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Contributions of Spatial Skills to Geometry Achievement:

Understand the impact of spatial skills on geometry achievement. Explore correlations, predictive factors, and instructional strategies. Research supported by Carnegie Mellon University and NSF grants.

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Contributions of Spatial Skills to Geometry Achievement:

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  1. Contributions of Spatial Skills to Geometry Achievement: Yvonne Kao & John Anderson Carnegie Mellon University

  2. …the first stages of removing obstacles in the way of pupils learning geometry are activities designed to improve the pupils’ understanding of their spatial world. If every teacher of geometry took steps to prepare the pupils ‘spatially’ before mathematizing the ideas, he or she would find the later work so much easier to teach on the base of those spatial experiences. And the pupils would, of course, realize that they already had some spatial foundations with which to secure their understanding of geometrical ideas (Bishop, 1986, p. 144).

  3. Background • Spatial Visualization“The ability to mentally manipulate, rotate, twist, or invert a pictorially presented stimulus object” (McGee, 1979) • Correlations between spatial visualization and mathematics achievement generally fall between 0.3 and 0.6 (Battista, 1990) • Spatial visualization predicts geometry achievement(Battista, 1990; Battista, Wheatley, & Talsma, 1992; Casey, Nuttall, Pezaris, & Benbow, 1995; Connor & Serbin, 1985)

  4. Background • Spatial factors that also predict geometry achievement: • Spatial orientation (Connor & Serbin, 1985) • …the ability to perceive and recognize multiple perspectives or representations of an object (Tartre, 1990) • Flexibility of closure (Hoz, 1981) • The ability to “break one gestalt and form another” (Lohman, 1988)

  5. But… • Problems: • Space-math correlations may not be greater than correlations between math and (Friedman, 1995): • verbal ability • reading comprehension • abstract reasoning • sports information • Studies have generally failed to establish a unique contribution of spatial skills to mathematics achievement that is distinct from general intelligence (Chipman, 2005) • The factor-analytic approach is not very useful for teachers (Bishop, 1980)

  6. Goal • To better define the relationship between spatial skills and geometry achievement so that we can identify targets for instruction. • To what extent do spatial skills contribute to geometry achievement, above and beyond other cognitive factors? • Do spatial skills matter more for specific geometry subdomains?

  7. Design • Exploratory study • Cognitive battery from Kit of Factor-Referenced Tests(Ekstrom, French, & Harman, 1976) • Collected data on students’ standardized test scores and course grades

  8. Cognitive Battery • General Reasoning • Necessary Arithmetic Operations Test

  9. Cognitive Battery • Verbal • Vocabulary • Word fluency

  10. Cognitive Battery • Spatial • Visualization • Orientation • Flexibility of closure

  11. Participants • 138 public high school students:

  12. Participants: PSSA

  13. * p < .0005 p = .077 p = .109 * * * * p = .020 p = .029 p < .0005 Results: Cognitive Battery

  14. Correlations w/PSSA Math Standardized math test scores were significantly correlated with: • General Reasoningr(132) = 0.67, p < .0005 • Verbal Indexr(132) = 0.43, p < .0005 • Spatial Indexr(132) = 0.39, p < .0005 • PSSA Readingr(132) = 0.67, p < .0005  = 88.354, t(129) = 6.71, p < .0005 59%  = .383, t(129) = 6.82, p < .0005

  15. Correlations w/PSSA Math Standardized math test scores were significantly correlated with: • General Reasoningr(132) = 0.67, p < .0005 • Verbal Indexr(132) = 0.43, p < .0005 • Spatial Indexr(132) = 0.39, p < .0005 • PSSA Readingr(132) = 0.67, p < .0005  = 119.659, t(129) = 9.08, p < .0005 50%  = 60.073, t(129) = 3.64, p < .0005

  16. Intermediate Geometry

  17. Intermediate Geometry Overall test performance in Intermediate Geometry significantly correlated with: • General Reasoning • Verbal Indexr(39) = 0.36, p = .010 • Spatial Indexr(39) = 0.26, p = .004  = .051, t(37) = 2.85, p = .007 17%

  18. Intermediate Geometry Overall test performance in Intermediate Geometry significantly correlated with: • General Reasoning • Verbal Indexr(39) = 0.36, p = .010 • Spatial Indexr(39) = 0.26, p = .004 • Flexibility of Closure  = .042, t(37) = 2.83, p = .005 19%

  19. Intermediate Geometry • Individual unit analysis

  20. Intermediate Geometry • Individual unit analysis • General Reasoning and Verbal Index did not significantly correlate with any individual units • Spatial Index and Congruent Triangles:r(51) = 0.41, p = .001 • Flexibility of Closure: = .054, t(37) = 2.16, p = .03711%

  21. Conclusions • Spatial skills do contribute to geometry achievement above and beyond other cognitive factors • …especially Flexibility of Closure • …especially for Congruent Triangles • To be continued…

  22. Thank You! Joan Son and the participating teachers Cynthia Peng This research was supported in part by the Institute of Education Sciences, U.S. Department of Education, through Grant R305B040063 to Carnegie Mellon University and in part by NSF ROLE grant REC-0087396 to Anderson.

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