[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.
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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.
An essential condition to use mathematics to solve problems is the ability to recognize, imagine and represent relations between quantities. In particular, covariational reasoning has been shown to be very challenging for students at all levels. The aim of the project Interactive Virtual Math (IVM) is to develop a visualization tool that supports students’ learning of covariation graphs. In this paper we present the initial development of the tool and we discuss its main features based on the results of one preliminary study and one exploratory study. The results suggest that the tool has potential to help students to engage in covariational reasoning by affording construction and explanation of different representations and comparison, relation and generalization of these ones. The results also point to the importance of developing tools that elicit and build upon students' self-productions
