應用模糊調查與統計方法於國中數學成就評量之難度分析

Abstract

應用模糊調查與統計方法去瞭解國中數學評量試題在教師與學生間以及學生不同背景（性別、對數學喜歡程度、課後數學練習時間及有無參加數學相關課外活動）對試題難易度的認知差異。結果顯示：在教師與學生之間、性別、學生對數學喜歡程度及課後數學練習時間方面有顯著差異，但是在參加課後數學相關活動方面對於數學科試題的難易度認知並沒有顯著的差異性存在。

Using fuzzy statistical methods to understand whether the cognitive difficulty scales of the junior high school mathematics assessment questions shows difference between those given by teachers and students, by students with different genders, with different preferences, with different amounts of time spent on math practice after school, with participation or not in various math related seminars.\r\nResult demonstrates that significant difference between teachers and students, between students with different genders, between students with different preferences, and between students with different amounts of time spent on math practice after school. However, there is no significant difference between students with participation or not in various math related seminars.

1. 前言...................................................1\r\n2. 數學成就評量............................................3\r\n2.1 傳統成就評量...........................................3\r\n2.2 模糊評量方法...........................................6\r\n2.3 整合型成就評量.........................................10\r\n3. 模糊統計量..............................................11\r\n3.1 模糊樣本平均數.........................................11\r\n3.2 模糊樣本眾數...........................................12\r\n3.3 模糊類別資料之卡方齊一性檢定............................18\r\n4. 實證探討.............................................. 20\r\n4.1 測驗分析..............................................20\r\n4.2 教師與學生對數學科試題難易度分析.........................24\r\n4.3 不同性別學生對數學科試題難易度分析.......................25\r\n4.4 學生對數學喜歡程度與數學科試題難易度分析..................26\r\n4.5 學生課後數學練習時間與數學科試題難易度分析................27\r\n4.6 學生參與課外活動與數學科試題難易度分析...................28\r\n5. 結論...................................................30\r\n參考文獻..................................................32\r\n附錄......................................................33\r\n附錄一：試題難易度調查表(教師版).............................33\r\n附錄二：試題難易度調查表(學生版).............................35\r\n附錄三：問卷調查結果........................................37\r\n附錄四：試題卷.............................................41\r\n附錄五：九年一貫數學領域分年細目.............................47