第五章 結論與未來研究
5.2 未來研究
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第五章 結論與未來研究
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加入新的遊戲元素
為了增加學生在使用系統上的興趣，希望未來在遊戲中加入新的遊戲要 素，例如新的獎勵方式、遊戲中的音效或是音樂，期望學生可以在更多回饋 的要素之下增加遊戲的使用、練習次數。
增加遊戲的難度
對於目前已經加入其中的教材，在實際測驗時曾有受測者表示教材(知 識卡)的難度不高，難以提起學習和遊戲之興趣。希望在未來可以加入不同 難度的教材，如此可廣泛針對不同學習程度的學生進行練習。
增加語言
目前遊戲的語言設定為中文，同時系統使用對象也為台灣的學生所使用。
另外，因本研究方向被國外研究學者採信(附錄七)，因此希望在未來可將語 言英文化，以利台灣之外地區的學習者使用系統及學習。
教材添加工具
本系統之內部教材，知識卡的內容編輯目前僅能靠了解程式碼的人進入 程式內部更改，若是教師對程式碼不熟則無法對現有教材做更動，若是時間 許可，將增加輔助工具幫助不了解程式碼的教師自行修改教材(知識卡)的內 容。
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參考文獻
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analysis of use cases‖, Graz, Austria: I-KNOW Conference, 2005
[2] Lim, D., ―Taking Students Out for a Ride: Using a Board Game to Teach Graph Theory.‖, 38th SIGCSE technical symposium on Computer science education, pp.
367–371. , 2007
[3] Goschnick, S., Balbo, S., ―Game-first Programming for Information Systems Students.‖, Second Australasian Conference on Interactive Entertainment, Creativity & Cognition Studios Press, pp. 71–74., 2005
[4] Komisarczuk, P., Welch, I., ―A Board Game for Teaching Internet Engineering.‖ , 8th Austalian conference on Computing education, vol. 52, pp. 117–123., 2006 [5] Amory A., Naicker K., J. Vincent, Adams C., ―The use of computer games as an
educational tool: identification of appropriate game types and elements‖, British Journal of Educational Technology v30 no4, pp.311-321, 1999
[6] Kirriemuir, J. and McFarlane, A., ―Literature review in game and learning.‖, Retrieved June 11, 2004,
from http://www.nestafuturelab.org/research/reviews/08_01.hrm
[7] 張春興，“現代心理學”，東華書局，pp. 233-242，民國 92 年 11 月。
[8] Prensky, M., Digital game-based learning. ACM Computers in Entertainment, Vol.
1, No. 1, pp. 1-4, 2003
[9] Ralph P. Grimaldi, ―Discrete And Combinatorial Mathematics An Introduction 3rd Edition Addison‖, Wesley, 1994
[10] http://en.wikipedia.org/wiki/Minimum_spanning_tree [11] http://en.wikipedia.org/wiki/Dijkstra%27s_algorithm
[12] http://www-b2.is.tokushima-u.ac.jp/~ikeda/suuri/dijkstra/Dijkstra.shtml
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[13] http://en.wikipedia.org/wiki/Prim%27s_algorithm
[14] http://www-b2.is.tokushima-u.ac.jp/~ikeda/suuri/dijkstra/Prim.shtml [15] http://en.wikipedia.org/wiki/Kruskal%27s_algorithm
[16] http://www-b2.is.tokushima-u.ac.jp/~ikeda/suuri/kruskal/Kruskal.shtml [17] Skinner, B. B., ―About Behaviorism‖, New York：Knopf, 1974.
[18] Thorndike, E. L., ―Animal Intelligence‖, New York：Maccmillan, 1911.
[19] Csikszentmihalyi, M., Flow: The Classic work on how to achieve happiness.
New York:Harper Perennial, 1992.
[20] http://en.wikipedia.org/wiki/Flow_(psychology)
[21] Thomas, L. G., Brophy, J., “當代教育心理學”，五南圖書出版公司，pp.
155-157, 民國 88 年 2 月。
[22] Ausubel, D., and Robinson, F., ―School learning: An introduction to educational to educational psychology‖, New York: Holt, Rinehart & Winston, 1969.
[23] Rajaravivarma, R., ―A Games-Based Approach for Teaching the Introductory Programming Course‖, ACM SIGCSE Bulletin archive. No 4, Vol. 37,
pp.98-102, 2005.
