Mediating students' mathematical learning through technology: The role of the graphical calculator.

The aim of this study has been to investigate the potential of the graphical calculator for mediating students' learning of functions in mathematics at GCE Advanced level. In carrying out this investigation, the study has been primarily concerned with three inter-related themes: How does the way in which individual students behave affect the shared construction of meaning in a graphical calculator environment? How does the visual imagery provided by the graphical calculator mediate students' understanding of functions? What are the implications for the role of the teacher in graphical calculator environments? In order to address these issues, the study has involved the development of materials and approaches that were subsequently trialled with Lower Sixth form students in a school and a college in the Local Education Authority of Sheffield. An ethnographic approach towards data collection and analysis was adopted, which entailed carrying out detailed studies of singularities in three key phases. The first phase consisted of the exploratory study and considered the learning experiences of novice graphical calculator users. The second phase involved experienced graphical calculator users and was concerned with identifying how knowledge construction might differ as a result of the longer-standing status of the graphical calculator as a tool for supporting mathematics learning. The third and final phase concentrated on the introduction of key function concepts to beginning Advanced level mathematics students and focused on the personal and social factors involved.The findings of this study have served to illustrate both the complexity and interdependence of the individual, social and affective factors involved in students' acquisition of meaning with the graphical calculator. Evidence from the research suggests that the social context has direct bearing on the functioning of the graphical calculator as a cognitive reorganiser. The graphical calculator was found to mediate the development of the visual capabilities of individual students via more intensive interaction between the students themselves and with the teacher. In this respect, the pairing of visualisers and non-visualisers amongst the students was found to be especially conducive to successful collaborative learning with the technology. In this study the graphical calculator acted as both a medium for communication and also as a new authority in the classroom, which empowered students to act as autonomous and independent learners. The potential of the technology for inspiring confidence, even in instances where it is not the main source of answers was also highlighted. An important part of successfully introducing new function concepts to students was found to lie in the creation of local communities of practice in the classroom, where the graphical calculator was seen as a means of drawing students into these practices. In this way, some of the more reluctant participants were encouraged to act as peer tutors. The importance of the role of the teacher in scaffolding the students' learning was also continually emphasised throughout, especially in relation to the interpretation of unexpected results and instances of dependency on the technology, which were linked to individual work. In illuminating all of these factors, the study has demonstrated the strength and relevance of a Vygotskian socio-cultural perspective for exploring students' learning with graphical calculators.