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http://dx.doi.org/10.7468/mathedu.2019.58.2.239

A study on the student's question about the existence of the inverse function for the task that connects the two correspondence relations  

Lee, Dong Gun (Seoul Education Research & Information Institute)
Publication Information
The Mathematical Education / v.58, no.2, 2019 , pp. 239-262 More about this Journal
Abstract
This study deals with the anxieties that originated from specific student questions. Through the analysis of the textbooks, we confirmed that the question was a sufficiently plausible question. Third interviews were also held with three high school students. Through the interviews, we analyzed students' expressions about the new correspondence relationship that the two correspondence relations are linked. In the determination of the composite function and the determination of the inverse function existence, We have observed a case of how the worries about domain are being reconstructed from students into meaningful mathematical knowledge. Through this, we confirmed that the question will be confusing to students in the field. In this study, we observed the transfer of domain in relation to student domain in composite function. In particular, a present study revealed that the students involved in the interview were influenced by this domain transfer phenomenon in determining whether the task given in the interview was a function. This was the same in determining the existence of a inverse function. The examples presented in this study are limited to specific cases in limited circumstances. Therefore, it can not be applied directly to teaching and learning situations. However, it is expected that this study will provide other researchers with insight into function learning related research.
Keywords
composition; composite function; function; one-to-one correspondence; inverse function;
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Times Cited By KSCI : 3  (Citation Analysis)
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