Third-year University Mathematics Education Students' Metaphorical Understanding of Mathematics Teaching and Learning

Abstract

This paper reports on the metaphors that 36 third-year university mathematics education students have about mathematics. These metaphors were investigated through a questionnaire with five open-ended items. An inductive analysis of the students' metaphors for mathematics indicated that students had well developed and complex metaphors about mathematics, mathematics learning, mathematics teaching and the mathematics teacher. Several common themes emerged, including the view that hard work, patience and perseverance are needed for success in mathematics. Some students emphasised their role in learning mathematics as active while others view their role of the teacher as crucial. Three mental images are common: firstly, the notion that mathematics learning is challenging and may involve anxiety; secondly, that perseverance is needed as continuing effort will bring reward; and lastly, that positive or negative mental images of mathematics are related to the perception of and the active vs passive role of the learner. Considering that the metaphors were collected from students with an extensive engagement with mathematics learning, the findings implied that these metaphors reflect the students' mental images formed as a result of experiencing mathematics learning.