The Mathematical Education (한국수학교육학회지시리즈A:수학교육)

Korean Society of Mathematical Education (한국수학교육학회)
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An Analysis of Errors in Describing Solving Process for High School Geometry and Vectors

고등학교 기하와 벡터 과목에서 풀이과정 서술의 오류 분석

  • Received : 2016.10.25
  • Accepted : 2017.02.11
  • Published : 2017.02.28
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Abstract

By analysing the examination papers from third grade high school students, we classified the errors occurred in the problem solving process of high school 'Geometry and Vectors' into several types. There are five main types - (A)Insufficient Content Knowledge, (B)Wrong Method, (C)Logical Invalidity, (D)Unskilled Expression and (E)Interference.. Type A and B lead to an incorrect answer, and type C and D cannot be distinguished by multiple-choice or closed answer questions. Some of these types are classified into subtypes - (B1)Incompletion, (B2)Omitted Condition, (B3)Incorrect Calculation, (C1)Non-reasoning, (C2)Insufficient Reasoning, (C3)Illogical Process, (D1)Arbitrary Symbol, (D2)Using a Character Without Explanation, (D3) Visual Dependence, (D4)Symbol Incorrectly Used, (D5)Ambiguous Expression. Based on the these types of errors, answers of each problem was analysed in detail, and proper ways to correct or prevent these errors were suggested case by case. When problems that were used in the periodical test were given again in descriptive forms, 67% of the students tried to answer, and 14% described flawlessly, despite that the percentage of correct answers were higher than 40% when given in multiple-choice form. 34% of the students who tried to answer have failed to have logical validity. 37% of the students who tried to answer didn't have enough skill to express. In lessons on curves of secondary degree, teachers should be aware of several issues. Students are easily confused between 'focus' and 'vertex', and between 'components of a vector' and 'coordinates of a point'. Students often use an undefined expression when mentioning a parallel translation. When using a character, students have to make sure to define it precisely, to prevent the students from making errors and to make them express in correct ways.

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References

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  1. 선다형 문제와 서술형 문제의 점수 차이와 이에 대한 학생들의 인식 -고등학교 기하 교과를 중심으로- vol.57, pp.3, 2017, https://doi.org/10.7468/mathedu.2018.57.3.197