Emergent mathematical worlds from teacher knowing in whole-class discourse: using an enactivist lens on the teaching of exponential functions

This paper reports findings related to the pursuit of describing a lived knowing for teaching mathematics. Specifically, we used an enactivist perspective to describe the knowing exhibited by three experienced high school teachers in their instructional actions while leading whole-class instruction on the topic of the equations of exponential functions. From classroom observations, we constructed maps of the emergent mathematical worlds of ideas and collective mathematical activity. Three major categories of ideas emerged in all three teachers' classrooms relating to the recursive multiplicative nature of exponential functions, the role of the independent variable, and the definition of exponential. Findings of this study suggest attending to teacher knowing for mathematical whole-class instruction must include describing the role of the mathematical activity in the emergence of the ascribed mathematical ideas. When teachers facilitated the collective mathematical activity as the means by which the mathematical ideas and justifications emerge, the mathematical worlds were diverse and complex, and connections among ideas were more robust in their comprehensibility.