Radian π: Concept images evoked by quantitative representations of radian angle measure

ABSTRACT

This article investigates evoked concept images (CIs) of seven secondary preservice mathematics teachers (PMTs) as they interact with different types of representations of radian angle measure. A thematic analysis indicates that representations emphasizing quantitative aspects of angle measure evoke conceptions that are attuned to quantitative elements of radian angle measure. Specifically, quantitative representations evoked CIs relating the length of the arc subtending the angle to the radius. Non-quantitative representations evoked CIs of radian in terms of π or in relation to degrees, even when the representation did not contain angles in these measurements. To foster a quantitative understanding of radian angle measure, teachers and curriculum developers are encouraged to consider how visual representations might support students in conceptualizing radian angle measure quantitatively.

KEYWORDS:

• Concept image
• radian
• angle measure
• representations
• preservice mathematics teachers

Disclosure statement

No potential conflict of interest was reported by the author(s).

Supplemental data

Supplemental data for this article can be accessed online at https://doi.org/10.1080/10986065.2024.2338893.

Notes

1. Moore et al. (2016) extended Moore’s (2013) work and demonstrated that acquiring a quantitative view of angle by attending to the angle’s measurable attributes could productively support learners’ conceptualization of angle measure.

2. Because textbook representations emphasize qualitative views of angle (Alyami, 2020), the only other quantitative textbook diagram I found was similar to Diagram 4 in that it also presents radian angle measure as iteration of the radius along the circumference.

3. See Supplementary File for more examples at each code for each diagram.

4. See the Supplementary File for more examples at each code for each diagram.

5. See the Supplementary File for more examples at each code for each diagram.