臺灣博碩士論文加值系統

動態評量對國小二年級數學學習障礙兒童數學解題之應用成效
摘　要
本研究旨在探索數學解題動態評量對數學障礙兒童應用成效之研究，而主要研究目的在於：一、瞭解數學學習障礙學生「動態評量」表現，與「原來數學能力」、「語文理解」、「非語文智力」彼此之間的關聯。二、以動態評量方式，分析二年級數學學習障礙學生對那些數學問題較感困難。三、以動態評量方式，診斷二年級數學學習障礙學生錯誤類型的結果。四、探討二年級數學學習障礙學生的「原來數學能力」、「語文理解」、「非語文智力」對「數學解題動態評量」之預測功能。五、瞭解接受動態評量的學生，對動態評量所持有之態度。
本研究以中部四縣市七所國小之二年級學生為研究對象，取樣方式兼採學習障礙特徵檢核表及差距標準，共計研究樣木34人，男生17人，女生17人。本研究工具為「自編二年級數學解題動態評量」、「自編二年級數學解題動態評量問卷」、「學障檢核表」、「國民小學中低年級數學診斷測驗」、「托尼非語文理解測驗（乙式）」、「魏氏測驗（語文量表）」。資料分析所使用的統計方法包含相關係數、線性多元迴歸、並以Excel計算平均數、標準差及百分比，製作圓形圖。最後再將個別晤談資料進行原案分析。
歸納資料分析結果，本研究發現：
(一) 二年級數學學習障礙學生數學解題動態評量得分與原來數學能力、非語文智力、語文理解彼此之間具有顯著關係。
(二) 二年級數學學習障礙學生對兩步驟的文字題、有多餘訊息的文字題、除法的預備經驗等題目較感困難。
(三) 二年級數學動態評量結果顯示：23﹪的情況，二年級數學學習障礙學生沒有提示就能答對題。5﹪的情況，解題過程正確但計算錯誤，提示後即算對。有9﹪的情況，語音提示有效，應屬閱讀認字問題。有19﹪的情況，關鍵字提示有效；這些學生應加強其對數學語言的理解。另有9﹪的情況，學生經簡化題目後，可以正確解題；這些學生可鼓勵其熟練基本題型。有19﹪的情況，以直式列出計算步驟，學生即會解題；這些學生基本計算並無問題。有11﹪的情況需要半具體提示；這些學生可鼓勵以圖解增進解題能力。需要具體物操作只有2﹪；只有2﹪的情況，數學障礙學生經動態評量協助後，仍然完全不會。
(四) 本研究結果顯示只有「原來數學能力」是預測「數學解題動態評量得分」之最主要變項。
(五) 由「態度問卷」和「個別晤談」的資料顯示，接受動態評量的學生，對動態評量持認同態度。以動態評量方式會令他們有自信、有成就感、有實際解題幫助。可增進學習動機、對數學的自我信念有較正面的看法。
研究者並依據以上發現，對數學解題動態評量與未來研究方向提出若干建議。
關鍵字：二年級數學學習障礙．動態評量

