| Summary: | 碩士 === 國立臺南大學 === 應用數學系碩士班 === 105 === The main purpose of this study is to explore schema university students utilize to perceive function related concepts (i.e., definition, domain, codomain, range, function value, one to one, onto, and composite functions) as well as to explore the link between core schema and various visual representations of functions (i.e., text, equations, tables, graphs, arrow diagrams, and ordered pairs). This study takes a qualitative approach with students from an engineering college in Tainan, Taiwan as the study subjects. The students were first divided into two groups, high ability and low ability, based on their scores from the “function concepts and its various representations test” created by the researcher. Eight students were selected from the high ability group to take part in the first stage interview. Of the eight, six were selected to participate in the second stage interview. From examining how the students conceptualize functions, the main results of this study are summarized as follows:
First, the cognitive processes used to conceptualize functions varies among university students.
The eight students that participated in the first stage interview used five different types of schema (machinery, arrow diagram, equations, mail and mailbox, and chefs) to express their understanding of functions. At the same time, most of the students were also able to use the same schema to integrate other function related concepts. This shows continued schema refinement, resulting in more accurate ability to distinguish functions and more advanced schema.
Second, most university students are able to link core schema to visual representations of functions.
Most of the six students that participated in the second stage interview were able to connect and integrate core schema with various visual representations of functions, further proving the comprehensive nature of their schema within the realm of function related concepts. Those unable to use core schema such as equations to integrate representations of functions (ordered pairs and arrow diagrams, etc.) show insufficient schema refinement in their learning process.
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