Browsing by Author "Pfeiffer, Cerenus"

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    A study of the development of mathematical knowledge in a geogebra-focused learning environment
    (Stellenbosch : Stellenbosch University, 2017-12) Pfeiffer, Cerenus; Ndlovu, M. C.; Smit, J. H.; Stellenbosch University. Faculty of Education. Dept. of Curriculum Studies
    ENGLISH ABSTRACT : This study was about a GeoGebra-focused learning environment in which students could develop mathematical knowledge. It was done during an intervention with a convenient sample of 48 Science and Mathematics bridging programme students at Stellenbosch University (SciMathUS). Students in the SciMathUS year have to improve their Mathematics marks in order to qualify for admission into Science, Technology, Engineering and Mathematics (STEM) oriented programmes the following year at any tertiary institution in South Africa. The teacher-researcher felt that these students needed to be exposed to a hybridisation of the student-centred approach and teacher as facilitator of learning approach which had the potential to enhance conceptual and deeper understanding of Mathematics. GeoGebra was a pivotal teaching tool in the teacher-researcher’s interactive lecturing. Students were afforded the opportunity to engage individually, or in groups, with the learning material on transformations of functions and circle geometry by making use of GeoGebra. The prepared tasks in the different learning trajectories used in this research were guided by a social constructivist view of learning, Realistic Mathematics Education (RME), the Van Hiele theory, the Theory of Instrumental Genesis (TIG) and the Technological Pedagogical and Content Knowledge (TPACK) framework for technology integration. A learning route for the students in the instruction of transformations of functions and circle geometry was established through the creation of learning trajectories intertwined with transformation geometry, straight line, triangle and quadrilateral geometry, respectively. The methodology used was a mixed methods exploratory case study. The quantitative part of the study was a pretest-posttest experimental design. This study utilised pre- and post-intervention questionnaires, pre- and post-tests for transformations of functions and circle geometry, observations, and in-depth and focus group interviews. The results of the quantitative and qualitative data were triangulated, with a higher priority given to analysis of the qualitative data to answer the research questions. The results from both quantitative and qualitative data showed that the pedagogical processes involved in using GeoGebra were more than just technology. They showed that real-life activities, guidance, exploration and interaction were important RME principles to be borne in mind when using GeoGebra. The results also underlined the fact that students had certain preferences on how GeoGebra could be used as a pedagogical tool. The qualitative and quantitative results also revealed that GeoGebra afforded students an opportunity to better understand transformations of functions, circle geometry and general solutions of trigonometric equations. The qualitative content analysis of pre- and post-test for both transformations of functions and circle geometry showed that students moved to higher levels of abstraction. Students attributed this to the instrumentation processes of GeoGebra, i.e. visual affordance, potentialities and enablements. Moreover, the results revealed that exploring with GeoGebra made the teaching and learning of mathematics more fun. The students utilised hand movements to articulate their ideas with a classmate, or the teacher-researcher. During Guide-and-explain orchestrations students explained to their group members, or teacher-researcher, how they understood the intended mathematics from the activities and in this way used informal reasoning (horizontal mathematising) and then moved within the discussions to formal reasoning (vertical mathematising). The results also showed that GeoGebra afforded the students an opportunity to acquire physical and logico-mathematical knowledge. Challenges observed whilst the students were working with GeoGebra in the computer lab and based on students’ responses in the interviews, were constraints posed by syntax and menu commands. A small percentage of students found the different teaching and learning approach to be challenging at times. A few others could not see the intended mathematics from activities with GeoGebra, or felt that it further confused them, or that this approach required more thinking. Consequently it is recommended that GeoGebra should be part of a teacher’s arsenal to teach mathematical concepts that lend themselves to technology integration.