Representations in mathmatical teaching

The idea of both inner and external representations in delivering mathematics teaching practice echoes with my own beliefs about math teaching. When we teaching math to children, it is easier for them to absorb the concept is to connect the abstract math signal concept with other external representations, include the external representation related with social life, or the other scientific phenomena. Through these activities, students can create the cognitive connection between the abstracted mathematics concept, like the signal formulas, with the phenomenon which they could see, touch, and feel.  

The connections between inner and external representations are important to recall abstract concepts and apply them to solve problems. For example, if the students connect the rectangle with their own bedroom setting, link the width and length with the room measurements, they are easier to understand and recall the concept of the area of the rectangle. Later, if the students can connect rectangle with other staff in their life, such as books, windows, etc. The more external representations they could collect and connect with the rectangle concept, the easier for them to recall the inner representations of the rectangle properties. Similarly, the more inner representations of the rectangle properties the students could learn, the more they could apply on external representations of real life, such as do a design to rearrange their rooms.