國小一般智能資賦優異學生數學解題能力之相關因素探討

本研究旨在探討國小資優生的數學解題能力與其相關因素(個人、家庭與學校)之研究。以中部地區資優生共146名為研究對象。以「數學解題能力相關因素調查問卷」與「數學科問題解決測驗」為工具進行研究，並透過t檢定、積差相關、單因子變異數分析、逐步多元迴歸分析、典型相關等統計方法進行分析，並獲得以下結論：1.國小資優生在數學解題能力方面，場地獨立型組優於場地依賴型組；數學態度「高積極程度」組優於「低積極程度」組。2.以「認知型式」、「數學探究動機」、「自我修正」為重要的預測變項。3.國小資優生的數學解題能力與其相關因素(個人、家庭與學校)之典型相關達顯著水準，後者三個因素可解釋前者總變異量的百分之二十九。

關鍵字

數學解題能力；認知型式；數學態度；後設認知

並列摘要

The purpose of the study was to investigate the differences of personal factors, family factors, school factors among elementary gifted students and their influence in mathematical problem solving ability. The subjects of the study included 146 fifth graders of gifted students at 7 elementary schools in the Taichung metropolitan area. The following research instruments were employed：＂Mathematics Problem Solving Questionnaire＂ and ＂Mathematics Problem Solving Test. The collected data were analyzed by descriptive statistics, t-test, one-way ANOVA, product-moment correlation, Shceffé method multiple comparison, step-wise regression analysis and Canonical correlation. The main findings of this study were indicated as followings: 1. There is a significant difference in mathematics problem-solving ability for gifted students with different cognitive style and mathematics attitudes.2.Cognitive style, explorative motive of mathematics attitudes and self-correcting are major predictors for mathematics problem-solving ability. The typical relationship among personal factors, family factors, school factors and mathematics problem-solving ability for elementary gifted students is significant. These three factors can explain 29% of the total variation of mathematics problem-solving ability.