徑路搜尋方法之加減法文字題知識結構分析

The Pathfinder Analysis on Knowledge Structure of Addition and Subtraction Word Problems

林原宏(Yuan-Horng Lin) ； 黃美盼(Mei-Pan Huang) ； 易正明(Jenq-Ming Yih)

《測驗統計年刊》 15期_上 (2007/06) Pp. 29-57

https://doi.org/10.6773/JRMS.200706.0029

摘要

本研究旨在進行國小學童的加減法文字題知識結構之徑路搜尋分析，以二年級學童為研究對象。利用試題反應理論和概念類似係數的計算，可獲得不同能力值下的加減法文字題知識結構。
「加減法文字題解題測驗」，根據實證資料之徑路搜尋分析，主要發現如下：
一、三個相似性指數均能對能力值做有效之預測，且GTD指數預測效果最高。
二、高能力值組知識結構圖與標準參照知識結構圖較為相似，中低能力值組知識結構圖與標準參照知識結構圖較不相似。
三、以集群分析方法將受試者分群，各群的知識結構有其特殊性。
四、高分群學童知識結構圖很接近標準參照知識結構圖，教師可進行充實活動。中分群學童答對率較低的概念位於同一區，教師應進行該區概念的補救教學。低分群學童在概念1和概念11有多餘鏈結，可能對概念不甚了解，教師須利用課外時間校正學生的錯誤概念。
根據結果，研究者提出未來知識結構方法論研究之建議，以及有關加減法概念的診斷及教學的參考。

關鍵字

加減法文字題 ； 知識結構 ； 徑路搜尋 ； 試題反應理論

並列摘要

The purpose of this study is to analyze addition and subtraction word problems knowledge structure by pathfinder. There are 324 pupils in this research. According to the response of addition and subtraction on word problems, the researcher wants to investigate the knowledge structure of addition and subtraction. Another methodologies, item response theory, factor analysis and cluster analysis, are applied so that the features of varied knowledge structure are discussed. The main results of this research are as follows:
1. All the three proximity indexes can explain the ability of pupils effectively. Moreover, the most effective index is GTD index.
2. The knowledge structure of high ability group is similar to the that of criterion-referenced one. On the contrary, the knowledge structure of middle and low ability group is relatively dissimilar to that of criterion-referenced one.
3. The method of cluster analysis can help group examinees effectively. There are lots of similarities on knowledge structure between each group.
4. Pupils in high score group have knowledge structures which are very close to that of criterion-referenced one. Therefore, teachers can carry out substantial activities. Pupils in middle scored group have low rate of correct responses and conception in the same area. Hence, teachers can carry out conceptual remedial instruction in that area. Pupils in low scored group have redundant links in concept 1 and concept 11. It is likely that they have no any idea with concepts so that teachers should design extracurricular to correct students' unpracticed section.
Based on the findings and results, some suggestions for practical teaching and future research are discussed.

並列關鍵字

addition and subtraction word problems ； knowledge structure ； pathfinder ； item response theory

參考文獻

江淑卿(1997)。知識結構的重要特性之分析暨促進知識結構教學策略之實驗研究。國立臺灣師範大學教育心理與輔導研究所博士論文（未出版）。

余民寧、林曉芳、蔡佳燕(2001)。國小學生數學知識結構認知診斷評量之研究。國立政治大學教育與心理研究。24，263-302。

呂玉琴()。

呂玉琴譯、Thomas P. Carpenter著(1988)。加、減法文字題的分類、解題策略及影響因素。國民教育。28(8, 9)，17-29。

林原宏(1996)。知識結構分析－徑路搜尋、多向度量尺和集群分析的方法論探討。測驗統計年刊。4，47-69。