Prospective Early Childhood and Elementary School Mathematics Teachers’ Concept Images and Concept Definitions of Triangles

This study presents a characterization of prospective early childhood teachers’ (ECEPTs) and prospective elementary school mathematics teachers’ (EMEPTs) concept images and concept definitions of triangles through a defining task and an example generation task. Data consisted of 62 EMEPTs’ and 72 ECEPTs’ written statements for the definition of a triangle, drawings for examples and non-examples of triangles, and written reasons for drawings. The results showed that most of the prospective teachers wrote inappropriate statements for the definitions of a triangle by using necessary but not sufficient conditions or using neither necessary nor sufficient conditions with frequent inaccurate terminology usage. The appropriate statements for the definition of a triangle included necessary and sufficient conditions, but were mostly considerably not minimal and/or included inappropriate mathematical terminology. A very large portion of the examples drawn by the prospective teachers consisted of acute triangles with typical positions rather than right and obtuse triangles, which can be evaluated as the indication of prototypical concept images. Drawings of non-triangles also revealed that the prospective teachers mostly drew non-triangular non-examples that can be immediately accepted as non-triangles with the lack of a relatively long list of missing critical attributes, but they provided a small number of triangular non-examples that bear significant similarity to valid examples of a triangle. This result indicates that the prospective teachers’ concept images regarding non-triangles also formed by intuitive non-examples which can be considered as prototypes for non-triangles.