Metacognition in Stock-flow Failure
Considering the nature of problems in dynamic systems, the systems thinking literature introduces various failures and oversimplified strategies while solving perceived problems of a system and possible reasons for failures. It is revealed that poor understanding of stocks and flows was due to the problems people have in their decision making processes. To understand the differences in individuals’ abilities in solving stock-flow problems, it is important to examine their decision making processes and thinking strategies while solving stock-flow problems. In particular, rather than just focusing on cognitive and contextual factors, individuals’ metacognition is identified as a crucial variable for gaining insight into stock-flow failure.
In this study, we introduce ‘metacognition’ from educational psychology as a possible way to approach to the failures in solving problems in dynamic systems. Metacognition in this context refers to the effective use of strategies for understanding the problem, and designing, monitoring, and executing an effective plan, and also evaluating the possible solution during stock-flow tasks. Individuals who perform these steps effectively are expected to be successful in interpreting the stock-flow tasks and constructing a solution. In order to investigate this issue, we attempt to systematically observe the problem-solving processes of individuals who solve the assigned problems and those who cannot, and compare their metacognitive strategies.
In the research design, we used a single-subject concurrent thinking-aloud technique to generate verbal protocol data of participants while they are solving two well-known systems tasks; “department store task” and the “bathtub task”. The participants’ behaviors and discourse as they were solving the tasks were also graded through systematic observation checklist. 40 pre-service mathematics teachers in their final year at their degree participated this study. It is a fact that improving students’ metacognition is an important part of mathematics teachers’ expertise and systems thinking contributes to the learning of mathematics in a more meaningful way. In this context, it was valuable for us to see how pre-service teachers used their metacognitive skills while solving systems tasks.
We identified difficulties in reading, planning, monitoring, and checking activities during the problem-solving sessions. And there is less likelihood of performing the metacognitive skills as you from reading to checking on the systematic observation checklist. Our study presents some direct quotations from the participants as they were solving the tasks and these serve as critical evidences of common misunderstandings and errors in reasoning. Besides, we identified some key phrases in the problem-solving sessions of the successful problem-solvers. “Over a 30-minute period” and “per minute” were some key phrases that indicate either sense of continuity for a stock or rate of change (i.e. flow), respectively.
The study has implications for both systems dynamics and mathematics education fields. The think-aloud protocol sheds light on the difficulties participants experienced while solving stock-flow tasks, such as considering instant flow and stock as the same. We realized that participants have difficulties in using strategies to control the accuracy and correctness of cognitive operations and results, while they easily use some metacognitive strategies such as reading and calculation based on readers’ previous knowledge or background information.
For future systems studies, metacognition could be incorporated in different designs and system tasks. Secondly, this study indicates that even pre-service mathematics teachers lacked some metacognitive skills. ‘Checking the answer’ was the least observed metacognitive activity. There should be more emphasis in mathematics education courses about these skills and more un-familiar problems such as system tasks should be introduced to pre-service teacher to diversify the context and structure of the problems they will study.
Gürsu and Zerrin are coauthors of “Metacognition in action as a possible explanation for stock-flow failure”, available on the System Dynamics Review.
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