Cognitive Foundations for a Multiplicative Structures Curriculum

乘法结构课程的认知基础

• 批准号: 8850623
• 负责人: James Kaput
• 金额: $ 26.68万
• 依托单位: Harvard University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1988
• 资助国家: 美国
• 起止时间: 1988-11-01 至 1990-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8850623&HistoricalAwards=false
• 关键词: Cognitive; Foundations; Multiplicative; Structures; Curriculum

The multiplicative structures curriculum in the middle grades, covering multiplication, division, rates, ratios, and proportional reasoning, is widely seen as the locus of serious curricular difficulty and underachievement. These investigators will conduct an intensive set of year-long teaching experiments involving 8 classes, 5 experimentals and 3 controls,intended to build a robust database and a theoretical foundation for a new, more effective multiplicative structures curriculum for the mid-upper elementary grades. Four experimental 6th grade classes and 1 below average ability level 8th grade class whose students have repeatedly failed to learn the topics will be taught using specially designed software and materials. Controls will be taught using conventional text materials. Whole-class written measures of conceptual change accumulated through the year will be overlaid with a year-long clinical study of a representative subsample of both experimentals and controls in each class. This research will utilize an elaborated sequence of software environments comprising a "concrete-to-abstract software ramp" developed at ETC. Lower levels of this ramp feature concretely enactive multiplication, division and ratios in object-based calculation environments, whereas upper levels include dynamically varying algebraically represented proportions linked to tables of data and coordinate graphs. Throughout, the software employs actively linked multiple representations of mathematical concepts and procedures, exploiting the representational power newly available in school affordable computers. The study will also compare 3 mid ability level classes taught by the same teacher, one of which uses it in the teacher-centered, one-computer mode only, and a third acts as control. The intent is to determine if and how the representational power of these types of learning environments can be used effectively in computer-scarce contexts apart from its interactive power, which requires computer-dense, hence more expensive, lab contexts. The Education Technology Center at Harvard and Weston Middle School are sharing the costs of conducting this project.

乘法结构课程在中等年级，包括 乘法，除法，比率，比率和比例推理，是 被广泛认为是严重的课程困难的所在地， 成绩不佳 这些调查人员将进行一系列密集的 为期一年的教学实验，涉及8个班，5个实验， 3个控件，旨在建立一个强大的数据库和理论 一个新的，更有效的乘法结构的基础 小学中高年级的课程。 4实验6 8年级班级和1个低于平均能力水平的班级， 学生多次学习失败的题目将采用 专门设计的软件和材料。 控制将被示教 使用传统的文本材料。 全班书面测量 一年来积累的概念变化将被一个 一项为期一年的临床研究， 实验和控制在每个类。 这项研究将利用 详细的软件环境序列，包括 ETC开发的“从具体到抽象的软件坡道”。 这个斜坡的特征具体地实现了乘法、除法和 基于对象的计算环境中的比率，而更高级别 包括动态变化的代数表示的比例 数据表和坐标图。 在整个过程中，软件 采用积极联系的数学的多重表示 概念和程序，重新开发代表权 在学校买得起的电脑。 该研究还将比较3 中等能力水平的班级由同一位教师授课，其中一位使用 它以教师为中心，只有一台计算机模式，第三个充当 控制 其目的是确定是否以及如何代表 这些类型的学习环境的力量可以有效地用于 计算机稀缺的背景下，除了它的互动能力， 需要计算机密集，因此更昂贵的实验室环境。 的 哈佛和韦斯顿中学的教育技术中心 共同承担这个项目的成本。