The mathematics "explorations" at MHC are 100-level courses that serve a number of purposes. First, and foremost, they are intended to convey the beauty, power, and utility of an area of mathematics. They are also intended to develop students' skills in mathematical communication and to dispel myths about mathematics, myths such as that

1. mathematics allows little creativity,

2.mathematics is a collection of rules to be memorized, and that

3.mathematics has little to do with human concerns.

The geometry exploration should draw each student into an exploration of visual thinking and the role of mathematical systems, the nature of space and mathematics as a system of knowledge. Although many students electing the geometry exploration course will not think of themselves as particularly 'mathematical people,' it is the hope of the mathematics department that their experience in this course will lead them to become more knowledgeable, confident, and appreciative mathematics consumers for both themselves, their communities, and on behalf of their children. We in mathematics also hope to develop some excitement about (as well as skill in) mathematics among the students who will be elementary and secondary school teachers. Finally, we also hope that some students in the seminar will become enthusiastic enough about mathematics to choose a math major or minor.

In the geometry exploration offered in Spring Term 2008, students will use dynamic geometry software that makes mathematical exploration easy. Students will be given, or will choose, or will devise a mathematical situation to investigate. As part of their investigations, they will create what is called a sketch in Geometer's Sketchpad terminology. Embedded in the sketch are mathematical constraints on the investigation at hand, but the sketch has the property that some geometric objects in it, like a line segment or a point, can be dragged around in the sketch plane, so that the appearance of the sketch changes but the underlying relationships remain. In this way, we see many specific instances of a general situation, and we can discover (if we're lucky!) something that is true about the situation in general.