Concepts for Game-Based Learning on Smartphones on the

Fakultät für Elektrotechnik, Informatik und Mathematik
Institut für Informatik
Fachgruppe Mensch-Computer-Interaktion
Fürstenallee 11
33102 Paderborn
Concepts for Game-Based
Learning on Smartphones on the
Example of Boolean Algebra
Bachelor’s Thesis
Submitted to the Human-Computer-Interaction Research Group
in Partial Fulfillment of the Requirements for the
Degree of
Bachelor of Science
by
Sergej Laas
Ellerbuscher Str. 124
32584 Löhne
Thesis Supervisor:
Prof. Dr. Gerd Szwillus
and
Prof. Dr. Johannes Magenheim
Paderborn, May 2015
Abstract
In the recent past, smartphones have taken on a pervasive role in everyday
life. Accompanying this trend, mobile gaming has seen a new advent as well.
However, the vast majority of games is still developed to merely entertain, rather
than to additionally allow the players to learn something useful for their lives. At
the same time, there is numerous research on educational games in general, while
approaches which take entertaining and playful learning on smartphone devices
into account remain scarce.
This thesis is an attempt to investigate the use of game-based features to
facilitate autodidactic learning on a smartphone. In this context, a diverse range
of literature and products was consulted. This led to the design and implementation of several problem scenarios related to Boolean algebra and playable on
a smartphone. The textual discussion explores the developed mapping between
didactic subject and game mechanics. It includes the conceptualization process
and a detailed depiction of the final implementation as well as technical specifics
and evaluation concepts. This study indicates the significance of conceptually integrating the characteristics of the educational subject into the core mechanics of
the game environment itself for effective knowledge transfer, while incorporating
the demands and possibilities offered by a smartphone device.
iii
Declaration
(Translation from German)
I hereby declare that I prepared this thesis entirely on my own and have not
used outside sources without declaration in the text. Any concepts or quotations
applicable to these sources are clearly attributed to them. This thesis has not
been submitted in the same or substantially similar version, not even in part, to
any other authority for grading and has not been published elsewhere.
Original Declaration Text in German:
Erklärung
Ich versichere, dass ich die Arbeit ohne fremde Hilfe und ohne Benutzung
anderer als der angegebenen Quellen angefertigt habe und dass die Arbeit in
gleicher oder ähnlicher Form noch keiner anderen Prüfungsbehörde vorgelegen
hat und von dieser als Teil einer Prüfungsleistung angenommen worden ist. Alle
Ausführungen, die wörtlich oder sinngemäß übernommen worden sind, sind als
solche gekennzeichnet.
City, Date
Sergej Laas
v
Contents
1 Introduction
1
1.1
Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1
1.2
Solution Idea . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2
1.3
Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3
2 Fundamentals
2.1
2.2
5
Digital Game-based Learning . . . . . . . . . . . . . . . . . . . .
5
2.1.1
Definition . . . . . . . . . . . . . . . . . . . . . . . . . . .
5
2.1.2
Games and Learning . . . . . . . . . . . . . . . . . . . . .
6
2.1.3
Existing Approaches . . . . . . . . . . . . . . . . . . . . .
8
Didactic Context . . . . . . . . . . . . . . . . . . . . . . . . . . .
10
2.2.1
Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . .
11
2.2.2
Fundamentals of Boolean Algebra . . . . . . . . . . . . . .
12
3 Concepts for Game-Based Learning
17
3.1
Conceptualization Process . . . . . . . . . . . . . . . . . . . . . .
17
3.2
Scenarios . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
19
3.2.1
Learning Boolean Axioms . . . . . . . . . . . . . . . . . .
21
3.2.2
Interpreting Boolean Formulae . . . . . . . . . . . . . . . .
30
3.2.3
Evaluating Boolean Formulae . . . . . . . . . . . . . . . .
41
3.2.4
Determining Satisfiability . . . . . . . . . . . . . . . . . .
44
3.2.5
Simplifying Formulae . . . . . . . . . . . . . . . . . . . . .
48
4 Implementation
61
4.1
Technical Overview . . . . . . . . . . . . . . . . . . . . . . . . . .
61
4.2
Graphical Specifics . . . . . . . . . . . . . . . . . . . . . . . . . .
62
vii
Contents
4.3
Developing for Smartphones . . . . . . . . . . . . . . . . . . . . .
63
4.3.1
Input . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
63
4.3.2
Interface . . . . . . . . . . . . . . . . . . . . . . . . . . . .
66
4.3.3
Game Sessions
67
. . . . . . . . . . . . . . . . . . . . . . . .
5 Evaluation Concepts
69
5.1
Prototyping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
69
5.2
External Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . .
70
5.3
Internal Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . .
71
6 Conclusion
73
6.1
Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
73
6.2
Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
74
Appendix
A Implementation Details
75
A.1 Info Texts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
75
A.2 DVD Content . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
77
A.3 Installation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
77
Bibliography
viii
79
List of Figures
3.1
The main menu of the prototype with access to the different scenarios 20
3.2
A black block representing the element 0 (false) . . . . . . . . . .
22
3.3
A white block representing the element 1 (true) . . . . . . . . . .
22
3.4
From left to right: A block with no assignment; a black block interior indicating a negative assignment, i.e. false or 0; a white block
interior indicating a positive assignment, i.e. true or 1 . . . . . . .
23
3.5
Conjunction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
23
3.6
Disjunction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
23
3.7
Negation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
23
3.8
White balls being stopped at a black block . . . . . . . . . . . . .
24
3.9
Balls inverting their color at the borders of a negation frame and
passing through a black block . . . . . . . . . . . . . . . . . . . .
24
3.10 A graphical representation of the formula a + (¬a · b) . . . . . . .
25
3.11 A graphical representation of the formula (a + ¬a) · b . . . . . . .
25
3.12 Representation of a + ¬a = 1 . . . . . . . . . . . . . . . . . . . .
25
a · ¬a = 0 . . . . . . . . . . . . . . . . . . . .
25
3.13 Representation of
3.14 Level 1-1: Introducing the goal of the game as well as the main
controls . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
27
3.15 Level 1-1 solved . . . . . . . . . . . . . . . . . . . . . . . . . . . .
27
3.16 Level 1-2: Two differently colored blocks in conjunction . . . . . .
28
3.17 Level 1-3: Two blocks of the same color in conjunction . . . . . .
28
3.18 Level 1-4: The 1 element . . . . . . . . . . . . . . . . . . . . . . .
28
3.19 Level 1-5: The 0 element and disjunction are introduced . . . . .
28
3.20 Level 1-6: An example for negation . . . . . . . . . . . . . . . . .
29
3.21 Level 1-6 with underlying formula . . . . . . . . . . . . . . . . . .
29
3.22 Level 2-1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
31
ix
List of Figures
3.23 Level 2-2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
31
3.24 Level 2-3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
31
3.25 Level 2-4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
32
3.26 Mockup demonstrating rewards and time limits . . . . . . . . . .
35
3.27 Mockup demonstrating an overlay once a level is passed . . . . . .
36
3.28 Mockup with an HUD element for an assignment counter and an
x
optimum indicator . . . . . . . . . . . . . . . . . . . . . . . . . .
37
3.29 Mockup demonstrating a theme . . . . . . . . . . . . . . . . . . .
39
3.30 Mockup demonstrating a level consisting of several formulae . . .
40
3.31 Mockup showing a subterm the player zoomed in on . . . . . . . .
40
3.32 Level 3-1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
42
3.33 Level 3-2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
42
3.34 Level 3-3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
42
3.35 Level 4-1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
45
3.36 Level 4-2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
45
3.37 Level 4-3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
45
3.38 The bonus round . . . . . . . . . . . . . . . . . . . . . . . . . . .
46
3.39 Disjunction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
49
3.40 Conjunction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
49
3.41 Negation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
49
3.42 Representation of (a + ¬a) · b . . . . . . . . . . . . . . . . . . . .
49
3.43 Context menu for a green block . . . . . . . . . . . . . . . . . . .
50
3.44 Context menu for a black block . . . . . . . . . . . . . . . . . . .
51
3.45 Context menu for a white block . . . . . . . . . . . . . . . . . . .
52
3.46 Level 5-1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
54
3.47 Level 5-2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
54
3.48 Level 5-3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
54
3.49 Solution for level 5-1 . . . . . . . . . . . . . . . . . . . . . . . . .
55
3.50 Solution for level 5-2 . . . . . . . . . . . . . . . . . . . . . . . . .
55
3.51 Solution for level 5-3 . . . . . . . . . . . . . . . . . . . . . . . . .
56
3.52 Mockup demonstrating a target constellation . . . . . . . . . . . .
58
3.53 Mockup showing the formal notation of a formula . . . . . . . . .
59
3.54 Mockup demonstrating an ambiguous layout . . . . . . . . . . . .
60
List of Tables
3.1
Overview of the implemented laws on the example of adjacent blocks 53
xi
1 Introduction
1.1 Motivation
Over the last few years, smartphones have seen a rapid spread and evolved into a
pervasive artifact of everyday life. With the ability of installing apps for a wide
variety of use cases, they constitute versatile tools used to assist with various tasks.
At the same time it is also frequented for entertainment purposes, particularly
when bridging idle time.1
Thus, with the advent of the smartphone, mobile games grew more popular as
well. The device has become the most used gaming platform, with mobile games
sales revenues steadily rising.2 However, the vast majority of smartphone games
– not unlike games for other platforms – is developed to merely entertain, rather
than to let a player “bring something from their recreation into their life” (cp.
Portnow 2008). Products which allow players to learn something useful while
keeping them engaged are rare.
While there are numerous studies and prototypes on educational games in
general (cp. Baker 2012, Bellotti et al. 2009, Harteveld et al. 2010), there is a
significant lack of research on portable educational games. Even more scarce are
actual implementations aimed at the general public and based on best practices
from both game design and didactics (cp. Kirriemuir & McFarlane 2004, p. 28).
As of yet, most examples of games with the premise of education either fail to
provide an enjoyable experience, or their pedagogical value stands to question.
1
Serviceplan (2014). Website accessed February 25, 2015 under
http://www.serviceplan.com/files/serviceplan.com/06_Press/Press-Releases/
14-07-16_Mediaplus_Pendler-Studie/Mobile-Nutzung-in-Wartesituationen.pdf
2
BITKOM (2014). Website accessed February 25, 2015 under
http://www.bitkom.org/files/documents/BITKOM-Praesentation_PK_Gaming_06_08_
2014.pdf
1
1. Introduction
Finally, games for smartphones differ significantly from those developed for
other platforms, like desktop PCs or stationary consoles. Most notably, the lack
of physical buttons and the limited screen space set the smartphone apart from
other gaming devices. This demands an adapted approach when developing for
this platform.
1.2 Solution Idea
Given the spread of mobile games and the deficit of educational games for smartphones, it seems reasonable to investigate whether and how it might be possible
to create a game with an educative motive for said platform.
In the context of this thesis, a prototype of a mobile game is designed to try and
take advantage of the popularity of casual gaming 3 for imparting knowledge about
Boolean algebra which can be seen as part of an information technology literacy.
Subjects related to computer science and especially logic lend themselves well
to be used in a game environment since they inherently concentrate on problem
solving which is at the core of every game (cp. Schell 2008, p. 35).
The learning contents are concurrently explored by the player in a series of 2D
puzzle games. Puzzle mechanics tend to emphasize the problem solving aspect in
particular. Learning the underlying principles of Boolean algebra is to take place
in a preferably concealed way. This kind of hidden or stealth learning (cp. Prensky
2003) is to be achieved by placing the game in a graphical context distant from
computer science. Part of the focus is on fast feedback cycles that allow the player
to concentrate on experimenting and thus stimulate autodidactic learning through
making mistakes. The use of formal notation in the game is kept explicitly and
strictly optional so as to make it easier for the player to casually get familiar
with the basic concepts of Boolean algebra. The playful aspect as a motivational
element is kept in the foreground, thus the learning content is intentionally limited
to the subject’s fundamental principles. In this way, an attempt is undertaken to
make a subject vital to information technology appeal to an audience distant to
computer science.
Game-based approaches are explored in five scenarios, each featuring distinct
3
2
A casual game typically features simple rules and targets a broad audience.
1.3 Overview
concepts grounded in educational games research and factoring in the specifics
of developing for smartphones. The first scenario (see section 3.2.1) serves as
an example for the introductory part of a game, also known as a tutorial. The
main game mechanics depicted therein are used in the following scenarios. These
demonstrate exploration- (see section 3.2.2) and quiz-based (see section 3.2.3)
concepts as well as a combination of both (see section 3.2.4). The last scenario
(see section 3.2.5) then presents a separate mechanic inspired by block moving
puzzle games.
As base technology, the Unity4 game engine is used, so as to be able to quickly
prototype and focus on the core mechanics (cp. Busch & Steinicke 2014, p. 23).
The choice of the open source Android5 platform is due to the rapid increase in
distribution and relevance of this platform which now lists the most active users
among mobile operating systems.6
The implementation is restricted to a prototype since developing a complete
game for a stationary platform would go beyond the scope of a work like this;
creating a mobile app instead of a game would disregard the motivation to use
such.
Actual play testing including evaluation and assessment of the concrete learning
effects is also not planned for the above restrictive reasons. However, concepts for
evaluation are presented in the thesis itself.
1.3 Overview
Textually, this work studies a digital game-based learning approach to the concepts
of Boolean algebra. Best practices for game-based design are investigated in the
light of developing for smartphones.
