An Error Pattern Analysis in a Volume of a Cylinder for Sixth Graders in Tainan City

• Main Authors: Wang, Te-Hsuan, 王德暄
• Other Authors: Huang, Chien-Chung
• Format: Others
• Language: zh-TW
• Published: 2018
• Online Access: http://ndltd.ncl.edu.tw/handle/w262p6

碩士 === 國立臺南大學 === 應用數學系碩士在職專班 === 106 === The purpose of this thesis was to investigate sixth graders’performance on calculating the volume of a cylinder in Tainan City. By generalizing their error patterns and analyzing the possible reasons why students made the mistakes was in order to know students' difficulties in learning to calculate the volume of a cylinder. The results could be taken as reference for teachers. To achieve the goal, I designed an achievement test of calculating the volume of a cylinder which was included 2 main aspects of volume of a cylinder. Furthermore,the test included 2 main aspects of a volume of a cylinder was classified into 3 categories each according to different types of questions.16 questions in 6 categories were included. There were 27 sixth graders in an elementary school of Tainan City selected to take the test and some of them were interviewed due to their performances and willingness. The results of the research were concluded as follows: 1. The performance of sixth graders on calculating a volume of a cylinder went variously in different categories of questions. a. There were 70% of the questions that students could answer correctly. It showed that most students could have the basic understanding of calculating a volume of a cylinder. b. The questions of a volume of a cylinder without illustrations and the questions of volume of composite solids only shown with illustrations received most incorrect responses and most students had the correct responses in the questions of volume of composite solids with illustrations and short description. c. Most of the students were willing to answer all the questions in this test but few students didn’t answer all of them due to the difficulties in reading and understanding the questions such as questions of a volume of a cylinder without illustrations,questions of a volume of a cylinder with illustrations and short description, the questions of volume of composite solidsonly shown without illustrations and the questions of volume of composite solids with illustrations and short description. 2. The error patterns were classified into 11categories: a. Students made calculation mistakes. b. Students misused the metric system units for volume or converted metric units of volume incorrectly. c. Students misread the questions. d. Students were not familiar with the definition of a trapezoid. e. Students were not familiar with the definition of a parallelogram. f. Students were not familiar with the definition of a triangle. g. Students answered the questions intuitively. h. Volume of composite solids were partitioned incorrectly. i. Misused the formula of a volume of a cylinder and area. j. Students were not familiar with the definition of a circle. k. Other reasons 3. The main reasons why sixth graders made errors in the unit of calculating the volume of a cylinder were as follows: a. False generalization and speculation were due to the influence of the previously learned knowledge. b. Students had incomplete understanding of geometric figures. c. Students misread, skipped or speculated the questions without reading thoroughly. d. Lack of basic arithmetic skills caused errors. e. Carelessness led to errors. f. Students were incapable of understanding the questions.