Diagrams Affect Choice of Strategy in Probability Problem Solving
| العنوان: | Diagrams Affect Choice of Strategy in Probability Problem Solving |
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| المؤلفون: | James E. Corter, Chenmu Xing, Doris Zahner |
| المصدر: | Diagrammatic Representation and Inference ISBN: 9783319423326 Diagrams |
| بيانات النشر: | Springer International Publishing, 2016. |
| سنة النشر: | 2016 |
| مصطلحات موضوعية: | Mathematical optimization, Theoretical computer science, Binary tree, 05 social sciences, Structure (category theory), Conditional probability, 050105 experimental psychology, Outcome (probability), 03 medical and health sciences, Tree (data structure), 0302 clinical medicine, Simple (abstract algebra), Table (database), 0501 psychology and cognitive sciences, Mathematical structure, 030217 neurology & neurosurgery, Mathematics |
| الوصف: | We investigated whether diagrams influence strategy choice and success in solving elementary combinatorics problems. Generic diagrams (trees or two-way tables) were provided to solvers as aids. Participants’ coded solution strategies revealed that problem solvers tended to utilize mathematical structures and solutions that easily mapped to the diagrams’ visuospatial relations. For example, when provided with an unlabeled N-by-N table, solvers tended to proceed by defining an equally-likely outcome space (an “outcome-search” solution); when provided with a binary tree, solvers tended to adopt a “sequential” solution defining stage-wise simple or conditional probabilities; when provided with an N-ary tree cuing equally-likely outcomes, choices were split between the two solution types. Furthermore, the tree and the table showed different patterns of characteristic errors, and perhaps for this reason, the tree led to higher accuracy for one problem that involved sequential sampling without replacement, while the table was best for the other problem, involving independent events. The results support arguments that the content and structure of diagrams must be congruent to that of the problem at hand and be easily and accurately perceived to be effective, and demonstrate that diagrams can influence strategy choice in problem solving. |
| ردمك: | 978-3-319-42332-6 |
| URL الوصول: | https://explore.openaire.eu/search/publication?articleId=doi_________::cd1dc6bd8f6195ac987fbedad06b3bae https://doi.org/10.1007/978-3-319-42333-3_1 |
| حقوق: | CLOSED |
| رقم الأكسشن: | edsair.doi...........cd1dc6bd8f6195ac987fbedad06b3bae |
| قاعدة البيانات: | OpenAIRE |
| ردمك: | 9783319423326 |
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