• Title/Summary/Keyword: levels of arithmetical thinking

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An Analysis on Levels of the Arithmetical Thinking and Development of the Arithmetical Thinking Level Test (산술적 사고 수준의 분석 및 검사 도구 개발)

  • Lim, Miin;Chang, Hyewon
    • Journal of Elementary Mathematics Education in Korea
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    • v.21 no.4
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    • pp.575-598
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    • 2017
  • This study aims to explore the level-specific characteristics of arithmetical thinking based on the arithmetical thinking factors and develop an arithmetical thinking level test that can identify students' arithmetical thinking levels by specifying the levels of arithmetical thinking based on the factors. In order to solve the research problems, we categorized the arithmetical thinking factors into 1~4 levels based on the literature review and constructed items of the arithmetical thinking level test considering both content and process based on the arithmetical thinking factors and the level-specific characteristics of the arithmetical thinking which conformed to the Guttman scale. To investigate the adequacy of the analysis of the arithmetical thinking levels, we reanalyzed the level-specific characteristics of the arithmetical thinking by checking that it matched the factors classified to the test developed by the Guttman scale. From the results of this research, the following conclusions were drawn. First, the arithmetical thinking factors are categorized into four levels which have different characteristics. Second, the arithmetical thinking level test of this study was developed satisfying the Guttman scale and it reflects the level-specific characteristics of the arithmetical thinking levels from 1 to 4. It is possible to determine the students' arithmetical thinking level using this test. Third, according to the results of the final application of the arithmetical thinking level test for 5th and 6th graders, teachers should provide more abundant learning experiences related to the relation level (the level 3) and the application level (the level 4) to increase students' arithmetical thinking level.

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An Analysis of the Arithmetical Thinking Levels of the Students in 5th Grade (초등학교 5학년의 산술적 사고 수준 분석)

  • Lim, Miin
    • Journal of Elementary Mathematics Education in Korea
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    • v.24 no.1
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    • pp.89-108
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    • 2020
  • Since arithmetic is the foundation of school mathematics, it needs to be taught meaningfully in the direction of improving arithmetical thinking levels of students beyond the fluency of computing skills. Therefore, in this study, the arithmetical thinking levels of 100 students in 5th grade were analyzed by applying the arithmetical thinking level test. As a result, 82 students were at 1st level and 15 students were at 2nd level of the arithmetical thinking. I analyzed the characteristics of arithmetical thinking and types of errors and misconceptions made by the students, and derived some didactical implications for arithmetic education in elementary school mathematics.

A Case Study on Levels of Arithmetical Thinking of an Underachiever in Number and Operation - Focusing on a 6th Grader - (수와 연산 영역 부진 학생의 산술적 사고 수준에 관한 사례 연구 - 초등학교 6학년 한 학생을 대상으로 -)

  • Lim, Miin;Chang, Hyewon
    • Journal of Educational Research in Mathematics
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    • v.26 no.3
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    • pp.489-508
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    • 2016
  • Number and operation is the most basic and crucial part in elementary mathematics but is also well known as a part that students have lots of difficulties. A lot of researches have been done in various ways to solve this problem but it can't be solved fundamentally by emphasizing calculation method and skill. So we need to go over it in terms of relevant arithmetical thinking. This study aims to diagnose the cause of an underachiever's difficulties about arithmetic and finds a prescription for her by analyzing her level of arithmetical thinking based on Guberman(2014) and understanding about arithmetic. To achieve this goal, we chose an 6th grader who's having a hard time particularly in number and operation among mathematics strands and conducted a case study carrying out arithmetical thinking level tests on two separate occasions and analyzing her responses. As a result of analyzing data, her arithmetical thinking corresponded to Guberman's first level and it is also turned out that student is suffering from some arithmetic concepts. We suggest several implications for teaching of arithmetic at elementary school in terms of the development of arithmetical thinking based on analysis result and discussion about it.