[24] Carrington, D.; Baker, A.; van der Hoek, A., ―It’s All in the Game: Teaching Software Porcess Concepts‖, Proceedings 35th Annual Conference Frontiers in Education, F4G-13 - F4G-18, 2005.
[25] Baker, A.; Navarro, EO.; van der Hoek, A., ―A. (2003) An experimental card game for teaching software engineering‖, Proceedings of 16th Conference on Sotware Engineering Education and Training, (CSEE&T 2003), pp.216-223, 2003.
[26] Baker, A.; Navarro, EO.; van der Hoek, A., ―Problems and Programmers: an educational software engineering card game‖, 25th International Conference on
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Software Engineering, 2003. Proceedings. pp.614-619, 2003.
[27] Chang, W.C. and Chen, Y.L., ―Cultivating Operation System Process Concept with Card Game‖, ICPPW 2007. International Conference on Parallel Processing Workshops, pp.23-23, 2007.
[28] Nevison, C., and Wells, B., ―Using a Maze Case Study to Teach Object-Oriented Programming and Design Patterns ―, Proceedings of the sixth Conference on Australasian computing education, pp. 207-215, 2004.
[29] Natvig, L., and Line, S., "Age of Computers:"An Innovative Combination of History and Computer Game Elements for Teaching Computer Fundamentals, in Proceedings of FIE 2004 , Lasse Natvig, Steinar Line and Djupdal, 2004.
[30] Makansi, J., ‖ Reactorland: A board game‖, IEEE, Volume 38 Issue 11, pp.42-43, 2001.
[31] Peitz, J., Björk, S., and Jäppinen, A., ―Wizard's apprentice gameplay-oriented design of a computer-augmented board game‖, 2006 ACM SIGCHI international conference on Advances in computer entertainment technology, 2006.
[32] Bekir, N., Cable, V., Hashimoto, I., and Katz, S., ―Teaching engineering ethics: a new approach‖, 31st Annual Education Conference, Vol 1, pp.T2G 1-3, 2001.
[33] http://en.wikipedia.org/wiki/Multigraph
[34] http://zh.wikipedia.org/wiki/%E6%9D%8E%E5%85%8B%E7%89%B9%E9%8 7%8F%E8%A1%A8
[35] 余民寧，“教育測驗與評量 第二版”，心理出版社，pp.266-268，民國 91 年 10 月。
[36] 吳宗正、吳育東，”LISREL 模式應用於行動電話消費者滿意度之研究”，
國立成功大學統計研究所碩士論文”，pp.29，民國 86 年 6 月。
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附錄一 Dijkstra 最小生成樹前測題目
前測題目 1:
請使用上圖中各路徑之權重值，以 u0 為起始點完成 Dijkstra 最小生成樹
前測題目 2:
請使用上圖中各路徑之權重值，以 a 為起始點完成 Dijkstra 最小生成樹
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附錄二 Prim 最小生成樹前測題目
前測題目 1:
請使用上圖中各路徑之權重值，以 u0 為起始點完成 Prim 最小生成樹 前測題目 2:
請使用上圖中各路徑之權重值，以 a 為起始點完成 Prim 最小生成樹
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附錄三 Dijkstra 最小生成樹後測題目
後測題目 1:
請使用上圖中各路徑之權重值，以 a 為起始點完成 Dijkstra 最小生成樹
後測題目 2:
請使用上圖中各路徑之權重值，以 a 為起始點完成 Dijkstra 最小生成樹
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附錄四 Prim 最小生成樹後測題目
