本研究之目的在設計觸控裝置上的十字交乘法遊戲式學習活動，透過遊戲情境激發學生的內在動機，使學生樂於練習並主動發展解題策略，以幫助學生理解十字交乘法的概念，並掌握將首項係數為一的二次多項式因式分解之運算。本研究使用Flash 與 ActionScript 3.0 設計十字交乘法之遊戲式學習活動，透過APOS理論安排十字交乘法的作業，依據遊戲式學習的相關理論建構遊戲情境，並將十字交乘法的學習內容與遊戲情境中過關所需的遊戲技巧進行內在整合，形成十字交乘法遊戲式學習活動。
本研究針對122名國中八年級學生進行實驗教學。採用2×2實驗設計，在遊戲式學習活動中以有無教學指引、觸控介面或滑鼠介面兩項變因為核心，形成四組實驗組，再以一組觸控介面上無遊戲情境有教學指引作為對照組，共分為五組。經由分析其前後測以及認知負荷與感受量表，再透過組間比較而探討有無教學指引、有無遊戲情境、觸控介面或滑鼠介面三項因素對學生在本學習活動中學習成效與認知負荷感受上的差異。
主要研究結果顯示五組學生在十字交乘法基本題前後測進步分數均達顯著水準。有無教學指引與觸碰滑鼠介面之雙因子間有交互作用，在觸控介面下無教學指引組前後測進步分數顯著優於有教學指引組；在滑鼠介面下有教學指引組前後測進步分數優於無教學指引組，但未達顯著差異。在觸控介面下無遊戲情境組十字交乘法基本題前後測進步分數與有遊戲情境組並無顯著差異；但在後測的遷移問題上無遊戲情境組顯著優於有遊戲情境組。
以學習成就與投入努力為軸分析五個組別的效率與投入情形，投入程度無教學優於有教學，有遊戲優於無遊戲；另外，在觸控介面、有遊戲情境、無教學指引位於高效率且高投入的區域。
本研究結合APOS理論與遊戲式學習理論發展出的十字交乘法的學習活動，使五組學生在十字交乘法基本題前後測進步分數均達高度顯著水準，可做為未來開發中學代數學習活動設計的參考。

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