David Hewitt Video Reflection

David Hewitt used a method of instruction that involved 'enacting', which is to actively use movement and gestures to get a point across. He used tapping on the board and counting the taps to teach counting, drew a number line and the concept of 'jumps' from point to point on the number line to simulate addition and subtraction. While I was quick to judge that this method of instruction trivializes the content and doesn't quite encapsulate the deep foundational roots of the mathematics being taught, I quickly realized the concepts he embeds in his pedagogy. For example, the 'jumps' along the number line quickly makes sense of the concept of a negative number. A negative number cannot be described as a quantity; one cannot 'show' a negative number like one can with a positive number (you can't 'show' -2 apples for example). In particular, the concept of a negative number is that of an OPERATION. One cannot have a negative number without TAKING AWAY something and the action of taking away is the key. This pedagogy would make further explorations in extending 'addition and subtraction' to more abstract abelian binary operations in ring theory much more intuitive. The one critique of his pedagogy is that while he was very engaging he didn't really pose 'real' problems, which one can hope to find in the realm of applied mathematics (like the math behind earthquakes, celestial systems, etc.)