The Effects of Problem-Based Instruction on the Geometric Knowledge of High School Students

美国学校数学课程与评价标准 全国数学教师理事会呼吁转变 从技能本位看中学数学教学范式 问题导向教学。 该提案描述了一个 研究项目中，基于问题的教学的影响， 高中几何学生的概念和思维过程将 被研究。 在拟议的三年项目期间， 以学生解决问题为中心的教学模式， 为不同能力的学生设计。 的 教学效果将从两个对比评估，但 互动观点-利用解决问题的过程和知识 特定的几何概念。 几何问题解决 要研究的过程包括以下能力：（a）概括 根据经验证据，（B）使用演绎证据进行归纳，（c） 处理反向思路，（d）灵活地重新调整思路， 思想，和（e）形象化的几何情况。 几何 要研究的概念包括（a）证明，（B） 无穷大，（c）相似性和一致性，（d）面积，周长，和 卷，（e）并行性，和（f）变换。 数据收集将 三个方面，包括（a）与个人的教学实验 学生评估特定的教学方法;及（B）教学 实验与完整的类，以评估不断变化的性质 教学和课堂互动;以及（c）状态测试， 记录开发概念和过程。 该项目由教材共同资助 发展计划。

The Curriculum and Evaluation Standards for School Mathematics of the National Council of Teachers of Mathematics calls for a shift in paradigm in the teaching of school mathematics from skills-based instruction to problem-based instruction. This proposal describes a research project in which the effects of problem-based instruction on the concepts and thought processes of high school geometry students will be studied. Over the course of the proposed three-year project, a teaching model which focuses on student solving of problems and which is accessible to students of varying abilities will be designed. The effects of the instruction will be assessed from two contrasting yet interactive perspectives--use of problem-solving processes and knowledge of particular geometric concepts. The geometric problem-solving processes to be investigated include the abilities to (a) generalize from empirical evidence, (b) generalize using deductive evidence, (c) deal with reverse trains of thought, (d) flexibly refocus a train of thought, and (e) visualize a geometric situation. The geometric concepts to be investigated include the concepts of (a) proof, (b) infinity, (c) similarity and congruence, (d) area, perimeter, and volume, (e) parallelism, and (f) transformations. Data collection will be three-fold, including (a) teaching experiments with individual students to assess particular instructional approaches; and (b) teaching experiments with intact classes to assess the changing nature of instruction and classroom interactions; and (c) status testing to document developing concepts and processes. This project is jointly funded by the Instructional Materials Development Program.