The groundwork is laid out in introductions to digital game-based learning
and the fundamentals of the didactic subject (chapter 2) to open up the main
discussion about the implemented learning concepts and the reciprocity between
4
A game creation software developed by Unity Technologies. Website accessed March 17, 2015
under http://www.unity3d.com
5
A mobile operating system developed by Google. Website accessed March 17, 2015 under
http://www.android.com
6
Net Applications (2015). Website accessed March 7, 2015 under
https://www.netmarketshare.com/operating-system-market-share.aspx?qprid=9&
qpcustom=iOS,Android,Linux&sample=29&qpcustomd=de
3
1. Introduction
learning and playing within the prototype (chapter 3). In that context, the proof of
concept is described in detail and suggestions for possible modifications are made.
An overview of the technical implementation follows (chapter 4), focusing on the
smartphone as target device. Finally, evaluation concepts are briefly described
(chapter 5), before closing with recommendations for possible future work (chapter
6).
4
2 Fundamentals
This chapter presents a short introduction to the two main domains of interest,
namely the idea of game-based learning and the subject of Boolean algebra.
2.1 Digital Game-based Learning
Following is a possible definition of the term as well as arguments for employing
a game-based approach to learning.
2.1.1 Definition
Although there is a growing body of literature on learning by playing games (cp.
Becker 2007, p. 122), the term Digital Game-Based Learning (DGBL) still eludes
a clear definition.
Busch and Steinicke describe it broadly as “the process of being taught
and/or learning via digitally enriched play-/gamelike activities or by playing/designing/creating/modifying digital games” (Busch & Steinicke 2014, p. 24).
Alternatively, there are attempts to curtail the idea by pointing out the differences to the anterior notion of Edutainment 7 which is defined as constituting a
media message to both entertain and educate (cp. Breuer 2009, p. 17). DGBL,
in contrast, focuses specifically on the playfulness of learning. Furthermore, it
is often not limited to any particular target group or area of education, while
the majority of Edutainment products concentrate on the academic sector (cp.
Breuer 2009, p. 17). The deficit of Edutainment is often seen in it using entertaining elements as intensifiers and stimuli before or after a learning passage, thereby
employing entertainment merely for disguising purposes (cp. Breuer 2009, p. 18).
Meanwhile, the more promising concept of DGBL aims at making the learning
7
Short form for Entertainment Education.
5
2. Fundamentals
process itself entertaining. The details on how this is tried to be achieved are
further investigated throughout this thesis.
2.1.2 Games and Learning
The parallels between playing and learning are manifold. Breuer points out the
following self-evident commonalities (cp. Breuer 2009, p. 12):
• There are preassigned, mandatory goals,
• in the best case, players/learners devote their complete attention,
• achievements give a sense of self-efficacy,
• progress is noticeable for players/learners,
• players/learners receive feedback for their performance,
• ideally, players/learners are motivated to accomplish an objective,
• the difficulty of the assignments increases over time,
• solving the assignments requires a certain degree of effort,
• players/learners should neither be challenged too much, nor too little,
• players/learners have to be active themselves.
As Breuer notes, this list already indicates the potential of digital games for
educational purposes (also cp. Tashiro & Dunlap 2007, p. 114). Becker goes as
far as declaring that “learning is really what games are all about” (Becker 2007,
p. 123). Doucet elaborates on this idea by stating that a game is “a formal system
of challenges to stretch the brain, coupled with rewards to encourage the player
to seek out the next learning high” (Doucet & Srinivasan 2010, p. 5). Thus, game
designers face a similar problem as educators do, namely how to motivate people
“to learn and master something that is long and challenging - and enjoy it” (Gee
2003, p. 1). Successful games arguably find effective ways to solve this dilemma,
enabling players to “achieve recreation and deep learning at one and the same
time” (Gee 2003, p. 3).
6
2.1 Digital Game-based Learning
One reason for using a game to convey the fundamentals of Boolean algebra
is the inherent notion of games as providing problems that demand to be solved.
Schell describes this as follows:
“When problem solving is removed from a game, it ceases to be a
game and becomes just an activity” (Schell 2008, p. 35).
Thus, a game is defined by a sort of conflict waiting to be resolved through
active participation on the side of the player.
Computer science subjects share this problem-focused methodology. Problems
concerning logic lend themselves particularly well for a game-based learning concept. Further investigation of this argument from a didactic vantage point is
carried out in section 2.2.1.
As a further argument for educational games, Greengard describes them as
being learning initiators:
“as children play an educational game and learn about a particular
period in history or an interesting concept, they often want to learn
more” (Greengard 2009, p. 19).
Games are well suited to pique curiosity for a subject and open the door for
further engagement. In this context, Breuer also constitutes games as stimulators
and motivators (cp. Breuer 2009, p. 33). Dealing with a subject in a playful way
can spark interest in the player to explore it more elaborately outside of the game.
Games can make use of this potential by placing hints as entry points to specific
topics, which would be described by Portnow as tangential learning (cp. Portnow
2008) and is also picked up in the implemented scenarios in the form of optional
overlays.
Games offer yet further attributes for application in learning, some of which
other media is not able to provide to such extent (cp. Breuer 2009, p. 10). Amongst
those is the notion of contextual bridging (cp. Tashiro & Dunlap 2007, p. 117),
meaning that learned content is used directly and in a situation that is meaningful
to the game itself. Thus, players can remember and make use of information in a
more effective way (cp. Gee 2003, p. 2). The interactive and immersive potential
of video games also eludes those of other media (cp. Bellotti et al. 2009, p. 23:2).
It enables players to actively participate and shape their experience.
7
2. Fundamentals
Finally, Prensky points out that there has been a shift in how people who grew
up with computer and video games process information, compared to those who
were raised without them (cp. Prensky 2003, p. 5). He sees this change as reason
to believe that “much, if not most of the data we have collected and the theories
we have formulated in the past about how people think and learn may no longer
apply” (Prensky 2003, p. 6). Based on this premise, he suggests “adding fun into
the process will not only make learning and training much more enjoyable and
compelling, but far more effective as well” (Prensky 2003, p. 4). The efficacy
of educational games is a much debated subject and needs to be evaluated on a
case-by-case basis. Thus, an evaluation concept is presented in chapter 5.
Whether or not a game is able to fully disclose a subject to a player is not the
only question of interest here. There is a clear benefit, even if a game merely
manages to introduce the user to a new concept. When having to learn a subject
sometime in the future (e.g. in school), players can draw on the experience of
having been confronted with the content in a playful way. Thus, barriers and
anxiety levels can be reduced since they already came into contact with the subject
in a positively marked context. The proof of concept hence aims at providing an
initial contact point to a subject, rather than trying to cover it in its entirety.
2.1.3 Existing Approaches
A variety of implementations for educational and non-educational games and apps
containing subjects from mathematics and computer science was consulted in the
process of designing the presented scenarios. Following is a short overview of some
of those.
A large portion of digital learning applications are designed for studying facts.
For example, Q&A8 provides a framework to create questions and answers and
compete against others in quizzes.
Other apps focus on guiding the user through a series of instructions. Math
42 9 is such an app, featuring tutor-like guidance on how to solve specific math
problems.
8
Developed by benntec. Website accessed April 7, 2015 under http://www.benntec.de/
elearningmultimedia/referenzen/qa-lern-app
9
Developed by Cogeon. Website accessed April 7, 2015 under http://www.math-42.com
8
2.1 Digital Game-based Learning
A third category of apps presents exercises with decorative elements (cp. Linehan et al. 2011, p. 1979). Math Blaster 10 is a representative product with this
characteristic. Here, the player switches between action sequences and exercise
passages. Besides creating an interruptive experience (cp. De Castell & Jenson
2003, p. 49), this kind of game typically exhibits a fundamental drawback by
trying to educate rather than to facilitate learning (cp. Portnow 2008). The developers try to force knowledge onto the player instead of letting them explore a
subject autonomously.
Other game-based approaches suffer from a similar problem. In Counting Kingdom 11 , players need to add up numbers in a tower-defense type of game. Yet
again, this presents a testing environment rather than a place to explore math.
A strong point of this specific game, however, is the implementation of consequences which goes along with the core defense mechanic. This is a more effective
way of checking for improvement, in contrast to tracking and record-keeping (cp.
De Castell & Jenson 2003, p. 49).
Finally, there are games that were developed with scientific research in mind.
Wu‘s Castle (cp. Eagle 2009) requires the player to solve problems by filling in
parameters of for-loops. Another game, developed by Heintz and Law (cp. Heintz
& Law 2012), uses blocks of code that need to be arranged. The Lost Java Code
(cp. Zhang et al. 2014) aims at helping to review concepts on decision structures
by switching between free play and quizzes, much like Math Blaster. Turtlet
(cp. Kasurinen et al. 2008) features controlling a character on a 2D game board
via user-defined commands, essentially providing a simplified visual programming
environment.
All of these approaches employ mechanics with elements very close to the didactic subject. While this seems necessary for transfer of knowledge in the context
of learning to write program code, it might also be a barrier when it comes to
accessibility. Communicating basic concepts could be accomplished by means of
mapping those concepts onto more intuitive game rules.
Rudder et al. use visualizations to create a bridge between real world situations
and programming concepts (cp. Rudder et al. 2007), requiring the user to
10
Developed by JumpStart Games. Website accessed April 7, 2015 under http://www.
mathblaster.com
11
Developed by Little Worlds Interactive. Website accessed April 7, 2015 under http://www.
countingkingdomgame.com
9
2. Fundamentals
comprehend the material on a semantic level. This comes closer to the presented
concepts, as they can be easily extended to enclose concrete settings as well,
effectively enhancing semantic understanding (see suggested features in section
3.2.2).
Although above methodologies might be suitable for specific areas of education, they all miss some crucial factors.
While apps largely disregard the
motivational aspect – would casual gamers voluntarily use them in their free
time? – and scientific approaches mostly lack entertaining ingredients as well,
games that are not explicitly devised for learning fail to deliver on the didactic
part. The key to effective learning within a digital environment seems to be the
conceptual integration of the mechanics contained in the subject that is to be
learned. This means identifying entertaining elements and moments of learning
that subject and making use of them for the game design to reflect those. In that
context, it is not enough to push learning content into playful form (cp. Breuer
2009, p. 18).
Furthermore, above approaches are arguably suboptimal when trying to convey the interplay of elements within a system of dependencies. They are in fact
decorated cloze tests, which are more suited for the learning of facts.
To conclude, most of the above-mentioned concepts are not suitable for the
general public since they were designed with an exclusively academic audience in
mind.
2.2 Didactic Context
While some reasons were given for the choice of a game-based approach, this
section goes into further detail on the motivation for the learning subject Boolean
algebra in particular, as well as covering its fundamentals in a concise manner and
confined to the context it is being used in.
10
2.2 Didactic Context
2.2.1 Motivation
George Boole12 introduced Boolean algebra in his books The Mathematical Analysis of Logic (1847) and An Investigation of the Laws of Thought (1854). These
titles already suggest the use of Boolean algebra outside of mere mathematics: It
is at the core of logical thinking and reasoning which are useful in everyday life.
Thus, the prototype developed in the context of this thesis targets the general
public since it is believed that development of logical and abstract thinking helps
to solve problems within non-scientific areas as well (cp. Kasurinen et al. 2008,
p. 3).
Besides being used in set theory and statistics, Boolean algebra plays a vital role
in computer science, where it provides the theoretical foundation for logic circuits.
These in turn form the basis for the vast majority of computing machines.
A good understanding of Boolean rules is essential when learning to write computer programs. There is a strong point for a computer science literacy with
the argument that “programming should be a universal skill for people in the
information society”(Kasurinen et al. 2008, p. 2). Bill Gates13 phrases it this way:
“Learning to write programs stretches your mind, and helps you
think better, creates a way of thinking about things that I think is
helpful in all domains.”14
To date, a large body of educational games has been developed to teach
programming in general (cp. Baker 2012, Bellotti et al. 2009, Heintz & Law 2012,
Kasurinen et al. 2008, Kumar 2014). Games which focus on specific computer
science related concepts, however, are rare (cp. section 2.1.3). This perceived
gap is a further reason for the development of a game concentrating on Boolean
algebra.
Finally, the content and the type of game should be matched (cp. Breuer
2009, p. 33). The subject at hand lends itself very well to being explored through
12
English mathematician. *1815, †1864. Coincidentally, the year of this work’s publication
marks the 200th birthday of George Boole which is commemorated under http://www.
georgeboole.com, accessed February 23, 2015.
13
Co-founder of Microsoft, the world’s largest PC software company.
14
http://www.code.org/quotes, accessed March 18, 2015.
11
2. Fundamentals
interactive game play (cp. Doucet & Srinivasan 2010, p. 5). As Schell points out,
areas, where games have some advantage against conventional education methods,
include the solving of problems and understanding systems of relationships (cp.
Schell 2008, pp. 444-446), which both apply to Boolean algebra. Schell goes on
to state:
“Lectures, readings, and videos all have the weakness of being linear,
and a linear medium is a very difficult way to convey a complex system
of relationships. The only way to understand a complex system of
relationships is to play with it, and to get a holistic sense of how
everything is connected.” (Schell 2008, p. 446)
Viewing the Boolean algebra as a system of dependencies also aided in the
design process of the prototype since “often the question of ‘game balance ’ is
already present in real-world trade-offs” (Doucet & Srinivasan 2010, p. 9). In this
case, the rules were already given by the Boolean axioms; the main effort lay in
mapping them onto a visual and more game-like system, which is covered in more
detail in section 3.2.
