The role of technology in the development of mathematical understanding through problem solving
Abstract
The use of digital technologies has incorporated new reflection elements to approach the problem of mathematics learning since these tools can uncover elements that could be hidden when students use pencil and paper to solve problems. For instance, to describe how the volume of a liquid in a container changes when the height of that liquid is modified requires the student to imagine how the change occurs. However, with the use of digital technologies,
the student can visualize such variation and focus his attention on other important aspects such as the rates of change or the way in which that change occurs. In this paper we report some results from a study conducted with a group of students that used GeoGebra to approach mathematical tasks aimed at exploring students’ understanding regarding functional relations derived from sketching graphs that describe volume as a function of the height of a liquid in a container. The tasks were solved by first semester students of a Bachelor Degree program in mathematics at a Mexican Public University. Collected data were analysed from a socioconstructivist epistemological perspective as well as a didactical view that privileges mathematical understanding through problem solving. The analysis units were the reasoning sequences developed by the students. The systematic use of technology fostered a development of students’ conceptual structures of quantitative and qualitative types. We also identified some limitations of the tool to promote the organization of ideas, especially those that refer to the concavity of the sketched graphs.
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References
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