Teaching Boolean logic realization: How to manipulate the difficulty of Boolean logic to assist students in easily observing the effects of specific logic operations.
Teaching real-world case formulation: How to manipulate the dissimilarity among different modified game scenarios to choose appropriate difficulty of game case for students' formulation practice.
3.2.1 The Game Context The elements of the Pac-Man game can be defined as follows: The main game scenario of the Pac-Man is that a player controls Pac-Man through a maze, eating pac-dots. When all dots are eaten, Pac-Man is taken to the next stage. Four ghosts including Blinky, Pinky, Inky, and Clyde roam the maze, trying to catch Pac-Man. If a ghost touches Pac-Man, a life is lost. When all lives have been lost, the game ends. Thus, the game objects include Pac-Man, ghost, pac-dot, power pill, and fruit. To simplify the discussion, the game rules which are embedded on the specific game object are controlling the behavior of the object. The definition of elements of the game rule is as follows:
Definition 1 (The Elements of the Game Rule). The game rule of a game is defined as , where the O is a set of game objects representing the scene objects and roles in the game scenario, the S is the actions in the game scenario including the change of events and status, and is a set of game rules with left side of compound event representing trigger conditions and right side the status changing actions.
In the Pac-Man game, the , the , and the R are shown in Fig. 4. Each game rule is composed with left-side compound conditions and right-side actions. There are three types of rules corresponding to different actions. The is the surviving rule, the and are the scoring rules, and the and are the ending rules.
3.2.2 The Platform Context The Scratch [ 21], [ 25] open source programming tool was developed by Resnick [ 26] from MIT Media Lab in 2007 for students to easily create games and share their creations. The Scratch is used as the learning platform in the Boolean logic learning. The Scratch programming tool is based on the self-defined object-oriented programming language with the support of the logical operators including the conjunction, disjunction, and negation. As shown in Fig. 5, the WYSIWYG (what you see is what you get) interface of the Scratch programming tool allows students to easily compare the game scenario (the left part of Fig. 5) and game rules (the right part of Fig. 5).
To provide the game-rule-tuning activity, the events and subroutines of original Pac-Man game, such as Ate_Power_ Pill, Touched_Ghost, and Score etc. are controlled by the corresponding global variables. For example, the game events of Ate_Power_Pill can be obtained from the global variable eat_pill in a period of time and the subroutines of Score can be activated by reconfiguring the global variable score. Therefore, the students can tune the logic expressions of game rules, using the Scratch components including global variables, if-statements, logical operations, and variable operations as shown in Fig. 6.
Definition 2 (Game Rule Boolean Logic Expression). The game rule Boolean logic expression is a context-free grammar as follows: Let be a set of terminal symbols representing the propositions of Boolean expression with S being the start symbol and N a nonterminal symbol. In each game rule, the implication operator ( ) appears once, where the left side represents the conditional propositions and the right side represents the game action propositions. Thus, the grammar of game rule Boolean logic expression R is as follows: .
Definition 3 (The Disjunctive Normal form of Game Rule). A Boolean logic expression or a formula is in disjunctive normal form (DNF) if it is a disjunction of clauses, where a clause is a conjunction of literals, for example, “ .”
Example 1 (The Game Rule of Scoring in Context-Free Grammar). For the game rule, “If (Ate_Pill AND Touched_Ghost) OR Ate_Fruit then Score,” let P, T, F, and C annotate the facts Pac-Man Ate_Pill, Touched_Ghost, Ate_Fruit, and player Scored, respectively. Then, the Boolean logic expression of the game rule is represented as “ .”
Definition 5 (Game Rule Case). A game rule case is a set of Boolean logic expressions, which are modified from Pac-Man game rules.
Definition 6 (Dissimilarity of Game Rule Cases). The dissimilarity of two propositional logic expression e1 and e2 is defined as , where is the number of different propositions between and . Thus, the dissimilarity of two cases of games A, B is .
Example 2 (Dissimilarity of Game Rule Cases). This example introduces the dissimilarity among Case 1, Case 2, and Case 3 in Fig. 6. First, the game rules of three cases are shown.
1. The pretest and posttest of students' scores have significant improvement in experimental group.
2. The posttest scores of students in experimental group have significantly greater achievements than students in control group.
5.1.1 Comparison of Learning Improvements The scores and the evaluations of the learning improvements between pretest and posttest are shown in Table 3. To evaluate the difference between two groups, the paired two-sample t-test for means of scores is applied. A statistically significant score is found for the pretest and posttest scores in experimental group with and . For the control group, the scores of pretest and posttest are not found to be statistically significant with , . Consequently, the t-test results of the experimental groups suggest significant differences but the control group has no significant differences. Finally, we may conclude that only the experimental group has significant learning improvement.
