This document analyzes the work of a group of university students in their attempts to comprehend the concept of derivative. In particular, we focus on analyzing the type of studentsâ€™ cognitive reorganization that they show as a result of using EXCEL as a problem solving tool. The cognitive changes developed by the students are identified through the connections they establish between systems of numeric, graphic and algebraic representations. The work of the students was oriented trough the discussion of problems that involve phenomena of the rate of change and linear approximation as fundamental ideas to the understanding the derivative concept.
The importance of employing different technological mediums in the learning of mathematics
has been sustained in the results obtained in different investigations (Santos, et al 2003), wherein the studentâ€™s understanding of mathematical ideas seems to be tied to the relationships they are able to establish among different representations. Recent curriculum proposals recognize that symbolic calculators and computer software, as well as spreadsheets, can become powerful tools for students to develop numeric, graphic and symbolic representations.
In order for technology to contribute to the exploration of connections, among different
representations and as a consequence to the construction of mathematics concepts for the students, the activities in which the students take part in the classroom with the help of technological mediums must be carefully designed and directed by the instructor. Thus, we document the cognitive reorganization shown by first year university students when they were asked to use EXCEL to solve a series of tasks that involved the concept of derivative. The tasks selected in this report focus on the ideas of the rate of change and linear approximation for approaching the derivative concept.
In the process of learning mathematics studentâ€™s understanding can be enhanced when
working with activities that involve the use of different representations. The relationships that students establish among different representation systems can be considered as indicators of change in their cognition. One method of seeing the connections that a student establishes among different representational systems is through the examination of external representations that the subject produces in writing, in speaking or in the manipulation of symbols such as algebraic symbols. By way of internal representations the individual constructs these external representations. Between the internal and external systems of representation, the subject establishes significant relationships, which can be modified throughout the development of the learning activities.
By assuming that individualâ€™s comprehension can be exhibited in terms of expressing
different representations, the activities implemented in the classroom, employing a cognitive tool such as a Excel can help students in the construction of connections among representations.
The term cognitive tool is used here â€śas whatever medium that helps transcend the limitations
of the mindâ€¦in thought, learning and activities involved in the problem solvingâ€ť (Pea, 1987 p. 91). In order for the students to utilize Excel as a cognitive tool, he or she should develop a psychological construct. This construct is found to be determined by the actions that are realized
All Academic Convention is the premier solution for your association's abstract management solutions needs.