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Teacher Knowledge Necessary to Analyze Student's Errors and Difficulties about the Concept of Irrational Numbers  

Kang, Hyangim (Korea National University of Education)
Choi, Eunah (Woosuk University)
Publication Information
School Mathematics / v.19, no.2, 2017 , pp. 319-343 More about this Journal
Abstract
In this study, we hope to reveal specialized content knowledge(SCK) and its features necessary to analyze student's errors and difficulties about the concept of irrational numbers. The instruments and interview were administered to 3 in-service mathematics teachers with various education background and teaching experiments. The results of this study are as follows. First, specialized content knowledge(SCK) were characterized by the fixation to symbolic representation like roots when they analyzed the concentration and overlooking of the representations of irrational numbers. Secondly, we observed the centralization tendency on symbolic representation and the little attention to other representations as the standard of judgment about irrational numbers. Thirdly, In-service teachers were influenced by content of students' error when they analyzed the error and difficulties of students. Lately, we confirmed that the content knowledge about the viewpoint of procept and actual infinity of irrational numbers are most important during the analyzing process.
Keywords
irrational number; concept and representations of irrational number; students' errors and difficulties; specialized content knowledge, SCK; analysis and explanation; decimal representation; geometric representation; incommensurability;
Citations & Related Records
Times Cited By KSCI : 4  (Citation Analysis)
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