Deepak Mavani | Rhodes University (original) (raw)
Papers by Deepak Mavani
Learning and Teaching Mathematics, 2014
Sketching and interpreting cubic functions is one of the main applications of differential calcul... more Sketching and interpreting cubic functions is one of the main applications of differential calculus for Grade 12 learners. However, when drawing graphs of functions using paper and pencil, a great deal of time is spent in performing repeated, tedious computations. As such, learners often do not get sufficient time to explore the nature and properties of functions and their graphs. Dynamic geometry software such as GeoGebra, The Geometer's Sketchpad and Cabri have immense potential for learners to explore functions and their graphs without the tedium of repeated calculations in order to sketch the graphs. The dynamic nature of such software environments makes them ideal for mathematical exploration in which students can experience the processes of conjecturing and discovering.
<jats:p>Visualisation in the mathematics classroom has its own pedagogical value and plays ... more <jats:p>Visualisation in the mathematics classroom has its own pedagogical value and plays a significant role in developing mathematical intuition, thought and ideas. Dynamic visualisation possibilities of current digital technologies afford new ways of teaching and learning mathematics. The freely available GeoGebra software package is highly interactive and makes use of powerful features to create objects that are dynamic, and which can be moved around on the computer screen for mathematical exploration. This research study was conceptualised within the GeoGebra Literacy Initiative Project (GLIP) – an ICT teacher development project in Mthatha in the Eastern Cape, South Africa. The focus of this study was on how GeoGebra could be used as a teaching tool by harnessing its powerful visualisation capacity. In the study, selected GLIP teachers collaboratively developed GeoGebra applets, then implemented and evaluated them. The research methodology took the form of action research cycles in which the design, implementation and evaluation of successive applets determined the data gathering and analysis process. My data consisted mainly of recorded observations and reflective interviews. The underlying theoretical foundation of this study lies in constructivism, which aligned well with the conceptual and analytical framework of Kilpatrick et al.'s (2001) description of teaching proficiency. An in-depth analysis of my classroom observations resulted in multiple narratives that illuminated how teachers harnessed the visualisation capabilities inherent in the software. My findings showed that dynamic visualisation and interactivity afforded by the use of technology are key enabling factors for teachers to enhance the visualisation of mathematical concepts. My analysis across participants also showed that technical difficulties often compromised the use of technology in the teaching of mathematics. The significance of this research is its contribution to the ongoing deliberations of visualisation and utilisation of technological resources, particularly through the empowerment of a community of teachers. The findings recognised that the integration of technology required appropriate training, proper planning and continuous support and resources for the teaching of mathematics. This action research provided insightful information on integrating Dynamic Geometry Software (DGS) tools in mathematics classrooms that could be useful to teachers and curriculum planners.</jats:p>
African Journal of Research in Mathematics, Science and Technology Education, 2018
This paper reports on an aspect of a larger research study conceptualised within a teacher develo... more This paper reports on an aspect of a larger research study conceptualised within a teacher development project in Mthatha, Eastern Cape Province. The project was initiated with the objective to develop appropriate skills to use dynamic geometry software (DGS) effectively and strategically as a teaching and learning tool for mathematics. The study reported in this paper aims specifically to ascertain how selected mathematics teachers integrated co-developed technologically aided visualisation tools in the observed lessons. The case study involved two teachers from different schools. The data sources were the classroom observations followed by stimulated reflective interviews with the teachers. The data were analysed to study the use of DGS visualisation tools in relation to Kilpatrick's framework of teaching proficiency. The lessons evidenced a displayed alignment with the elements of teaching proficiency in the context of teaching geometry. The dynamic visualisation opportunities offered by DGS proved to supplement the teaching repertoire for the participating teachers. Pedagogical practices influence the use of DGS, as evident from the lessons when the participating teachers incorporated collaboratively developed GeoGebra applets into their classrooms. We argue that the collaborative engagement between teachers appears to be a positive way forward in closing the gap between having access to technology and adapting it for effective use in mathematics classrooms.
Learning and Teaching Mathematics, 2016
The points of intersection of p and g can be found by setting L(x) = 0 since the distance QP will... more The points of intersection of p and g can be found by setting L(x) = 0 since the distance QP will be zero at these points. Solving L(x) = 0 gives x = −2 and x = 5 4 . In order to determine the maximum length of QP all we need to do is determine the turning point of the parabola represented by L(x). We can do this by (i) completing the square and writing L(x) in the form a(x − p) + q from which the turning point can be read, (ii) determining the axis of symmetry of L and using it to find the corresponding y-value, or (iii) setting L′(x) = 0 to determine the point at which the gradient is zero and then finding the corresponding y-value. Using any of these methods gives the turning point of L to be (− 3 8 ; 169 32 ). The maximum length of QP is thus 5,28 to two decimal places.
