Measuring and Modeling: Towards a Conceptual Understanding of Science and Mathematics

这个项目将考察9年级和10年级学生对科学和数学概念的学习情况。研究人员打算进行一系列教学实验，旨在研究在真实科学情景下的测量和建模活动如何影响学生学习微积分的基本概念(变化率，累积水平-正式称为导数和积分)。学生将用涉及物理变量(落物、流水、加热物质等)随时间变化的动态系统样本进行实验；实验仪器将包括基于微型计算机的实验室探头来测量和表示相关物理量。符号系统将使用计算机程序实现，并将提供软件环境，学生将能够构建模型并表示由特定模型预测的任何内容。研究问题中心的研究问题是，“测量和建模活动对学生理解科学实验以及变化率和积分的基本微积分概念有什么影响？”另外两个相关的研究问题是：(1)学生如何使用不同的表示法(图形、数字数据、图标网络等)，当他们努力理解一个实验和一个模型时？(2)哪些符号系统对学生的学习最有效，最佳符号系统可能在多大程度上随领域的不同而不同？结果这项研究的一个成果将是对学生通过测量和建模活动刺激的认知模型进行分析。这一分析将被用来制定：(1)教育应用指导方针：结合测量和建模活动，丰富学生对科学情境的理解的教学策略。(2)软件设计者指南：有助于学生构建模型的符号系统和用户界面的设计准则。

This project will examine the learning of both science and mathematics concepts by 9th and 10th grade students. The investigators intend to conduct a series of teaching experiments designed to study how measuring and modeling activities with real science situations influence student learning of basic notions of calculus (rates of change, level of accumulation-formally called derivative and integral). The students will conduct experiments with sample dynamic systems involving the variation of physical variables over time (falling objects, flowing water, heating substances, etc.); the experimental apparatus will include Microcomputer-based Laboratory probes to measure and represent the relevant physical quantities. The symbol system will be implemented using a computer program with the software environment that will be provided, students will be able to construct models and represent whatever is predicated by a particular model. RESEARCH QUESTIONS The central research question is, "What is the effect of measuring and modeling activities upon students' understanding of science experiments and the underlying calculus concepts of rate of change and integration?" Two additional, related research questions are: (1) How do students use different representations (graphs, numerical data, iconic networks, etc.), as they work to understand an experiment and a model? (2) Which symbol systems are most effective for student learning, and to what extent may the optimal symbol system vary with the domain? OUTCOMES A product of the research will be an analysis of the cognitive models that are stimulated in students by measuring and modeling activities. This analysis will be used to formulate: (1) Guidelines for educational applications: Instructional strategies that enrich students' understanding of science situations combining activities of measuring and modeling. (2) Guidelines for software designers: Criteria for the design of symbol systems and user interfaces that will facilitate the construction of models by the students.