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A Cognitive Study of Modeling during Problem-solving: An integrated problem solving model

Introduction

A fundamental issue in engineering education is the question of how to improve students’ analytical skills.1 Analysis skills are central to engineering students’ abilities to interpret and solve problems and the question of how to improve these skills is a fundamental issue in engineering education research. In recent years, there have been several programs developed to improve students’ analysis skills. Amongst these are programs to improve problem solving skills2, software modules that teach concepts3, and concept inventories to assess misconceptions4. Each of these programs is grounded in a set of beliefs about the underlying causes of students’ disappointing analytical skills. If one believes, for example, that students use ineffective problem solving strategies, one is more likely to develop and adopt a program that teaches these strategies. On the other hand, if one’s belief is that the quality of underlying knowledge is the critical factor in determining analysis skills, one will turn toward efforts to improve students’ knowledge.

Our belief is that there are multiple causes for students’ troubles with analysis skills. In the literature, we have found three approaches to understanding analysis that we find to be the most promising. These three are: problem solving processes,5 translations between symbol systems,6 and domain knowledge.7 We are attracted to these approaches because each has compelling empirical and theoretical support. In this article, we report on a cognitive model of the analysis process that was developed by melding these three approaches. This model, the Integrated Problem Solving (IPS) model, treats each of the three approaches as a separate dimension of problem solving and proposes that high quality problem solving processes requires their integration. These three dimensions are organized into three phases with each phase corresponding to a different step of analysis. Because the IPS model incorporates all three dimensions of problem solving, symbol system transformations, and domain knowledge, it is more comprehensive than previous models.

In this research, we collected verbal protocols from engineering students as they constructed free-body diagrams (FBD). We compared the cognitive processes reported in protocols to our model. Verbal protocols were analyzed through a thematic analysis of processing to better understand students’ difficulties with analysis skills. The results are used to uncover the source of students’ difficulties and to generate suggestions about effective instructional interventions. In the sections that follow, each of the three dimensions contained in the IPS model are discussed independently. This discussion is followed by a presentation of the model itself.

Problem Solving Process

Since Polya’s seminal work in mathematics,8 the utility of learning and using a sequence of steps during problem solving has been widely accepted. Although several specific models exist, a generic 4-step model captures most: (1) Represent the Problem, (2) Goal Setting and Planning, (3) Execute the Plan, and (4) Evaluate the Solution. In the first step, problem representation, the student must read the problem statement and discern the objective. Correct execution of this step is heavily dependent upon the student’s ability to determine the deep structure of the problem

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Litzinger, T., & Van Meter, P., & Wright, M., & Kulikowich, J. (2006, June), A Cognitive Study Of Modeling During Problem Solving Paper presented at 2006 Annual Conference & Exposition, Chicago, Illinois. 10.18260/1-2--211