Mathematical Cognition and Affect During Non-Routine Problem Solving

非常规问题解决过程中的数学认知和影响

• 批准号: 0203225
• 负责人: Shandy Hauk
• 金额: $ 5万
• 依托单位: University of Northern Colorado
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2002
• 资助国家: 美国
• 起止时间: 2002-01-15 至 2003-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0203225&HistoricalAwards=false
• 关键词: Mathematical; Cognition; Affect; During; Non

The objective of the proposed work is two?fold. At the level of the individual the objective is to advance understanding of the complexities of cognition and affect during problem?solving. The other objective is at the level of community: cognition?and?affect interaction in the context of collegiate mathematics classroom culture. In pursuing these objectives, the relationships among affect and cognition during non?routine problem solving should prove particularly important.The Proposal incorporates one of the most effective methods developed to date for research in collegiate mathematics education: research working groups involving graduate students as well as junior and senior researchers. The research methodology ensured by the make?up of the working groups is both broad: quantitative methods (e.g. survey), experimental methods (e.g. teaching experiment) and deep: qualitative methods (e.g. interview), experiential methods (e.g. case study).Investigating the relationships and causalities among what problem?solvers think of their feelings, attitudes, beliefs, and selves in mathematics and how those aspects of affect interact with cognitive efforts during problem solving would, of course, take more than the next year. What this Proposal provides for is the organizing of research working?groups around the objectives given above. One result of this cooperation will be the design, implementation, and completion of at least one pilot study. A second result will be the creation of a research design for continued work on both individual and community cognition?and?affect interaction in the various contexts of mathematics learning.At the individual?level, it is well known that significantly reducing the anxiety of a mathematically anxious student is challenging (at best, and often fails). What does show promise, however, is meta?affective self?control. Rather than insisting a student no longer feel anxious, an individuallevel pilot study would investigate ways to encourage an empowering meta?affect. Most work in this area has been at the school level. The proposed pilot?study would be at the collegiate level. A pilot study aimed at the community?level objective could offer a way to revitalize curricular reforms. Many curricular reforms in mathematics lose momentum because their "one?size fits all" approach fails to influence enough instructors. A community?level pilot study could investigate for which cognition?and?affect profiles an existing reform appears to be effective and then work through teaching experimentation and research to create several "sizes," i.e. tailor curricula for classroom and/or distance?learning formats based on the goals of the original reform efforts.The proposed avenue of research addresses one of the large issues confronting higher education today: distance learning. The format of an internet education site has, implicitly, assumptions about cognition?and?affect; i.e. a cognition?and?affect profile can be compiled from the forms and processes at a website. In many distance learning settings, the interaction of teachers and students does not disappear, but rather is made more complex by the mediation of the website (or other vehicle). This is especially so as distance learning in this country is shifting from a concern mainly with procedural knowledge to the teaching of conceptual knowledge (for example, in non?routine problem solving or theorem proving). As an area for research and development, this three?way relationship between students, teachers, and a mediating website has been little studied (in mathematics education) and is very promising. The proposed work would contribute to the foundation for future investigations of this topic.

拟议工作的目标有两个方面。在个体层面上，目标是在解决问题过程中促进对认知和情感复杂性的理解。另一个目标是在社区层面：认知和？大学数学课堂文化背景下的影响互动。在追求这些目标的过程中，情感和认知在非？解决日常问题应该被证明是特别重要的。该提案结合了迄今为止大学数学教育研究中最有效的方法之一：包括研究生以及初级和高级研究人员在内的研究工作组。研究方法的保证是什么？Up的工作组既有广泛的：定量方法（如调查），实验方法（如教学实验），也有深入的：定性方法（如访谈），经验方法（如案例研究）。调查哪些问题之间的关系和因果关系？解题者思考他们在数学中的感受、态度、信念和自我，以及在解题过程中这些方面的影响如何与认知努力相互作用，当然，这将需要一年以上的时间。该提案规定的是组织研究工作？围绕上述目标分组。这一合作的一个成果将是设计、实施和完成至少一项试点研究。第二个结果将是创建一个研究设计，以继续研究个人和社区认知？影响数学学习中各种情境下的互动。就个人而言？水平，众所周知，显著减少一个数学焦虑的学生的焦虑是具有挑战性的（充其量，经常失败）。然而，什么才是有希望的呢？控制情感自我?。与其坚持让学生不再感到焦虑，一项个人层面的试点研究将探讨鼓励增强元影响的方法。这一领域的大部分工作都是在学校层面进行的。拟议中的飞行员？学习将在大学水平。一项针对社区的试点研究？水平目标可以为课程改革的振兴提供一条途径。许多数学课程改革因为“一？“一刀切”的方法无法影响足够多的教师。一个社区?水平的初步研究可以探讨哪些认知？影响档案，现有的改革似乎是有效的，然后通过教学实验和研究来创建几个“大小”，即为课堂和/或远程定制课程？学习形式基于原有目标的改革努力。提出的研究途径解决了当今高等教育面临的一个大问题：远程学习。互联网教育网站的格式隐含着对认知和影响的假设；即认知？和？可以从网站上的表格和流程编译影响配置文件。在许多远程学习环境中，教师和学生的互动并没有消失，而是通过网站（或其他工具）的中介变得更加复杂。尤其是在这个国家，远程教育正从主要关注程序性知识转向概念性知识的教授(例如，在非？解决常规问题或证明定理)。作为研发领域，这三个？学生、教师和中介网站之间的关系研究很少（在数学教育中），是很有前途的。建议的工作将有助于为今后研究这一专题奠定基础。