21st century schools face significant challenges as they move towards providing opportunities for learners which recognize and build on their strengths and abilities. The process of supporting young people to develop the desire and the confidence to recognise personal potential and to manage their ongoing learning is a priority. Communication and collaboration are key to learners becoming informed active participants in their own learning and experiencing successful outcomes in today's society. Our old models of learning where pre packaged parcels of knowledge were delivered to students by teachers will no longer suffice. As we respond to the new meaning of knowledge in the 21st century and begin to view knowledge as an active process, it is clear that many of the top down structures and organisational practices present in New Zealand secondary schools need change. The idea of personalisation in order to support independent learners to reach their potential is a familiar one for many teachers and is one of the ideals which may have brought them into the teaching profession. However, the institutional contexts in which they operate can act not as a driving force for personalised learning but as a barrier to it. In seeking to find one possible way in which secondary school systems can be re shaped around the needs of the learner, this study examines the role of online mentoring with experts outside the school. This small scale qualitative study uses ethnographic methods to gather data from twelve secondary school year thirteen physical education students and their teacher as they engage in an eight week online project with expert sports coaches at Auckland University of Technology. Eleven of the students were boys. In examining the impact which online mentoring might have on this group of learners and their teacher, rich data was collected via web transcripts, observation, image data and interviews. The research findings reveal that students found a high degree of satisfaction with the process and placed value on having the opportunity to pursue personalised goals as they worked with mentors in a collaborative online environment. Teacher behaviour and practice underwent change in the project with the teacher becoming repositioned within the group in the role of learner. In a process where authoritarian approaches were replaced by collaborative group action and inquiry, students reported an enhanced ability to think deeply, to manage their own learning and to relate in highly skilled ways with others. Students' perceptions about the ways in which they were working were analysed using the New Zealand Curriculum Key Competencies. As students focused their inquiry past the level of curriculum goals and onto real world personal goals, several experienced a shift in perception concerning their own learning potential and expressed surprised at their own level of competence. The fact that eleven out of the twelve students were boys makes this shift in personal learning expectation worthy of further investigation in the quest for improving academic outcomes for boys. Finally, this study may have relevance for the ways in which the Key Competencies have meaning in secondary schools. The study demonstrated that the emergence of competencies such as self management and relating to others was assisted by changes in teacher behaviour and action. As authoritarian approaches were replaced by a collaborative model where independent learning with others was supported, learners began to exhibit the personal competencies described by the New Zealand Curriculum (2008). These competencies which include Thinking, Using Language, symbols and texts, Managing self, Relating to others and Participating and contributing occurred as a natural consequence of a learning model which was shaped to fit the learner; a personalised approach to learning with support from online mentors.

Philosophiae Doctor - PhD / The use of technology in mathematics education has many potentially positive outcomes. There is, however, little evidence to show where the use of technology has made a significant impact on mathematics education in South Africa. This study aims to address the issue of how computer tablets are currently used in the mathematics classroom. The researcher drew a comparison between learners who were taught with computer tablets and learners who were taught in the traditional way by evaluating the learners' progress after being taught on the topic of 3D images. This assessment was done in the form of a pre-test and a post-test that were administered to both classes on a topic of 3D images that was taught during this allocated time. The research is located in the third-generation activity theory. It is based on the socio-cultural theory of Lev Vygotsky, but it is blended with modern western theories as described by Engeström. The researcher made use of a mixed methods approach starting with a qualitative survey, followed by a pre-test, observations and concluding with a post-test. The pre-test and post-test determined whether cognitive knowledge was gained. The participants in the study were a group of 15-year-old learners at a private school where the one class was taught using computer tablets in the mathematics classroom, and the other class was taught the same content without computer tablets. A qualitative survey was sent to 27 schools within a particular school group where teachers indicated the popular Apps that were used in the mathematics classroom in this school group. Teachers also gave reasons why these were the Apps of choice and elaborated on how they were using these Apps. The quantitative part of this research was guided by the results of the survey and the 5 most popular Applications (Apps) were used in the teaching experiment. The quantitative part focused on two classrooms within the same school where the one class were taught with computer tablets and the other class were taught without the use of computer tablets. The t-test for this research showed that the group of learners who were taught with computer tablets achieved significantly better results than the class of learners who were taught using hard copy textbooks with traditional methods of teaching. This study showed that having computer tablets in schools can be effective in the mathematics classroom. The recommendations emanating from this study indicates that school who are planning to use computer tablets in the mathematics classroom should first plan their wi-fi capabilities with enough access points and internet access. These schools also need to decide on a type of computer tablet and what operating system to use. This decision has implications to the accessibility of quality Apps, battery life and storage space of the computer tablet. Schools are recommended to have a plan for training teachers in the use of this computer tablets especially regarding the pedagogical practice when interacting with learners. A last recommendation is to nurture a culture of computer tablet use amongst the learners to discipline themselves to charge and maintain their computer tablets and apply it to educational use. This study includes a pedagogical framework in respect of the effective use of computer tablets in the mathematics classroom.