Educational Studies in Mathematics

, Volume 93, Issue 2, pp 223–243 | Cite as

Turn vs. shape: teachers cope with incompatible perspectives on angle

  • Igor’ Kontorovich
  • Rina Zazkis


This study is concerned with tensions between the two different perspectives on the concept of angle: angle as a static shape and angle as a dynamic turn. The goal of the study is to explore how teachers cope with these tensions. We analyze scripts of 16 in-service secondary mathematics teachers, which feature a dialogue between a teacher and students around the following statement: “The sum of the exterior angles of a polygon is 360°.” The findings show that while addressing a variety of intellectual needs of their student characters, in many cases, the teachers compromise the mathematical rigour of the concept of angle.


Angles Polygons Scriptwriting Intellectual needs Teacher knowledge Intuitive rules 


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Copyright information

© Springer Science+Business Media Dordrecht 2016

Authors and Affiliations

  1. 1.The University of AucklandAucklandNew Zealand
  2. 2.Simon Fraser UniversityBurnabyCanada

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