臺灣博碩士論文加值系統

本研究旨在發展三階段評量診斷工具，探討國小五年級學童比率問題的解題表現。主要目的有：一、發展用以診斷學童比率問題解題表現之三階段評量。二、根據三階段評量，探討學童於比率問題在後設認知之表現。三、根據三階段評量，分析學童於比率問題的解題類型。
　　本研究以五所國民小學五年級學童，共272人為研究對象，採用自編「國小五年級數學比率單元的三階段評量」為研究工具。研究結果顯示，學童在比率問題的表現，部分量未知的表現優於比率未知的表現，在三種數值類型中，分數與小數的表現優於百分率的表現。此外後設認知的表現與三階段評量的結果相似，且敘述性知識的表現與後設認知的表現具有相關性。因此三階段評量可以從學童解題類型中診斷出迷思概念，與展現學生多元的解題想法。
本研究之結果與發現，教師依據學童所展現的解題想法，可提供教師在數學教學設計與進行補救教學上的參考，以及對未來相關研究的建議。

This thesis aims to develop a three-tier assessment to evaluate the performance of the fifth-grade students for the ratio problem. There are three phases in this research. To start with, design a three-tier assessment for the participants, which focuses on the ratio problem mainly. Next, investigate the performance of metacognition based on the three-tier assessment. Lastly, analyze students problem-solving types, which apply to the test.
This study includes 272 subjects in fifth-grade who come from five different elementary schools. We adopt “Three-tier Assessment of Ratio for Fifth Graders” developed by ourselves. The results indicate that the participants performed better on unknown within a part of the whole problems than unknown within ratio problems. Besides, we uncover the fact that fractional type and decimal type have better effects than percentage type. In our experiments, metacognition results are similar to the three-tier assessment, which imply that declarative knowledge is well correlated with metacognition. We conclude that the three-tier assessment can show students' diversity of ideas and diagnose the misconception via the problem types.
The results and findings of this study can provide teachers with reference for teaching design and remedial teaching for school children, and the researcher also make suggestions for further researches in the future based on the research results.

目錄
摘要 I
目錄 III
表次 V
圖次 VII
第一章 緒論 1
第一節 研究動機 1
第二節 研究目的 4
第三節 名詞解釋 5
第四節 研究範圍 6
第二章 文獻探討 8
第一節 比率與百分率的意涵與相關研究 8
第二節 三階段評量意涵與編製 16
第三節 建構反應題之相關研究 23
第四節 後設認知的意義與評量 30
第三章 研究方法 40
第一節 研究架構 40
第二節 研究步驟 41
第三節 研究對象 42
第四節 研究工具 44
第五節 分析方法 55
第四章 結果與討論 56
第一節 學童在比率問題的表現情形 56
第二節 後設認知與解題表現之相關分析 62
第三節 學童於建構反應題的解題類型分析 66
第五章 結論與建議 101
第一節 結論 101
第二節 建議 106
參考文獻 109
一、中文部分 109
二、英文部分 112
附錄 117
附錄一 正式施測卷 117
附錄二 解題類型分析 　119

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