Abstract
This study investigated, in the context of mathematical problem solving by secondary school students, the nature of the visual schemata which Johnson (1987) hypothesises mediate between logical propositional structures and “rich” specific visual images. Four groups of grade 10 students were studied, representing all combinations of high and low operational ability in mathematics (equivalent to Johnson's logical propositional structures) and high and low vividness of visual imagery (corresponding to Johnson's “rich” images). The results suggested first, that success at problem solving was related to logical operational ability, but not to vividness of visual imagery. Second, a variety of visually based strategies were used during problem solving which differed in their level of generality and abstraction, and use of these strategies appeared related to either logical operational ability or vividness of visual imagery, depending on their level of abstraction. The results supported Presmeg's (1992b) continuum of abstraction of image schemata.
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Throughout the paper, the first “High” or “Low” denotes logical operational ability, and the second, vividness of visual imagery.
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Campbell, K.J., Collis, K.F. & Watson, J.M. Visual processing during mathematical problem solving. Educ Stud Math 28, 177–194 (1995). https://doi.org/10.1007/BF01295792
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DOI: https://doi.org/10.1007/BF01295792