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 [1], 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.
[1] With thanks to Susanna Epp for her much appreciated work in updating the Illustrative Resources.
Access pdf files of the CUPM Curriculum Guide 2004 and the Curriculum Foundations Project: Voices of the Partner Disciplines.
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.
David Bressoud
is DeWitt Wallace Professor of Mathematics at Macalester College in St. Paul,
Minnesota, and president-elect of the MAA. You can reach him at bressoud@macalester.edu.
This column does not reflect an official position of the MAA.