POWRE: School-Work Connections: Generalizing Mathematics Learning

学校教学的一个中心目标是促进知识的泛化或将知识从最初的学习环境转移到新的环境中。最近，对于学校数学是否足以让学生为未来的工作场所做好准备的担忧，给学习转移带来了新的相关性。然而，近年来，由于发现转移很难在实验室中进行工程设计，转移研究一直举步维艰。此外，文献中的两个争论表明迁移的建构存在理论问题。通过以下研究和教育活动，本研究扩展了首席调查员已经开始的工作，即建立一种新的迁移理论方法：1)确定一个特定的数学概念(即，斜率)如何在两个工作或日常环境中使用；2)与高中教师合作，设计一个单元教学，将先前研究和人种学的建议付诸实施；3)确定学生在学校和非学校环境中构建的相似性(或常识)关系的类型；以及4)开发可以纳入首席调查员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。第一项研究涉及对数学概念在工作或日常环境中的使用进行人种学分析。第二项研究包括学生在访谈中解决问题的录像数据和学生在高中课堂上学习坡度概念的视频数据。这些分析在很大程度上是定性的，基于对录像带进行细粒度分析的方法学技术，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.