CONTEXTUAL-EMPIRICAL RESEARCH: Longitudinal Investigation of the Effect of Curriculum on Algebra Learning from the Middle Grades through High School

本研究计划将对参加不同中学数学课程的学生进行纵向研究。这项拟议中的研究将分析密尔沃基10所公立高中的4000多名学生的数据。这些学生将在高中四年的时间里被跟踪，直到他们完成12年级的学业。该研究有两个研究问题：1)连接数学项目（CMP）和非CMP学生如何在各种任务中表现出广泛的数学思维和推理能力，重点是高中代数？2) CMP和非CMP学生在高中所接受的课程和教学与他们在初中所接受的课程和教学有什么异同？这项研究将由特拉华大学和马奎特大学的一个团队进行。准实验研究设计将用于比较具有CMP背景的学生与具有更传统数学方法的学生。项目设计包括使用多个学生成绩的措施以及观察的课堂实践。数据将使用多变量统计进行分析，包括HLM和嵌套数据的ANCOVA。最初的样本量将是近1000名在10所高中中的一所中学学习CMP的学生，以及3000多名在中学学习其他数学课程的学生。由于学生将被跟踪到高中四年，预计在12年级之前学习数学的人数将至少下降25%。该研究的结果将报告国家科学基金会支持的中学数学项目对学生在八年级毕业后四年进入高中的代数概念知识的长期影响。结果将在会议和期刊文章传播。该项目通过分析数学课程的长期影响的有效性，解决了一个深深植根于数学教育的具有强制性国家重要性的研究问题。

The proposed research project will conduct a longitudinal study of students who took different middle school mathematics curricula. The proposed study will analyze data from over 4,000 students enrolled in the 10 Milwaukee public high schools. The students will be tracked over four years of high school through their completion of 12th grade. The study has two research questions: 1) How do Connected Mathematics Program (CMP) and non-CMP students perform on various tasks measuring a broad spectrum of mathematical thinking and reasoning, with a focus on algebra in high school? 2) What are the similarities and differences between the curriculum and instruction that CMP and non-CMP students are receiving in high school and the curriculum and instruction they received in middle school? The research will be conducted by a team at the University of Delaware and Marquette University. A quasi-experimental research design will be used to compare students with a CMP background to students with a more traditional mathematics approach. The project design includes using multiple measures for student achievement along with observations of classroom practices. Data will be analyzed using multivariate statistics including HLM and ANCOVA with nested data. The initial sample size will be nearly 1000 students who took CMP in middle schools who enrolled in one of the 10 high schools and over 3,000 students to took some other mathematics curriculum in middle school. Since students will be followed through their four years in high school, it is anticipated that the group who will be taking mathematics through 12th grade will decline by at least 25%. Results from the research will report on the longer term impact of a NSF supported middle school mathematics program on students' algebraic conceptual knowledge into high school up to four years after leaving 8th grade. Findings will be disseminated at conferences and through journal articles. The project addresses a research problem of compelling national importance deeply rooted in mathematics education by analyzing the efficacy of the long range impact of a mathematics program.