• Journal of Educational Research in Mathematics
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• v.27 no.3
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• pp.431-449
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• 2017

Acute triangles and obtuse triangles are defined according to the classification of triangles by angles. The definitions of acute triangles and obtuse triangles are difficult for students because they are related to different logical elements. The purpose of this study is to seek desirable methods for teaching the classification of triangles by angles related to logic. To do this, based on the theoretical consideration and the longitudinal analysis of the elementary mathematics textbooks, some implications are found for teaching. And then the lesson was planned and applied to $4^{th}$ graders. After the lesson, we reviewed and analyzed their worksheets and test results for examining the effects by teaching methods. Based on the result, we discussed and made some didactical suggestions for teaching the classification of triangles by angles.

• Education of Primary School Mathematics
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• v.18 no.1
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• pp.45-59
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• 2015

This study focused on the classification of triangles by angles in elementary school mathematics. We examined Korean national mathematics curriculum from the past to the present. We also examined foreign textbooks and the Euclid's . As a result, it showed that the classification is not indispensable from the mathematical and the perceptual viewpoint. It is rather useful for students to know the names of triangles when studying upper level mathematics in middle and high schools. This study also suggested that the classification be introduced in elementary school mathematics in the context of reasoning and inquiring as shown foreign textbooks, and example topics for the reasoning and inquiring.

• Communications of Mathematical Education
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• v.24 no.2
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• pp.325-344
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• 2010

The purpose of this study is to investigate what influences students' preferences on empirical and deductive proofs and find their relations. Although empirical and deductive proofs have been seen as a significant aspect of school mathematics, literatures have indicated that students tend to have a preference for empirical proof when they are convinced a mathematical statement. Several studies highlighted students'views about empirical and deductive proof. However, there are few attempts to find the relations of their views about these two proofs. The study was conducted to 47 students in 7~9 grades in the transition from empirical proof to deductive proof according to their mathematics curriculum. The data was collected on the written questionnaire asking students to choose one between empirical and deductive proofs in verifying that the sum of angles in any triangles is $180^{\circ}$. Further, they were asked to provide explanations for their preferences. Students' responses were coded and these codes were categorized to find the relations. As a result, students' responses could be categorized by 3 factors; accuracy of measurement, representative of triangles, and mathematics principles. First, the preferences on empirical proof were derived from considering the measurement as an accurate method, while conceiving the possibility of errors in measurement derived the preferences on deductive proof. Second, a number of students thought that verifying the statement for three different types of triangles -acute, right, obtuse triangles - in empirical proof was enough to convince the statement, while other students regarded these different types of triangles merely as partial examples of triangles and so they preferred deductive proof. Finally, students preferring empirical proof thought that using mathematical principles such as the properties of alternate or corresponding angles made proof more difficult to understand. Students preferring deductive proof, on the other hand, explained roles of these mathematical principles as verification, explanation, and application to other problems. The results indicated that students' preferences were due to their different perceptions of these common factors.

• Education of Primary School Mathematics
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• v.20 no.2
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• pp.163-175
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• 2017

The purpose of the study is to identify the effect of length and right angle indication on the understanding of the concept of the figure when presenting the task of classifying the plane figures. we recorded thirty three 4th grade students' performance with eye-tracking technologies and analyzed the correct answer rate and gaze duration. The findings from the study were as follows. First, correctness rate increased and Gaze duration decreased by marking length in isosceles triangle and equilateral triangle. Second, correctness rate increased and Gaze duration decreased by marking right angle in acute angle triangle and obtuse triangle. Based on these results, it is necessary to focus on measuring the understanding of the concept of the figure rather than measuring the students' ability to measure by expressing the length and angle when presenting the task of classifying the plane figures.