Examining the Impact of a Standards-Based Program on Student Performance

本提案的目的是申请资金，以深入研究过去三个学年（1997 - 2000）收集的数据，用于“纵向/横断面研究：‘情境中的数学’对学生表现的影响”，该研究由美国国家科学基金会资助。本研究为复杂教育情境下学生数学学习的研究范例。本研究的研究模型是一个监测学校数学变化的结构模型，旨在捕捉学习的社会背景、课程内容和材料、课堂实验和学生动机的动态、复杂的相互作用对学生表现和进一步追求数学的影响。该模型由14个变量及其理论相互关系组成。该研究还采用了非等效对照组，准实验设计。约80%的学生和教师使用“情境中的数学”；其余20%的学生使用学校现有的传统课程。研究的纵向部分包括跟踪三组学生在三年学习期间的表现，横断面部分包括三次跨年级的年度比较和三次跨年级的年级比较。来自4个学区5年级、6年级、7年级和8年级的教师、管理人员和学生的信息已经被收集起来，现在正在进入一个数据库。分析将针对纵向和横向比较，以及一系列关于基于标准的课程实施的问题，例如：“学生在这样的课程中是否继续发展数字技能？”或“这些课程对不同背景的学生有效吗？”或“教师在以非传统方式呈现内容时是否改变了他们的教学方法？”为了进行比较并回答这些问题，分析将包括对模型中每个变量相关信息的探索性描述，简化模型的线性回归，在完整模型中估计路径系数的结构方程，以及一系列深入研究数据中关系模式的子研究。最后，在这些分析的基础上，规划了一系列的报告。目前正在编写一套技术报告，内容涉及数据构建工具的创建、每个变量的索引和已收集的原始数据。本提案的资金将使报告横断面和纵向研究结果以及我们对“上下文中的数学”的一系列问题的回答成为可能（国家数学科学教育研究中心& Freudenthal研究所，1997-98）。

The purpose of this proposal is to request funds to examine in depth data collected during the past three school years (1997 - 2000) for the "Longitudinal/Cross-Sectional Study of the Impact of 'Mathematics in Context' on Student Performance," funded by the National Science Foundation. This study is an example of a research study on student learning of mathematics in complex educational contexts. The research model for the study is a structural model for monitoring changes in school mathematics designed to capture the impact that the dynamic, complex interaction of social context for learning, curricular content and materials, classroom experiments, and pupil motiviation have on student performance and further pursuit of mathematics. The mo9del is composed of 14 variables and their theoretical interrelationships. The study also featured a nonequivalent control-group, quasi-experimental design. about 80% of the students and teachers used "Mathematics in Context"; the remaining 20% of the students used conventional curricla already available in the schools. The longitudinal parat of the study involves tracking the performance of the three cohorts of students over the three years of study, and the cross-sectional part includes three cross-grade comparisons by year and three cross-year comparisons by grade. Information from teachers, administrators, and students in grades 5, 6, 7, and 8 in four school districts has been collected and is now being entered into a database. The analyses will be directed toward both the longitudinal and cross-sectional comparisions an dtoward a set of questions about the implementation of standards-based programs, such as: "Do students continue to develop number skills in sucha a program?" or "Are such programs effectivie with students with differing backgrounds?" or "Do teachers change their pedagogy when presenting content in non-traditional ways?" To make the comparisons and to answer such questions the analyses will include exploratory descriptions of information related to each variable in the model, linear regression for a simplified model, structural equations to estimate path coefficients in the complete model, and a series of sub-studies examine in depth some patterns of relationships in the data. Finally, based on these analyses a series of reports are palnned. Currently a set of technical reports are being written on the creation of the data consturction instruments, the indicies for each variable, and the raw data that has been collected. Funds in this proposal would make it possible to report on the cross-sectional and longitudinal findings and our answers to the set of questions about the "Mathematics in Context" (National Center for Research in Mathematical Sciences Education & Freudenthal Institute, 1997-98).