數學的加減法是小學生一項重要的基本能力，也是傳統教室中一項重要而且重複性練習的活動。本研究探索在無線網路與電腦技術支援環境下，應用縱橫數謎(Cross Number Puzzle)遊戲方式促進學生的學習。研究中共發展出三個版本的算術數謎遊戲（Arithmetic Puzzle Game, APG），而第三代的APG 3根據國小四年級「數與量」和「代數」的能力指標課程，並利用美國史丹佛大學國際教學科技中心所開發的Group Scribbles 2.0的電腦輔助學習軟體為平台，將縱橫數謎遊戲與回饋機制，融入到加減法未知數當中，內容結合共同解題的合作學習模式，以促進學生對於未知數的理解與喜愛。 研究中的實驗對象為國小四年級三個班級的學生共83人為樣本，進行一般傳統學習班級、個別操作學習班級與合作學習班級的學習成就比較，以探討不同學習模式的差異。經由前後測發現，傳統學習班級的前後測成績是未達顯著，個別操作學習班級與合作學習班級前後測成績皆有達顯著水準，而合作學習班級進步幅度又大於個別學習的班級，其中低成就組的學生進步幅度更明顯增加。從實驗前後的問卷與訪談中也發現，二個使用APG 3系統的班級，學習信心都有明顯成長，其中合作學習班級87.5%的學生認為APG 3系統可以增加她們對數學學習信心。合作學習班級80%的學生喜歡這種合作學習的模式。而超過85%的學生認為APG 3系統可以讓學生更容易了解算術運算，並且增加學生們的學習動機。 分析錄影與觀察紀錄表得知，合作學習班級的溝通互動模式有三種，分別為理想的溝通、私下交談的溝通及無反應的溝通。而由實驗結果分析來看，理想溝通模式會有最好的學習成效。 雖然研究中得到不少正面的實驗結果，但不能驟下結論APG 3可以取代傳統教室內的算術練習活動。我們需要更多的實驗對象與實驗內容，更多的統計資料以驗證APG 3系統對學習成效的貢獻。 While addition and subtraction is a key mathematical skill for young children, a typical activity for them in classrooms involves doing repetitive arithmetic calculation exercises. In this study, we explore a collaborative way for students to learn these skills in a technology-enabled way with wireless computers. Three versions of learning game system were developed: “Arithmetic Puzzle Game version 1 (APG 1)”, “Arithmetic Puzzle Game version 2 (APG 2)”, and “Arithmetic Puzzle Game version 3 (APG 3)”. In APG the third version system, 83 students in three classes in Grade 4 were asked to solve arithmetic problems with three different methods: via playing an adapted “cross number puzzle” game on Group Scribbles (GS) collaboratively, via playing the same game on GS individually, and via the traditional method of teaching and learning, i.e. with no games at all. Students used the Group Scribbles software to run an adapted version of the “Cross Number Puzzle” that was designed with the “feedback” mechanism to assist students’ problem solving. Analysis of the pre and post learning achievement data reveals that the two classes who played the game performed better than the control class, with the collaborative class students achieving better than the individual class students. The low-ability students in the collaborative and individual class were found to have made the most significant progress in arithmetic skills through playing this game. From pre and post questionnaire, the mean for the collaborative class students’ confidence is higher than that of individual class. Another statistical data was shown that 87.5% students in collaborative class had their confidence enhanced in this system. The result of interview from students also support that the cross number puzzle game can enhance confidence. More than 80% of the participants stated that they liked to work with their group members to solve problems. Over 85% of them thought that they could easy understand arithmetical skills in game processing. It indicates that their strong willingness in learning through playing the cross number puzzle game and consequently they were fully motivated to learn. Three dominant interactive collaboration patterns, one contributing to productive interactions and two to less productive interactions, were also identified in the students’ collaboration and the ideal interactive patterns made more performance. Although we have some positive results for the APG 3 system were shown, they are not strong enough to conclude that the APG 3 system can replace part of the current elementary school mathematics curriculum. These experiments should take into consideration different mathematics content and problems for students and gather more data. It would be interesting to see if adding the elements of game play and technology if larger groups will still show high learning achievement.
