文字題，沒有解題速度的問題，而 MLD-RD 學生則無法完成所有的題目，有明顯解題速度的問 題。策略觀察顯示兩組學生在列出算式後，均會以數數策略進行計算，而且四位個案在解文字 題中有三個數字的題型時，均採二階段列式的方式進行解題，無法完整地進行一次列式並進行 解題，錯誤類型主要都是「運算符號錯誤」，MLD-only 組學生在兩種文字題題型共解 32 題，其 中 6 題出現此錯誤，犯「運算符號錯誤」的比例為 18.75％，MLD-RD 組學生共解 24 題，其中 17 題出現此錯誤，犯「運算符號錯誤」的比例為 70.83％。據此推論，雖然 MLD-only 學生仍然 會在「運算符號錯誤」有所掙扎，但 MLD 學生合併 RD 後，犯此錯誤類型的比例明顯增加，因 此文字題解題出現「運算符號錯誤」可能和 RD 的關係較為明顯，文字題解題能力似乎不是 MLD 的核心缺陷。進一步分析 MLD 學生合併 RD 後，除主要影響其解題速度的表現外，如果 RD 除 了識字困難，也包括閱讀理解的困難，如 MLD-RD1 學生，則會進一步影響其解題的正確性，
因此 MLD-RD1 和 MLD-RD2 在文字題解題能力上所呈現的正確率差異，可能在於 RD 亞型之 不同。
MLD 幼童比正常的同儕在數數時犯錯的機率高（Bull & Johnston, 1997; Geary, 1990; Geary, Widaman, Little, & Cormier, 1987; Jordan & Hanich, 2000），原因可能在於 MLD 孩童對數數原則 的概念不了解所致（Geary, et al., 2000），但是這種和正常的同儕所產生的數數犯錯機率之差異，
到了國小二年級結束時就消失了（Geary, et al., 2000）。
一般成就水準的學童到了國小二年級結束時，數學事實提取就成為他們主要的計算策略，
但是 MLD 學生到了國小六年級，甚至國中七年級，數學事實的提取仍未成為他們主要的策略，
而且持續運用與不斷練習 min-counting 程序，也無助於強化 MLD 學生能以記憶的方式直接提取 數學事實做為他們主要的策略（Goldman, Pellegrino, & Mertz, 1988; Ostad, 1997），本研究支持上 述文獻的結果與觀點，經過國小的補救教學持續至國中階段的 MLD-only 和 MLD-RD 學生，在 個位數加法和減法的計算上，依然未採取最有效率的數學事實提取策略來進行計算，仍相當程 度地依賴數數策略，並將個案的年級延伸至九年級的 MLD 國中生。MLD-only 和 MLD-RD 學 生的個位數加法和減法的正確率高，但主要使用數數策略進行計算，導致計算速度緩慢。此外，
兩組學生的數數策略發展呈現了 min-counting 和 count-from-first 程序的差異，由於 min-counting 程序可以說是數數策略的最高發展階段，因此讓 MLD-RD 學生從 count-from-first 進展到 min-counting 程序是教學上重要的課題。
本研究利用大數字，以二位數或三位數的加法和減法，但未涉及進、借位的複雜題型進一 步探討數學事實提取能力，在控制大數字的「答對題數」與「全部題數」依個位數型式進行調整 計分後發現，兩組學生的計算速度均有下降趨勢，而且 MLD-RD 學生比 MLD-only 學生的計算 速度緩慢問題更顯嚴重，原因之一可能在於兩組學生遇到大數字時，導致計算負擔加重而在心 理上產生焦慮感，因此觀察到回到使用較熟悉且有把握的數數策略之頻率相對提高，加上兩組 學生在數數策略的發展階段之不同，MLD-RD 學生使用 count-from-first 的數上去策略，一定比 MLD-only 學生之 min-counting 的數上去策略，在計算速度上更為緩慢。然而，這種大數字複雜 題型的正確率也產生組間差異，為何 MLD 學生合併 RD 後，在二位數以上的大數字但未涉及 進、借位的計算，其正確率會下降，仍需進一步研究加以探討。
