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Students’ structure for the understanding of the axis of reflective symmetry in mathematics. (English)
Acta Didact. Univ. Comen., Math., No. 9, 41-62 (2009).
Summary: The present study explores students’ constructed definitions of the concept of the axis of reflection for a function in relation to their abilities in dealing with tasks involving different forms of representations and problem solving tasks. A major concern is also to examine interrelations between these three ways of thinking about or dealing with the concept of the axis of reflection. The sample of the study consisted of 139 students attending the second class of the lyceum (17‒18 years). A test was developed which involved nine items: two items requested students to provide a definition of what the axis of reflection is, six items were developed in order to investigate students’ ability to transfer information from one representation to another and an item for problem solving ability. Findings revealed students’ difficulties in giving a proper definition for the concept and resolving tasks involving conversions between diverse modes of representations (algebraic, graphical, tabular). Several inconsistencies among students’ constructed definitions, their competence to use different representations of the axis of reflection and their problem solving ability were also uncovered, indicating lack of flexibility between different ways of approaching the concept.
Classification: I24 C34 D23
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