後測題目 1:
請使用上圖中各路徑之權重值，以 a 為起始點完成 Prim 最小生成樹
後測題目 2:
請使用上圖中各路徑之權重值，以 a 為起始點完成 Prim 最小生成樹
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附錄五 最小生成樹實驗時間結果表
組別 學生 Dijkstra 前測
Prim 前測
試玩 時間
組員對戰 時間
Dijkstra 後測
Prim 後測 乙 8 A1 6:02 2:32 14:39 15.00 2:00 1:03
A2 6:03 3:02 14:39 15.00 4:27 2:02 乙 3 B1 6:50 2:38 8:00 15:00 3:03 1:49 B2 15:00 2:48 8:00 15:00 6:30 8:00 甲 8 C1 23:01 7:01 8:00 12:00 8:51 3:24 C2 19:45 4:01 8:00 12:00 5:30 2:17 乙 2 D1 27:38 3:07 8:00 12:00 6:09 2:14 D2 23:05 7:27 8:00 12:00 4;01 3:08 甲 6 E1 15:02 5:13 16:00 16:00 7;13 2:55 E2 23:15 9:10 16:00 16:00 17:43 3:31 甲 4 F1 13:06 2:09 16:00 16:00 1:25 1:07 F2 22:12 2:09 16:00 16:00 4:57 3:14 乙 4 G1 13:37 7:12 10:00 15:00 5:28 6:38 G2 31:12 9:18 10:00 15:00 15:02 4:28 乙 6 H1 6:27 10:54 15:00 15:00 4:52 2:42 H2 10:29 2:19 15:00 15:00 5:09 1:15 甲 5 I1 14:10 10:01 10:00 10:00 5:50 3:05 I2 13:05 7:01 10:00 10:00 5:54 4:12 甲 3 J1 9:45 2:33 8:00 21:00 2:41 1:40 J2 8:55 2:16 8:00 21:00 4:01 2:04 乙 5 K1 7:16 3:31 10:00 24:00 2:28 4:58 K2 2:15 3:10 10:00 24:00 1:45 1:17 甲 2 L1 19:11 5:07 13:00 23:00 6:45 3:37 L2 21:18 7:42 13:00 23:00 6:39 5:42 乙 7 M1 7:20 16:12 10:00 21:00 6:34 6:04 M2 17:08 20:10 10:00 21:00 10:02 5:18 甲 1 N1 8:49 3:20 17:00 18:00 1:40 3:50 N2 9:01 1:15 17:00 18:00 3:10 3:15 乙 1 O1 22:14 12:56 10:00 15:00 3:18 9:14 O2 6:49 4:00 10:00 15:00 2:29 3:06 單位:XX 分-OO 秒，
以組別乙 1，學生 O1 為例，Dijkstra 前測時間為 22 分 14 秒
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附錄六 實驗問卷
請您於使用過本系統後填寫此問卷，本問卷結果將作為學術研究用，並會保密您 的資料，謝謝您!
(問卷選項:A-非常同意 B-同意 C-無意見 D-不同意 E-非常不同意) 1 2 3 4
請問您目前就讀的年級 □ □ □ □
(<2) (2-5) (5-8) (8<)
請問您平均一個星期中，花費於電腦之時間(小時) □ □ □ □ 是 否
請問您之前有無接觸過原始版的鐵道任務? □ □
請問您之前有無接觸過最小生成樹的概念? □ □
A B C D E
我覺得遊戲功能容易了解 □ □ □ □ □
我覺得遊戲按鍵容易找到 □ □ □ □ □
我覺得學習過程容易 □ □ □ □ □
我覺得我可在 20 分鐘內獨立摸索出遊戲中的功能和 用途
□ □ □ □ □
此系統提供良好學習最小生成樹概念的環境 □ □ □ □ □
此系統能幫助學習最小生成樹概念 □ □ □ □ □
此系統可輔助課前預習 □ □ □ □ □
此系統可輔助課中學習 □ □ □ □ □
此系統可輔助課後學習 □ □ □ □ □
此系統可將抽象的最小生成樹概念實體化 □ □ □ □ □
我喜歡使用此系統學習 □ □ □ □ □
此系統會增加學習最小生成樹概念的興趣 □ □ □ □ □ 我覺得使用此系統學習時會有較高的專注度 □ □ □ □ □ 我願意在沒有記分壓力的情況下使用此系統自我學習 □ □ □ □ □ 我願意在沒有課業壓力的情況下使用此系統自我學習 □ □ □ □ □
我覺得此系統比傳統教學方式有趣 □ □ □ □ □
我覺得此系統遊戲過程中是有趣的 □ □ □ □ □
我覺得遊戲中有競爭的感覺 □ □ □ □ □
我覺得競爭的感覺會使遊戲更有趣 □ □ □ □ □
我覺得遊戲過程中得分高者未必最後會得勝 □ □ □ □ □
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附錄七 英文論文
發表於 International Conference on Web-based Learning, Jinhua, China, August 20-22, 2008, pp. 275-284
Learning Kruskal's Algorithm, Prim's Algorithm and Dijkstra's Algorithm by Board Game
Wen-Chih Chang, Yan-Da Chiu and Mao-Fan Li
Deparment of Information Management, Chung Hua University Hsinchu, Taiwan, R.O.C.
