results. Twenty-four (N = 25) first-year algebra-based college physics courses took part in this case study. The pretest showed that the students did not realize that taking limits would help them answer questions requiring using that technique. The instructional unit, whose goal was to bring forth the notion, enabled the students to apply the techniques of limits to evaluate formulas as covariate functional representations. Posttest results supported the study thesis that converting formulas to functions helps students with transferring their mathematical knowledge and opens up a gate for advancing their scientific inquiry skills.