Teaching Introductory Combinatorics by Guided Group Discovery

数学科学（21）本项目为组合学第一门本科课程提供教学材料，大量学生将学习所涵盖的大部分材料。这些材料是基于一系列的问题，旨在引导学生理解组合数学的过程，将这些过程抽象为一般原则，并应用一般原则。虽然有一些文本材料提供定义，解释共同的主题，并帮助学生反思他们所学的知识，但绝大多数知识内容都在问题本身。咨询委员会就主题的选择提供建议，对所开发的材料进行评论，在他们自己的机构中测试或安排对材料的测试，并帮助向整个社区介绍这些材料。所编写的材料正由一家商业出版商作为一本薄书出版，并在出版商的网站上提供补充材料。还有一个教师版本的书，包含完整的解决方案的问题，以及协议使用的材料。协议包括使用小组工作的方式来增强学生对材料的体验。小组活动包括确保提出的解决方案是可信的和可理解的，帮助学生决定他们对重新提交的选定问题的重写是否对教师的评论有反应，并对教师选择的问题给予小组成员反馈，只是“抽查”。该项目最后举办了一个讲习班，目的是为渴望在自己的机构中使用这些材料的教员提供基础。

Mathematical Sciences (21)This project is producing materials for teaching a first undergraduate course in combinatorics where a large number of students learn most of the material covered. The materials are based on a sequence of problems designed to lead students to understand the processes of combinatorial mathematics, abstract these processes to general principles, and apply the general principles. While there is some textual material to provide definitions, explain common themes, and help students reflect on what they learn, the vast majority of the intellectual content is in the problems themselves. An Advisory Board is advising on the selection of topics, critiquing the materials developed, testing or arranging for a test of the materials at their own institutions, and helping introduce the materials to the community at large.The materials developed are being published as a slim book by a commercial publisher, with supplementary material on the publisher's website. There is also an instructor's version of the book that contains complete solutions to the problems as well as protocols for using the materials. The protocols include ways of using group work to enhance students' experiences with the materials. Group activities include making sure that the solutions proposed are believable and understandable, assisting students in deciding whether their rewrites of selected problems for resubmission are responsive to instructor comments, and giving group members feedback on problems the instructor chooses only to "spot check."The project concludes with a workshop designed to provide a base of instructors who are both eager and well-equipped to use the materials in their own institutions.