• School Mathematics
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• v.12 no.3
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• pp.371-388
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• 2010

The goals of this study are to inquire middle school students' understanding about prime number and to propose pedagogical implications for school mathematics. Written questionnaire were given to 198 Korean seventh graders who had just finished learning about prime number and prime factorization and then 20 students participated in individual interviews for member checks. In defining prime and composite numbers, the students focused on distinguishing one from another by numbering of factors of agiven natural number. However, they hardly recognize the mathematical connection between prime and composite numbers related on the multiplicative structure of natural number. This study suggests that it is needed to emphasize the conceptual relationship between divisibility and prime decomposition and the prime numbers as the multiplicative building blocks of natural numbers based on the Fundamental Theorem of Arithmetic.

• The Mathematical Education
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• v.58 no.1
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• pp.1-20
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• 2019

As the importance of algebraic thinking in elementary school has been emphasized, the links between fraction knowledge and algebraic thinking have been highlighted. In this study, we analyzed the solution methods and characteristics of thinking by fifth graders who have not yet learned fraction division when they solved 'reverse fraction problems' (Pearn & Stephens, 2018). In doing so, the contexts of problems were extended from the prior study to include the following cases: (a) the partial quantity with a natural number is discrete or continuous; (b) the partial quantity is a natural number or a fraction; (c) the equivalent fraction of partial quantity is a proper fraction or an improper fraction; and (d) the diagram is presented or not. The analytic framework was elaborated to look closely at students' solution methods according to the different contexts of problems. The most prevalent method students used was a multiplicative method by which students divided the partial quantity by the numerator of the given fraction and then multiplied it by the denominator. Some students were able to use a multiplicative method regardless of the given problem contexts. The results of this study showed that students were able to understand equivalence, transform using equivalence, and use generalizable methods. This study is expected to highlight the close connection between fraction and algebraic thinking, and to suggest implications for developing algebraic thinking when to deal with fraction operations.