A qualifying paper submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Mathematics Education. Abstract: This qualifying paper explores the processes of reification (Sfard, 1987, 1989, 1991, 1992) and encapsulation (Dubinsky, 1991a, 1991b; Dubinsky & Harel, 1992a), as they apply to the concept of mathematical functions, and attempts to determine how both ... read moreprocesses contribute to explaining the formation of the concept of function. The review of empirical studies on students' understanding of functions leads to the conclusion that neither reification nor encapsulation is without flaw; however, they have contributed significantly to partially explaining the formation of the function concept. This implies that more theoretical and empirical work needs to be conducted within this area in order for researchers and educators to have a complete explanation of the formation of the function concept.read less
