Mathematical Connections unveiled within Selfies - By Axelle Faughn

This will be a short post as I only have one picture on the menu for you today. But it will hopefully convince the skeptic of the power of Selfies to build stronger understanding of the underlying structures of mathematics, as well as provide a rationale for their place in what educators label as "doing mathematics".

I collected the picture below during a middle school teacher workshop. The teacher who submitted it categorized it as an illustration of geometric translation. Indeed the equal distance between the vertical bars allows us to easily imagine how this could be the same bar and its subsequent images repeatedly translated by a horizontal vector of length the space between two adjacent bars.

Translation or Number Line?

However as we reviewed and discussed the various participants' representations that day, another teacher argued that the same picture could also illustrate the notion of number line and therefore be classified in the number sense category. Interestingly enough, the last workshop I lead in South Africa 2 weeks ago for a varied group of Math Club facilitators, provided the same opportunity for connecting number line and geometric translations with the picture of a slatted roof.

What I want to emphasize here, is that this is precisely the kind of situations that make Mathematical Selfies assignments so rich during discussion and sharing of ideas. The mathematics that one sees may not be the same as their neighbor, but opening such perception actually allows us to establish connections between concepts, connections that may not have been obvious to a single pair of eyes. Indeed, what is the number line but a unit translation to infinity? And would the teachers, facilitators, and students who discover this not be doing mathematics by bridging the various strands of study, unveiling connections, and creating new knowledge?