Pre-service middle school mathematics teachers' personal concept definitions of special quadrilaterals

The purpose of the current study was to explore pre-service middle school mathematics teachers' personal concept definitions of a trapezoid, parallelogram, rectangle, rhombus, square, and kite. The data were collected by a self-report instrument through which the pre-service teachers provided their answers in written form. The participants' definitions were coded by using Zazkis and Leikin's (Educational Studies in Mathematics, 69(2), 131-148, 2008) framework, which includes the following four main categories for determining mathematical correctness: necessary and sufficient, necessary but not sufficient, sufficient but not necessary, and neither necessary nor sufficient. The findings revealed that about half of the all definitions were correct. More specifically, the participants generated considerably higher proportion of correct definitions for a parallelogram and rhombus, while they displayed a very low performance in defining a kite. The possible reasons of the participants' varied performance levels in defining the six basic quadrilaterals are discussed based on the linguistic (syntactic, semantic, and lexical) structure of the Turkish names given to the these quadrilaterals. The current study may provide some feedback to teacher education programs regarding the extent of knowledge that should be possessed by the pre-service teachers about definitions of special quadrilaterals before they leave their programs. Such feedback may also help mathematics teacher educators ponder on more fruitful approaches that may promote the development of pre-service teachers' knowledge and understanding of definitions of special quadrilaterals.