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首页> 外文学位 >Teachers' definition constructions and drawing productions of basic plane figures: An investigation using the van Hiele theory.
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Teachers' definition constructions and drawing productions of basic plane figures: An investigation using the van Hiele theory.

机译：教师的定义构造和基本平面图形的图形制作：使用van Hiele理论进行的调查。

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摘要

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.
机译：全国数学教师委员会和纽约州教育部强调了几何在数学课程中的重要性。几何内容知识，多种表示形式和认知发展是几何课程的主要重点。本文报告了为探索未来和新手数学老师对基本平面图的知识而进行的分析结果。;使用纸笔工具从21位教师的样本中收集数据。要求教师定义和绘制乐器中的12个图形，包括：圆形，三角形，四边形，垂直角度，等腰三角形，矩形，平行四边形，弦，风筝，梯形，扇形和菱形。考试成绩的解释表明，教师对基本平面图形的知识不完整。圆（M = 1.98，SD = 1.07），风筝（M = 1.43，SD = 1.09）和扇形（M = 1.17，SD = 1.16）的平均值表明教师对数字关键要素的认识不足。;非参数Spearman的rho = 0.691（p = 0.001）和参数Pearson的r（19）= 0.551（p = 0.010）值的解释表明，分配给教师对定义任务的反应的得分之间存在中等正相关以及分配给他们对绘图任务的响应的分数。非参数Mann-Whitney U检验统计量U = 131（p = 0.025两尾），而参数t检验统计量t（20）= 2.43（p = 0.025）提供了证据，表明分配给教师对定义任务的响应的分数，以及分配给教师对绘图任务的响应的分数，有利于定义任务的响应。这些结果支持以下观点：教师对定义任务的答复中包含的关键要素数量与他们对绘图任务的答复中包含的关键要素数量相对缺乏一致性。非参数Mann-惠特尼（Whitney）U检验统计量U = 69.5（p = 0.314两尾），以及参量t检验统计量t（19）= -1.20（p = 0.246），提供了证据，证明先前几何课程工作中的不同背景无法辨别对教师对定义任务和绘画任务的反应得分的影响；教师对定义任务和绘画任务的反应对应于van Hiele模型低水平的认知活动。大多数教师对定义任务和绘画任务的回答提供了证据，表明他们的认知活动处于van Hiele分析水平，并且符合国家对3-5年级的期望。一些教师对定义任务和绘画任务的反应表明，其认知活动处于最低的van Hiele水平，可视化水平，并且符合国家对K-2年级以前的期望；非参数Spearman的rho = 0.569（p = 0.007）和参数Pearson的r（19）= 0.526（p = 0.014）值提供了证据，表明分配给教师对定义任务的反应的van Hiele值与分配给他们对图形的响应的van Hiele值之间存在中等正相关任务。解释非参数Mann-Whitney U检验统计量U = 279.5（p = 0.142两尾），以及参数t检验统计量t（20）= -1.73（p = 0.099），表明两者之间无统计学差异。分配给教师对定义任务的响应的van Hiele等级值和分配给教师对绘图任务的响应的van Hiele等级值。这些结果提供了证据，表明无论使用哪种表示系统，对于本研究中考虑的12个数字，教师的反应都处于相同的认知水平。

著录项

  • 作者

    Viglietti, Janine M.;

  • 作者单位

    State University of New York at Buffalo.;

  • 授予单位 State University of New York at Buffalo.;
  • 学科 Education Mathematics.
  • 学位 Ph.D.
  • 年度 2011
  • 页码 182 p.
  • 总页数 182
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类
  • 关键词

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