Generative Aspects of Mathematical Thinking: Formulating Conjectures and Posing Problems

这个研究项目将仔细检查和开发一个认知 数学生成的某些方面的描述和分析 思考-提出问题，并以 需要解决的问题-因为这些过程被人们使用， 不同程度的数学经验和成熟度，从 六年级学生到中学数学教师。 小心 将注意个体之间和内部的差异， 不同的受试者人群，以及对频率的影响 和/或使用支持机制的过程的有效性， 如使用计算机软件支持或配对解决问题。 的 从观察性研究中获得的对这些过程的理解 将在第三年开始运作， 教学研究中的一个项目，其中一套教学 根据描述性分析， 这些生成过程的发展，被用于中学 学生 拟议的研究是针对重要的扩展， 与数学思想和问题有关的现存科学发现 解决 此外，这里提出的工作与目前的努力有关 改革学前数学教学，使其更 为学生提供智力刺激， 教学时间给予学生的教学和 调查 因此，建议的研究计划的结果 这不仅是因为他们可以为世界做出贡献， 不断增长的数学认知科学知识基础， 解决问题的能力，同时也是他们对大学预科的实际意义 数学教育

This research project will carefully examine and develop a cognitive description and analysis of certain generative aspects of mathematical thinking - posing problems and formulating conjectures in the form of problems to be solved - as these processes are used by persons at varying levels of mathematical experience and maturity, ranging from sixth-grade students to secondary school mathematics teachers. Careful attention will be paid to individual differences among and within the various subject populations and also to the effects on the frequency and/or effectiveness of use of the processes of support mechanisms, such as the use of computer software support or paired problem solving. The understanding of these processes obtained from observational studies during the first two years will be operationalized in the third year of the project in an instructional study in which a set of instructional activities, based on the descriptive analysis and devised to promote the development of these generative processes, is used with middle school students. The proposed research is directed at important extensions of extant scientific findings related to mathematical thinking and problem solving. Moreover, the work proposed here is related to current efforts to reform precollege mathematics instruction to make it more intellectually stimulating for students by increasing the amount of instructional time given over the student conjecturing and investigation. Thus, the results of the proposed research program should be significant not only for the contribution they can make to the growing scientific knowledge base concerning mathematical cognition and problem solving but also for their practical relevance for precollege mathematics education.