# Putting the unit in pre-service secondary teachers’ unit circle

## Abstract

We discuss a teaching experiment that explored two pre-service secondary teachers’ meanings for the unit circle. Our analyses suggest that the participants’ initial unit circle meanings predominantly consisted of calculational strategies for relating a given circle to what they called “the unit circle.” These strategies did not entail conceiving a circle’s radius as a unit of measure. In response, we implemented tasks designed to focus the participants’ attention on various measurement ideas including conceiving a circle’s radius as a unit magnitude. Against the backdrop of the participants’ actions on these tasks, we characterize shifts in the participants’ unit circle meanings and we briefly describe how these shifts influenced their ability to use the unit circle in trigonometric situations.

## Keywords

Unit circle Trigonometry Pre-service secondary teachers Measurement Teaching experiment Quantitative reasoning## Notes

### Acknowledgments

This material is based upon work supported by the National Science Foundation under Grants No. DRL-1350342 and EHR-0412537. All opinions expressed are solely those of the authors and do not necessarily reflect the views of the National Science Foundation. Thank you to SIGMAA on RUME for the opportunity to present a previous version of this manuscript. Thank you to Patrick Thompson for his feedback on previous versions of the manuscript and his suggestions for important clarifications.

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