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。研究者打算进行一系列教学实验，旨在研究真实科学情境下的测量和建模活动如何影响学生对微积分基本概念（变化率、累积水平——正式称为导数和积分）的学习。学生将使用样本动态系统进行实验，涉及物理变量随时间的变化（落体、流水、加热物质等）；实验装置将包括基于微电脑的实验室探针来测量和表示相关的物理量。符号系统将使用计算机程序和将提供的软件环境来实现，学生将能够构建模型并表示由特定模型预测的任何内容。研究问题研究的中心问题是，“测量和建模活动对学生理解科学实验和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)当学生努力理解实验和模型时，他们如何使用不同的表征（图表、数值数据、图标网络等）？(2)哪种符号系统对学生学习最有效，最优符号系统在多大程度上随领域而变化？本研究的一个成果将是对通过测量和建模活动激发学生认知模型的分析。这一分析将用于制定：(1)教育应用指南：结合测量和建模活动，丰富学生对科学情境理解的教学策略。(2)软件设计师指南：符号系统和用户界面的设计标准，将有助于学生构建模型。

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.