Addressing the disconnect between radians and degrees in secondary school. Moore’s (2013) teaching experiment

The Plato’s protractor series draws on a teaching experiment by Kevin Moore (2013). This experiment aimed at addressing a perceived disconnect in secondary mathematics teaching between the understanding of degrees and radians. Degree based angle measure is taught at primary school and is based on understanding the geometric structure of angle and on connecting that structure to rotation. In secondary school, students are exposed to radians, which are introduced as intersected arc with the circle’s radius as the unit. This is seen as creating a disconnect, which is explained further in the next paragraph. In Moore’s (2013) study students are taught to quantify angle as a ratio of arc lengths and to see units such as radians and degrees as measuring the same underlying concept.  The six Plato’s protractor investigations build on the lessons in Moore’s experiment to challenge the Mathomat kids to see the opening in the angle concept they had developed earlier in the Explorer manual as openness, being a ratio of arc lengths. This leads to understanding of angle as one quantity that can be measured by different units such as radians and degrees.  A quantity is a mental construction of angle as a concept which makes it measurable.

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