In Resnick's 1994 book, Turtles, Termites, and Traffic Jams - Explorations in Massively Parallel Microworlds, he writes about StarLogo as a tool for exploring ways of thinking about things. In the chapter on New Turtle Geometry he discusses "two major reasons for developing new ways of doing geometry."
Heck, it's not just geometry to which these lines apply!
First, different people find different approaches more accessible. … Too often, schools give special status to particular ways of thinking about mathematical and scientific ideas. By privileging certain types of thinking, they exclude types of thinkers.
Second, everyone can benefit from learning multiple ways of thinking about things. Understanding something in just one way is a rather fragile kind of understanding. Marvin Minsky has said that you need to understand something at least two different ways in order to really understand it. Each way of thinking about something strengthens and deepens each of the other ways of thinking about it. Understanding something in several different ways produces an overall understanding that is richer and of a different nature than any one way of understanding.