2.2.2 Fundamentals of Boolean Algebra
The following briefly covers the concepts of the two-element Boolean algebra that
are relevant in the context of this thesis.15
A Boolean algebra, as part of mathematics, is a class of elements B with two
binary operations ⊕ and , which satisfies the following postulates (cp. Whitesitt
1995, p. 28):
1. The operations ⊕ and are commutative.
2. There exist in B distinct identity elements 0 and 1 relative to the operations
⊕ and , respectively.
3. Each operation is distributive over the other.
4. For every element a in B there exists an element a0 in B such that a ⊕ a0 = 1
and a a0 = 0.
15
For convenience, the two-element Boolean algebra will be referred to as simply Boolean algebra
throughout the remainder of this thesis.
12
2.2 Didactic Context
The binary operations can be denoted by any two symbols; throughout the
remainder of this thesis, they will be written as + and · as well as ∨ and ∧,
or and and, and disjunction and conjunction, respectively. For an element or
variable a in B, its complement (see postulate 4) will be symbolized as ¬a, a and
not a interchangeably. The elements 1 and 0 can be seen as true and false values,
respectively.
Considering the above postulates, the following laws can be established for any
Boolean algebra, where x, y, z are elements of a Boolean algebra and the symbol ⊗
denotes either of the binary operations (for proofs cp. Whitesitt 1995, pp. 29ff.):
x ⊗ (y ⊗ z) = (x ⊗ y) ⊗ z
x⊗y =y⊗x
(Associativity)
(Commutativity)
x ∧ (y ∨ z) = (x ∧ y) ∨ (x ∧ z)
(Distributivity of ∧ over ∨)
x ∨ (y ∧ z) = (x ∨ y) ∧ (x ∨ z)
(Distributivity of ∨ over ∧)
x∨0=x
(Identity for ∨)
x∧1=x
(Identity for ∧)
x∨1=1
(Annihilator for ∨)
x∧0=0
(Annihilator for ∧)
x⊗x=x
(Idempotence)
x ∧ (x ∨ y) = x
(Absorption 1)
x ∨ (x ∧ y) = x
(Absorption 2)
x ∧ ¬x = 0
(Complementation 1)
x ∨ ¬x = 1
(Complementation 2)
¬(¬x) = x
(Double negation)
¬x ∧ ¬y = ¬(x ∨ y)
(De Morgan 1)
¬x ∨ ¬y = ¬(x ∧ y)
(De Morgan 2)
13
2. Fundamentals
A literal denotes a variable or the negation of a variable. A clause is a disjunction of literals or a single literal. A Boolean propositional formula is a composition
of elements of Boolean algebra, which in turn satisfy the conditions for Boolean
terms. A formula is in conjunctive normal form (CNF) if it is a conjunction of
clauses or a single clause.
Mapping all variables in a formula to logical values, e.g. values of 0 and 1, is
called a truth assignment or interpretation. The truth value of such an interpretation is then determined by computing the value of this term and can be 0 or
1.
A formula is satisfiable, if there exists at least one interpretation that makes
its truth value equal 1. An unsatisfiable formula is known as a contradiction. A
formula is called a tautology, if every truth assignment yields a truth value of 1.
Considering these definitions, there are several kinds of interesting problem
statements when beginning to learn about Boolean algebra, some of which are the
basis for the educational scenarios developed in this thesis. These are elaborated
upon in the respective subsections of section 3.2. Below, they are briefly listed
from a didactic viewpoint.
Getting to know the above axioms is a reasonable starting point to get a feeling
for Boolean algebra. This is explored in the introductory levels of the prototype
under Learning Boolean Axioms (see section 3.2.1).
Given a formula, another possible problem is finding a concrete truth assignment
for its variables so as to yield a certain truth value for the resulting interpretation,
which is covered in Interpreting Boolean Formulae (see section 3.2.2).
Computing the truth value corresponding to a given interpretation of a formula
is a sensible next step in the learning process and is addressed in the scenario
entitled Evaluating Boolean Formulae (see section 3.2.3).
Determining the satisfiability of a formula, i.e. deciding if its variables can be
mapped to 0 and 1 values in a way so as to yield a truth value of 1, is known
as the Boolean satisfiability problem (SAT) and is especially relevant to computer
science. It constitutes the first known NP-complete problem and every decision
problem in NP can be reduced to it. It is explored under Determining Satisfiability
(see section 3.2.4).
A Boolean expression can have a number of equivalents. These are formulae
14
2.2 Didactic Context
which have the same truth values under identical interpretations. Often, a formula
can be simplified, i.e. Boolean laws can be repeatedly performed so that the
amount of elements and operations is reduced, eventually yielding an equivalent
formula with a minimum number of symbols. In computer science, such formulae
are of particular importance for the efficiency of logic circuits. For this problem,
a special type of level was implemented under Simplifying Formulae (see section
3.2.5), which focuses specifically on transforming formulae by manipulating their
elements.
15
3 Concepts for Game-Based
Learning
Thus far, Boolean rules and game-based concepts were discussed only briefly in
an introductory form. This chapter connects the two domains by discussing the
proof of concept in detail.
3.1 Conceptualization Process
Since educational game development is a highly interdisciplinary endeavor, a
variety of commercial and scientific approaches was consulted in the course of
developing the concepts presented in this thesis.
The process of designing a mapping between didactic context and game
environment involved balancing the educational content with the entertaining
characteristics of a game. Early approaches exhibited deficits in either one of
those areas. This section discusses a selection of design ideas that led to the
developed concepts. Some of those were discarded for the above reason, others
because of platform restrictions.
As a starting point, the prototype was to feature a collection of levels,
where each one would present a specific computer science related subject.
This was dismissed in favor of a design that would allow to gradually build
understanding of one particular subject. Once Boolean algebra came into focus
as said subject, several game mechanics were experimented with.
Game ideas which would not fit the target device were the first ones to be
turned down. These included concepts with complex control schemes that would
require several on-screen buttons or a designated controller as well as mechanics
17
3. Concepts for Game-Based Learning
that demanded larger screens or high computing resources. With that and the
limited scope of the work in mind, 3D graphics were also dismissed in favor of a
simple, two-dimensional environment.
Relating to core game mechanics, the manipulation of formulae using formal notation was considered, yet discarded early on since it limits possibilities
for playful endeavor. The closeness to the formal system rendered this mechanic
unfit for the general public which the game aimed for. Also, replacing symbols of
a formula with abstract forms or concrete objects would mean a mere decorative
treatment of the subject, which was also deemed inapt for above target group.
Being too closely related to the didactic context, these approaches lack inherent
motivation to be pursued in game-like form (cp. De Castell & Jenson 2003, p. 49).
Concepts biased toward entertainment turned out to be problematic as well.
These would disregard or divert from the didactic subject at hand and thus lead
to games where transfer of knowledge was very unlikely. Ideas in this direction
involved story-driven and action-oriented games. It quickly became clear that
the core mechanic needed to match the structures and dependencies within the
subject itself (cp. Doucet & Srinivasan 2010, p. 5).
The presented solution was reached by employing those mechanics and systems which correlate to the ones contained in the educational content, creating
what Clark and Martinez-Garza describe as a “conceptually integrated game”
(Clark & Martinez-Garza 2012, p. 280). This was accomplished by translating
the elements of Boolean algebra appropriately into game rules, without resorting
to mere decorative game mechanics.
However, it also included identifying
entertaining moments of learning and using them for the game (cp. Breuer 2009,
p. 31). In the context of Boolean algebra, these were seen in discovering the
interplay between variables and their interpretation in relation to the truth
value of a formula. Another interesting aspect to seamlessly integrate learning
and gameplay (cp. Van Eck 2006, p. 18) was found in transforming formulae.
The challenge then became finding a coherent mapping of the core ideas and
relationships of the didactic subject onto game-based mechanics (cp. Clark &
Martinez-Garza 2012, p. 281).
18
3.2 Scenarios
A first concept relating to the above areas featured free-floating objects,
e.g. circles, squares and triangles, representing Boolean variables with the goal of
the game being the simplification of the visualized formula by combining those
objects. This proved problematic with regard to an intuitive mapping of the
operations and and or, which either would have turned out unintuitive or too
close to formal notation. Eventually, transforming formulae was implemented
(see section 3.2.5) as a combination of the above and some of the concepts that
relate to the following design idea.
Focusing on experimenting with the truth value of a formula, a visualization
using pipes or corridors was investigated. Here, much like in logical circuits,
operations could be intuitively integrated with the structure of the level itself
(cp. section 3.2.1). Variables were to be represented by blocks positioned in
those corridors, with black blocks representing variables with an interpretation
of 0 and white blocks denoting 1. To enable an intuitive understanding of the
formula’s truth value, a fluid was meant to be directed vertically through the
corridors, with black blocks polluting it. The pollution state of the fluid leaving
the system of corridors would then determine the truth value of the underlying
formula: non-polluted fluid would mean true and polluted would represent false. A
problem concerning an intuitive mapping arises with this setup when considering
the following simple situations: Given the axiom 0 · 1 = 0, it would be represented
by a single corridor featuring two blocks which the fluid would have to pass in
succession. The first (black) block would pollute the fluid, the second (white)
block must leave it polluted, as the truth value is 0. Looking at the formula
0 + 1 = 1, where the fluid would pass the two blocks in separate corridors and
subsequently merge into one corridor, it becomes clear that the polluted fluid
would have to change its state to clean, when mixed with polluted parts. This
poses a contradictory behavior with respect to intuitive mechanics. Thus, the
concept was adapted to feature more self-explanatory characteristics (see sections
3.2.1 through 3.2.4).
3.2 Scenarios
As stated, the aim of the developed prototype is to introduce the player to Boolean
algebra. Five scenarios were designed to cover a set of problems connected to this
19
3. Concepts for Game-Based Learning
subject. The first four scenarios explore the role of assignments and truth values
of Boolean formulae, while the fifth scenario approaches the subject of simplifying
formulae by transformation.
Each scenario corresponds to a specific sort of problem relating to Boolean
algebra (see also section 2.2.2) and features several levels for demonstration. Each
level is identified in the form of “level <scenarioNumber>-<levelNumber>” (e.g.
level 1-3 addresses the third level of 3.2.1) throughout the remainder of the thesis,
where the scenario number is the last number of the corresponding subsection of
section 3.2.
In the prototype, the levels are accessible via the Main Menu (cp. Figure 3.1).
Tapping on the Info icon in the bottom center displays a short description of
the main mechanics and the information that hints can be accessed by tapping
the top area of any level.16 Additionally, there is a Quit button for quitting the
application in the left bottom corner and a Resume button on the right to load
the lastly played level.
Figure 3.1: The main menu of the prototype with access to the
different scenarios
16
For the full info texts, see A.1.
20
3.2 Scenarios
Each level – independent of the scenario it belongs to – represents a Boolean
formula in a graphical way, using 2D graphics. The specifics of this mapping as
well as the characteristics of each scenario are described in the sections below.
Several elements were designed, yet not implemented to keep the proof of concept manageable and within the scope of the thesis. Nonetheless, these modifications are also mentioned per scenario since they portray sensible means to extend
the game environments and adapt the presented concepts to different requirements
and conditions, e.g. to shift the target group in an uncomplex way.
The scenarios present different game-based approaches, with scenario 3.2.1 implementing a tutorial design, scenario 3.2.2 focusing on an exploration and trialand-error method, scenario 3.2.3 featuring a quiz-like mechanic and scenario 3.2.4
combining exploration and quiz elements. These can be seen as individual games
or used consecutively in the above order to foster an understanding of Boolean
algebra. Finally, scenario 3.2.5 marks a separate approach.
The mapping of didactic context to game mechanics is identical for scenarios
3.2.1 through 3.2.4; thus it will be covered once in the beginning of section 3.2.1.
Scenario 3.2.5 employs a mapping which is uncoupled from the aforementioned
scenarios and therefore features a distinct description of its mechanics.
3.2.1 Learning Boolean Axioms
The first scenario covers the basic laws of Boolean algebra (see section 2.2.2).
Following is a detailed discussion on the motifs for this scenario and the game
mechanics introduced here as well as DGBL- and device-related arguments for its
design.
Motivation
Beginning to play a new game confronts a novice player’s mind with the challenge
to form a coherent model of the game rules, much like starting to learn a new concept or subject would. In this phase of learning, generalizations are formed about
the game or subject at hand. Thus, the make-up and order of initial problems is
key to a good foundation of the player’s and learner’s knowledge “about what will
work well later when they face more complex problems” (Gee 2003, p. 2).
Approaching the subject of Boolean algebra, the first concepts to be grasped
21
3. Concepts for Game-Based Learning
are the fundamentals of operations and elements (see section 2.2.2). Therefore,
a series of introductory levels were designed to familiarize the player with these
basic components of Boolean algebra.
Mechanics
Before discussing the implemented levels, the mapping of Boolean algebra onto
the game world is illustrated.
The elements 0 (false) and 1 (true) are visualized by black (cp. Figure 3.2) and
white (cp. Figure 3.3) blocks, respectively. These are not interactable.
