for the learning of mathematics

an international journal of mathematics education

Dave Hewitt - Vol. 44 Num. 3 (2024)
 The ring of conscious awareness

36-41
 ABSTRACT:

Building on Caleb Gattegno’s work, I distinguish between awareness and memory as different ways in which we come to know things. The idea that there are things we know, or know how to do, which are at a conscious level, and other things which are at an unconscious level, is developed into a model which I call the Ring of Conscious Awareness (RCA). This model highlights the interaction between what we perceive from outside, through our senses, and what comes from within us. The model includes those parts of ourselves which maintains our past learning which we can now utilise without the need for conscious attention (inside the ring), and the awarenesses we have at a conscious level (within the ring itself), as we engage with what comes from our senses (originating from outside the ring). Through this model, I discuss four different ways in which we learn, and consider some implications for teaching and research.