• Title/Summary/Keyword: 대수적 사고 요소

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Understanding of Algebraic Proofs Including Literal Expressions: Expressions or Contexts? (문자식을 포함한 대수 증명에 대한 중학교 3학년 학생들의 이해 연구 - 문맥과 문자식, 어느 것을 보는가 -)

  • Chang, Hyewon;Kang, Jeong Gi
    • Journal of Educational Research in Mathematics
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    • v.24 no.3
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    • pp.359-374
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    • 2014
  • Students' difficulties and errors in relation to mathematical proofs are worth while to say one of the dilemmas in mathematics education. The potential elements of their difficulty are scattered over the process of proving in geometry as well as algebra. This study aims to investigate whether middle school students understand the context of algebraic proof including literal expressions. We applied 24 third-grade middle school students a test item which shows a proof including a literal expression and missing the conclusion. Over the half of them responded wrong answers based on only the literal expression without considering its context. Three of them were interviewed individually to show their thinking. As a result, we could find some characteristics of their thinking including the perspective on proof as checking the validity of algebraic expression and the gap between proving and understanding of proof etc. From these, we also discussed about several didactical implications.

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Development of Hazard-Level Forecasting Model using Combined Method of Genetic Algorithm and Artificial Neural Network at Signalized Intersections (유전자 알고리즘과 신경망 이론의 결합에 의한 신호교차로 위험도 예측모형 개발에 관한 연구)

  • Kim, Joong-Hyo;Shin, Jae-Man;Park, Je-Jin;Ha, Tae-Jun
    • KSCE Journal of Civil and Environmental Engineering Research
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    • v.30 no.4D
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    • pp.351-360
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    • 2010
  • In 2010, the number of registered vehicles reached almost at 17.48 millions in Korea. This dramatic increase of vehicles influenced to increase the number of traffic accidents which is one of the serious social problems and also to soar the personal and economic losses in Korea. Through this research, an enhanced intersection hazard prediction model by combining Genetic Algorithm and Artificial Neural Network will be developed in order to obtain the important data for developing the countermeasures of traffic accidents and eventually to reduce the traffic accidents in Korea. Firstly, this research has investigated the influencing factors of road geometric features on the traffic volume of each approaching for the intersections where traffic accidents and congestions frequently take place and, a linear regression model of traffic accidents and traffic conflicts were developed by examining the relationship between traffic accidents and traffic conflicts through the statistical significance tests. Secondly, this research also developed an intersection hazard prediction model by combining Genetic Algorithm and Artificial Neural Network through applying the intersection traffic volume, the road geometric features and the specific variables of traffic conflicts. Lastly, this research found out that the developed model is better than the existed forecasting models in terms of the reliability and accuracy by comparing the actual number of traffic accidents and the predicted number of accidents from the developed model. In conclusion, it is expect that the cost/effectiveness of any traffic safety improvement projects can be maximized if this developed intersection hazard prediction model by combining Genetic Algorithm and Artificial Neural Network use practically at field in the future.