Figure 3.2: A black block representing the element 0 (false)
Figure 3.3: A white block representing the element 1 (true)
Boolean propositional variables are represented by colored blocks (cp. Figure
3.4), where each block of the same color represents one variable, e.g. if there are
two green blocks (and one presumed the arbitrary mapping of the color green
to the variable a) and one blue block (again, arbitrarily mapping this color to a
variable denoted by b) in a level, then the corresponding formula contains two
variables (a and b), where the first one (a) appears twice and the second one (b)
appears once in mentioned formula.17
Concrete assignments are visualized by mapping 0 to a black and 1 to a white
block interior (cp. Figure 3.4). Toggling the truth value of a variable is done by
tapping on the corresponding block, resulting in all blocks of the same color also
changing their value since they all represent one variable.
17
Note: Mapping variable identifiers to colors will be kept arbitrary throughout the remainder
of the thesis.
22
3.2 Scenarios
Figure 3.4: From left to right: A block with no assignment; a black block interior
indicating a negative assignment, i.e. false or 0; a white block interior
indicating a positive assignment, i.e. true or 1
The main operations, the conjunction and the disjunction are implemented by
corresponding corridors in the level (cp. Figures 3.5 and 3.6, respectively), while
the negation is denoted as a black frame around any of the blocks of a level (cp.
Figure 3.7).18
Figure 3.5: Conjunction
Figure 3.6: Disjunction
Figure 3.7: Negation
Depending on the type of level, white balls fall from the top to the bottom
through a system of such corridors, comparable to the concept of a current running
through a logic circuit. At negation borders, their color is toggled between black
and white (cp. Figure 3.9). White balls pass through white blocks and stop at
black blocks (cp. Figure 3.8), while black balls pass through black blocks, being
stopped by white blocks. In this context, black and white blocks denote completely
black and white blocks representing the element 0 and 1, respectively, as well as
meaning blocks with a black or white interior depicting variables with a concrete
value assignment.
18
The screenshots here contain place holders instead of actual blocks. The introductory levels
with variables are presented in the next section.
23
3. Concepts for Game-Based Learning
Figure 3.8: White
balls
being
stopped at a black block
Figure 3.9: Balls inverting their color
at the borders of a negation frame and passing
through a black block
Given a concrete assignment of all the blocks of a level, the interpretation of
the underlying formula becomes true, if – and only if – the afore-mentioned balls
can pass through to the bottom ground and false, otherwise.
A necessary auxiliary feature so as to avoid incorrect outcomes is that balls
below a tempered-with block disappear; otherwise it would be possible to let
balls reach the ground with an assignment that does not match the truth value
of the formula.
Taking all of the above into account, this mapping makes it possible to
represent any Boolean formula in a graphical way. All the components of Boolean
algebra are mapped to corresponding visual representations, which can be
combined in very much the same way as their formal counterparts. Elaborately,
all postulates which define a Boolean algebra hold for this mapping (cp. section
2.2.2):
• The operations · and + are implemented in a way that ensures commutativity since the order of two or more blocks in an and - or an or -corridor is
irrelevant (cp. Figures 3.5 and 3.6),
• the 0 and 1 elements are incorporated as black and white blocks, respectively
(cp. Figures 3.2 and 3.3)),
• distributivity is given, for operations are combined in the same way as in
24
3.2 Scenarios
formal notation, with parentheses indicated by the level structure itself19
(cp. Figures 3.10 and 3.11),
• negation is mapped via a frame around blocks; its behavior corresponds to
its formal counterpart, as for any element a, it holds: a + ¬a = 1 (cp. Figure
3.12) and a · ¬a = 0 (cp. Figure 3.13).
Figure 3.10: A graphical representation of the formula a + (¬a · b)
Figure 3.11: A graphical representation of the formula (a + ¬a) · b
Figure 3.12: Representation
a + ¬a = 1
Figure 3.13: Representation
a · ¬a = 0
19
of
of
Precedence rules are omitted here since they are merely used to reduce the number of necessary
parentheses; those will always be employed in case of ambiguity.
25
3. Concepts for Game-Based Learning
Aside from the introductory levels, these mechanics are used for scenarios 3.2.2,
3.2.3 and 3.2.4 to demonstrate a game-based approach to assignments in Boolean
algebra.
Game-based Design
Having defined a coherent mapping between Boolean algebra and game logic, the
actual design and order of the introductory levels come into focus.
A crucial part of the design was to make the game rules as self-explanatory and
intuitive as possible, so as to allow the player to start playing right away. Thus,
tutorial levels should be perceived by the player as part of the game and act as a
substitute for any pre-game instructions. Notably, the use of text as a necessary
element was avoided altogether, as research indicates that “users hardly ever read
the text at all” (cp. Prensky 2003, p. 13). This might be particularly true for
players of casual and mobile games.
As a result, not only is there a necessity for the levels themselves to be designed
in a clear, straightforward and short way, but also the order of these introductory
levels appears to be relevant to facilitate a conclusive model in the player’s mind.
Starting out with a very basic case of just one variable, the first level (cp.
Figure 3.14) confronts the player with a manageable amount of options for the
beginning, where they do not know anything about the game rules yet. They
see a static black block and a steady stream of balls falling down to stop at the
block. Without any instructions, the most likely action on user-side is tapping
on the screen. Since the block is in the center of the level and it stands out
against the rest of the environment, players ought to be able to quickly come to
an understanding of how to interact with it and also draw conclusions about the
goal of the level as it ends when the first balls touch the ground (cp. Figure 3.15).
26
3.2 Scenarios
Figure 3.14: Level 1-1: Introducing the
goal of the game as well as
the main controls
Figure 3.15: Level 1-1 solved
Several things are discovered by the player via just this one simple level. When
they finish it, they will arguably suspect that the goal is to get the balls to touch
the ground. They also will know how to interact with a block and they will have an
idea about the conditions for the balls to pass through a block. These assumptions
are supposed to broaden and manifest to actual knowledge throughout the series
of intro levels.
The second tutorial level (cp. Figure 3.16) features a conjunction of two differently colored blocks. Having figured out how to solve the first level, players are
likely to pass this level rather quickly. Nonetheless, it is necessary for creating the
notion of assignments to blocks of differing color.
This is especially relevant in the light of the third level (cp. Figure 3.17),
where the same level structure is presented to the player with the two blocks
sharing the same color. Here, an important game rule will be observed by the
player for the first time, namely that blocks of the same color always have the
same assignment. Additionally, levels 1-2 and 1-3 both introduce the player to
conjunction in Boolean algebra.
27
3. Concepts for Game-Based Learning
Figure 3.16: Level 1-2: Two differently colored blocks in
conjunction
Figure 3.17: Level 1-3: Two blocks
of the same color in
conjunction
Levels four and five of the introductory series (cp. Figures 3.18 and 3.19)
respectively debut the 1 and 0 elements of Boolean algebra in much the same
obvious way as the preceding levels depicted other aspects of it. Moreover, level 1-5
arranges the blocks in disjunction, establishing the corresponding part of Boolean
algebra.
Figure 3.18: Level 1-4: The 1 element
28
Figure 3.19: Level 1-5: The 0 element and disjunction are
introduced
3.2 Scenarios
Finally, an example for negation is shown in the sixth level (cp. Figure 3.20).
Here, the setup was carefully designed so as to allow the player to experiment
with the top, negated block, without directly solving the level. This way, they
have a good chance of figuring out that balls reverse their color and their passing
condition at the borders of a negation frame.
Figure 3.20: Level 1-6: An example for
negation
Figure 3.21: Level 1-6 with underlying
formula
In addition to the mechanics described above, another specific feature to foster
the link to Boolean algebra was implemented: If the player touches the bottom
part of a level, the formal equivalent of that level’s structure is shown (cp. Figure
3.21). This presents a non-intrusive integration of semi-formal notation since its
use is not necessary to play the game, yet it provides additional information to
support the transfer of knowledge. Thus, it is in compliance with the idea of
tangential learning described by Portnow (cp. Portnow 2008).
Immediate feedback throughout the levels as well as at the completion of a
level serve as reinforcement as well as encouragement (cp. Rudder et al. 2007).
The instant response of all interactable elements further makes for a reactive
game environment.
The introduction is kept fast-paced across these very short, but descriptive
levels and the momentum built is used to keep the initial curiosity of the player
29
3. Concepts for Game-Based Learning
alive, introducing new concepts with each new level, comparable to the puzzles
found in The Witness 20 . At the same time, the amount of tutorial levels is kept
to a bare minimum to be able to convey the basic laws of Boolean algebra while
not losing the player’s interest with redundant challenges (cp. Redwood 2012).
With this design, players are believed to be able to learn the controls and
goals of a game simply by playing it. Simultaneously, they get a feeling for the
main elements and operations of Boolean algebra by autonomous exploration of
the game rules. Associativity and commutativity are implicitly grasped through
the graphical design. The direct mapping between didactic subject and game
elements ought to allow for an efficient transfer of knowledge between the two
domains, although a custom-designed evaluation would shed more light on this
subject (see chapter 5).
To conclude, this scenario aims to build and keep the attention of players,
letting them discover the objectives autonomously and provide clear feedback of
their actions (cp. Breuer 2009, p. 32).
3.2.2 Interpreting Boolean Formulae
Building upon the main mechanics introduced in the tutorial levels, this scenario
aims at making the player familiar with the truth value of a Boolean formula by
manipulating the assignments of its variables.
Motivation
To get a feeling for a system of relationships, a player, viz. a learner, needs to be
able to experiment with it (cp. Schell 2008, p. 446). Thus, a tweakable simulation
which allows players to fail without punishment is preferable.
Considering Boolean algebra, one way of developing an understanding for the
interplay between elements of a formula is to assign concrete values to its variables
and observe the effect this has on its truth value. Hence, this scenario provides a
playground for the player, where they can manipulate assignments as they please
and observe the outcome in real-time.
20
Puzzle Game developed by Thekla, Inc., to be released 2015. Website accessed March 24,
2015 under http://www.the-witness.net
30
3.2 Scenarios
Game-based Design
Using the mapping between Boolean algebra and the game mechanics introduced
in section 3.2.1, this scenario also keeps the conditions for completing a level. The
goal of the game remains to allocate concrete values to blocks so as to yield a truth
value of 1 for the underlying satisfiable formula under that specific interpretation.
However, the focus here is on more complex level structures. Several exemplary
levels were designed to demonstrate the playability (cp. Figures 3.22, 3.23, 3.24
and 3.25).
Figure 3.22: Level 2-1
Figure 3.23: Level 2-2
Figure 3.24: Level 2-3
The structure of level 2-1 corresponds to the formula (a · 0) + (1 · b). This level
presents a light increase in complexity compared to the tutorial levels. Here, the
player has to show an understanding of the 1 and 0 elements of Boolean algebra
which were introduced in scenario 1. The initial values are set so as to yield a
truth value of 0 when the level starts, which is maintained throughout the scenario.
That way, the levels are not in a solved state when starting out. The solution to
this level lies in recognizing the difference between the black and white blocks and
their behavior, thus setting the blue block to white.
Level 2-2 can be written in formal notation as (b+a)·(d+b). While setting each
variable to 1 would solve this level, the underlying aim is to sensitize the player
to the idea of yielding a truth value of 1 by manipulating the minimum amount of
variables. In this case, the optimal solution is reached by tapping on either of the
31
3. Concepts for Game-Based Learning
blue blocks, while all other possibilities of solving the level would include more
than one assignment.
Level 2-3 is the graphical representation of (b+¬a)·(¬b+a+c)·¬b. This marks
the first level with a nontrivial solution, as negation prevents the truth value from
becoming 1 by merely setting all variables to 1. Here, the experimental aspect
comes fully into play, as insights are gained by assigning values and observing the
effects. The solution requiring the least assignments is setting the green blocks to
black.
Level 2-4 shows a larger structure and demonstrates additional control schemes.
To be able to confidently manipulate blocks, zooming and panning features have
been implemented for large levels, which will be further discussed in section 4.3.1.
Furthermore, this level features negations that extend over multiple variables,
which should be intuitive since the concept of inversion could be seen in several of
the previous levels and the effect of the negation frame can be directly observed.
Figure 3.25: Level 2-4
As addressed briefly before, this type of gameplay allows the player to get a
hands-on experience of Boolean logic, as opposed to just reading about it, for
example. Schell elaborates:
32
3.2 Scenarios
“There is a tremendous difference in understanding between people
who have merely read about these things [systems of relationships],
and people who have played with simulations of them.” (Schell 2008,
p. 446)
The player is explicitly encouraged to experiment within the game environment,
which is supported by the lack of instructions in this scenario. All game rules can
be deduce by performing actions and drawing conclusions on the consequences
observable through the feedback of the game environment (cp. Squire et al. 2004,
p. 25).
The concept of losing is currently not incorporated in the game design. Thus,
players can develop knowledge at their own speed, as “the pace of learning varies
from one individual to another” (Joyce et al. 2009, p. 159). They may try activities
as often as they want, choosing different ways to solve a level (cp. Tashiro &
Dunlap 2007, p. 117).
Along with this exploration-based approach, players have an implicit permission
to “fail” (cp. Schell 2008, p. 446) since the scenario setup imposes no penalties
for playing around with the game constraints. This correlates to the notion of
games as being “safe private laboratories” (Breuer 2009, p. 12), where self-guided
and autonomous learning is supported through exploration. It also stands in
contrast to classic educational methods which do not focus on learning by failing
and encouraging multiple attempts, but rather frown upon and even punish such
behavior (cp. Breuer 2009, p. 15).