earnest@chu.edu.tw, griffin.chu@msa.hinet.net, m09610030@chu.edu.tw
Abstract. This paper describes the reasons about why it is beneficial to combine with graph theory and board game. Forbye, it also descants three graph theories: Dijkstra’s, Prim’s, and Kruskal’s minimum spanning tree. Then it would describe the information about the board game we choose and how to combine the game with before-mentioned three graph theories. At last, we would account for the advantage of combining with these three graph theories and the game specifically.
1. Introduction
For computer sciences, graph theories are important. There are many computer science’s concepts relate with graph theory, and many researchers try to combine these science to games. For example, we can connect the concept of network and Prim’s minimum spanning tree1, or link the graph and the concept of searching[2]. Therefore, learning and teaching graph theory much more efficiently aid learning computer sciences.
About some knowledge in computer science, using graph theories assist in teaching is useful. It helps to describe some virtual concepts, like network connection. Some computer science, often combine with graph theories in class recently.
There many kinds of concepts of graph theories, but we contact the concept of minimum spanning tree mostly. And, we choose minimum spanning tree theories as our target.
Accordingly, how to make student to learn graph theories more efficiently and boost the interest in learning for them is administer to learn computer sciences. In order to increase the interest in learning and absorbing knowledge, using board game to help learning is a good method.
Learning graph theories well help to learn computer sciences. By the reason, we combine the board
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game Ticket to Ride with three graph theories Dijkstra’s, Prim’s, and Kruskal’s minimum spanning tree. Except some saving rules, we change and create some rules in the game. By the new board game, students can understand the graph theories more efficiently and can get interest in learning.
In the follow sections, we will describe these: 1. The concept of minimum spanning tree theories:
Dijkstra’s, Prim’s, and Kruskal’s minimum spanning tree (section 2). 2. Related work (section 2). 3.
The information about board game Ticket to Ride (section 3). 3. The design of combining graph theories and the board game Ticket to Ride (section 4). 4. Conclusion and evaluation about the board game in helping learning.
2. Related Work
In the early centenary, games were just played for fun. The games, especially board games are.
With the time goes, computers’ knowledge and technologies are developing. So, computer science was becoming an important science. Accent on the materiality of board games, many researches tried to combine teaching computer sciences with playing board games. For example, Andre J. Henney and Johnson I. Agbinya used board game to explain the idea about mobile connection 3. And Steve Goschnick and Sandrine Balbo linked programming to board games[4].
In these researchers’ concepts, the most access to combine with computer sciences and board game is – shows the network or graph theory on board game. For example, Peter Komisarczuk and Ian Welch used board game to teach internet engineering 5.
Darren Lim shows the graph theory on the board game 1.
Using games can help teaching computer sciences much more efficiently. Especially teaching graph theory or network concepts on board games. It can use the materiality of board games to describe the virtual of graph theories and network well. In this paper, we try to explain the three of ideals of graph theories - Dijkstra’s, Prim’s, and Kruskal’s minimum spanning tree on the board game Ticket to Ride
3. Brief describe the three minimum spanning tree theories we use
Between many connected nodes, they are undirected graph. Spanning trees means all of the nodes connection. If we give the weight to every path from node to another and the sum of all paths will be the least in the minimum spanning tree 1, 6.
3.1 Dijkstra’s minimum spanning tree
It describes a concept of minimum spanning tree. The theory can be use in teaching network, like the paths of router and router 7. It goes from a start node, than it will begin to run follow steps: 1.Finding the connected node. 2. Calculating the sum of start node to next node. 3. Choosing the least sum of
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node as start point next round and avoiding account for loop. It will cuckoo the three steps until finishing the spanning tree 1, 8.
3.2 Prim’s minimum spanning tree
Similar to Dijkstra’s minimum spanning tree, the theory has a start node too. It can also use the same knowledge area in network. After choosing a start node, it finishes the minimum spanning tree by repeating the follow steps: 1.Finding the connected nodes. 2. Choosing the least weight of paths to next node, and avoiding account for loop 1,9. After repeating the two steps, a Prim’s minimum spanning tree is created.