5.1.2 Comparison of Learning Outcomes The evaluations of the learning achievements of posttest are shown in Table 4. To evaluate the difference between two groups, the unpaired two-sample t-test for means of scores is applied. The t-test result for pretest shows that F-value is 1.35117 and p-value is 0.3774. Consequently, the t-test results of the two groups suggest no significant differences for scores of pretest at a confidence interval of 95 percent. The t-test result for posttest shows that F-value is 1.56083 and p-value is 0.01946. Consequently, the t-test results of the two groups suggest significant differences for the scores of posttest at a confidence interval of 95 percent. Finally, we may conclude that the experimental group has higher learning achievement than control group.
Although the game-based learning is interesting for students, the game is additive for students. Therefore, the teacher should control the progress of the teaching stages and provide a clear and well-designed learning goal.
Since teaching the realization of Boolean logic is our main objective, choosing the well-known game with simple game scenario is better for students to quickly catch the point.
The learning materials and learning platform should be prepared for students to avoid wasting time in getting familiar or while installing the preliminarily used tools.
Understanding the application of Boolean logic affecting the interesting games is surprisingly attractive for students to actively engage in the learning activities.
J.-F. Weng and T.-J. Lee are with the Department of Computer Science, National Chiao Tung University, EC447 KDELab, No. 1001, Ta Hsueh Road, Taiwan 300, R.O.C.
E-mail: email@example.com, firstname.lastname@example.org.
S.-S. Tseng is with the Department of Information Science and Applications, Asia University, EC447 KDELab, No. 500, Lioufeng Rd., Wufeng, Taichung 41354, Taiwan, R.O.C. E-mail: email@example.com.
Manuscript received 9 Dec. 2009; revised 17 Apr. 2010; accepted 26 Aug. 2010; published online 14 Oct. 2010.
For information on obtaining reprints of this article, please send e-mail to: firstname.lastname@example.org, and reference IEEECS Log Number TLTSI-2009-12-0193.
Digital Object Identifier no. 10.1109/TLT.2010.33.
Jui-Feng Weng received the BS and MS degrees from the Department of Computer and Information Science, National Chiao Tung University, Taiwan, in 2000 and 2002, respectively. He is currently working toward the PhD degree at the Department of Computer Science, National Chiao Tung University, Taiwan. His current research interests include e-learning, knowledge engineering, expert systems, and data mining.
Shian-Shyong Tseng received the PhD degree in computer engineering from National Chiao Tung University in 1984. From 1983 to 2009, he was on the faculty of the Department of Computer and Information Science at National Chiao Tung University. From 1991 to 1992 and 1996 to 1998, he acted as the chairman of the Department of Computer and Information Science. From 1992 to 1996, he was the director at the Computer Center, Ministry of Education, and the chairman of Taiwan Academic Network (TANet) Management Committee. In December 1999, he founded the Taiwan Network Information Center (TWNIC) and was the chairman of the board of directors from 1999 to 2005. He was the dean in the College of Computer Science, Asia University, from 2005 to 2008. He is currently a vice president of ASIA University and the chairman of the board of directors of TWNIC. He is an editor-in-chief of the International Journal of Digital Learning Technology and an editor of the International Journal of Fuzzy Systems, the Journal of Internet Technology, and the International Journal of Computational Science. He is also a co-editor-in-chief of the Asian Journal of Health and Information Science. He was named an Outstanding Talent of Information Science of the Republic of China in 1989. He obtained the 1992, 1994, and 1995 Outstanding Research Awards of the National Science Council of the Republic of China. He was the winner of the 1990, 1991, 1998, and 2000 Acer Long Term Awards for outstanding MS Thesis Supervision and the winner of 1992 and 1996 Acer Long Term Awards for outstanding PhD Dissertation Supervision. He was also awarded the Outstanding Youth Honor of R.O.C. in 1992. His current research interests include expert systems, data mining, computer-assisted learning, and Internet-based applications. He has published more than 100 journal papers. He is a member of the IEEE and Phi Tau Phi Societies.
Tsung-Ju Lee received the BS degree in mathematics from TungHai University in 2000 and the MS degree in applied mathematics from National Chiao Tung University, Taiwan, in 2002. He is currently working toward the PhD degree in the Department of Computer Science, National Chiao Tung University, Taiwan. His current research interests include machine learning, data mining, and various applications, especially in network security, e-learning, and software testing.