Having played the tutorial beforehand, players are confronted with familiar
mechanics in this scenario. By trying to solve the levels provided here, their
assumptions and concepts of the game rules – and thus, Boolean algebra – is
expected to strengthen and consolidate. The design of the mapping between
didactic context and game logic (see section 3.2.1) makes learning “incidental to
and a by-product of the player’s action and interaction [...] within the game”
(De Castell & Jenson 2003, p. 49). Integrating the didactic subject tightly into
the game mechanics increases the likelihood of effective knowledge transfer.
The game sessions are still kept short, despite the fact that the level structure
is more complex than the one of the introductory levels (see section 3.2.1). Thus,
the player can leave and pick up playing at any time. This is especially important
33
3. Concepts for Game-Based Learning
on a mobile platform and is further elaborated upon in section 4.3.3.
Additional Features
Several possible modifications are worth mentioning since they present feasible
means to alter the above mechanics and produce games for other target groups, as
well as opening up possibilities for a general enrichment of the game environment.
It needs to be noted that these are supplementary elements; the core of the
game is implemented in the prototype and constitutes the fundament. Without
the conceptual integration of the educational content, the following suggestions
would result in a decorative gameplay at best. However, as the core mechanics are
well founded in the didactic subject, these modifications allow for an extension of
that foundation.
Another aspect to keep in mind is that some of the following features would
have to be introduced either through an extension of the presented tutorial, or
by offering explanations and hints as the features come into play (cp. Tashiro &
Dunlap 2007, p. 117).
To further broaden this scenario’s target audience, elements promoting entertainment and extra incentives can be added, including general features like
sound effects, animations and extended interaction possibilities like the use of the
phone’s gyroscope. Following are suggestions of a more concrete nature.
A common motivator in digital games is a high score or a point system (cp.
Breuer 2009, p. 23). These can be used to allow the player to get a sense of their
own progression. High scores can be included in the form of an ever-increasing
number on the HUD21 , accumulating as players solve levels. Alternatively, rewards
can have the form of collectible objects, e.g. stars or coins.
These can be used in combination with time limits. One can imagine a setup,
where each level has specific time constraints. Depending on how quickly players
solve the level, they earn a certain amount of points or objects. For example, a
level might offer three stars if the player manages to solve it in under five seconds,
two stars if they stay within five to ten seconds, and one star for any solution
beyond ten seconds. The running countdown can be implemented as a thin bar
21
Head-Up Display, a part of the user interface displaying specific game-related information.
34
3.2 Scenarios
with a noticeable centered strip inside, which is shrinking as the time runs out.
Simultaneously, the amount of rewarded stars is indicated. An example for this
concept can be found in the game Huerons 22 as well as in an edited screenshot
of level 2-3 (cp. Figure 3.26). The mockup shows a situation that would occur
approximately seven seconds into the level, given the above rules: The countdown
indicator is just past the five-second-markers, but has not run out yet, while the
stars at the top indicate that two of those were to be earned if the level was
completed at that moment. An additional Replay-button is useful in this context
as well since it can be expected that the player may want to quickly restart the
level to try and score a higher reward.
Figure 3.26: Mockup demonstrating rewards and time limits
This modification would allow players to explore a level at their own pace, yet
at the same time provide an incentive to practice, becoming quicker in comprehending a level’s structure.
22
Puzzle Game developed by BulkyPix. Website accessed March 27, 2015 under http://www.
huerons.com
35
3. Concepts for Game-Based Learning
Playing the same level several times is arguably only sensible, if the variable
allocation is random with each start of a level, which denotes another alteration to
the implemented mechanics. The tutorial, however, is excluded from this feature
since it is designed specifically to be played only once and the initial assignments
are crucial for the introduction to the game rules.
Finally, unlockable elements might incentivize players to continue playing (cp.
Redwood 2012). These can be levels themselves as well as certain items that
may be used to help advance inside a level. Earned points could be utilized as
currency toward unlockables. In this context, a clear indicator of passing a level
with information on how many points were claimed is also advisable (cp. Figure
3.27). Simultaneously, navigational elements should be displayed to allow the
player to go back to the main menu, replay the level or move on to the next level.
The time required to solve the level may also be of interest.
Figure 3.27: Mockup demonstrating an overlay once a level is passed
The above ideas can be used in similar form in either of the developed scenarios.
Following are a few modifications which are specific to scenario 2.
36
3.2 Scenarios
In the depicted levels 2-1 through 2-4, the concept of “something at stake”
(Prensky 2003, p. 17) is neglected in favor of supporting experimentation. Thus,
they can be solved by simply keeping assigning random values to the variables
until a satisfying combination is found. To provide an additional incentive, a
reward for the least assignment actions needed might be implemented, driving
the player to think about the minimum amount of allocations required to finish
a level. An HUD element could be used to relay information about how many
assignments were made, as well as indicating the optimum number of assignments
for the current level (cp. Figure 3.28). This mechanic can be used in combination
with time limits, making the reward dependent on the time needed to solve a level
and the amount of performed assignments. It would, however, evidently introduce
a counterpoint to the experimental character of the implemented scenario.
Figure 3.28: Mockup with an HUD element for an assignment counter and an
optimum indicator
To further foster the semantic understanding of Boolean logic, levels could feature a setting. Additionally, the goal of a level would not be restricted to only
37
3. Concepts for Game-Based Learning
aiming for truth values of 1, but allow levels where it needs to be turned to 0
instead. The context given by the setting would require players to determine the
target truth value by themselves. For example, one such setting could interpret
the balls as hazardous objects falling down on something of value. The player
then needs to deduce that the goal of the level is to stop the falling objects from
reaching the ground, effectively yielding a truth value of 0. In another level, the
balls might be seeds or water and the ground might represent dry soil (cp. Figure
3.29). Here, the goal would be to make assignments so the truth value becomes
1 and the seeds or the water reach the ground. Designs with sequential goals are
also conceivable in that context.
This kind of setup is more likely to induce a feeling for the meaning and importance of Boolean algebra for logical thinking in general since players need to
decide on the goal of a level on their own. It would also increase the intrinsic
motivation to solve the levels, as it allows adding content that lets players engage
in the game in a more personal way (cp. Portnow 2008) and makes the game
activities be perceived as being useful to them (cp. De Castell & Jenson 2003,
p. 50). “Motivation is the most important factor that drives learning” (Gee 2003,
p. 3), thus including a theme could aid in the learning process as well.
A side effect of this modification, however, is that levels would need to start
out with all blocks containing no assignments and balls only starting to fall once
all blocks had a concrete interpretation. Otherwise, the goal of a level would be
too obvious by the initial truth value. Furthermore, the amount of balls might
have to be limited to a certain fixed amount to create a restriction. Once they all
are destroyed or at the ground, the outcome is evaluated and the level is either
passed or failed. Yet, this would again compromise the experimental character of
the currently implemented mechanics.
Another setting that additionally allows for a natural inclusion of time limits,
is defusing a timed detonation device, for instance. Here, the corridors might be
interpreted as wires with the blocks representing points along those wires which
are cut in case of assigning 0. The task then is to induce a truth value of 0 in a
given time limit, effectively disarming the harmful device.
Themes like the ones suggested above could also be used in alternation to provide a diverse and varied experience.
38
3.2 Scenarios
Figure 3.29: Mockup demonstrating a theme
Arguably, even with all the above-mentioned additions, gameplay might become
repetitive rather quickly. To allow for long-term engagement, further objectives
would need to be devised. An example for an extending mechanic in this sense
would be to expand the game environment in a spacial way. Formulae could be
combined and nested to form very large and complex structures. As an additional
incentive, players would then need to solve subparts of such a large level, while
still keeping in mind the connections between the parts.
One can imagine a setup where a level consists of multiple terms, each visually
distinguished from blocks themselves, yet connected by corridors much like the
structure within each such term. A level might begin zoomed out, only allowing
to see a representation of each subterm’s truth value and the connections between
them (cp. Figure 3.30). A player then might zoom in on the different parts by
tapping on them to reveal the contained structure (cp. Figure 3.31), manipulate it
in the same way as presented in the prototype and then zoom out to see the bigger
picture again. Deeper nesting of terms would also be possible with the described
39
3. Concepts for Game-Based Learning
design. This would likely demand more cognitive processing on different levels on
player side and thus provide longer and more immersive game sessions.
Figure 3.30: Mockup demonstrating a
level consisting of several
formulae
Figure 3.31: Mockup showing a subterm the player zoomed in
on
The final features to be mentioned here concern minor shortcomings of the current implementation. While the prototype features data persistence by saving the
lastly played level and allowing to resume when restarting the game, a dedicated
Pause button would further aid in providing confidence to the user. Similarly,
a visible Help button would yield a clear entry point to additional hints, while
accessing those via tapping the top area of a level may not be evident enough.
A problem with large levels like level 2-4 is denoting the underlying formulae. These can get very long and thus would only fit on screen if split into
multiple lines or scaled down, which in turn would have a negative impact
on the readability on a small display. Another solution would be to provide
a scrollable representation, letting the user scroll horizontally through the formula.
To conclude this list of shortcomings and amendments, it is worth noting
that, despite the concept and implementation not being a flawless example,
simulations like this do not necessarily need to be completely accurate to be
instructive (cp. Schell 2008, p. 447).
insights.
40
Loopholes can also provide productive
3.2 Scenarios
3.2.3 Evaluating Boolean Formulae
Having explored free-play mechanics in the last scenario, this concept introduces
quiz-like features by confronting the player with a specific interpretation of a
formula and letting them determine the truth value.
Motivation
The rules learned in the preceding scenarios can be manifested by recitation.
Zhang et al. have created a game (cp. Zhang et al. 2014, p. 62) with a similarly
open exploration phase as scenario 2, where players are able to play without
restrictions in Free Play levels, before they advance to Learning and Practicing
levels to challenge themselves. Levels of this more demanding type are covered
in this scenario. The free exploration aspect is reduced in favor of problems that
require pondering over.
Game-based Design
The initial setup of each level contained in this scenario is a Boolean formula with
a concrete assignment for all variables, much like in the preceding scenarios. A
crucial change in mechanics is the absence of falling balls as well as the lack of
interaction possibilities with the blocks that make up the formula. The goal in
this type of level is to find out whether the given interpretation results in a truth
value of true or false. Instead of interacting with blocks, the player is presented
with two areas at the bottom of the screen (cp. Figures 3.32, 3.33 and 3.34), one
for each possible outcome. They then need to choose the correct truth value of
the underlying formula given the presented interpretation by tapping either on
the white or the black area. These represent a truth value of 1 and 0, respectively,
which is consistent with the mapping of those colors to Boolean values. The colors
aid in hinting to the functions, yet to further help the player, instructions can be
accessed by tapping the top area of the level.
41
3. Concepts for Game-Based Learning
Figure 3.32: Level 3-1
Figure 3.33: Level 3-2
Figure 3.34: Level 3-3
Level 3-1 demonstrates an easy-to-solve introduction to this scenario, visualizing
the formula a · (a + b) with an interpretation of a = 0 and b = 1. Containing
no negations, this level only demands a very rudimentary understanding of the
concepts treated in the previous scenarios. The role of this level is to sensitize the
player to the fact, that determining the truth value of a formula is nearly trivial,
if no negations are present. The correct solution is easily determined to be 0, as
one merely needs to consider the top green block, which already constitutes the
deciding bottleneck.
Level 3-2 has the same structure as level 2-3, representing the formula (b + ¬a) ·
(¬b + a + c) · ¬b. This is yet another way to alleviate the introduction to the
new type of gameplay since the player is presented with a familiar setup. As the
objective is different in this scenario, the level still provides a new perspective.
The interpretation is a = 1, b = c = 0 and yields a truth value of 0. The use of
negations offers a more challenging setup.
Level 3-3 correlates to the formula (a · ¬b) + (¬a · c) + (b · ¬c). Given the
interpretation a = c = 0 and b = 1, the correct answer is 1 or white. It was
included to add diversity to the presented level structures.
While the first scenario demonstrated a tutorial-like introduction and the
second served as a presentation of a free-play game mode, the above levels
42
3.2 Scenarios
propose a quiz-like mechanic. This reinforces the assimilation of the didactic
subject (cp. Rudder et al. 2007). Players were able to explore the assignment
of variables and the effect on the truth value in scenario 2.
To foster the
understanding of this system of dependencies, scenario 3 then requests them
to mentally simulate the balls falling and recall the blocks’ behavior that was
observed in the preceding scenarios. Thus, the learned concepts are applied in a
restricted environment.
This scenario can be used to gauge a player’s understanding of the principles of
the preceding scenarios (see also section 5.3). Furthermore, it presents a bridge
to the next scenario, as it introduces the quiz mechanic.
Additional Features
Given its passive character, this scenario is more appropriate for an academic
context. Nevertheless, the game mechanics could be modified to better suite the
general public.
Alterations to be considered include some of those mentioned in the discussion
about scenario 2, namely the inclusion of random initial variable allocations to
facilitate replayability, as well as high scores in combination with time limits.
Here, the latter is of special interest since it challenges the player to quickly grasp
the structure of a formula. A point system ought to prevent players from simply
testing all possible answers, as it would introduce stakes. These features can be
implemented in the same way as described in the previous scenario.
Other modifications would need to be specifically adapted for this scenario.
