本研究旨在探討「關係子題」與「線圖」對國小三年級數學低成就學生（依不同工作記憶問題，可分為語意記憶困難型、視覺空間困難型）理解比較型文字題中難度最高「參照量未知」題之助益。研究過程包含兩階段，第一階段透過「基礎數學概念評量」、「語文工作記憶測驗」、「視空間工作記憶作業」三項篩得41名語意記憶困難數低生及57名視覺空間困難數低生；第二階段兩類數低生均須接受研究者參考葉雪梅（民79）實驗材料所改編之「原始參照量未知題」、「附加『綜合關係子題』參照量未知題」、「附加『線圖』參照量未知題」等三份試題。結果主要有三點發現：（一）工作記憶為一可區分數學低成就群體之關鍵認知特質；（二）綜合關係子題對語意記憶困難數低生最具促進理解之效；（三）線圖對視覺空間困難數低生最具促進理解之效。最後，基於研究結果及限制，針對學術、實務兩個面向提出具體建議。

The purpose of this study is to discuss the effectiveness of “relative subproblem” and “line diagram” on mathematics underachievers’ comprehension of “unknown reference set problems”, which are the most difficult compare problems.
98 third-graders children were recruited from 8 elementary schools in Taoyuan City, and divided into 2 groups by their working memory difficulty: representation or retrieval of arithmetic facts from semantic memory (N=41); visuospatial representation of numerical information (N=57).
The process of this study includes 2 stages. At stage 1, all participants were divided into 2 groups via completing “Basic Math Concept Test” (Ko, 1999), “Working Memory Test” (Tzeng, 1999), “Visuospatial Working Memory Tasks” (Chen, 2004); at stage 2, they had to finish 3 types of unknown reference set problems, referred to the experimental materials of Yeh’s study (1990).
The major findings of this study are as follows: (1) Working memory is a critical cognitive component that can distinguish mathematics underachievers. (2) “Integrative Relative Subproblems” have great effectiveness on mathematics underachievers with the difficulty of representation or retrieval of arithmetic facts from semantic memory. (3) “Line Diagram” have great effectiveness on mathematics underachievers with the difficulty of visuospatial representation of numerical information.
Lastly, this study provides recommendations on academic and practical perspectives according to the study results and its restriction.

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