Self-construction and interactive simulations to support the learning of drawing graphs and reasoning in mathematics

In mathematics, sciences and economics, understanding and working with graphs are important skills. However, developing these skills has been shown to be a challenge in secondary and higher education as it involves high order thinking processes such as analysis, reflection and creativity. In this study, we present Interactive Virtual Math, a tool that supports the learning of a specific kind of graphs: dynamic graphs which represent the relation between at least two quantities that covary. The tool supports learners in visualizing abstract relations through enabling them to draw, move and modify graphs, and by combining graphs with other representations, especially interactive animations and textual explanations. This paper reports a design experiment about students’ learning graphs with this tool. Results show that students with difficulty in generating acceptable graphs improve their ability while working with the tool.