For instance, the inclusion of a setting differs from the one presented in scenario
2. Here, the decision whether the given interpretation yields true or false can
be connected with a meaningful outcome. As an example, one can imagine a
setup where the fate of something of value depends on the player’s correct decision. Using themes as a motivator in this way might especially be interesting in
combination with time limits, such as a visibly running countdown.
43
3. Concepts for Game-Based Learning
3.2.4 Determining Satisfiability
After having introduced a free-play mechanic in scenarios 3.2.1 and 3.2.2 and a
quiz-based format in scenario 3.2.3, this game mode combines the two approaches
to study their interplay.
Motivation
SAT (see section 2.2.2) is an important problem for computer science. Its definition lends itself very well to be used as the basis for a game-like scenario, as
it provides a clear goal, namely determining whether a given Boolean formula is
satisfiable or not.
Game-based Design
The game logic of this scenario builds on the mechanics introduced in section
3.2.1. At the beginning of each level, the player is presented with a formula, much
like in scenarios 3.2.1 through 3.2.3 (cp. Figures 3.35, 3.36 and 3.37).
The goal is slightly – but significantly – shifted, however. Instead of merely
finding an interpretation to yield a specific truth value (cp. sections 3.2.1 and
3.2.2) or evaluating a given assignment (cp. section 3.2.3), the focus here lies on
determining whether there actually exists an interpretation with a truth value of
1. While scenarios 1 and 2 presupposed that the formula was satisfiable, this is not
a given in scenario 4. Players need to think about the satisfiability for themselves.
They may experiment with assignments until they are confident to have found the
correct answer.
An additional objective is identifying any blocks that do not contribute to the
outcome of a level. These are variables whose assignments have no influence on
the truth value of a formula.
44
3.2 Scenarios
Figure 3.35: Level 4-1
Figure 3.36: Level 4-2
Figure 3.37: Level 4-3
Level 4-1 depicts a·¬a, which constitutes a contradiction. Following the practice
of the preceding scenarios, an elementary formula was chosen as an introduction
to the new rules.
Level 4-2 features the formula used in levels 2-3 and 3-2: (b+¬a)·(¬b+a+c)·¬b.
The player may thus remember that it is at least satisfiable. This level was used
once again since encountering a level structure repeatedly makes it more likely to
reinforce its intricacies in the player’s mind (cp. Rudder et al. 2007). The objective
then becomes to determine the variables that have no influence on the truth value,
which in this level is only a single variable represented by the red block.
Level 4-3 shows a tautology, in formal notation: (b + ¬b) · (a + b + 1) · 1. The
structure is identical to the formula of the preceding level, yet the variables are
not the same and the answer differs. This aims to further sensitize the player to
the characteristics of Boolean algebra by showing that formulae with the exact
same structure can still have different properties.
This kind of setup opens up the possibility to explore various assignments
as in scenario 3.2.2, yet at the same time it conserves the quiz-like character
of scenario 3.2.3. Specific interface elements have been added to facilitate this.
In particular, three designated areas at the bottom of the screen represent
the decisions “Tautology” (white), “Satisfiable” (gray) and “Contradiction”
45
3. Concepts for Game-Based Learning
(black). For the purpose of simplicity and a clear interface, these are depicted as
semantically exclusive here. This is technically incorrect since every tautology is
also satisfiable.
Once players feel confident, they can tap on the area which they deem to correlate to the correct answer. If they chose the right one, and in case of that one
being a contradiction (level 4-1) or a tautology (level 4-3), the level is instantly
completed.
Should they correctly pick ”Satisfiable”, however, an extra round is initiated
and the decision areas are hidden (cp. Figure 3.38). In this special mode, the
player is asked to identify any variable whose assignment does not have an impact
on the value of the truth table.
Figure 3.38: The bonus round
Players can continue to experiment with assignments until they want to pick
the variables in question. For every block color present in the current level, there
appears a special block at the bottom of the screen once the bonus round begins.
Tapping on the ones deemed to meet above criteria, if any, players finish by
activating a special button in the bottom right corner of the screen. In case of a
correct answer, the level ends.
46
3.2 Scenarios
Since this scenario’s rules are not self-explanatory and arguably difficult to
grasp by mere experimentation, there is a need to indicate what the specific
options and interface elements mean. Giving hints through the color of the answer
buttons aids in this. As an additional help for the player, detailed information is
displayed when tapping the top area of a level.
The mechanics presented here require the player to recall their experience
from the preceding scenarios (cp. Kirriemuir & McFarlane 2004). Thus, “the
learning is not only relevant but applied and practiced within that context”
(Van Eck 2006, p. 18). Concluding, this scenario provides means to use the
accumulated knowledge in the course of the game (cp. Breuer 2009, p. 32).
Additional Features
As in the preceding scenarios, several modifications to enhance the play and
learning experience are sketched out here. Once again, a point system would
provide an additional incentive, especially for the bonus round. Players could be
awarded extra points for spotting variables which do not have an impact on the
outcome of the simulation.
Given the implemented design, players can experiment with assignments as
long as they wish. The introduction of time limits would be an option to create
restriction in this context. Nonetheless, it seems less frustrating to implement
the time component in a positive form, for example as described in scenario 2:
Instead of letting the player fail a level after a certain amount of time, one might
reward them with points depending on how fast they come to a correct solution.
This way, players can still take as long as they like, yet at the same time they
have a motivation to arrive at the solution as quickly as possible.
47
3. Concepts for Game-Based Learning
3.2.5 Simplifying Formulae
For the final sort of problem, a different approach was chosen to show how simplifying Boolean formulae can be performed in a graphical environment.
Motivation
The previously presented game environments were deemed unfit to be used for
transforming formulae, the main reason being the static nature of the corridors
which make up the structure of the underlying formula. Thus, the arrangement of
blocks was adapted to enable transformation via moving the blocks themselves.
On the didactic level, simplifying formulae arguably benefits the understanding
of parts of Boolean algebra since the basic laws are trained in combination with
each other.
Mechanics
As in the preceding scenarios, variables are visualized by colored blocks, where the
colors red, yellow, green and blue were implemented. However, assigning concrete
values has been omitted to focus on transforming formulae.
The mapping between game logic and elements of Boolean algebra has been
adapted as well. Omitting corridors, the position and proximity of blocks in
relation to one another define which operation is used between them. Horizontally
adjacent blocks represent two variables in disjunction (cp. Figure 3.39), while
blocks that touch each other on the top or the bottom edge are in conjunction
(cp. Figure 3.40). This becomes more intuitive in the context of the previous
scenarios, when considering objects that fall from the top and through the blocks.
As with the corridor system, neighboring blocks on a horizontal axis allow for the
operation or to be mapped since either of the blocks need to be set to true –
viz. passable – to let the objects pass. Blocks which are placed on a vertical axis
represent and, for all of them need to let the objects through if these are to pass
that corridor.
48
3.2 Scenarios
Figure 3.39: Disjunction
Figure 3.40: Conjunction
Negation is visualized via black borders, similar to the concept of the preceding
scenarios (cp. Figure 3.41).
Figure 3.41: Negation
Brackets are mapped by employing gaps between blocks (cp. Figure 3.42).
Figure 3.42: Representation of (a + ¬a) · b
This results in a similar mapping of a formula to a visual representation as in
the previous scenarios. To enable the simplification of the structure, two main
actions were implemented: extending and combining parts of a formula. These
correspond to the Boolean axioms (see section 2.2.2) which are used to transform
a formula in formal notation.
49
3. Concepts for Game-Based Learning
Expansion is usually performed on one single variable at a time. For example,
given the variable a, it can be expanded to the following equivalents (cp. Figure
3.43):
a+a
(Idempotence),
a·a
(Idempotence),
a+0
(Identity),
a·1
(Identity).
Figure 3.43: Context menu for a green block
50
3.2 Scenarios
The element 0 (cp. Figure 3.44) is equal to
a·0
a · ¬a
(Annihilator),
(Complementation).
Figure 3.44: Context menu for a black block
51
3. Concepts for Game-Based Learning
The element 1 (cp. Figure 3.45) is logically the same as
a+1
(Annihilator),
a + ¬a
(Complementation).
Figure 3.45: Context menu for a white block
These equivalents are accessible in the proof of concept via a context menu.
Depending on the type of block – colored, black or white – performing a long tap
on it will display the equivalents of that block, while dimming all other elements
on the screen. Moving the finger to one of the options and releasing it results in
the replacement of the original block with the selected term.
52
3.2 Scenarios
Law
Initial
Result
Identity for ∧
Identity for ∨
Annihilator for ∧
Annihilator for ∨
Idempotence for ∧
Idempotence for ∨
Complementation 1
Complementation 2
Table 3.1: Overview of the implemented laws on the example of adjacent blocks
The other main technique used when transforming formulae is the combining
of elements, which includes reversing the actions described in the passage above.
Mainly, the laws listed in section 2.2.2 are applied, most of which were implemented for demonstration (cp. Table 3.1).
The proof of concept allows to combine different parts of a formula by using a
pinching motion. For this, two fingers need to be placed on the screen simultaneously, one on each of the blocks which should be combined. For blocks with a gap
between them, moving the fingers toward each other results in the action to take
place. For adjacent blocks, the fingers need to be moved apart. The motivation
behind this control scheme is discussed in section 4.3.
53
3. Concepts for Game-Based Learning
Besides those, factorizing is often used to arrive at simpler solutions. This is
comparable to the same technique in elementary algebra and is possible because
of distributivity. It is demonstrated in the levels 5-2 and 5-3 and elaborated upon
in the next section.
Game-based Design
Three levels were implemented for demonstration (cp. Figures 3.46, 3.47 and
3.48). For convenience, all feature a formula which can be reduced to a single
variable. This is a special case, yet it can be expanded to any kind of formula.
These levels show very basic situations while still conveying the main aspects of
this concept.
Figure 3.46: Level 5-1
Figure 3.47: Level 5-2
Figure 3.48: Level 5-3
Level 5-1 depicts the formula (a + a) · (a + 0) · (a + 1), which is in conjunctive
normal form. After simplification (cp. Figure 3.49), only a remains. The following
laws can be applied to reach this:
(a + a) · (a + 0) · (a + 1)
Idemp.
=
a · (a + 0) · (a + 1)
Ident.2
=
a · a · (a + 1)
Annih.
=
a·a·1
Ident.
a · 1 = a.23
23
Note: The first three steps are performed simultaneously in the corresponding figure.
54
Idemp.
=
3.2 Scenarios
Figure 3.49: Solution for level 5-1
Level 5-2 represents the formula (a · b) + (a · ¬b). The solution (cp. Figure 3.50)
makes use of the laws listed in section 2.2.2, namely distributivity, complementation and identity. It is arrived at via the following transformations:
Distr.
(a · b) + (a · ¬b) = a · (b + ¬b)
Compl.2
=
Ident.
a · 1 = a.
Figure 3.50: Solution for level 5-2
Level 5-3 shows the formula a + (a · b). Here, the derivation of the Absorption
law is effectively shown, including the extension of a variable (cp. Figure 3.51):
Ident.
Distr.
a + (a · b) = (a · 1) + (a · b) = a · (1 + b)
Annih.
=
Ident.
a · 1 = a.
55
3. Concepts for Game-Based Learning
Figure 3.51: Solution for level 5-3
Technically, a game using above mechanics requires a custom-built tutorial
series to introduce the player to the game rules. A complete discussion concerning
this subject is omitted here to avoid redundancy of concept since the design ideas
for introductory levels are already covered in section 3.2.1. Nevertheless, it is
important to point out a necessary extension of the principles discussed in the
first scenario. In short, a similar approach would be chosen for these mechanics
by breaking them down to essential actions, i.e.
the expanding of elements
via context menu and the combining through pinching motions. The controls
would need indications, however. This is in contrast to the self-explanatory style
of the tutorial levels presented in detail in scenario 1. While those featured
a very simple control scheme to interact with the elements of a level (namely
tapping on them), the variety of possible control schemes introduced in this final
scenario requires additional instructions. Even so, a text-based solution can be cir-
56
3.2 Scenarios
cumvented by employing overlays or animations before the first usage of a control.
As it stands, the scenario effectively employs common touchscreen gestures
to map them onto elements of Boolean algebra. Accessing Boolean axioms via
a context menu and combining elements by dragging them across the screen
provides a close, yet very graphic translation. This should support the knowledge
transfer, especially when adding formal notations of formulae which reflect the
depicted structure and update in real-time to any changes.24
While players experiment with different structures, they incidentally learn the
main axioms. Additionally, switching between equivalents of terms makes transformations apparent.
This scenario, more than anything, places “the control of learning itself into
the hands of the learner” (cp. Downes 2005, p. 1). Players can discover the
dependencies contained in Boolean algebra in an autonomous way since there are
no constraints other than the ones present in the didactic subject itself.
Additional Features
As in the preceding scenarios, several modifications are listed which could enhance
the implemented mechanics.
Incorporating a theme would again help to transport the presented concept to
a wider audience. Blocks could be replaced by concrete objects, where it might
be more intuitive to combine those. Additionally, to facilitate understanding the
meaning of the block’s positioning in relation to each other, assignments could
be incorporated and a fluid might be directed through them from top to bottom.
This would directly show the semantics of horizontally or vertically aligned blocks,
similar to the implementation in scenarios 1 through 4. A combination of the
mechanics used therein with the ones introduced in scenario 5 remains a further
researchable subject.
Connecting a theme to a point system could be an additional entertaining factor.
For each combination, points could be rewarded. Combinations toward the correct
goal would get more points. This way, players would have an incentive to solve
levels in the most efficient way.
