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Geometry Problems and Children's Cognitive Styles

Summary:
All children have a cognitive style which is their preferred way to process information. Here, we introduce a paper on the relation between cognitive styles and performance in geometry. Entitled "Performance on Middle School Geometry Problems with Geometry Clues Matched to Three Different Cognitive Styles," by Karen L. Anderson, M. Beth Casey, William L. Thompson, Marie S. Burrage, Elizabeth Pezaris, and Stephen M. Kosslyn, it reports the results of tests on seventh graders at a middle school in Massachusetts. This article appeared in Mind, Brain, and Education, Vol. 2, No. 4, p. 188-197. The objective was to determine a correlation between a specific cognitive style and the types of clues in problems that resulted in good performance.
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Keywords: Children, Noboru Kobayashi, Geometry, academic results, Brain Science, Neuroscience, Linguistics, Cognition, the Brain and Education




All children have a cognitive style which is their preferred way to process information. Here, we introduce a paper on the relation between cognitive styles and performance in geometry, a subject of great practical interest to teachers. It is entitled "Performance on Middle School Geometry Problems with Geometry Clues Matched to Three Different Cognitive Styles." The authors are researchers in the United States: Karen L. Anderson, Department of Education Studies, Stonehill College; M. Beth Casey, Applied Developmental and Educational Psychology, Lynch School of Education, Boston College; William L. Thompson and Marie S. Burrage, Department of Psychology, Harvard University; Elizabeth Pezaris, Department of Counseling and Applied Educational Psychology, Northeastern University; and Stephen M. Kosslyn, Department of Neurology, Massachusetts General Hospital. This article appeared in 2008 in Mind, Brain, and Education, Vol. 2, No. 4, p. 188-197 and it reports the results of tests on seventh graders at a middle school in Massachusetts.

From the perspective of neuroscience, ability-based cognitive styles can be classified into three types.

  • 1) Verbalizers use verbal deductive reasoning to process information linguistically.
  • 2) Object imagers use object imagery to process information based on the visual characteristics of the object.
  • 3) Spatial imagers process information based on spatial relations of the object.

Much research has been reported on cognitive styles since the mid-1990s, but little has been done from the perspective of neuroscience. In general, a higher percentage of males than females are spatial imagers. Spatial imagers are able to visualize objects in space, by mentally rotating them or otherwise manipulating them, which is an ability considered important in mathematics.

This project was carried out with the participation of 186 students in Massachusetts ranging in age from 12 to 14 years. Ability in the three cognitive styles was measured as follows.

1) Verbal Reasoning ability was measured using the Word Reasoning subtest of the Wechsler Intelligence Scale for Children.

2) Object Imagery Ability was measured using the Shape Memory Test from the Education Testing Service Kit.

3) Spatial Imagery Ability was measured with a mental rotation task designed by Shepard and Metzler.

The participants were categorized according to cognitive style. They were then given geometry problems together with different types of clues for the solving the problem. The aim was to examine which participants having a particular cognitive style scored higher on problems using a particular type of clue.

The results were as follows.

-Students who were verbalizers and spatial imagers performed well on geometry problems with mental rotation clues. Furthermore, females who were spatial imagers performed significantly better.

-Students who were spatial imagers and verbalizers performed well on problems with shape memory clues. Females who were spatial imagers performed significantly better.

-On problems with verbal deductive reasoning clues, students who were verbalizers and spatial imagers performed significantly better.

Students who were spatial imagers, verbalizers, or those who had both cognitive styles performed well on geometry problems. There was no correlation between whether a participant was an object imager or not and the ability to solve geometry problems. These results were corroborated by previous studies. A relationship was found between females who were spatial imagers and their results of geometry performance. This suggests that providing training in spatial working memory to females may improve performance. This may lead to better performance because when solving geometry problems with verbal clues, spatial imagers convert this information into spatial imagery, their area of proficiency. This indicates the need for geometry education that fully acknowledges the important role of visual and spatial imagery.

Moreover, object imagers did not do well on the geometry problems with shape memory clues. The authors consider that this may be due to the fact that object imagery skill assessed in the present did not require using working memory to process the different information that is necessary for solving geometry problems.


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