• 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.

• 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.