Probing interactions in exploratory teaching: a case study

ABSTRACT

This study investigates an exploratory teaching style used in an undergraduate geometry course to help students identify an ellipse. We attempt to probe beneath the surface of exploration to understand how the actions of teachers can contribute to developing students’ competence in justifying an ellipse. We analyse the complex interactions between student, content, and teacher, and discuss explicit pedagogical strategies that help students develop a higher level of geometric reasoning. The findings indicate that students engaged in guided explorations by the teacher and in group discussions with peers were able to identify an ellipse and justify their reasoning.

KEYWORDS:

• Exploration
• explanation
• justification
• geometry
• undergraduate mathematics

SUBJECT CLASSIFICATION CODE:

• 51

Acknowledgements

The authors wish to thank the anonymous reviewers for their helpful comments. Special thanks to Arleen Schenke for her numerous suggestions for improving the text.

Disclosure statement

No potential conflict of interest was reported by the author.

Additional information

Funding

Preparation of this paper was supported in part by the Social Sciences and Humanities Research Council of Canada [grant number 435 2014 0305].