As Geometry is Lost - What Connections are Lost? What Reasoning is Lost? What Students are Lost? Does it Matter?

In a North American curriculum preoccupied with getting to calculus, we witness an erosion of geometric content and practice in high school. What remains is often detached from "making sense of the world", and from reasoning (beyond axiomatic work in University). We see the essential role of geometry in science, engineering, computer graphics and in solving core problems in applications put aside when revising math curriculum. A second feature is that most graduates with mathematics degrees are not aware of these rich connections for geometry.

We will present some samples of: what we know about early childhood geometry.; and then of the critical role of geometry and geometric reasoning in work in multiple fields outside of mathematics. With a perspective from "modern geometry", we note the critical role of transformations, symmetries and invariance in many fields, including mathematics beyond geometry.

With these bookends of school mathematics in mind, we consider some key issues in schools, such as which students are lost when the bridge of geometry is not there to carry them through (caught in endless algebra) and possible connections other subjects. We also consider the loss within these other disciplines. We will present some sample investigations and reasoning which can be supported by a broader more inclusive set of practices and which pays attention to geometric features and reasoning in various contexts. In particular, we illustrate the use of dynamic geometry investigations, hands on investigations and reflections, and making connections to deeper parts of the rest of mathematics and science.