The Performance of Sixth Graders on Geometry Problems that are Conducive to the Use of the Equality Axioms
| Autor: | Chien-Hua Cheng, 鄭鈐華 |
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| Rok vydání: | 2003 |
| Druh dokumentu: | 學位論文 ; thesis |
| Popis: | 91 The Equality Axioms in this study mean “If equals be added to equals, the wholes are equal.” and “If equals be subtracted from equals, the remainders are equal.”; the former is an additional type, and the latter is a subtractive type. There are two main purposes for this study. The first one is to understand sixth graders’ performance of using the Equality Axioms in solving different addional and subtractive geometry problems. The second is to understand how students recognize to solve problems with Equality Axioms, and what problem solving strategies the other students use and why they do. This study was a investigation through the written test designed by the researcher, and the way of case study matched with interview. The structure of the instrument was based on Equality Axioms’ three components by Tam & Lien (2002). There were 29 students in this study. They were chosen from a sixth class of an elementary school in Taipei County. And eight different achievers were chosen for the interview. To understand students’ performance in using Equality Axioms, this study took the way of descriptive statistic in the quantitative analysis, and also adopted the protocol analysis in qualitative analysis. To get the realistic data, we also used the data triangulation. By these methods, we could understand sixth graders’ performance of using Equality Axioms in different geometry problems. The results in the study were: (a)The performance of different backgrounds’ sixth graders of using Equality Axioms was different. (b)High achievers used Equality Axiom better in area and length problems in 「a=b,c=d」type, and they usually used.other strategies to solve area problems in 「a=a,c=d」type. (c)High achiever used Equality Axioms in additional geometry problems better than subtractive ones. (d)No matter in what geometry problems, low achievers tended to use other strategies to solve problems.(e)Students thought of using Equality Axioms by paying attention to equal conditions, recognizing out the equal parts in the sketch, or trying to use numbers to calculate, use symbles, or write algebra equations. (f)Most of students who didn’t use Equality Axioms usually followed intuitive rules to solve problems. |
| Databáze: | Networked Digital Library of Theses & Dissertations |
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