到目前為止，探討 MLD-only 和 MLD-RD 兩組學生在多位數計算和文字題解題能力差異之 研究仍是相當有限，本研究指出單純 MLD 學生到了國中階段，他們在多位數計算能力的主要困 難是在計算速度的緩慢，並不影響其計算正確性，而且越複雜或大數字的題型，計算速度就越 緩慢，在合併 RD 後，除了會加重他們在計算速度問題之嚴重性，也會影響其計算正確性，錯誤 類型主要是「數學事實提取錯誤」。觀察與訪談兩組學生在多位數計算策略運用的情形時發現，
核心缺陷仍是在數學事實自動化提取的困難，兩組之間計算策略的運用沒有明顯的差異，因此 造成此種組間正確率差異的原因，須進一步地研究加以釐清。
文字題解題能力方面，本研究指出在國中階段核心缺陷仍為加法和減法事實自動化提取困 難之 MLD-only 學生，在解題速度方面不受影響，至於正確性方面則偶而會出現「運算符號錯 誤」；MLD 合併 RD 後，解題速度明顯下降，至於正確率是否受到影響可能視 RD 亞型而定，
「識字兼閱讀理解困難」亞型的 RD 學生會進一步影響其解題正確率，錯誤類型主要也是「運 算符號錯誤」，因此文字題解題能力可能不是 MLD 的核心缺陷，建議在 MLD 的鑑定實務上可 予以排除，僅作為判斷可能合併 RD 之參考。到目前為止，文獻上在探討 MLD 是否合併 RD 的 研究時，尚未進一步將 RD 做更細部的亞型區分，本研究以 MLD 合併不同的 RD 亞型（亦即
「識字困難」亞型與「識字兼閱讀理解困難」亞型）的方式進行分析時，發現他們在文字題解題 的正確性、速度與錯誤型態上可能有所差異，此議題亦值得進一步地探討。
最後，本研究最大的限制在於個案研究的樣本數問題，這些研究結果是建立在四位個案所 進行的標準化測驗量化分析與深入的觀察與訪談資料之質性分析與比較所獲得，因此只能得到 初步的計算能力特徵與差異的可能趨勢，上述研究結果有待進一步地增加大樣本數的實徵研究 加以驗證。
誌謝
本文承科技部專案補助（專案編號 NSC 98-2511-S-003-010-M），特此致謝。
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通訊作者：陳埩淑，e-mail：tg0002@mail.tut.edu.tw 收稿：2016 年 9 月 27 日；
接受刊登：2017 年 3 月 17 日。
陳埩淑（2017）。
幼童重複樣式教學之探索性研究。
臺灣數學教育期刊，4（1），63-92。
doi: 10.6278/tjme.20170317.003
幼童重複樣式教學之探索性研究
陳埩淑
臺南應用科技大學師培中心
本研究為提升幼童樣式推理能力設計樣式教學模式，從尋找樣式、辨識樣式單位、標示單位、延伸單位、
臆測單位到驗證樣式，教導幼童會複雜重複樣式推理。本研究採探索性研究，以南部一所大學附設幼兒園 兩班大班實施樣式推理教學，每班各三十名，平均年齡約 6 歲。其中一班實施樣式教學模式為實驗組；
另一班維持原來樣式教學方式即為控制組。為瞭解樣式教學模式的成效，教學前後兩組接受樣式作業評 量。資料蒐集包括觀察、攝影教師樣式教學，以及對研究對象訪談，之後進行量化分析與質性分析，以瞭 解樣式教學成效及教師如何進行樣式教學。研究結果發現兩組經教學後，後測成績皆有提升，且實驗組的 後測成績顯著優於控制組。顯然，樣式教學模式介入明顯提升幼童的推理能力。另一方面，教師在教導幼 童樣式推理時會循序漸進以故事、遊戲引導幼童，再透過操作增進幼童的樣式概念。實驗組進行複雜重複 樣式教學時，分解複雜重複樣式結構為簡單重複樣式，幫助幼童掌握核心單位及延伸樣式，擴展幼童複雜 重複樣式推理能力。
關鍵詞：幼兒數學、重複樣式、樣式教學
