Аннотация: Mason and Spence’s (1999) work demonstrate a detailed view into the concept of knowing. Although they highlight the importance of not-knowing as a first step, it is a topic that is not well researched. This study aims at expanding that research, by analyzing not-knowing expressions from teacher to student and possible connections to be found. During a course of geometric reasoning student teachers were asked to reason with a tangram while simultaneously recording their expressions of not-knowing and reflecting on it periodically. Student teachers were then tasked to teach this lesson to their students, who would also reflect and express their forms of not-knowing. Findings presented no real link between teacher-student expressions of not-knowing, but two major conclusions were made. Individuals altogether struggle conveying their not-knowing clearly and when they did express it, these expressions leaned heavily on not-knowing-that and not-knowing-how forms. A discussion follows to interpret said findings. A conclusion is made detailing key points in the study and what comes next for the concept of not-knowing.

Аннотация: Education researchers often cite a statement from Anatole France: "An education isn't how much you have committed to memory, or even how much you know. It's being able to differentiate between what you know and what you don't." In this paper, we show how this statement can be transformed into an exact theorem.