本研究旨在探討國小兒童對「比較」類應用問題的解題行為。過去研究顯示，「比較」類應用問題中的「參照量未知」題要此「被比較量未知」題困難。

Nesher等人( 1982) 認為：能夠正確解答「被比較量未知」題，而無法解答「參照量未知」題者，是為「第三層次」兒童，由於其限於「非逆轉性比較基模」只能對「比較」類問題形成「單一方向不對稱性」的問題表徵，未能進行「逆轉推論」，因此尚無法解答「參照量未知」題，要到「第四層次」兒童，擁有「可逆轉性比較基模」能夠「逆轉推論」，方能夠正確解題。

本研究的主要目的即是(1) 被驗Nesher等人(1982) 所提有關「逆轉推論」之假設。(2) 以增加「逆轉問句」等方式來改寫題目，探討其對兒童解答「參照量未知」題的影響。

本研究採實驗法，以篩選測驗來挑選實驗的受試者：能夠解答「被比較量未知」題，而無法解「參照量未知」題的「第三層次」兒童；與能夠解答兩類題目的「第四層次」兒童。在實驗操作上，是以增加「逆轉問句」的相關處理方式，將受試者分為五組：控制組、非逆轉組、逆轉組、綜合組(此四組皆屬第三層次兒童)與第四層次組，分別給予附加不同問句的「被比較量未知」題及「參照量未知」題。實驗的目的在探討各組學童在「被比較量未知」與「參照量未知」題中，對「增加問句」及「原問句」的答題情形。

本研究的主要發現如下： (1)「非逆轉組」、「綜合組」、與「第四層次組」學童在「增加問句」上之得分均顯著高於「逆轉組」。 (2)「逆轉組」學童能否正

確回答「逆轉問句」，與其能否正確回答「參照量未知問句」，二者之間確有密切的正向關係。(3)「非逆轉組」學童在「非逆轉問句」上答題之正確率為90% ；「逆轉組」學童在「逆轉問句」上答題之正確率為74 克；「綜合組」學童中，在「非逆轉」及「逆轉」之「增加問句」上答題之正確率高達94% 0 (4) !「第四層次組」、「綜合組」、「逆轉組」與「非逆轉組」學童在「原參照量未知問句」上之得分，均顯著高於「控制組」。

研究結果顯示：(1) Nesher等人(1982) 雖提出有關「逆轉推論」之假設，但並未能充份解釋為何兒童能夠正確解答「被比較量未知」題，郤無法解答「參照量未知」題；部份原因可由Flavell (1970~ 1977) 等人所提有關監控認知( metacognition) 的論點加以闡釋。(2)以增加「逆轉問句」等方式來改寫題目，確可引導兒童，進行「逆轉推論」的思考，建構完整的問題表徵，進而正確解答「參照量未知」題。

【中文部份】
唐淑華(民78) 。「語文理解課程」對增進國一學生數學理解能力與解答應用問題能力之實驗研究。國立臺灣師範大學教育心理與輔導研究所碩士論文。
張春興(民77) 。知之歷程與教之歷程：認知心理學的發展及其在教育上的應用。行政院國家科學委員會認知與學習第二次研討會專集論文。
鄭昭明(民76) 。知識的傳遞與理解歷程。行政院國家科學委員會認知與學習第一次研討會專集論文。
鄭昭明、翁家英(民78) 。國小兒童解數學應用問題的認知歷程。行政院國家科學委員會認知與學習第三次研討會專集論文。
劉錫麒(民77) 。統合認知與數學問題解決教學。台灣省立師範學院76學年度教學研究學術研討會論文集。

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