• Education of Primary School Mathematics
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• v.27 no.2
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• pp.155-171
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• 2024

This study compared and analyzed students' reasoning processes and justification methods when introducing the concept of "the sum of angles in a triangle" in mathematics classes with a focus on both measurement and geometric aspects. To confirm this, the research was conducted in a 4th-grade class at H Elementary School in Suwon, Gyeonggi-do, South Korea. The conclusions drawn from this study are as follows. First, there is a significant difference when introducing "the sum of angles in a triangle" in mathematics classes from a measurement perspective compared to a geometric perspective. Second, justifying the statement "the sum of angles in a triangle is 180°" is more effective when explained through a measurement approach, such as "adding the sizes of the three angles gives 180°," rather than a geometric approach, such as "the sum of the angles forms a straight angle." Since elementary students understand mathematical knowledge through manipulative activities, the level of activity is connected to the quality of mathematics learning. Research on this reasoning process will serve as foundational material for approaching the concept of "the sum of angles in a triangle" within the "Geometry and Measurement" domain of the Revised 2022 curriculum.

• Education of Primary School Mathematics
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• v.21 no.1
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• pp.75-91
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• 2018

This study examines the educational meaning of the sum of the angles of a triangle in elementary school mathematics and discusses the introduction and explanation methods to convey the meaning faithfully. First, we investigated how to introduce the sum of the angles of a triangle in the Korean national mathematics curriculums from the past to the present and surveyed the experiences and opinions of the teachers. The results of the survey are summarized and discussed in three parts: The context of 'arranging angles activities' and 'measuring angles activities', the methods to convey the meaning of the sum of the angles of a triangle as an invariance, and other details.

• School Mathematics
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• v.12 no.1
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• pp.45-60
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• 2010

In school mathematics, gakdo(korean, ie angular measure in english) lost effectiveness as a term, on the other hand, an expression gak-ui-kugi(korean, ie size of angle in english) is prevalent these days. So it is necessary to accept this expression. It is necessary to specify in textbook that the size of angle rely on the degree of gap between two edges regardless of the length of edges. The content of curriculum manual and the content of textbooks must be reconciled. Random units for measuring the size of angle are not contained in textbooks. It can be possible, but it is not carried out actually. So, it is necessary not to require it in curriculum manual considering this circumstance. In curriculum manual, it is necessary to specify the role of 1-right angle as a standard unit, and situations to use it must be presented in textbooks. In cut-paste method of finding the sum of the size of three angles in a triangle and the sum of the size of four angles in a quadrilateral, keeping a straight angle and one rotation in mind, an explanation is based upon a premise that students know how to express the $180{^{\circ}}$ and $360{^{\circ}}$ in figure as a result. It is a leap of logic.