3.3 Kruskal’s minimum spanning tree
Unlike upper two theories of minimum spanning tree, the theory needn’t any start node. The point of the theory are choosing the least paths and avoiding account for the loop. It finishes the minimum spanning tree by repeating two steps: 1.Choosing the least weight path. 2. Connecting the nodes and avoiding the loop 1, 10. The concept can be used in network, too.
Fig. 1. Ticket to Ride Portugal Edition
99 4. What is “Ticket to Ride”
This is a board game; it contains the city name and tracks from one city to another. The game has many kinds of maps like Europe, South America, and Portugal etc. An example is shown in Figure 1.
The main ideas of this game are: 1.Players can choose the mission about connects one city to another, and try to finish the mission to get points. 2. Players have to use their source in hand much more efficiently. 3. There are game plans in the game; players try to interrupt others finish their missions expect for finishing their missions. During playing the game, players get points by finishing missions or building the longest tracks. Player who gets the highest points is the winner. Altogether, this is a game needed chicanery.
5. Design of Combining minimum spanning tree theories and Ticket to Ride
In the section we fixed some rules based on original rules, and created a new edition of board game Ticket to Ride. The new edition of Ticket to ride is combined with the concept of board game Ticket to Ride and three minimum spanning tree theories: Dijkstra’s, Prim’s, and Kruskal’s minimum spanning tree.
5.1 Necessary properties of the game
In this game, we need these things:
(1) Railway map (We use Portugal railway map as an example in Figure 1.) (2) Each player has 45 railway carriages with its special color.
(3) Starting Point Card (It presents the start point of each player.)
(4) Ticket Card (It indicates the link from Starting point station to Destination station, and the score after the player completed the route.)
(5) Knowledge Card (It identifies which algorithm has to apply on the railway stations and the completed score. The related algorithms are Dijkstra’s algorithm which is applied in shortest path algorithm, Prim’s algorithm and Kruskal’s algorithm which are used in minimum spanning tree.
(6) Railway Card (Each section railway of the map has a specific color which is composed of white, black, red, yellow, orange, blue, purple, green and full-color.)
(7) The Number of each color card (white, black, red, yellow, orange, blue, purple, green) are thirty five, and the number of full-color is fifteen.
5.2 The Limitation of this game
There are the limitations of this game:
(1) Players range :2-3 players
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(2) End conditions of single round game:
a. When one of the players ran out of the 45 railway carriages b. When one of the players cannot put his/her railway carriages c. When one of the players reached scores over 150
(3) Completed conditions of the entire game: (A game consists of two single round games.) a. When one of the players reached scores over 300
b. When one of the players completed all the three knowledge card missions which involved Dijkstra, Prim and Kruskal algorithms. The winner has to complete each knowledge card.
(4) All the players have to learn the related knowledge about the shortest path algorithm and minimum spanning tree.
5.3 Game Progress
In the new edition of Ticket to Ride, we fixed some rules based on original rules because of our ideal – combining the board game and three minimum spanning tree theories. The progress is likely the original game. The difference between new and old edition games is that we gave the new game an additional element. The element is the concept of start location and minimum spanning tree theories cards. First, players should cast a start point and knowledge card. Then, they should choose if they want them. After casting start point and knowledge cards, players begin to a single turn.
In the single turn, players can do three actions:
(1) Draw two of the railway cards or choose one which is opened directly.
(2) Draw three of the 3 ticket cards, and reserve the selected ticket.
(3) Re-cast new start point card and knowledge cards.
(4) Put the railway carriages on the map to establish the route. Players also can skip the step if there is no available condition.
In principle, the game will repeat these four steps until a player rich the end conditions of single round game. The game progress graph is shown in figure 2.
5.4 Game regulations
There are the descriptions of the game regulations.
(1) The station recorded in the starting point card has to match the stations in the knowledge card else the player cannot play the game (example is shown in Table 1).
(2) Regulations of drawing the railway card:
a. Railway card color: white、black、red、yellow、orange、blue、purple、green、full-color.
b. In the beginning of each round, the railway cards are divided into two piles. One is composed of five opened cards and the other one is covered pile of cards.