24
This feature was left for future work due to its implementation complexity which goes beyond
the scope of this work.
57
3. Concepts for Game-Based Learning
Another feature would be adding extended multi-touch controls, effectively allowing for combination of more than two blocks at a time. In a formula with three
clauses, which all share one variable, factorizing could be performed by dragging
that variable out of every clause, using three fingers simultaneously.
Enabling a more diverse range of target constellations and communicating them
to the player could be achieved by adding an HUD element which displays the
final structure (cp. Figure 3.52). This term could be shown in a corner of the
screen. Employing such an element would aid in relaying a clear goal to the
player (cp. Tashiro & Dunlap 2007, p. 117). An alternative could be to only hint
at the amount of remaining blocks in the target structure by showing that number,
resulting in a more ambiguous description of the objective.
Figure 3.52: Mockup demonstrating a target constellation
As mentioned, showing the formal equivalent of the depicted structure would
arguably enhance the knowledge transfer (cp. Figure 3.53).
58
3.2 Scenarios
Figure 3.53: Mockup showing the formal notation of a formula
To be able to map the didactic subject completely to this graphical environment, several problems of the current implementation would need addressing. Although the developed prototype demonstrates some prominent and useful aspects
of Boolean algebra, it exhibits limited support for other areas. One of those are
nested parentheses. These would be viable by adding frames around blocks, denoting brackets. Without additional elements like these, the layout is restricted with
respect to the depth of nested parentheses. Since the only indicator is whether
there is a gap between blocks, the maximum depth that can be clearly depicted
is 1. Resorting to the distance between blocks to define nested parentheses is not
advisable for lack of clarity.
A related problem with the current state of implementation is also the layout
of blocks, even without taking parentheses into account. Given an initial setup
of two differently colored blocks which are horizontally adjacent, it is possible to
expand those to two vertically arranged blocks each. This results in a square
structure built by four blocks (cp. Figure 3.54). Defining parentheses merely by
gaps, as it stands, causes this representation to be ambiguous since it is not clear
in what order the variables would appear in the corresponding formula.
59
3. Concepts for Game-Based Learning
Figure 3.54: Mockup demonstrating an ambiguous layout
Finally, larger structures would be problematic, since the blocks would be too
small for the player to confidently manipulate them. The solution presented for
level 2-4 could be implemented in this case: Zooming and panning functionalities
can provide means to navigate and thus circumvent the issue of undersized
elements.
A solution would need to adapt the current control scheme since
pinching is also used to drag blocks across the screen, thus interfering with the
pinch zoom control. A possible way to evade this would be to check if blocks
were touched when starting to pinch. Alternatively, only the singe-finger version
of zooming might be implemented.
Concluding, while this scenario leaves ample room for improvement, the
current implementation already shows interesting possibilities of transforming
formulae in a very graphical way.
60
4 Implementation
This chapter depicts specifics concerning the technical realization of the concepts
presented above. A special focus is on particular design adjustments for the target
device.
4.1 Technical Overview
The Unity game engine was used as base technology. It provides tools to quickly
create and test games for a variety of platforms, including the Android operating
system. Details of the game logic were implemented using the C# programming
language.
The game engine builds on the concept of every part of the game world being
abstracted as a Game Object, be it a graphical element, an audio file or parts
of the game logic itself. A Game Object can have various types of Components
which extend its functionality. In particular, one kind of Component is a Script,
where the specific behavior of the corresponding Game Object can be defined by
code written in C# and using a variety of APIs25 .
This was exploited to define the behavior of a block, for instance. The differing
goals of each scenario were implemented in a similar way, where a GameControllerScript was written for each scenario, defining the specific rules for the corresponding educational concept.
The integrated physics engine was used to implement physically accurate behavior for the falling balls.
Finally, the use of the game engine’s tools made it possible to keep the amount
of code manageable, resulting in approximately 2,100 lines of manually written
code in 14 custom scripts to implement the rules for all five scenarios combined.
25
Application Programming Interface, provides a set of tools and functionalities to facilitate
writing programs for specific domains.
61
4. Implementation
4.2 Graphical Specifics
The graphical interface was kept as simple as possible so as to be able to concentrate on the game mechanics. Busch and Steinicke argue, that the effort for a
game production of this type is more of a content-didactic, rather than being of
a financial nature (cp. Busch & Steinicke 2014, p. 28). Games with high development budgets often spend a large amount of it on creating complex graphics.
Yet, for educational games, it is deemed more important for the game design to
effectively reflect the didactic concepts, than for those concepts to be covered
with decorative graphics. The proof of concept was designed to shed light on this
paradigm.
Opting for minimalist graphics is further justified by the choice of a mobile
platform and the game itself aiming for casual puzzle game characteristics. In
the last years, an increasing amount of titles succeeded with abstract or reduced
graphical fidelity (cp. Breuer 2009, p. 34), which is particularly well received
in mobile games. For example, Thomas Was Alone 26 lets the player control
characters which are plain rectangles in a very abstract environment, yet the
game managed to create emotional identification with these simple forms and has
become a critically acclaimed success.
Breuer points out another argument for choosing a simplistic art style when developing games with an educational agenda: It lowers the technical requirements
and barriers, which is a special concern for educational institutions (cp. Breuer
2009, p. 34).
The proof of concept, although aiming at the general public, was designed
with this in mind, restricting itself to 2D graphics. A further reason for a twodimensional environment is that the structure of a level can be grasped directly
and there is no need for decorative elements. Finally, the touch controls of a
smartphone are very well suited for manipulating elements on a plane, which is
discussed in the next section.
26
Developed by Mike Bithell.
Website accessed April 7, 2015 under http://www.
mikebithellgames.com/thomaswasalone
62
4.3 Developing for Smartphones
4.3 Developing for Smartphones
Since the prototype was designed for a mobile platform, several problems specific
to a mobile and particularly touch-controlled game arose and were considered in
its development.
4.3.1 Input
Smartphones use a capacitive touchscreen as their main means of interaction.
These screens enable direct input by touching the screen. The location of a touch
is determined and can then be used to manipulate elements, for example.
Most modern touch-controlled devices support multi-touch input, where multiple simultaneous touches can be registered on the screen. While this presents a
useful extension of possible touch control mechanisms, it is largely neglected in
the first four scenarios of the developed prototype. The reason for this is that
these scenarios were explicitly designed to be used with one hand and in portrait
mode, where the device is vertically oriented. The controls of the prototype are
kept simple so as to further encourage manipulation by a single finger, notably
the thumb, while holding the device in the same hand. This ensures that these
scenarios can be played with one hand free, amplifying the use as casual games.
To be able to interact with the elements of the game with only one finger,
commonly used gestures were considered. These are predefined motions which
Android users are generally familiar with since most are a de facto standard for
current smartphone apps and games.27
The most basic among these is the simple touch or tap, executed by pressing on
the screen with one finger and quickly lifting it again. This is commonly associated
with selecting an element on the screen. Thus, it is used as the primary action in
scenarios 1 through 4, toggling the values of blocks as well as choosing answers.
In larger levels (cp. level 2-4), it can become necessary to navigate within the
environment. Hence, a control scheme for dragging has been implemented for this
level, which is executed by pressing on the screen and moving the finger while
still maintaining contact to the display. A drag is a precise way of moving visible
27
Google lists a core gesture set supported by Android. Website accessed April 17, 2015 under
https://www.developer.android.com/design/patterns/gestures.html
63
4. Implementation
objects, or in this case panning the camera. While the finger is on the screen, the
player can move the view within the level constraints.
In the context of large levels, interactable elements, viz.
blocks, can get
quite small. This leads to input becoming unreliable since finger touches are
relatively coarsely positioned in contrast to mouse clicks, for example. Operating
the device primarily via the thumbs is adding to this inaccuracy. A recommended
minimum touch target size for any interactable on-screen elements, e.g. buttons,
is 44pt28 by 44pt (cp. Gage 2012). Additionally, there should be enough space
between the elements so as to reduce incorrect hits.
One solution to achieve areas that are large enough to be hit confidently is
to provide a zooming functionality, allowing the player to enlarge any area of
the game environment. In combination with panning, this enables complete and
convenient navigation within a two-dimensional space. Two main gestures are
associated with this concept on Android devices and can be found in most image
viewing29 and navigation apps30 , amongst others.
The double touch drag constitutes the one-finger version and is executed by a
single short touch followed in quick succession by a second tap and drag up or
down on the screen. Dragging up decreases the size of the visible elements, while
dragging down zooms in on them. On an intuitive level, this can be viewed as
pushing something further away or pulling it close, respectively.
The second possibility, the pinch, involves using two fingers, where moving
them apart on the screen – pinch open – results in zooming in and bringing them
closer together – pinch close – zooms out. For the sake of compliance with default
or expected control schemes and for demonstration purposes, this gesture was
also implemented in above-mentioned level. It can thus be used as a multi-touch
alternative to the single-finger version.
Having discussed the controls, the problem of communicating these to the
1 typographic point (pt) = 352.78 · 10−6 m.
For instance, QuickPic by Q-Supreme team. Website accessed April 17, 2015 under http:
//www.alensw.com/en
30
The most prominent example for Android is the Google Maps mobile app by Google Inc.
Website accessed April 17, 2015 under https://play.google.com/store/apps/details?
id=com.google.android.apps.maps
28
29
64
4.3 Developing for Smartphones
players themselves arises. Most computer and console games need tutorials to
explicitly describe the game controls since the mapping of actions to keyboard,
mouse and dedicated gamepads generally differs between games. In contrast,
the interaction possibilities of a smartphone, mainly its touchscreen, allow for
intuitive and instant gameplay without the feeling of playing a tutorial. Players
can be expected to be familiar with the touch input, thus enabling the designer
to completely forego text-based instruction in a lot of cases (for a detailed game
design discussion on this issue, see 3.2.1).
While the touchscreen makes for a very direct user interface, there are
drawbacks. A common problem with mobile games is a high input-consequence
ratio, i.e. interactions trigger relatively few reactions observable on screen. To
counter this prevalent deficit, games tend to utilize decorative means, such as
particles and other visual effects that are triggered each time a player touches
the screen. Although this seems a legitimate supplementary technique, it also
wears off quickly since it does not provide any direct value to the gameplay itself.
Considering scenarios 1 through 4, the designed prototype thus confronts the
problem of too much input with too little effect directly in its core mechanic.
Every level that contains blocks of the same color appearing more than once
inherently has a lower input-consequence identifier, as touching one of the blocks
not only changes its state, but also the states of all other blocks of the same
color. Additionally, there is a real-time effect on the balls falling down from the
top, which also builds toward a reactive environment.
Finally, the control scheme has been kept rather simple to facilitate intuitive operation of the game.
In scenarios with answer areas or buttons (see
sections 3.2.3 and 3.2.4), these are placed conveniently at the very bottom of the
screen. This way, the player can easily reach them with their thumb without
using a second hand.
As for scenario 5, multi-touch controls were implemented more vigorously.
Thus, it is best operated with two hands or with the device resting on a surface.
One of the two main gestures is the long press drag which is performed by
pressing the finger on the screen, letting it rest there for a while and then moving
65
4. Implementation
it. In the context of the scenario, this will open up the context menu displaying all
equivalents of the block that the long press was performed on. Without releasing
the finger, a drag onto one of the options followed by a lift lets the player make a
selection. This presents intuitive behavior as long presses usually display context
sensitive information.
The other action is a pinching motion. In contrast to the preceding scenarios it
is necessary that each finger starts out on a block since this gesture moves blocks
instead of controlling the camera. While prototyping, it became clear that it was
necessary to adapt the game mechanics so as to allow the player to confidently
pinch inwards or outwards. Using one sort of pinch was deemed not feasible as, for
instance, pinching two adjacent blocks together yields rather unsatisfying results:
The fingers need to be very close at the beginning of the pinch, which makes
performing a follow-up pinch close impractical as there is no room for the fingers
to move. Thus, both pinch close and pinch open were implemented. Depending
on the proximity of two blocks, players can perform the pinch type which is more
convenient for them. With adjacent blocks, this means a pinch open, while distant
blocks are easier moved together with a pinch close.
An additional benefit was also observed on the implementation side. Determining the nature of a pinch – viz. checking if the fingers were moved outwards or
inwards, vertically or horizontally – could be done with a lot more confidence and
certainty given longer drag distances that are encouraged by the above mechanic.
Finally these dragging and swiping gestures were used to add to a more pleasurable experience (cp. Gage 2012) as players transform the game environment by
their finger movements.
4.3.2 Interface
Complementing the control paradigm, a lightweight interface design presents itself
as particularly significant in the context of developing for a device with a small
screen. Thus, the prototype was designed with the screen real estate, i.e. the
amount of space available on a display, and usability concerns in mind.
A typical smartphone has a shortage of tactile controls which a player can
blindly interact with. A large amount of games tries to solve this issue by placing
numerous buttons on the screen, which becomes problematic since this means
66
4.3 Developing for Smartphones
that players need to constantly shift their visual focus to those designated areas,
effectively leaving the game environment. These frequent interruptions can quickly
build up a barrier to the game (cp. Redwood 2012). The developed scenarios were
designed without such buttons that would require constant interaction. The main
manipulation – namely assigning values to blocks or moving them – takes place
at the position of the blocks themselves, thus allowing the user to concentrate on
the game environment rather than switching to HUD elements. Furthermore, the
feedback of each interaction is instant and unobtrusive, communicating “to users
that their action has been registered” (Redwood 2012).
