POWRE: School-Work Connections: Generalizing Mathematics Learning

学校教学的一个中心目标是促进知识的推广或转移，使其超越最初的学习环境，适应新的环境。 最近关注学校数学是否足以让学生为明天的工作场所做好准备，这给了学习的转移新的相关性。 然而，近年来，由于发现转移很难在实验室中进行，转移研究陷入了困境。 此外，在文献中的两个争议表明理论问题的建设转移。 这里提出的研究扩展了主要研究者已经开始的工作，通过以下研究和教育活动，建立一个新的理论方法来转移：1）确定一个特定的数学概念如何（即斜坡）用于拖曳工作或日常设置; 2）与高中教师合作，设计一个单元教学，实施先前研究和民族志的建议; 3）识别学生在学校和非学校环境中构建的相似性（或一般知识）关系的类型;以及4）制定可纳入主要研究者为未来教师教授的数学课程的教学建议。 将采用几种分析方法。 第一项研究涉及在工作或日常环境中使用数学概念的民族志分析。 第二项研究涉及学生解决问题的访谈和学生在高中课堂上学习有关斜坡的概念的录像带数据。 这些分析主要是定性的，基于对录像带进行细粒度分析的方法技术，并将遵循扎根理论发展中使用的解释技术。

A central aim of school instruction is to facilitate the generalization or transfer of knowledge beyond the initial learning context to new circumstances. Recent concerns over the adequacy of school mathematics to prepare students for the workplaces of tomorrow give the transfer of learning new relevancy. However, transfer research has floundered in recent years due to findings that transfer is difficult to engineer in the laboratory. Furthermore two controversies in the literature indicate theoretical problems with the construct of transfer. The research study proposed here extends the work that the principal investigator has already begun in building a new theoretical approach to transfer, through the following research and educational activities: 1) identifying how a particular mathematical concept (namely, slope) is used in tow work or everyday settings; 2) working with a high school teacher to design a unit instruction that implements suggestions from prior research and from the ethnographies; 3) identifying the types of relations of similarity (or general knowledge) that students construct across school and non-school settings; and 4) developing instructional recommendations that can be incorporated in the mathematics courses that the principal investigator teaches for prospective teachers. Several methods of analysis will be employed. The first study involves ethnographic analysis of the use of mathematical concepts in work or everyday settings. The second study involves the video-taped data of students solving problems in interviews and of students learning about slope concepts in high school classrooms. The analyses are largely qualitative, based on methodological techniques for fine-grained analyses of videotapes and will follow interpretive techniques used in the development of grounded theory.