Educators in engineering and science disciplines are well aware of student difficulties in formulating problems. Correct problem formulation is a critical phase in the problem solving process because the solution follows directly from the formulation.
Students in this phase are engaged in reasoning and argumentation activities that result in support for a specific formulation. Empirical evidence from our work in ill-structured STEM problem solving indicate that more research is needed to understand the nature of problem formulation and what the cognitive challenges are for STEM students.
Students work in teams to solve ill structured problems in the Problem Solving Learning Portal (PSLP). In this study we examine the use of scaffolding in the problem formulation stage in the context of an Engineering Economy course having students from multiple engineering disciplines.
Correct problem formulation is critical at the onset of problem solving because the solution process follows directly from the formulation. The ability to recognize a problem type is considered to be an essential cognitive skill in problem solving.
This recognition of the nature of a problem is an important step within problem formulation and adds some immediate structure to the problem that can evolve during problem solving. Problem formulation could be instantaneous for simple problems, or may require some investigation, analysis, evaluation, and iterative development.
French et al. suggested that problem formulation is iterative in nature and recommended that students should revisit individual steps in the formulation until they converge on an acceptable formulation.
We introduced scaffolding in the problem formulation stage to address the following
- Does scaffolding of the problem formulation help students solve ill structured problems?
- When do complete the problem formulation relative to the solution stage?
Problem Solving Learning Portal:
This study was performed within the Problem Solving Learning Portal (PSLP), a web-based collaborative environment that is intended to help students improve their problem solving skills using ill structured real world problems.
The PSLP is a unique active learning environment where teams of students solve complex problems using the tools and domain-specific knowledge learned in class. Students are presented with a description of the problem, a series of tasks that must be completed, and information resources such as reports, spreadsheets, databases, design specifications, drawings, pictures, or streaming video.
The Problem Formulation stage provided scaffolding for each problem. The scaffolding in the first problem was much more extensive than the second problem. The contents of the scaffolding for both problems included cash flow and balance diagrams as shown in Figure 1. The intent here was to encourage students to reflect on what is important in the problem.
ASSESSMENT OF STUDENT SOLUTIONS
Each stage is included in the overall assessment of student work. The rubrics for problems 1 and 2 are the same except for a slight modification in the Robustness criterion. Students received a grade in the range of 0-30 based on the rubrics.
The average grades for problems 1 and 2. The grade ranges and standard deviation indicate that students had greater difficulty with problem 2. The range for problem 1 was 22-29 (standard deviation of 2.1) while problem 2 had a range of 14-29 (standard deviation of 4.0).
Was the observed change in grade between problems 1 and 2 due to the use of more general scaffolding or the increased difficulty in the second problem? Given the lack of a control group in this study, performance data is not available to address this question. However, based on the problem descriptions, the second problem is more ill structured than the first problem.
We have conducted some initial investigations into the use of scaffolding to help students improve their problem solving skills. Teams of students were presented with a sequence of two problems with different levels of complexity and different levels of scaffolding.
Scaffolding (in the form of diagrams and questions) was implemented in the problem formulation stage to encourage students to reason about the problem before examining the data. We may have undermined this scaffolding by putting too much detail and data in the problem description for problem 2.
The assessment of student solutions indicates that the second problem was indeed more complex. Teams that did not find the scaffolding helpful tended to complete that section after the problem was solved. Those who found it helpful usually completed the scaffolding questions towards the beginning of the problem solving process.
Teams who found the first problem scaffold most helpful tended to perform as well as the other students indicating that it may have helped them solve the problem. When we reduced the scaffolding level in problem 2, teams that found it most helpful had a much wider variation in grade, suggesting that for some of them the scaffold may be sufficient and for others additional scaffolding is warranted.
This is reinforced by looking at the change in grade from problem 1 to 2 for the teams that found them most useful. Two groups performed better and three groups performed worse (i.e., scaffolding was insufficient for some groups). A greater spectrum of scaffolding may be needed, especially in more difficult ill-structured problems.
These results will be used to further refine our use of scaffolding and explore other approaches to scaffolding in the next course offering. In addition, we are expanding the study to another domain, a Physics course required by all engineering students. The use of scaffolds in the problem formulation stage for ill structured physics problems will be investigated in a similar fashion.
Source: Iowa State University
Authors: John K. Jackman | Sarah M. Ryan | Craig A. Ogilvie | Dale Niederhause