As many researchers have studied, calculators may not be appropriate for all educational situations or all mathematical subjects. However, Ellington (2003) reported that the improvement to problem solving skills was most significant when (a) special curriculum materials were designed for use with the calculator and (b) the type of calculator used was the graphing calculator. The purpose of the study was to identify strengths and limitations in how prospective mathematics teachers use the graphing calculator in teaching mathematics concepts and procedures. This study included both quantitative and qualitative data collection and analysis methods, providing an opportunity for presenting a greater diversity of views. , discussion thread and essay data were qualitatively analyzed in the context of the TI-Nspire study in search of recurring themes, informed by the Technological Pedagogical Content Knowledge (TPCK) framework (Niess, 2008).

First, the effective use of TI-Nspire lies in the resequencing and reorganization of traditional mathematical topics, i.e., it is essentially an instructional design issue. Under sound instructional principles such as those of MFL, the new technology affords students opportunity to model and explore a variety of mathematical ideas at increasingly complex level and ultimately develop a holistic view of the mathematics in terms of their multiple connections and representation (NCTM, 2000, 2003). Second, the new technology plays the roles of cognitive amplifiers and organizers (Heid, 1997) in support of students’ mathematical problem solving. Third, the new technology stands as a challenge to collaborative learning in small group. The project team’s initial findings are consistent with those of Doerr and Zangor (2000). Through multiple experiences including a hypothetical teaching scenario involving TI-Nspire, class reflections, and lesson plans participants responded to a variety of aspects of teaching with technology. The initial analysis of their responses unveiled five major themes. First, the new technology served as a tool or stimulator in fostering pedagogical reflection among the participants. Second, faced with the challenges and alternatives of the new technology, participants experienced the tension between traditional curricular materials (e.g., the textbook) and the need to recreate their instructional tasks. Third, the new technology stands as a challenge to the traditional paper-n-pencil approach to school mathematics, causing a tension or, at times conflicts between participants’
traditional view of mathematics teaching and their awareness of innovative alternatives. Fourth, the new technology
stimulated among the participants a willingness to learn on their own and with their students. There is evidence that
the new technology might have fostered the emergence of certain openness in their approach to teaching. They
explicitly identified the need for further support, training and peer assistance. Fifth, participants’ beliefs and prior
experience played an important role in their justification of their proposed ways of teaching and assessment. Their
beliefs shaped their learning experiences on the TI-Nspire project, which further challenged their beliefs. Teachers in general are not well prepared to take advantage of technologies such as the graphing calculator to support mathematics education. Deficiencies are not easily categorized and seem to involve what is now being called technological pedagogical content knowledge (TPCK) (AACTE Committee on Innovation and Technology, 2008). Deficiencies with regard to TPCK have not been addressed by traditional teacher preparation or professional development. Rather than support teachers, the graphing calculator in many cases makes it evident that teachers lack the appropriate TPCK.
According to Mishra and Koehler (2006) effective technology integration for pedagogy around specific subject matter requires developing sensitivity to the dynamic, transactional relationship between all three components. The expertise demonstrated by a teacher capable of negotiating these relationships represents a form of expertise different from, and greater than, the knowledge of a disciplinary expert (say a mathematician or a scientist), a technology expert (a computer scientist) and a pedagogical expert (an experienced educator). Furthermore, the incorporation of a new technology (e.g., TI-Nspire calculator) suddenly forces teachers to confront basic educational issues because this new technology reconstructs the dynamic equilibrium among the elements of
technology, pedagogy and content. Through the design of effective learning tasks utilizing technology integration
teachers are confronted with new decisions about the content and pedagogy. Future studies need to further examine the dynamic interplay between elements such as connections,
interactions, and constraints between and among content, pedagogy, and technology. The identification of centrally
held beliefs about the nature of mathematics and the learning of mathematics in contexts involving the use of technology for teaching mathematics is another area that merits further examination. Finally, curriculum development leading to units of content that are supported by NSpire are needed to examine the effectiveness of the use of the calculator learning different levels of mathematics and the interplay of multiple representations in the learning process.