Learning mathematical thinking and reasoning is a main goal in mathematical education. Instructional tasks have an important role in fostering this learning. We introduce a learning sequence to approach the topic of integrals in secondary education to support students mathematical reasoning while participating in collaborative dialogue about the integral-as-accumulation-function. This is based on the notion of accumulation in general and the notion of accumulative distance function in particular. Through a case-study methodology we investigate how this approach elicits 11th grade students’ mathematical thinking and reasoning. The results show that the integral-as-accumulation-function has potential, since the notions of accumulation and accumulative function can provide a strong intuition for mathematical reasoning and engage students in mathematical dialogue. Implications of these results for task design and further research are discussed.
DOCUMENT
[Paper abstract]: The aims of the Interactive Virtual Math-project are to design and develop a digital tool for learning covariation graphs at high school (14-17 years old students) and to explore the use of new technologies for learning in classroom. Research provides some didactical directions to develop instruction that supports the learning of covariational reasoning. For instance, engaging students in the mental activity to visualize a situation and construct relevant quantitative relationships should be prior to determining formulas or graphs. Also, learners can be helped to focus on quantities and generalizations about relationships, connections between situations, and dynamic phenomena. Digital tools can be designed in order to meet these and other didactical requirements. In this talk we present the prototype of such tool: IVM (Interactive Virtua Math) and discuss the didactical principles behind the tool. We use results of a small scale experiment at secondary and tertiary education involving four classes and their students and teachers that used IVM during one lesson to illustrate the working of the tool and the challenges of developing digital didactical tools for learning mathematics. This abstract is submitted to the workgroep didactic considerations with respect to digital tools for the teaching of mathematics.
MULTIFILE
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.
DOCUMENT
