## Projects

*CoMInDS (College Mathematics Instructor Development Source)*

www.maa.org/cominds

Funded by the National Science Foundation, DUE project #1432381

Graduate students play substantial roles in undergraduates’ opportunities to learn mathematics. For graduate students planning on employment in academia, the teaching they do in graduate school serves as professional preparation for future pedagogical responsibilities. Over the past several decades increased attention has been paid to the professional development of graduate students for their teaching-related responsibilities. The primary goal of this project is to promote dialogue and collaboration among practitioners, researchers, and others involved in the professional development of mathematics graduate students and to create the infrastructure to support the creation and distribution of professional development materials. Project activities include the development of web-accessible repositories of professional development materials and research as well as workshops for faculty wishing to start or enhance programs in their departments.

**Mathematics Capstone Course Resources: Preparing Secondary School Mathematics Teachers**

Funded by the National Science Foundation, IUSE project #1504551

The preparation of the highest quality teachers and learners of mathematics is a national imperative. As undergraduates, future secondary school teachers take many courses from professors with advanced degrees in mathematics. However, university faculty members often do not possess deep knowledge of the kinds of teaching demands faced by new school teachers. There is a notable need for instructional materials that deliberately and explicitly connect undergraduate mathematics content to the knowledge needed for teaching secondary mathematics. This project will leverage the existence of Capstone Courses for future teachers found in many universities, which bring together ideas from across the college mathematics experience, as well as recent developments in policy and school accountability, to create and refine activities for use by university faculty in mathematics pre-service teachers Capstone Courses. This project will develop Capstone Course modules which provide access to advanced mathematical ideas along with opportunities to unpack mathematics in ways helpful for teaching it in middle and high school settings. The proof-of-concept work of the project has two parts. One is the development and refinement of two full modules, each designed to take about a week of instructional time in a Capstone Course. The second aspect is refining the module development process itself.

*Videocases for Novice College Mathematics Instructor Professional Development*

Funded by the Dept. of Ed., Fund for the Improvement of Post-Secondary Education (FIPSE)

This project involves the development of authentic, video-based cases for use in professional development activities and programs for mathematics graduate students and novice faculty instructors. The associated research program includes examinations of roles of videocases and instructional materials in helping college mathematics instructors enrich their knowledge of student thinking and ability to use that knowledge in instructional decisions. Click here for a preview of the web portal for the project.

*Maine Physical Sciences Partnership*

Funded by the National Science Foundation, Mathematics-Sciences Partnership program

This partnership brings together nearly 50 rural Maine schools, the University of Maine, three Maine non-profits with expertise in science education, and science and technology leaders at the Maine Department of Education to target the teaching and learning of physical sciences in grades 6-9 and the preparation of science teachers at the University of Maine. Activities include collaborative selection, refinement, and implementation of a coherent, research-supported curricula and ongoing intensive professional development for school teachers. At the university level, activities include refinement of university-level instruction through reform, a Faculty Fellows program to support implementation of active learning and other research-supported instructional practices, enhanced professional development for graduate students and implementation of a Learning Assistant program. For more information, see Maine PSP.

*Mathematicians’ Knowledge for Teaching*

Funded by The Spencer Foundation

As a result of research on elementary school mathematics teachers, there is now broader recognition that effective teaching relies on knowledge of more than just mathematical facts and ideas. Kinds of knowledge that are key to effective teaching include (a) how students think about particular mathematical ideas and (b) mathematics that is “specialized” for the work of teaching (e.g., evaluating validity of student-generated solutions). These developments have prompted and enabled creation of courses and materials to enhance teachers’ “mathematical knowledge for teaching.” Unfortunately, the same cannot be said of developments in *college-level* mathematics. Although there have been advances (primarily focused on graduate student teaching assistants), similar changes in views of what knowledge is used in and necessary for teaching have not occurred. Reasons are likely numerous and complex but the case of elementary mathematics demonstrated that research-driven change is possible. However, a key ingredient is missing: We lack an *existence proof* that experienced, expert teachers of *college mathematics* possess and make use of knowledge of student thinking and teaching-specific mathematics. The goal of this project is to provide that missing ingredient and raise awareness in the college mathematics community that experienced instructors have a wealth of knowledge (of various kinds) that they use in teaching. This will be accomplished by gathering teaching-related task-based interview data as well as video data of the teaching practices of mathematicians from around the country who have been recognized for their expertise in teaching. Armed with such an existence proof, the college mathematics education community may be better able to offer, and have supported, programs that help novice instructors develop such knowledge, thus enriching learning opportunities they provide for students.

**On The Job Learning: Graduate Student Instructors’ Development of Knowledge for Teaching**

Over the past two decades education researchers have demonstrated that various types of knowledge influence teachers’ instructional practices. Pedagogical content knowledge (PCK) and other teaching-specific types of knowledge have been productive foci for research. Researchers have documented correlations between measures of these types of knowledge and teachers’ practices and/or their students’ achievement. It is apparent that teachers have opportunities to develop such knowledge while engaged in the work of teaching, however, to date, very little research has captured the actual genesis of such knowledge. Knowing more about how teachers develop such knowledge on-the-job is especially important when the teachers are college-level instructors who typically receive little to no teaching-focused professional development during their careers. In this project, we analyze data from interviews with novice college physics instructors as they examined students’ written work. In the course of the discussions, some instructors built new teaching-related knowledge and some did not. We examine the factors that enabled and/or inhibited the development of the new knowledge.