삼각형의 넓이를 두 직사각형의 넓이의 합 또는 차로 구하는 변형 문제 고찰
A Study on the Transformation for Finding the Area of a Triangle as the Sum or Difference of the Areas of two Rectangles
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This study focuses on using the concept of ‘double area transformation of a right triangle’ to solve triangle problems. The usage rate of this method among pre-service elementary teachers was low, revealing a lack of manipulative skills emphasized in elementary mathematics education. Students tend to rely on existing knowledge to solve problems, which relates to Piaget's cognitive development theory. The difference in response rates between inscribed and non-inscribed triangle problems highlights issues in manipulative skills. Through the partitioning shown in [Table V-1] and [Table V-2], which reflects the results of manipulative activities, students can experience an application that justifies the well-known area formula for a triangle with known vertex coordinates. This is done without using the distributive property and only permits operations involving multiplying by negative numbers to ensure the side lengths of rectangles are positive, providing valuable learning material.
Abstract
This study focuses on using the concept of ‘double area transformation of a right triangle’ to solve triangle problems. The usage rate of this method among pre-service elementary teachers was low, revealing a lack of manipulative skills emphasized in elementary mathematics education. Students tend to rely on existing knowledge to solve problems, which relates to Piaget's cognitive development theory. The difference in response rates between inscribed and non-inscribed triangle problems highlights issues in manipulative skills. Through the partitioning shown in [Table V-1] and [Table V-2], which reflects the results of manipulative activities, students can experience an application that justifies the well-known area formula for a triangle with known vertex coordinates. This is done without using the distributive property and only permits operations involving multiplying by negative numbers to ensure the side lengths of rectangles are positive, providing valuable learning material.