Elaborating reflective abstraction for instructional design in mathematics: Postulating a Second Type of Reflective Abstraction

The goal of our research program is to explicate the learning of mathematical concepts in ways that are useful for instructional design and to develop design principles based on those explications. I review one type of concept and our elaboration of reflective abstraction, coordination of actions (COA) that accounts for its construction. I then postulate a second type of concept and a second type of reflective abstraction that accounts for its construction, the abstraction of commonality (AOC).