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The role of dynamic software in the identification and construction of mathematical relationships.

Article Excerpt
What features of mathematical thinking do students exhibit when



they use dynamic software in their problem solving approaches? To what extent does the systematic use of technology favour students development of problem solving competences? What type of reasoning do students develop as a result of using a particular tool? This study documents features of mathematical practice that students display when they systematically use dynamic software in problem solving. In particular, the use of the software involves the construction of simple geometric configurations that become a platform to formulate questions that lead them to the construction or recognition of mathematical relationships. In this process, students can build their own repertoire of mathematical results and also utilize their previous knowledge to support, justify, or explain their conjectures. Here, it becomes important for students to develop methods and strategies to observe particular relationships, express them using specific notation, and provide arguments to demonstrate and communicate their results.

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Recent curriculum reforms suggest that students need to utilize distinct technological tools in their process of learning mathematics. It is well recognized that students need to develop distinct strategies to identify and examine relevant information to deal with problems or situations that involve the use of mathematical resources. Given this perspective, it is common that they pose questions, explore particular conjectures, use distinct representations, and develop ways to communicate their ideas or results. The presence of technological tools in mathematical classrooms tends to influence not only the content and organization of the curriculum studied, but also ways in which students approach and learn it ((National Council of Teachers of Mathematics (NCTM), 2000). It is also recognized that there are multiples ways in which students can employ those technological tools and, as a consequence, there is a need to investigate what aspects of mathematical practice actually enhance students' learning as result of using particular tools. The intent of this study is to investigate aspects of reasoning exhibited by high school students while using dynamic software to construct and examine a set of geometric configurations. In particular, mathematical results emerge from exploring the behavior of parts of a certain configuration as a result of moving other elements within such a figure or configuration. Hence, it becomes important to characterize types of questions, conjectures, explanations, and forms of communication that students develop during their problem solving experiences.

DISCUSSION

A Problem Solving Scenario: Elements of a Conceptual Framework

Mathematical problem solving has become a central activity in students learning of the discipline (NCTM, 2000). However, it is important to recognize that there are different scenarios in which students can be engaged in problem solving practices. Thus a problem solving approach may be based on creating a mathematics microcosm in the classroom where students openly discuss a set of well-selected non-routine problems (Schoenfeld, 1998). What happens when students are asked to participate in the process of formulating questions? What is the role of the use of technology in achieving this goal? To what extent are students'...

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