Effects Of Conceptual Understanding, Math And Visualization Skills On Problem Solving In Statics
Kelli Higley, Thomas Litzinger, Peggy Van Meter, Christine B. Masters, Jonna M. Kulikowich
Abstract
Abstract NOTE: The first page of text has been automatically extracted and included below in lieu of an abstract Effects of Conceptual Understanding, Math and Visualization Skills on Problem-solving in Statics Introduction Although non-technical skills are increasingly important to successful engineering careers in the global marketplace of today, problem-solving remains a critical skill for most young engineers. In many cases successfully solving problems requires engineers to use their analytical skills. The central importance of problem-solving and analytical skills in engineering motivates the work presented in this paper, which is the first phase of a program aimed at answering two main questions: What are the major difficulties that students encounter when they perform modeling during problem-solving? What are the necessary components of instructional interventions to improve engineering students’ modeling during problem-solving? The work is being done in Statics classes because this is one of the first places that engineering students encounter the engineering problem-solving process. In this study we are paying particular attention to the early steps in problem-solving when students ‘model’ the system being studied to create a set of equations describing the system. In Statics students typically read a problem statement and then create a model of the system, the free body diagram, that contains all of the salient forces on the body. Then, based on the free body diagram, they create a mathematical model of the system. Clearly there are many different ways in which students can go wrong as they solve problems in Statics. They may, for example, have inadequate knowledge of the forces and moments for particular types of joints, an inability to visualize forces, or inadequate math skills. Our working hypothesis is that students will cluster into different groups based on their abilities and knowledge, and that these groups will demonstrate differing abilities to solve Statics problems. Therefore, improving the problem-solving skills of these groups will require different interventions. The work presented in this paper is designed to answer two research questions: can such clusters be identified, and if so, can they be used to identify the specific needs of the students in those clusters? The results presented include a summary of a cluster analysis, which did identify statistically significant clusters, and a comparison of the characteristics of the best and worst performing clusters to illustrate how the data can be used to identify the specific needs of the students in a cluster. Relationship to Previous Work This study has been influenced by a number of studies of problem-solving in general and of problem-solving in engineering specifically. The relationship to past work was discussed at some length in a previous paper1 and therefore it is only briefly summarized here. Three subsets of the literature have had the most influence on our work: Problem-solving processes, translations between symbol systems, and domain knowledge.