Reuse in Algebra-Based Physics : Implementation of Strategies

This paper summarizes the practical implications and limitations of a project that investigated students’ development of problem solving schemata while using strategies that facilitate the process of using solved examples to assist with a new problem (case reuse). Over a two year span, focus group learning interviews were used to explore students’ perceptions, understanding and use of several problem solving strategies. Individual clinical interviews were conducted and classroom quantitative examination data were collected to assess students’ conceptual understanding, knowledge organization and problem solving performance on a variety of problem tasks. FACILITATING CASE REUSE IN ALGEBRA-BASED PHYSICS 3 Introduction Individuals, including experts of science and mathematics, commonly extrapolate information collected and stored from previous events to determine how it might be comparable to a new circumstance. Experts refine their approach to reusing cases over years of experience. This refinement includes a more sophisticated organization of knowledge elements and their associations (Jonassen, 2006). Our goal with this project was to assist novices with refining this approach early in their studies, easing both cognitive load and the perceived difficulty associated with physics problems. With the continual decline of students choosing physical science as either a major or even a science elective, research focus has turned toward students’ attitudes toward science and how the current decline might be reversed (Osborne, Simon, & Collins, 2004). This qualitatively intense study presented promising evidence of how implementing strategies that accommodate students’ pre-existing problem solving methods positively affect student performance and their overall attitude towards physics problem solving. This work was not intended to be turned into a stand-alone curriculum, only a framework that faculty could assimilate into their existing teaching methodology. This paper discusses the research methods used for each phase of the project, the results for each phase and how our promising results using limited outside intervention can have considerable implications for further research and instruction. Theory Meets Practice This study, like many in science education research, remained well-informed by previous research studies and student and faculty perception of problem solving. FACILITATING CASE REUSE IN ALGEBRA-BASED PHYSICS 4 The pilot and three phases of this project were all built upon the same foundation: valuing worked examples (Maloney, 1993; Ward & Sweller, 1990), active reflection of case comparison (M. T. H. Chi, P.J. Feltovich, & R. Glaser, 1981; Gentner, Loewenstein, & Thompson, 2003; Graesser, Baggett, & Williams, 1996; Jonassen, 2006), emphasis on deep-structure elements within problem sets (Catrambone & Holyoak, 1989) and assessing students’ development of problem solving schemata using non-traditional problem tasks. The non-traditional problem tasks used were text editing (Low & Over, 1990), problem posing (Mestre, 2002), and physics Jeopardy (Van Heuvelen & Maloney, 1999). As this project adapted, researchers continued to use and update the literature review to inform the next viable research phase. We focused our observations on measurement of schema development and collected information regarding students’ perceptions of implemented strategies. Pilot The study began with a short, one-time treatment of two independent research-based strategies chosen to facilitate case reuse (Mateycik, Hrepic, Jonassen, & Rebello, 2007). The problem solving strategies used in this phase of the project were chosen for their focus on organization of knowledge and their ease of accommodating case reuse. The questioning strategy was based upon Graesser’s questioning strategy template, a generated question list that solicits students to openly communicate information relevant to the question resolution (Otero & Graesser, 2001). It trains students to trigger questions with each problem that look to extract the interdependent relationships of given information as it pertains to a described event. It is not intended to force a particular process of resolution, but to incorporate quality questioning in students’ problem solving framework. FACILITATING CASE REUSE IN ALGEBRA-BASED PHYSICS 5 The structure mapping strategy used visual representations of quantities and associations created by experts to model the appropriate mental organization of knowledge elements for a given type of physics problem. The structure maps are a type of concept map (Novak, Gowin, & Johansen, 1983), but are developed using Gentner’s theoretical representations of learners’ implicit cognitive associations between concepts, principles and quantities (Gentner, 1983). For each strategy, volunteers enrolled in an algebra-based physics course were required to indicate quantities given and asked for in a work-energy problem statement, the associations between these quantities, and how these compare with another similar problem. Each strategy was used in conjunction with paired problems of similar physical principles, work and energy. The two strategies chosen were never used together. Our objective was to determine whether treatments conducted only once as extra-credit tasks, each using separate problem solving strategies, would affect student perception of problem solving strategies and/or implicitly affect student performance on solving concept-related problems. A third control group was used to identify any changes in students’ examination performance. The control group participants were required to work out homework style problems as extra credit. The time on task was approximately equivalent between the three groups. Pilot – Results and Limitations The one-time treatment of each strategy made no difference between treatment and control group students’ average examination scores nor did individual groups perform better on any specific work-energy problem. This result was somewhat expected due to the very short treatment application. It would have been preferred to implement both strategies using multiple assignments across the semester. Unfortunately, any sizeable in-class implementation would require substantial control over the course. That level of control and course/treatment integration FACILITATING CASE REUSE IN ALGEBRA-BASED PHYSICS 6 could not be obtained for this pilot or any other phase of this project. In fact, it was only for this pilot project that the primary instructor of the course agreed to our request for extra-credit data collection. Further data collection for subsequent studies would be done using small groups of paid volunteers. Exploration of students’ perceptions of the extra-credit tasks using semi-structured interviews with eight volunteers indicated that students believed both these strategies are helpful, giving them good problem visualization and facilitating their ability to identify important information from the problem. All interview participants agreed that the purpose of the strategies was to help them work out problems, though the intended purpose of some of the questions from the questioning strategy was not clear to the students. Since the phrasing of given questions used in the questioning strategy was prone to be misinterpreted, investigators determined the structure mapping strategy would be a more effective strategy for a full semester implementation. It was impossible to study both strategies across the next semester given the limited availability of human resources. Phase I Eleven student volunteers enrolled in an algebra-based physics course participated in the semester long study. These participants met in two groups of five and six students a total of nine times during the semester. During these focus group learning interviews, students were asked to solve a set of similar deep-structure problems and discuss the contrast between each of the problems. The selected problems were variations of problems asked in Physics: Principles with Applications, Giancoli, 6th Edition. Students were also introduced to structure maps or visual representations of the associations between quantities for a given broad concept. Maps were FACILITATING CASE REUSE IN ALGEBRA-BASED PHYSICS 7 created by expert faculty and graduate students and covered several first semester algebra-based physics topics including kinematics, forces, circular motion, work and energy and waves. Upon request, students would identify how, if at all, a given map might represent the information given or asked for in a problem statement. These ‘marked’ maps would then be compared between problems. Students’ perceptions of the usefulness of these maps as well as the students’ problem solutions and examination data were collected throughout the hour long weekly meetings with our student volunteers. Following the sixth focus group learning interview, students’ feedback regarding the design of the maps was used to generate a new, more complex map. Phase I – Results and Limitations. Data obtained from student solutions, examination and interviews offered no evidence of improved problem solving schema (Mateycik, Jonassen, & Rebello, 2009). The 11 contact hour study was barely sufficient time for students to become comfortable using the maps. This led researchers to believe that the strategy may not be easily assimilated into the classroom. Previous concept map research (Novak, et al., 1983) suggests that student use of concept maps requires significant training. This was something we just could not hope to achieve in a single semester at one meeting per week. Students perceived only some of the initial maps useful. Maps that were designated as not useful were expressed to have discontinuity between how the ‘given’ problem quantities linked to the ‘asked for’ quantities. Students also determined that the redesigned maps were useful because they acted like equation shee