Graphing calculators and the zone of proximal development : a study of fourteen year old Malaysian students development of graphical concepts with technology
This study investigates 14 year-old students' development of graphical concepts using graphing calculators. Two learning models based on two broad interpretations of Vygotsky's "zone of proximal development" were implemented to gauge the role of graphing calculators in technology-based learning. Epistemological case studies were used to ascertain the extent to which the graphing calculator facilitated the learning of key graphical concepts. To this end, students of different levels of mathematical attainment were observed to determine the different kinds of understanding they derived from using the technology. The 24 students participating in the study were pre and post tested, and formed into two groups. One group was taught according to a structured, teacher-led learning model, and the other group was taught according to an open-ended, activity-led learning model. What emerges from the study is the complexity of the teaching and learning situation when technology is incorporated. A student's learning of graphical concepts with the graphing calculator was the result of an interplay between his/her knowledge of the functionality of the graphing calculator, existing mathematical knowledge and the nature of teacher intervention. The use of the graphing calculator raises the issues of the ordering or sequencing of learning of graphs from simple linear equations to those perceived as more complex polynomials. With the graphing calculator, students were able to learn much more than was thought possible. Changes in students' mathematical learning were accompanied by a change in the role of the calculator from a static display tool to a mediational tool. The study also highlights the issues of teachers' roles when technology is incorporated including teacher's content knowledge, and the ways in which teachers intervene with students, in particular how teachers deal with students' semantic and syntactic errors in using the calculator.