Teaching Introductory Combinatorics by Guided Group Discovery

数学科学（21）该项目正在制作组合学第一门本科课程的教学材料，其中大量学生学习所涵盖的大部分材料。这些材料基于一系列问题，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理，并应用一般原理。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到的，绝大多数的知识内容是在问题本身。一个咨询委员会正在就主题的选择提供咨询意见，对编写的材料提出批评，在自己的机构测试或安排测试材料，并帮助向整个社区介绍这些材料，编写的材料正由一家商业出版社出版成一本小书，出版社的网站上有补充材料。这本书还有一个教师版本，包含了问题的完整解决方案以及使用材料的协议。这些协议包括使用小组工作的方式，以提高学生的经验与材料。小组活动包括确保提出的解决方案是可信的和可理解的，帮助学生决定他们重新提交的选定问题的重写是否符合教师的意见，并对教师选择的问题给予小组成员反馈。“该项目最后举办了一个讲习班，旨在为那些渴望在自己的机构中使用这些材料并具备良好条件的教员提供基础。

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.