The ring of conscious awareness

I start by making the statement that what you read is not what I wrote. Or, in a spoken context, what you hear is not what I said. If this makes no sense to you now, my hope is that it will by the end of this paper.

I have been influenced throughout my time in mathematics education by the work of Caleb Gattegno. He made extensive use of the word awareness whereas much educational literature from a psychological perspective talks about memory (for example, Justicia-Galiano, Martín-Puga, Linares & Pelegrina, 2017). This has, amongst other things, led me to consider the relationship between the two and resulted in a model I call the Ring of Conscious Awareness. In this paper I gradually introduce this model and how it can offer an image for four different ways in which we learn. In doing so, I have tried to bring together several different ideas, and I am aware that in doing so I have restricted the detail which could be given to each of them. I will start by considering the way in which I will use the terms memory and awareness and build the model from there. [...]