Students’ reasons for introducing auxiliary lines in proving situations

Alik Palatnik (1) , Tommy Dreyfus (2)

1 Shaanan Academic Religious Teachers' College
2 TAU - Tel Aviv University

We study proving situations in geometry where students introduce auxiliary lines. We examine students’ reasons for introducing auxiliary lines. The overarching theme of the tasks proposed to the students is the comparison of areas of triangles and/or parallelograms. The students gave a wide spectrum of reasons when introducing auxiliary lines. Two main groups of reasons have been discerned for modifying a given situation by introducing auxiliary lines: recalling a learned procedure using some known results or definitions, and anticipating more information from the modified situation. We present a case study of a pair of students who combine reasons of recalling and anticipating nature when introducing auxiliary lines.

Mots clés: High school geometry; proof; auxiliary lines; reasoning; task-based interviews

Domaines: Mathématiques [math]; Education

Alik Palatnik, Tommy Dreyfus. Students’ reasons for introducing auxiliary lines in proving situations. Eleventh Congress of the European Society for Research in Mathematics Education, Utrecht University, Feb 2019, Utrecht, Netherlands. ⟨hal-02402251⟩