Student representation and understanding of geometric transformations with technology experience
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The primary purpose of this study was to investigate how and to what extent 'representations'affect the students'understanding and the growth of understanding in a technology [GSP ]-based collegiate mathematics classroom.There are three themes in the framework of the study to support this purpose:1)technology in mathematics education; 2)images on computer screen -visualization and representation;3)understanding and growth of understanding.|The following three research questions guided this study:1)How do students present each component of representations when they study 'transformations'in a technology [GSP ]-based classroom?If there is any difference between the first and second presentation for each component,how are they different?;2)How and to what extent do representations affect the students'understanding and the growth of understanding in a technology [GSP ]-based classroom?;3)What types of benefits and obstacles are there when students study 'transformations'in a technology [GSP ]-based classroom?|This study was conducted during spring semester of 2001.A qualitative methodology study was used,especially case study,which is the most powerful and appropriate method for intensive examination (Goetz &LeCompte,1984).Two college students were purposefully chosen based on three criteria and voluntarily participated for this study.Data were collected from descriptive notes,reflective notes,archival data, interviews,and concept maps.The collected data were analyzed using 'constant comparison method'described by Corbin and Strauss (1990)along with analytic induction.|Findings indicated unbalanced students'representations of what they learned in the classroom.Pictorial representation was dominant and verbal representation came along with it.However,written representation was often avoided unless participants were specifically asked to use it.Students'growth of understanding in transformations was based on a)their understanding basic concepts,b)the applicability of these basics,and c) their mathematical understanding of the given situations.If paper and pencil were the main tools for this course,written representations might play a major role in the whole process.Due to the complexity of mathematical contents,'don't need boundary'in Pirie and Kieren's model (1994)was not significantly featured in this study,whereas 'folding back'was.|There were obstacles and benefits with technology experiences.As for obstacles, first,images on computer screen restrict learners'logical thinking;second,images on computer screen might lead learners nowhere or to misconception.As for benefits:first, students could quickly make a solid conjecture with accurate constructions with technology;second,the dynamic function of technology plays a significant role;third, well-constructed figures lead learners to efficient problem solving and psychological relief.|Finally,this study suggests that further researches with various perspectives relating to technology should be conducted for students'better understanding of mathematics so that we can use technology that we have more efficiently.Further,we need to develop a theory or a tool to recognize students'understanding and growth of understanding.