MATtours of discrete mathematics

History and philosophy of MATtours

This site contains a set of materials supporting courses in discrete mathematics, focusing on graph theory, combinatorics, and recursion. It was developed by ISEM, the Institute for Studies in Educational Mathematics, for SciMath Minnesota. For information about obtaining copies of the site, contact Larry Copes at ISEM and Augsburg College.

ISEM, the Institute for Studies in Educational Mathematics, is a non-profit research organization founded in 1980 to help its members explore ways of encouraging human development through the study of mathematics. It has served as a vehicle for acquiring grant moneys for members not associated with particular academic institutions or when consortia of institutions are engaged in a project.

The MATtours project began in 1996 when some of us developed a demonstration site on ellipses. In 1998, SciMath Minnesota hired us, through ISEM, for a longer-term project to develop materials in discrete mathematics. We continue to seek funding for tours of calculus.

Goals of SciMath Minnesota include preparing middle- and high-school teachers to teach to new state graduation standards in mathematics. The biggest concerns of teachers seem to be:

the content of discrete mathematics; and
the inquiry skills students are supposed to acquire.

To address those concerns, these tours deliver a discrete mathematics curriculum in an inquiry-based, hypertext format.

We intend that these materials support courses for teachers but not replace them. Instructors are still needed to guide learners through the tours, to supplement these pages with activities and other written materials, to provide the delicate balance between support and challenge, and to assess learning. It is up to these course instructors to determine how to promote communication while touring and how to use the journaling feature of the tours.

MATtours invite tourists to engage in the processes of doing mathematics. As users construct mathematical concepts on the forefront of their own knowledge, they are using methods that professional mathematicians use to create mathematics on the frontiers of the community's knowledge. For this reason we've tried to take a non-authoritative attitude to the material. That is, we try not to act as if we know all of the answers and are playing games to get users to see them our way. Instead, we put travelers in the position of those functioning without odd-numbered answers in the back of the book.

We know from our own teaching experiences that inexperienced investigators will need support in becoming comfortable with less familiar creative aspects of mathematics. We also know from experience that the approach can bring about much deeper understanding of the ideas and new insights into the nature of knowledge, mathematics, and learning.