The Concept and Performance on Both Reduced and Enlarged Graphs of Seventh Grade Students.

• Main Authors: Yi-ching Wu, 吳宜靜
• Other Authors: None
• Format: Others
• Language: zh-TW
• Online Access: http://ndltd.ncl.edu.tw/handle/97270810976506172546

碩士 === 國立臺南大學 === 應用數學研究所 === 93 === Four main goals of this research included: (1) Exploring the directing-viewing comprehension and recognition of both reduced and enlarged shapes by the 7th grade students (2) Exploring the basic comprehension of properties and characteristics of both reduced and enlarged shapes by the 7th grade students. (3) Understanding the mapping skills of both reduced and enlarged shapes by the 7th grade students. (4) Exploring the overall performance and misconceptions of both reduced and enlarged shapes by the 7th grade students. To achieve above goals, this research used methods including paper-and-pencil tests, writing tests, and interviews. The subjects are from first-year students of two public junior high schools and 135 valid questionnaires were collected. All collected data was entered into the computer for statistical analyses. Findings of this research include: (1) The directing-viewing comprehension and recognition of both reduced and enlarged shapes by the 7th grade students are easily affected by the positioning of these shapes. Children tend to neglect the properties of similar shapes. (2) The 7th grade students can recognize both reduced and enlarged shapes based on the scale and their symmetries but are easily affected by the positioning of the shapes. They tend to neglect the scale proportion uniformity. The differences between the perimeter and area cannot be detected when the 2-dimensional shapes is enlarged or reduced. (3) The comprehension of the basic properties of both reduced and enlarged shapes affect students’ mapping skills more than the recognition of those shapes. (4) The 7th grade students can not fully apply the concepts they learned on both reduced and enlarged shapes on their mapping skills. Based on these findings, an explicit definition of the “reduced shapes”, “enlarged shapes”, and the “similar shapes” should be lectured in elementary school math class. And teacher can provide a diversity of thinking ways to develop the abilities of applying transformations and using symmetry to analyze mathematical situations about geometric relationships.