Dynamic evaluation on the effectiveness of the math question solution for 2nd grade learning retarded children in elementary schools
Abstract
This research is for the purpose of finding out the effectiveness on the dynamic evaluation of math question solution for mathematically learning retarded children. The main purposes are to: 1.Understand mathematically learning retarded students’ exhibition on “Dynamic evaluation” and the correlation between “Original mathematic ability”, Verbal comprehension” and “nonverbal intelligence”. 2. Analyze what kinds of math question are most easily confusing the 2nd grade mathematically learning retarded students with “dynamic evaluation” method. 3. Find out the types of the wrong answers of those 2nd grade learning retarded students with “Dynamic evaluation” method. 4. Discuss about the forecasting function of the 2nd grade learning retarded students’ “Original mathematical ability”, “Verbal comprehension” and “nonverbal intelligence” for “Math question solution dynamic evaluation”. 5. Understand the attitude of those students, who took the dynamic evaluation, for the “Dynamic evaluation”.
This research is made on the 2nd grade students of 7 elementary schools in 4 counties/cities in Taiwan middle area as the objects of study. Sampling is using learning retarded features checking list and difference standard. The total research samplings are 34 people-17 boys and 17 girls. The research tools are “Self-edited 2nd grade math question solution dynamic evaluation”, “Self-edited 2nd grade math question solution dynamic evaluation poll sheet”, “Learning retard checking list”, “Mathematic diagnosis test for lower grade students of elementary schools”, “Test of nonverbal intelligence, TONI (Type B)” and “Wei-shi Test (Verbal Measure Sheet)”. The statistics method used in information analysis include related modulus, and linear multiple regression and then figure out the average value, standardized difference, percentage proportion, and make round chart with EXCEL. At last, the information of individual interview is to be analyzed.
After summing up all analysis results, we found:
（一） The scores that 2nd grade learning retarded students got in “Math question solution dynamic evaluation” have remarkable relationship with “Original math ability”, “Nonverbal intelligence” and “Verbal comprehension”.
（二） The 2nd grade mathematically learning retarded students are confused mostly with the questions of “two-step verbal question”, “Verbal question with extra information” and “Division preparation experience”, etc.
（三） The result of the math dynamic evaluation shows: In 23% cases, 2nd mathematically retarded students can answer correctly without cue. In 5%, the solution process is correct, but with calculation error. After cued, the answer is correct. In 9%, cuing key words works. It belongs to the reading problem. In 19%, cuing key words works, but these students shall strengthen their comprehension ability for mathematic language. In 9%, students can answer correctly after the question being simplified. These students shall be encouraged to do more basic questions. In 19%, students can answer correctly only when the counting steps being listed in vertical type. Basically, these students’ counting ability is fine. In 11%, students need more specific cues. These students shall be encouraged with illustration method to improve their solution ability. Only 2% need concrete demonstration. In only 2%, the mathematically learning retarded students are still able to answer after assisted by dynamic evaluation.
（四） The result of this research shows that only “Original math ability” is the primary variable to forecasting “Math question solution dynamic evaluation score”.
（五） Base on the “Attitude poll” and “Individual interview”, it shows the students, who took dynamic evaluation, have positive attitudes. Dynamic evaluation makes them feel confident and have sense of achievement. It practically helps improve the learning motive and have positive attitude of self-confidence to math. Depending on the above findings, the researchers offered several suggestions for “Math question solution dynamic evaluation” and “Future research direction”.
Keywords: 2nd grade mathematically learning retarded students. Dynamic evaluation.

目　　　錄
第一章 緒　論…………………………………………………………1
第一節 研究動機………………………………………………………1
第二節 研究目的與待答問題…………………………………………3
第三節 名詞解釋………………………………………………………4
第二章 文獻探討………………………………………………………5
第一節 動態評量的起源、理論基礎及特性…………………………5
第二節 動態評量的介入模式……………………………………….17
第三節 數學學習障礙學生之數學解題困難……………………….23
第四節 數學文字題解題策略……………………………………….26
第三章 研究設計與實施…………………………………………….33
第一節 研究架構…………………………………………………….33
第二節 研究假設…………………………………………………….33
第三節 研究對象…………………………………………………….34
第四節 研究工具…………………………………………………….36
第五節 研究程序…………………………………………………….41
第六節 資料分析………….………………………………………….43
第四章 結果與討論………………………………………………….45
第一節 二年級數學學習障礙學生動態評量得分與原來數學能力
、語文理解、非語文智力之相關分析…………….……….45
第二節 二年級數學學習障礙兒童對那些數學問題較感困難的統
計分析……………………………………………………….46
第三節 動態評量在診斷二年級數學學習障礙兒童錯誤類型的統
計分析……………………………………………………….47
第四節 二年級數學學習障礙學生的原來數學能力、語文理解、
非語文智力對數學解題動態評量的線性多元迴歸預測分
析………………………………………………….………….50
第五節 「數學解題動態評量態度問卷」及「個別晤談」之結果
與討論……..…..………………….…………….……………52
第六節 討論……………………………………………….………….55
第五章 結論與建議………………………………………………….57
第一節 結論…………………………………………………….…….57
第二節 建議…………………………………………………….…….57
參考文獻…………………………………………………………………61
附錄一：二年級數學解題動態評量………………………………….…73
附錄二：二年級數學解題動態評量評量表…………………………..147
附錄三：數學解題動態評量態度問卷………………………………...151
附錄四：個別晤談逐字稿..……………………………….…………..155

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