Another problem of on-screen buttons manifests itself in them taking up a large
amount of screen space, reducing the already small area available. Since the prototype was developed for upright display position, the answer buttons of scenarios
3 and 4 could be added to the bottom of the screen, without compromising too
much of the screen space available for the level structure. Additionally, zooming and panning functionalities could aid in compensating for some of the lost
space. All other scenarios completely refrain from using specific control elements,
resulting in an uncomplicated user interface (cp. Duff et al. 2014, p. 332). Scenario 5 in particular makes use of context sensitive overlays, effectively saving a
large amount of space that would be needed, given that these elements were to be
displayed permanently.
4.3.3 Game Sessions
A final important aspect of playing a game on a smartphone, which is discussed
here, is the design and duration of the individual game sessions.
The proof of concept aims for short game sessions, respecting the nature of a
casual game which can be played in any situation and place. Short gameplay is
promoted with clear goals and manageable level sizes. Additionally, the simplicity
in the control scheme targets casual smartphone gamers (cp. Duff et al. 2014,
p. 332).
Sessions can be started, interrupted and ended quickly at any given time. Each
level is directly accessible via the main menu, making it possible to start playing
with only one tap after starting the game. All instructions are optional, further
supporting a quick game start. This is important to facilitate the game’s claim at
67
4. Implementation
being suited for quick sessions in any environment, effectively minimizing waiting
time before actual gameplay can occur (cp. Redwood 2012).
Interrupting or pausing a game is an essential concern for games on mobile
devices like smartphones. There are numerous sources which might force the user
to take an instant break from playing, like receiving a phone call or a text message.
This means the game needs to pause and save user data automatically on being
pushed to the background. If a game fails to accomplish this, users are likely
to develop an anxiety for fear that another interruption will cause them to lose
their progress (cp. Redwood 2012). The prototype implements data persistence
on the example of saving the last level a user played. Without additional data
like high scores, this is a viable way of demonstrating permanent data which is
stored on the device and loaded once the game starts. Via the main menu, players
can access the most recently played level by tapping on the Resume button. This
feature adheres to the need of the target group to be able to quickly pick up and
play a game session “while on the move and in short bursts” (cp. Redwood 2012).
Ending the game can be accomplished by simply pressing the home button of
the phone. Alternatively, to confidently close the application and release reserved
memory, the Back soft key of the phone can be used in any level to get to the
main menu, where a dedicated Quit button exists to quit the game.
While quick interruption possibilities like the above are crucial for a mobile
game, it is at the same time important to maintain an ongoing experience within
the game itself. Constant interruptions rooted in the game design can quickly
disturb this and lead to frustration and rejection of a game [cp.][p. 49]De Castell
& Jenson (2003). These include constant passages which can’t be skipped and
abrupt changes in the game environment and controls in general, as well as
intrusive advertisement. The implementation thus tries to stay consistent in its
graphical appearance and control scheme, specifically within a scenario.
68
5 Evaluation Concepts
Having presented the implemented designs, this chapter discusses evaluation concepts related to educational games in a threefold manner. Firstly, games can be
tested and evaluated during development to improve them iteratively. Second,
elements might be added to a game, which evaluate the progress of a player’s
knowledge and skills within the game environment over time. Finally, external
evaluation tries to measure the influence of a game on a player’s cognitive processes; in the context of educational games this means determining the effectiveness of knowledge transfer.
5.1 Prototyping
“The process of game design and development is necessarily iterative” (Schell 2008, p. 79).
As with all other software products, it is very hard to estimate, how much
time the completion of a satisfiable version is going to take up. Games have the
additional difficulty of being expected to entertain. Educational games further
aim to enable learning on top of that (cp. Portnow 2008).
Predicting the effectiveness of elements concerning fun and learning becomes
unfeasible for even very simple games without a working prototype. This is used
to observe the interplay of the core features. As games provide experiences, these
can only be truly comprehended by playtesting an actual implementation, where
the most defining mechanics are present.
Aside from the developers themselves, it is crucial to let outsiders test the prototype, without instruction or comment. This is the only way to get independent
feedback and evaluation, which is then used to improve on the implementation,
only to start the loop all over again.
69
5. Evaluation Concepts
To conclude, an iterative design process using prototyping presents an effective
way to detect bugs and design flaws.
5.2 External Evaluation
“Even though playing a conceptually integrated game engages the
player constantly in the targeted relationships, the player may never
articulate or even identify those relationships” (Clark & MartinezGarza 2012, p. 281).
After discussing the design of the learning scenarios in section 3.2, a reasonable objection is the question of their effectiveness on the learning of concepts
related to Boolean algebra. In fact, for research on games in general, “the topic of
methodologies for evaluation is gaining increasing relevance“ (Bellotti et al. 2009,
p. 23:8). Several studies have been designed and conducted to detect any actual
learning outcome from playing specific games (cp. Bellotti et al. 2009, Doucet &
Srinivasan 2010, Eagle 2009, Heintz & Law 2012, Kasurinen et al. 2008).
The most common way of evaluating the impact of a game on the knowledge
of a player is the utilization of a question catalog or survey. Two main areas
of knowledge transfer can be identified in the context of this work: The impact
of playing the prototype on the cognitive ability of semantically relevant logical
thinking and the effect on formal understanding.
A possible experimental setup to detect changes in the first area might be defined in the following way. Subjects are selected from a group of individuals with
no knowledge of Boolean algebra. They are presented with problems relating to
that subject; yet with a semantic context rooted in real-world situations. These
persons are then asked to play the scenarios of the prototype – here, scenario 2 including the suggested modification of adding a semantically relevant theme would
be of special interest – with no additional external instruction. Afterwards, similar tests as before are conducted. Finally, the pre- and post-exposure results are
compared. If the game has any positive impact on logical thinking in a semantic
context, the expected outcome would be an increase of correct answers.
Detecting changes in handling Boolean logic in formal notation could be done
in a similar way. The prototype’s feature of offering a non-intrusive layer by
70
5.3 Internal Evaluation
displaying formal notation is expected to enhance the cognitive mapping between
the game environment and the mathematical counterpart. Questionnaires with
Boolean algebra problems could shed light on the knowledge transfer qualities of
the implemented scenarios.
A problem with evaluating the learning efficiency after letting the subject play
the game is that the testing situation itself can affect their motivation in a negative
way (cp. Breuer 2009, p. 25). One possibility to face this problem is to employ
evaluation within the game itself.
5.3 Internal Evaluation
Games can continuously evaluate their player’s learning and skill development with
means that are incorporated into the game design. This presents an opportunity
to determine the player’s way of learning and playing and adapt the game to it.
The gathered information can be used to adapt the game to the player’s individual style in real-time, viz. while they are playing. In this way, games enable “personalization that allows tailoring of learning to the individual learner”
(Tashiro & Dunlap 2007, p. 117), becoming comparable to a personal teacher who
constantly monitors a student’s progress, detects the problematic areas and offers
just the right mixture of help and challenges to optimize the learning process (cp.
Tashiro & Dunlap 2007, p. 117).
Internal evaluating elements also present a more useful way to gauge the
learning process with respect to knowledge transfer, as they don’t necessarily
interfere with the player’s experience. They can be integrated into the game
mechanics themselves in the form of puzzles or quizzes (see sections 3.2.3 and
3.2.4), allowing “embedded” or “stealth assessment” (Breuer 2009, p. 26).
To further observe and evaluate the quality of a player’s progression, several elements can be added to the presented scenarios.
Some of those were
already mentioned in the suggested features in section 3.2.
Additionally, for scenarios 3.2.2 through 3.2.4, the aforementioned time limits
in combination with randomized initial states of a level’s interpretation would
offer a tool to detect and measure any progress in processing speed. Each time
a level is played, the player is confronted with a random initial assignment of
71
5. Evaluation Concepts
the variables so as to avoid picking up on improvement that is based on mere
memorization of specific constellations. This would also provide an additional
incentive for the player to practice each level, which in turn supports the learning
effect. Assuming a large arsenal and range of levels, the information gathered
through this procedure could then be used to offer specific types of levels. Drawing
conclusions on the measured times and attempts, possible adaptations might be
changing the problem order, adding new problems changing difficulty (cp. Eagle
2009, p. 340). Additionally, if the player takes too much time to grasp a specific
concept, hints can be displayed to assist and prevent frustration, allowing for
adjustment of instructions “to a learner’s level of mastery” (Tashiro & Dunlap
2007, p. 117).
72
6 Conclusion
The aim of this thesis has been to investigate the use of game-based features to
facilitate learning on a smartphone. To conclude the work, this chapter offers a
short summary and the deduced insights as well as impulses for further research
in this area.
6.1 Summary
Chapter 1 provided the context for the thesis, pointing out the motivation for
studying this particular problem and laying out the proposed ideas to meet it.
Chapter 2 gave a more detailed overview of the two main domains, namely gamebased learning approaches and Boolean algebra. The core discussion took place
in chapter 3, bringing together learning and playing by elaborating on their roles
in the implemented prototype. Chapter 4 covered the technical implementation,
including device-specific aspects, while chapter 5 framed different ways of approaching an evaluation of the implemented concepts.
In the context of this thesis, a diverse range of literature and implementations
was consulted. Throughout the research, the main theme proved to be the importance of conceptually integrating the characteristics of the didactic subject
into the core mechanics of the game environment itself. Recommended literature
on this topic includes Breuer (2009), Portnow (2008), Prensky (2003) and Schell
(2008).
In the process of compiling this work it became clear that it is very unlikely
for there existing a universal solution or recipe for effective game-based learning
implementations. Scientific researchers and commercial game designers alike provide useful impulses and advice. Conceptualizing a concrete educational game
on the basis of a given didactic subject, however, requires a case-by-case analysis
of that subject and highly customized game mechanics. The developed concepts
73
6. Conclusion
illustrate how this can be accomplished by providing a detailed discussion on the
mapping between Boolean algebra and game environment.
To conclude, designing an effective educational game requires incorporating
strong scientific research and insights from commercial and educational games as
well as taking into account the specifics of the target platform.
6.2 Future Work
The developed concepts are very specific as for the didactic subject, yet they employ general best practices, most notably the idea of conceptual integration. This
is believed to have been accomplished in a way which can provide insights for other
approaches as well. Most notably, the elaborate discussion on establishing a balance between the entertaining elements and the educational contents constitutes
a transferable outcome.
As discussed in chapter 3, the implemented concepts leave room for improvement. The suggested additional features present reasonable extensions for the
prototype. Chapter 5 further illustrates why games thrive on iterative development. The evaluation concepts discussed therein can be utilized to conduct an
external evaluation of the game’s efficacy, as well as include evaluative elements
inside the game. Moreover, the prototype could be extended to combine the
mechanics from scenarios 1 through 5 and support more laws and other aspects
of propositional logic, such as implications and quantifiers to promote semantic
understanding.
Since educational game development requires a highly pluridisciplinary approach, it would be useful to incorporate research from other areas for the enhancement of the presented concepts. In particular, pedagogical methodologies,
insights from tutoring systems and Human-Computer-Interaction research and
principles for creating flow (cp. Eagle 2009, p. 339) were included here on an
expandable level only.
Finally, the discussions on the contextual mapping of didactic elements onto
the game mechanics can provide insight that might be used for other games with
differing learning contents and target platforms as well.
74
Appendix A
Implementation Details
Additional information about the implementation is listed here.
A.1 Info Texts
Following are all help texts implemented in the proof of concept.
Main Menu
In any level, tap the top area
of the screen to see hints.
Press the ’back’ button
to get to the main menu.
Axioms
Tutorial.
Get the balls to the bottom of the level.
Interpretation
Get the balls to the bottom of the level.
Evaluation
Could balls get through to the bottom?
75
A. Implementation Details
Satisfiability
Is it possible to get the balls through?
Are there any blocks that have no
influence on that?
Simplification
Reduce the structure to one block.
Scenario 1
Get the balls through.
Scenario 2
Get the balls through.
Scenario 3
Would the balls get through?
Press white for yes, black for no.
Scenario 4
Is it possible to get the balls through?
Tap white if any assignment lets balls through.
Tap black if no assignment lets balls through.
Tap gray if some assignment lets balls through.
If gray is correct and you chose it,
see if there are any blocks that have
no influence on the balls getting through.
Scenario 5
Reduce the structure to one block.
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A.2 DVD Content
Long-tap on a block opens the menu.
Pinching two close blocks apart
or two distant blocks together
combines them, if possible.
A.2 DVD Content
Following is the file structure – reduced to the essential files and folders and including annotations – found on the data storage medium accompanying this thesis.
Implementation
Assets
Prefabs
Manually created game files
Files for templates of game objects
Scenes
Level files
Scripts
Manually written scripts
Sprites
Image files
Installation Files
Prototype.apk
UnitySetup64-5.0.1f1.exe
Installation file for the prototype
Installation file for the game engine
Sources
Surveys
Thesis
Videos
ReadMe.txt
Screen captures
Text file containing A.2 and A.3
A.3 Installation
Before being able to install apps from sources other than the Google Play Store, the
corresponding setting needs to be changed on the device under Settings/Security.
The .apk-file located under Implementation/Assets/Builds needs to be copied
to the Android device. There, it can be opened with the default packet installer
and installed directly.31
31
The prototype supports Android versions starting with and higher than Android 2.3.1.
77
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