Mathematical Reasoning Ability and Error Comparison through the Descriptive Evaluation of Mathematically Gifted Elementary Students and Non-Gifted Students

초등수학영재와 일반학생의 서술형 평가를 통한 수학적 추론 능력 및 오류 비교

  • 김동관 (대구도남초등학교) ;
  • 류성림 (대구교육대학교 수학교육과)
  • Received : 2014.03.17
  • Accepted : 2014.04.28
  • Published : 2014.04.30

Abstract

The purpose of this study is to figure out the perceptional characteristics of mathematically gifted elementary students by comparing the mathematical reasoning ability and errors between mathematically gifted elementary students and non-gifted students. This research has been targeted at 63 gifted students from 5 elementary schools and 63 non-gifted students from 4 elementary schools. The result of this research is as follows. First, mathematically gifted elementary students have higher inductive reasoning ability compared to non-gifted students. Mathematically gifted elementary students collected proper, accurate, systematic data. Second, mathematically gifted elementary students have higher inductive analogical ability compared to non-gifted students. Mathematically gifted elementary students figure out structural similarity and background better than non-gifted students. Third, mathematically gifted elementary students have higher deductive reasoning ability compared to non-gifted students. Zero error ratio was significantly low for both mathematically gifted elementary students and non-gifted students in deductive reasoning, however, mathematically gifted elementary students presented more general and appropriate data compared to non-gifted students and less reasoning step was achieved. Also, thinking process was well delivered compared to non-gifted students. Fourth, mathematically gifted elementary students committed fewer errors in comparison with non-gifted students. Both mathematically gifted elementary students and non-gifted students made the most mistakes in solving process, however, the number of the errors was less in mathematically gifted elementary students.