The purpose of this study was to investigate the quantifier structuring processes of teacher candidates doing the Abstract Mathematics course of the Elementary School Mathematics Teaching program. Educational activities assisting the students’ structuring of quantifiers were provided through transitions between verbal (written) expressions and symbolic expression in open statements that contained first, second, and third order quantifiers. The data of this study, based on an APOS (Action, Process, Object, and Schema) theoretical framework, were obtained by using a problem form. This form consists of four questions on quantization prepared by the researcher to investigate the cognitive development of the students; clinical interviews were performed at the end of the study period with five students. At the end of the study, it was determined that the students were unable to fully understand expressions regarding first and high order quantifier structures, and that they developed opinions according to their own perceptions. Furthermore, important results were obtained during the study that demonstrated the level of comprehension of students regarding first, second, and third order quantifier structures.

 

Key words: The quantifier concept, universal quantifier, existential quantifier, genetic decompositions, APOS.