David M. Bressoud February, 2008
This column was started three years ago to promote the CUPM Curriculum Guide 2004 and to help make people aware of the accompanying Illustrative Resources. The latter is a web-based compendium of resources chosen to help those seeking to improve undergraduate mathematics education whether through assessment, the planning of individual courses, the development of interdisciplinary programs, the use of technology, advising, faculty support, or curriculum development. Lots of people are doing lots of interesting things, and many of them can be found within the Illustrative Resources.
These web pages have just been updated , and I encourage everyone to browse through them. There are ten web pages of descriptions of papers, projects, and programs, together with links. These pages are organized according to the recommendations in the Curriculum Guide. I list them together with a hint of the riches to be found in each.
The MAA is considering ways of keeping the Illustrative Resources current and valuable, but one of the most important consists of your suggestions. If you know of something we are missing, please go to the website www.maa.org/cupm/cupm_ir_submit.cfm and let us know what it is.
I.1. Understanding our students
This includes assessment resources such as the project reports produced by MAA’s committee Supporting Assessment of Undergraduate Mathematics. There are also examples of placement tests and discussion of their effectiveness as in the Rueda and Sokolowski paper Mathematics Placement Test: Helping Students Succeed. There are also resources for advising and suggestions from different departments on what information needs to be disseminated to potential majors.
I.2. Developing thinking and communication skills
There are a lot of resources here that discuss how to get students to read the textbook, and how to help them learn how to read a textbook. There are many suggestions of writing assignments, and a lot of discussion of how to assess student writing in math classes. There is information on Inquiry-Based Learning, and links to many Java applets designed to help students understand formal logic.
I.3. Communicating the breadth of mathematics
Some of the newest contributions in this section deal with Mathematics and Art and with Mathematics and Music, and there are many websites devoted to these combinations. The connections between mathematics and art are especially helpful in communicating some of the fundamental concepts of geometry, a field that too often is short-changed in the undergraduate curriculum.
I.4. Promoting interdisciplinarity
From image processing to mathematical biology to the mathematics of geology to Integrated Physics and Calculus or Patterns in Poetry and Mathematics, there is a wide variety of interdisciplinary programs, courses, and projects that are listed on this page.
I.5. Use of Technology
This page provides links to many websites filled with java applets, mathematical software, and technology based projects. I mention just five of them: Alexander Bogomolny’s Interactive Mathematics Miscellany and Puzzles, Manipula Math with JAVA, MathTools, The New Mathwright Library and Café, and GeoGebra. The last of these is free dynamic mathematics software for exploring questions in geometry, algebra, and calculus.
I.6. Support for Faculty
This page includes links to reports on the importance of supporting faculty engaged in improving undergraduate education, including the MAA report Guidelines for Programs and Departments in Undergraduate Mathematical Sciences. There are links to information on Teaching and Learning Centers and links to many professional development opportunities, including the MAA’s own PREP workshops.
II.A. General Education Courses
This page includes syllabi, descriptions of different types of courses, and suggestions for textbooks. There are also links to research on the effectiveness of different types of general education courses.
II.B. Partner Disciplines and Prospective Teachers
Among the many resources on this page are links to the results of the MSRI series of workshops on Critical Issues in Education, including the 2007 workshop on Teaching Teachers Mathematics. There is a link to the website of Center for the Study of the Mathematics Curriculum, an NSF-sponsored consortium of universities that studies the K-12 mathematics curriculum as it is practiced across the United States and seeks to explain “what is important, what is expected, how it is organized and sequenced, how it is taught, and what students learn.” This piece of the Illustrative Resources also lists many resources for teaching teachers through the use of video clips of actual classroom situations, both in the United States and from overseas. These have proven to be very valuable in training prospective teachers and helping in-service teachers recognize what is happening and what could be happening in their classrooms.
II.C. Math Majors
This page includes examples of departments that have been successful in recruiting math majors as well as a discussion of why they are successful. One useful link is to the collection of papers that came from a contributed paper session on Innovative Mathematics Majors in Small/Medium Departments. There are links to resources to help with the transition to proof needed for higher level math courses, and recommendations for and links to examples of a wide variety of capstone courses and programs, including tips for evaluating senior presentations. There also is material on advising and encouraging students to become mathematics majors.
II.D. Preparing for Post-Graduation
This last page looks at specific student audiences: those preparing to teach high school mathematics, those preparing for the workforce, and those preparing for graduate school. There are links to career information, to information on internships and summer programs, and to information on professional master’s programs, as well as tips on what students need to know and when.
Purchase a hard copy of the CUPM Curriculum Guide 2004 or the Curriculum Foundations Project: Voices of the Partner Disciplines.
Find links to course-specific software resources in the CUPM Illustrative Resources.
Find other Launchings columns.