Learning and Teaching Mathematics, 2014
Sketching and interpreting cubic functions is one of the main applications of differential calcul... more Sketching and interpreting cubic functions is one of the main applications of differential calculus for Grade 12 learners. However, when drawing graphs of functions using paper and pencil, a great deal of time is spent in performing repeated, tedious computations. As such, learners often do not get sufficient time to explore the nature and properties of functions and their graphs. Dynamic geometry software such as GeoGebra, The Geometer's Sketchpad and Cabri have immense potential for learners to explore functions and their graphs without the tedium of repeated calculations in order to sketch the graphs. The dynamic nature of such software environments makes them ideal for mathematical exploration in which students can experience the processes of conjecturing and discovering.
<jats:p>Visualisation in the mathematics classroom has its own pedagogical value and plays ... more <jats:p>Visualisation in the mathematics classroom has its own pedagogical value and plays a significant role in developing mathematical intuition, thought and ideas. Dynamic visualisation possibilities of current digital technologies afford new ways of teaching and learning mathematics. The freely available GeoGebra software package is highly interactive and makes use of powerful features to create objects that are dynamic, and which can be moved around on the computer screen for mathematical exploration. This research study was conceptualised within the GeoGebra Literacy Initiative Project (GLIP) – an ICT teacher development project in Mthatha in the Eastern Cape, South Africa. The focus of this study was on how GeoGebra could be used as a teaching tool by harnessing its powerful visualisation capacity. In the study, selected GLIP teachers collaboratively developed GeoGebra applets, then implemented and evaluated them. The research methodology took the form of action research cycles in which the design, implementation and evaluation of successive applets determined the data gathering and analysis process. My data consisted mainly of recorded observations and reflective interviews. The underlying theoretical foundation of this study lies in constructivism, which aligned well with the conceptual and analytical framework of Kilpatrick et al.'s (2001) description of teaching proficiency. An in-depth analysis of my classroom observations resulted in multiple narratives that illuminated how teachers harnessed the visualisation capabilities inherent in the software. My findings showed that dynamic visualisation and interactivity afforded by the use of technology are key enabling factors for teachers to enhance the visualisation of mathematical concepts. My analysis across participants also showed that technical difficulties often compromised the use of technology in the teaching of mathematics. The significance of this research is its contribution to the ongoing deliberations of visualisation and utilisation of technological resources, particularly through the empowerment of a community of teachers. The findings recognised that the integration of technology required appropriate training, proper planning and continuous support and resources for the teaching of mathematics. This action research provided insightful information on integrating Dynamic Geometry Software (DGS) tools in mathematics classrooms that could be useful to teachers and curriculum planners.</jats:p>
African Journal of Research in Mathematics, Science and Technology Education, 2018
This paper reports on an aspect of a larger research study conceptualised within a teacher develo... more This paper reports on an aspect of a larger research study conceptualised within a teacher development project in Mthatha, Eastern Cape Province. The project was initiated with the objective to develop appropriate skills to use dynamic geometry software (DGS) effectively and strategically as a teaching and learning tool for mathematics. The study reported in this paper aims specifically to ascertain how selected mathematics teachers integrated co-developed technologically aided visualisation tools in the observed lessons. The case study involved two teachers from different schools. The data sources were the classroom observations followed by stimulated reflective interviews with the teachers. The data were analysed to study the use of DGS visualisation tools in relation to Kilpatrick's framework of teaching proficiency. The lessons evidenced a displayed alignment with the elements of teaching proficiency in the context of teaching geometry. The dynamic visualisation opportunities offered by DGS proved to supplement the teaching repertoire for the participating teachers. Pedagogical practices influence the use of DGS, as evident from the lessons when the participating teachers incorporated collaboratively developed GeoGebra applets into their classrooms. We argue that the collaborative engagement between teachers appears to be a positive way forward in closing the gap between having access to technology and adapting it for effective use in mathematics classrooms.
Learning and Teaching Mathematics, 2016
The points of intersection of p and g can be found by setting L(x) = 0 since the distance QP will... more The points of intersection of p and g can be found by setting L(x) = 0 since the distance QP will be zero at these points. Solving L(x) = 0 gives x = −2 and x = 5 4 . In order to determine the maximum length of QP all we need to do is determine the turning point of the parabola represented by L(x). We can do this by (i) completing the square and writing L(x) in the form a(x − p) + q from which the turning point can be read, (ii) determining the axis of symmetry of L and using it to find the corresponding y-value, or (iii) setting L′(x) = 0 to determine the point at which the gradient is zero and then finding the corresponding y-value. Using any of these methods gives the turning point of L to be (− 3 8 ; 169 32 ). The maximum length of QP is thus 5,28 to two decimal places.