| The National Council of Teachers of Mathematics and the New York State Education Department emphasize the importance of geometry in the mathematics curriculum. Geometry content knowledge, multiple representations, and cognitive development are primary foci of the geometry curriculum. This paper reports the results of analyses conducted to explore future and novice mathematics teachers' knowledge of basic plane figures.;A paper and pencil instrument was used to collect data from a sample of 21 teachers. The 12 figures in the instrument, which the teachers were required to define and draw, included: circle, triangle, quadrilateral, vertical angles, isosceles triangle, rectangle, parallelogram, chord, kite, trapezoid, sector, and rhombus. Interpretation of test scores suggested that the teachers' knowledge of basic plane figures was incomplete. Mean values for circle ( M = 1.98, SD = 1.07), kite (M = 1.43, SD = 1.09), and sector (M = 1.17, SD = 1.16) revealed deficits in the teachers' knowledge of the key components of the figures.;Interpretation of non-parametric Spearman's rho = 0.691 (p = 0.001) and parametric Pearson's r(19) =0.551 (p = 0.010) values indicated that a moderate positive correlation between the scores assigned to the teachers' responses to the definition tasks and the scores assigned to their responses to the drawing tasks. Non-parametric Mann-Whitney U test statistics, U = 131 (p = 0.025 two-tailed), and parametric t-test statistics, t(20) = 2.43 ( p = 0.025), provide evidence that a statistically significant difference between the scores assigned to the teachers' responses to the definition tasks and the scores assigned to the teachers' responses to the drawing tasks in favor of the definition task responses. These results support the notion that there was a lack of consistency in the number of key components included in the teachers' responses to the definition tasks and the corresponding number of key components included in their responses to the drawing tasks.;Non-parametric Mann-Whitney U test statistics, U = 69.5 (p = 0.314 two-tailed), and parametric t-test statistics, t(19) = -1.20 (p = 0.246), provide evidence that differing backgrounds in prior geometry course work had no discernable impact on the scores assigned to the teachers' responses to the definition tasks and drawing tasks.;The teachers' responses to the definition tasks and drawing tasks corresponded to cognitive activity at low levels of the van Hiele model. Most teachers' responses to the definition tasks and drawing tasks provided evidence that their cognitive activity was at a van Hiele level of analysis and corresponded to national expectations for grades 3-5. Some teachers' responses to the definition tasks and drawing tasks suggested cognitive activity at the lowest van Hiele level, visualization, and corresponded to national expectations for grades Pre-K-2.;Non-parametric Spearman's rho = 0.569 (p = 0.007) and parametric Pearson's r(19) =0.526 (p = 0.014) values provided evidence that a moderate positive correlation between the van Hiele level values assigned to the teachers' responses to the definition tasks and the van Hiele level values assigned to their responses to the drawing tasks. Interpretation of non-parametric Mann-Whitney U test statistics, U = 279.5 (p = 0.142 two-tailed), and parametric t -test statistics, t(20) = -1.73 (p = 0.099), indicated no statistically significant difference between the van Hiele level values assigned to the teachers' responses to the definition tasks and the van Hiele level values assigned to the teachers' responses to the drawing tasks. These results provide evidence that regardless of the representational system being used, the teachers' responses were at the same cognitive level for the 12 figures under consideration in this study. |
