Symbolic_Problems

Symbolic_Problems - Same to Us, Different to Them: Numeric...

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Same to Us, Different to Them: Numeric Computation versus Symbolic Representation Eugene Torigoe and Gary Gladding Department of Physics, University of Illinois Urbana-Champaign, Urbana, IL, 61801 Abstract. Data from nearly 900 students was used to measure differences in performance on numeric and symbolic questions. Symbolic versions of two numeric kinematics questions were created by replacing numeric values with symbolic variables. The mean score on one of the numeric questions was 50% higher than the analogous symbolic question. An analysis of the written work revealed that the primary identifiable error when working on the symbolic problems was a confusion of the meaning of the variables. The paper concludes with a discussion of possible theoretical explanations and plans for future follow-up studies. Keywords: physics education research, kinematics, symbolic algebra. PACS: 01.40.Fk. 01.30.Cc. INTRODUCTION Algebra is an essential skill for students in physics. For some students the lack of algebraic facility acts as a barrier to success in physics. Studies from the mathematics education research community have shown that many students learning algebra have difficulties understanding the meaning of symbolic variables and dealing with unevaluated expressions [1]. We performed a study to measure the effect of such algebraic difficulties in the context of a physics exam. We modified exam questions to see the effect of numeric computational and symbolic representational cues on student performance. We hypothesized that changing the numeric quantities in the problem to symbolic variables would change the way students thought about and approached the solution to the problems. Specifically, we thought that students would have difficulties with problems that required them to plug an unevaluated symbolic expression into another symbolic equation. METHODS The subjects of the study were students who were enrolled in the calculus-based introductory mechanics course, Physics 211, at the University of Illinois, Urbana-Champaign in the spring 2006 semester. Students in Physics 211 take three multiple-choice midterm exams and a cumulative final. While numeric questions are the most common type of question, symbolic questions are not uncommon. There were 894 students who completed one of the two randomly administered versions of the final exam. We placed a pair of kinematics questions dealing with cars on each version of the final exam. On final exam 1, numeric values were used and on final exam 2, symbolic variables were used. The questions are shown in Figure 1. Minor modifications were made to discourage cheating. The order of the problems and the order of the choices were reversed from one final to the other. The same choices are present in both versions of each
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Symbolic_Problems - Same to Us, Different to Them: Numeric...

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