DescriptionI have explored the instructional value of using multiple-possibility problems (MPPs) in introductory physics courses. MPPs are different from problems we most often encounter in textbooks. They are different from regular problems since 1) they have missing information, vaguely defined goals or unstated constrains, 2) they possess multiple solutions with multiple criteria for evaluating the solutions, 3) they present uncertainty about which concepts, rules, and principles are necessary for the solution or how they are organized.
Real-life problems and professional problems are MPPs. Students rarely encounter such problems in introductory physics courses.
Kitchener (1983) proposed a three-level model of cognitive processing to categorize the thinking steps one makes when faced with such problems (cognition, metacognition, epistemic cognition). The critical and distinctive component of MPP solving is epistemic cognition. At that level individuals reflect on the limits of knowing, the certainty of knowing, the underlying assumptions made. It is an important part of thinking in real life.
Firstly, I developed and tested a coding scheme for measuring epistemic cognition. Using the coding scheme I compared the epistemic cognition level of experts and novices by conducting think-aloud problem-solving interviews with them. Although experts had higher epistemic cognition level than novices, I documented some instances where a novice showed an expert-like epistemic cognition. I found that prompting question during interviews were 50% effective for students.
Secondly, I tested the following two hypotheses by conducting two experimental design and one pre-post treatment design investigations in an algebra-based physics course at Rutgers University: Hypothesis 1: Solving MPPs enhances students' epistemic cognition;
Hypothesis 2: Solving MPPs engages students in more meaningful problem solving and thus helps them construct a better conceptual understanding of physics.
I found supporting evidence for both hypotheses. Although not all of my studies produced the results that would unquestionably support the hypotheses strongly, I can say that they show much promise for the use of MPPs in introductory physics courses. I have also created a bank of MPPs freely available for use.