Handheld graphing technologies have fundamentally been utilized in the teaching and learning of many secondary school and college mathematics concepts. In order to observe the effects of these new kinds of technologies on students' learning of mathematics, their teachers need to decide whether it is reasonable to do, learn, and teach mathematics with a calculator, and moreover, if graphing calculators are worth using in their classrooms as an instructional tool. With this aim in mind, this study utilized two conceptual frameworks--the possible roles of advanced calculators in mathematics teaching and learning, as well as technological pedagogical content knowledge--to investigate the views of preservice secondary mathematics teachers on the use of calculators in mathematics instruction. Open-ended survey questionnaire and group interviews were the main data collection methods for this study. Results revealed preservice teachers' views on the use of handheld technology in mathematics instruction and the roles that they assigned to the calculators such as a visualization tool, a transformational tool, a computational tool or a discovery tool. Their beliefs about advantages and disadvantages of using graphing calculators and when and why they would prefer to use graphing calculators were discussed. (Contains 2 tables and 1 figure.)