First year mathematics undergraduates’ settled images of tangent line

This study concerns 182 first year mathematics undergraduates’ perspectives on the tangent line of function graph in the light of a previous study on Year 12 pupils’ perspectives. The aim was the investigation of tangency images that settle after undergraduates’ distancing from the notion for a few months and after their participation in university admission examination. To this end we related the performances of the undergraduates and the pupils in the same questions of a questionnaire; we classified the undergraduates in distinct groups through Latent Class Analysis; and, we examined this classification according to the Analytical Local, Geometrical Global and Intermediate Local perspectives on tangency we had identified among pupils. The findings suggest that more undergraduates than pupils demonstrated intermediate perspectives on tangency. Also, the undergraduates’ settled images were influenced by persistent images about tangency and their prior experience in the context of preparation for and participation in the examination.

Research highlights▶ Student images of tangent line are influenced by geometrical properties. ▶ Participation in university admission examination influences student understanding. ▶ The domain in which a concept is exemplified determines student concept images. ▶ Adequate knowledge of the formula does not necessarily imply accurate images. ▶ Teaching mathematics at university should consider student previous knowledge.