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
[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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Explicit language objectives are included in the Swedish national curriculum for mathematics. The curriculum states that students should be given opportunities to develop the ability to formulate problems, use and analyse mathematical concepts and relationships between concepts, show and follow mathematical reasoning, and use mathematical expressions in discussions. Teachers’ competence forms a crucial link to bring an intended curriculum to a curriculum in action. This article investigates a professional development program, ‘Language in Mathematics’, within a national program for mathematics teachers in Sweden that aims at implementing the national curriculum into practice. Two specific aspects are examined: the selection of theoretical notions on language and mathematics and the choice of activities to relate selected theory to practice. From this examination, research on teacher learning in connection to professional development is proposed, which can contribute to a better understanding of teachers’ interpretation of integrated approaches to language and mathematics across national contexts.
