A geometric construction or a series of them may be thought of a function. Here is an example: Construct the three medians of a triangle. Reflect the point of concurrence of the medians over each of the sides of the triangle. These operations define a new triangle. Taken together these operations are a function from the domain of point triples in the plane to the range of point triples in the plane. This collection of applets allows for the exploration of such functions on shapes.
This collection of tasks is part of a series entitled "Making and Exploring Conjectures - Expanding Teachers' and Students' Mathematical 'Habits of Mind'". They are designed primarily to help teachers think more deeply about aspects of mathematics that they know and are expected to teach.
Along with his colleagues and students, Judah L. Schwartz has been writing prize-winning educational software for more than thirty years. For several decades he taught physics at the Massachusetts Institute of Technology and taught and did research on mathematics and science education at the Harvard Graduate School of Education. After retiring from MIT and Harvard, he taught pre-service and in-service teachers of mathematics for nine years at Tufts University.
Professor Schwartz and colleagues are available to conduct small scale workshops to help people think more creatively about the mathematics they know. Interested schools, school systems and organizations can contact him at math.habits.of.mind@gmail.com