Chapter 7 Applications
7.1 Application: teaching Boolean Logic through game rule tuning
The Boolean logic is the logical calculus with algebra of truth values 0 and 1 representing false and true. Numerous subjects studied in schools such as describing scientific theorem in Mathematics and Physics or causal statements in History and Literature use the Boolean logic as the formulation language. There are also many problems about decision making or rule designing in our daily life can use the skill of Boolean logic to help clarify the possible effects for different situations.
Since the Boolean logic is a tool for representing the cognitive principles or rules, the Truth table, Logic gate and Venn diagram approaches are usually used in traditional lecturing to visualize the behavior of different operators and the results of various logic expressions. However, these traditional approaches lack meaningful scenario to connect students‟ experiences, the mappings between Boolean logic and real world case spaces are usually difficult for students to imagine and comprehend.
Teachers usually need to explain the concepts with real world cases including the formulation from the real world cases to Boolean logic space and the realization from the Boolean logic expressions to the real world space. It motivates this dissertation of applying the game-based learning approach to assist students in manipulating and observing the relationship of two spaces.
To support the teaching of Boolean logic and solve the issues above, the game-based learning with game rule tuning activity is proposed. The game rule tuning activity design process is shown in Figure 7.1. The initial process of selecting the suitable game is the most important process. For example, the logic learning should select the puzzle game focused on logic training, the management learning should select the strategy game focused on decision making, the clinical learning should select the simulation or action game focused on reaction training, etc. Next, the process of mapping learning objective to game property instantiates the abstract learning objective to the meaningful game scenarios or obvious scores. The process of modeling difficulty of learning activity allows the teachers to provide suitable tasks following the pedagogical need. In this dissertation, the classical game Pac-Man is chosen as the teaching material and the Scratch programming tool is used as the learning platform.
Figure 7.1 The Game rule tuning activity design process
With our observation, a game is composed of game rules, game script, and game roles. The popular game such as Pac-Man involves well-designed game rules, simple game scenario and characteristic game roles to interest players. In this dissertation, we define the grammar of game rules to represent the Boolean logic expressions space and the game scenarios to represent the real world case space. For example, the rule
“Ate_Pill AND Touched_Ghost Score” includes the conjunction and implication operators for one scoring scenario that “if the Pac-Man ate the pill and touched the ghost then the player gets one point of score”. Thus, the students can practice the realization of Boolean logic from the game rules to the game scenario and vice versa.
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Accordingly, our goal aims to provide several modified game scenarios from original Pac-Man game to stimulate students to comprehend the specific Boolean logic in game rules in terms of teacher‟s teaching objectives. Therefore, how to model and manipulate the rules of the game cases is our first concern.
The Scratch open source programming tool was developed by Resnick 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 Figure 7.2, 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 Figure 7.2) and game rules (the right part of Figure 7.2).
Figure 7.2 The Scratch programming tool
To evaluate the hypotheses we made, there are 67 random selected 9-th Grade students (14 to 15 years old) in Minzu Junior High School, Taipei, Taiwan
participated the experiment in semester 2009-2010. There are 27 students in control group and 40 students in experimental group and their background including semester grade of Mathematics and ratio of boys and girls are shown in Table 7.1.
Table 7.1 Students joined the experiment
Groups size Term Math Score Boys / Girls
Control group 27 2009-2010 66.33 12 / 15
Experimental group 40 2009-2010 62.6 19 / 21
The experiment tool of the learning achievement evaluation is the self-designed test sheet for Boolean logic realization.
Comparison of learning improvements
The testing score of the learning achievement is shown in Table 7.2. To evaluate the difference between two groups, the paired two-sample T-test for means of scores is applied. 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 the experimental group has higher learning improvement.
Table 7.2 The score for each group (total score=100)
Pretest Posttest
Mean Std. Div. Mean Std. Div. Paired t-test
Control group
(size=27)
54.44 20.82 54.81 20.64 t(26)=0.0997, p=0.9214 Experimental group 54.5 17.68 64 12.77 t(39)=3.9141,
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(size=40) p=0.0004*
*p<.05
Comparison of learning outcomes
The testing score of the learning achievement is shown in Table 7.3. To evaluate the difference between two groups, the un-paired two-sample T-test for means of scores is applied. The null hypothesis H0 assumes that population variances are equal.
The t-test results show that F-value is 2.61181 and p-value is 0.0065. Consequently, the t-test results of the two groups suggest significant differences at a confidence interval of 95%. Finally, we may conclude that the experimental group has higher learning achievement than control group.
Table 7.3 The score for each group (total score=100)
Size Mean Std. Dev.
Control group 27 54.81 20.63
Experimental group 40 64 12.77
F=2.61181, p-value=0.0065*
*p<.05
From the experiment, our findings of applying the game tuning activity in the game-based learning can be concluded in following points:
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 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 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.
Though this works, we have some suggestions of applying game to learning. For the game platform selection, the game should be easy to manipulate and the factors of the game should be easy to observe. For the reinterpretation of the game, teachers should connect the game scenarios, roles and rules with the knowledge in order to apply the pedagogical theory to the game-based learning activity. For the activity control, the teacher should be able to control the learning progress by dividing the game playing into several rounds, and thus the explanation can be provided before each round. For the activity design, the learning objectives of each activity are better to be limited in one or two specific concepts.
The effectiveness of the game-based learning for realization of basic operations of Boolean logic has been shown in our experiment. Currently, the Pac-Man game rule tuning activity only supports the learning of simple Boolean logic expressions for junior high school students. In the nearly future, we will further apply the game rule tuning activity for the complex logic expressions or higher order logic with quantifiers (existential and universal). Since the key point of game-based learning is the selection of the suitable game type, the simulation games or strategy games which contain more criteria for decision making can be selected as the game context for the learning of complex logic expressions.
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