• Education of Primary School Mathematics
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• v.27 no.4
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• pp.481-500
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• 2024

This study examined argumentation in lessons for mathematically gifted elementary students, focusing on two tasks: 1) proving how many convex polygons can be formed using all the pieces of a seven-piece puzzle, and 2) proving which convex polygons cannot be formed with a seven-piece puzzle in practice. The argumentation in the classroom was analyzed from the perspectives of 'proving as problem-solving,' 'proving as convincing,' and 'proving as socially-embedded practice,' as suggested by Stylianides et al. (2017). Additionally, Toulmin's model of argument, as applied by Zhuang and Conner (2024), was used as an analytical framework to structurally understand the argumentation process. The research findings indicated that students successfully proved both tasks. Moreover, the specific conditions described in the data played a key role in enhancing argumentation in the classroom. Finally, in lessons emphasizing argumentation, teachers needed to develop classroom practices that encouraged the exploration of tasks based on mathematical reasoning.

• Journal of Korea Multimedia Society
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• v.20 no.12
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• pp.1890-1900
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• 2017

Tangram game consists of seven pieces of polygons such as triangle, square, and parallelogram. Typical methods of image processing for object recognition may suffer from the existence of side thickness and shadow of the puzzle pieces that are dependent on the pose of 3D-shaped puzzle pieces and the direction of light sources. In this paper, we propose an image processing method that recognizes simple convex polygon-shaped objects irrespective of thickness and pose of puzzle objects. Our key algorithm to remove the thick side of piece of puzzle objects is based on morphological operations followed by logical operations with edge image and background image. By using the proposed object recognition method, we are able to implement a stable tangram game applications designed for tablet computers with front camera. As the experimental results, recognition rate is about 86 percent and recognition time is about 1ms on average. It shows the proposed algorithm is fast and accurate to recognize tangram blocks.

• Journal of Educational Research in Mathematics
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• v.17 no.3
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• pp.221-232
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• 2007

In school mathematics, activities to make particular convex polygons by attaching edgewise some pieces of tangram are introduced. This paper focus on deepening these activities. In this paper, by using Pick's Theorem and 和 草's method, all the convex polygons by attaching edgewise seven pieces of tangram, Sei Shonagon(淸少納言)'s tangram, and Pythagoras puzzle are found out respectively. By using Pick's Theorem to the square seven-piece puzzles satisfying conditions of the length of edge, it is showed that the number of convex polygons by attaching edgewise seven pieces of them can not exceed 20. And same result is obtained by generalizing 和 草's method. The number of convex polygons by attaching edgewise seven pieces of tangram, Sei Shonagon's tangram, and Pythagoras puzzle are 13, 16, and 12 respectively.