本研究之目的有三：1.初探加法應用題之學習層次。2.探討學習層次對輕度智障兒童學習加法應用題解題成績之影響。3.探討教學策略對輕度智障兒童學習加法應用題解題成績之影響。針對上述三項研究問題，依序進行下列三項研究子題。
研究子題一「加法應用題學習層次之建立」，以二百名國小三、六年級的普通學童為研究對象，採用測驗法，測試每位受試者在「基本加算和解題能力測驗」上的作業成績，由於此套研究者自編的測驗卷上，包含七類加法應用題，每類題均有九題，總共六十三題，故根據全體樣本的施測結果，可以分別求出各類型題的通過百分比，與其間的相互依賴關係。資料採用通過百分比和Novillis模式加以處理。研究結果發現：通過百分比計算各類型題的答對比率來界定各類型題的難易度，Novillis模式則是計算每位受試者的平均答對題數來確認兩種類型題之間的難度階層。經過本研究的探討，三位數加三位數之內加法應用題的學習層次，初步建構如下：「合併類」或「改變類1」→「改變類2」→「比較類1」 →「平衡類1」→「平衡類2」→「比較類2」。
研究子題二「學習層次對輕度智障兒童學習加法應用題解題成績之影響」，根據研究子題一的結果，研究者使用加法應用題的學習層次來選題，作為本研究的實驗材料。選取國小卅二名三至六年級的輕度智障學生為研究對象，依其智力和解題技能分成兩個實驗組，分別接受不同學習層次加法應用題的實驗教學，採單因子實驗設計，自變項為不同學習層次組別，依變項為前後測作業的得分。資料採用相依樣本單因子變異數分析和重複量數單因子共變數分析加以處理。研究結果發現：輕度智障學生經過教學之後，在教學類型題和遷移類型題的前後測得分達到組內的顯著差異。而不同學習層次組別之輕度智障兒童經過教學之後，在教學類型題和遷移類型題的後測得分並未達到顯著差異。
研究子題三「教學策略對輕度智障兒童學習加法應用題解題成績之影響」，根據研究子題二的結果，選取兩名在前測、教學和後測得分均為０分的輕度智障學生為研究對象，依其解題錯誤的情形接受個別化教學，採交替處理實驗設計，自變項為教學策略，依變項為各項數學作業的得分。施測所得資料分別採用答對百分比和曲線圖分開處理。研究結果發現：實驗教學開始之後，教學策略產生立即性的教學效果，且進行到第四天之後，兩名受試者都達到滿分的標準，且維持了穩定的進步情形。惟受試者在加法應用題之進步量和有效促進受試者解題得分之教學策略類別有其個別差異。
根據上述結果，本研究對數學應用題之教學及未來研究提出數點建議。

THE EFFECTS OF LEARNING HIERARCHIES AND PROBLEM-SOLVING STRATEGIES ON THE ADDITION WORD PROBLEMS FOR THE
MILDLY RETARDED STUDENTS FROM THE ELEMENTARY SCHOOLS
Min-Huey Lin
Abstract
The purposes of this study were as follows : 1) to study the learning hierarchies of the addition word problems, 2)to study the influence of the learning hierarchies
on the abilities in solving the addition word problems from mildly retarded students’ , 3) to study the influence of the problem-solving strategies from the same group.
This study comprised three researches. The research 1. was designed to find out the learning hierarchies of addition word problems. The subjects of the study were 200 students from third and sixth grades students in elementary schools. The students had to answer the addition word problems in different context of language knowledge. The word problems used in this study included the patterns of change, combine, compare, and equalicy problems. The percentage and rate of correct responses in addition word problems were used as the indexes of learning hierarchies. The main finding of this research was that the patterns of the addition word problems were
in difficult order. The learning hierarchies of the addition word problems were
“combine“ or “change 1”, “change 2”, “compare 1”, “equalicy 1”, “equalicy 1”, and “compare 2”.
The research 2, based on the results of the research 1, was designed to explore the influence of the learning hierarchies on 32 mildly retarded students’ abilities in problem-solving. There were two experimental groups in these 32 students . In training stage, the group1 received the instruction of the lower learning hierarchies
in problem-solving, and the group2 received the instruction of the higher learning hierarchies in problem-solving. In pre-test and post-test stages, both groups answered on both different levels of the difficulty in problem-solving. The scores of correct responses in problem-solving were used as the index of the improvement of the students. They were found that the instruction of the learning hierarchies could improve problem-solving performance of the students, and the improvement was not significant between the two groups.
The research 3, based on the results of the research 2, was designed to investigate
the effect of three problem-solving strategies for two of the mildly retarded students with serious problem-solving difficulties. These Strategies included the object
strategy, the diagram strategy, and the cognitive strategy. An alternating treatment design was used. The percentage and rate of correct responses in problem-solving were used as the indexes of the improvement of the students. The clinical interviews and the protocol analysis were used to understand the error of the students’ problem-solving process . The main findings of this study were as follows: 1)during the instruction period , the correct percentage of the specific type of the problem was increased. But individual improved scores and problem-solving strategies were different. 2)after the instruction period, the percentage of correct responses of two
students increased obviously, whether the rate of correct responses was increased during instruction stage and maintain stage. 3)during the transfer period, the performances of the students in both groups was not superior to that of the pre-test period.
According to the aforementioned findings, application of the mathematical word problem instruction and further research were recommended.

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