This article adressses the relationship between characteristics of on-line mathematical mini-games and their flow, apparent in their actual user statistics. A set of educational mini-game characteristics is identified. An instrument is developed for determination of the game characteristics of the mini-games involved. The instrument, which was validated by an international forum of game expert, was enabled the determination of ‘GameLike Scores’ of twenty mathematical mini-games. Through comparison of the GameLike Scores with the actual user statistics of three months online use, the relationship between game characteristics and game flow is established. A regression model quantifies this relationship and allows for predicting game flow from its characteristics. The results show that a higher Gamelike Score leads to a higher ActualUse Score. The conclusion is that the model has a significant predictive power
Vincent Jonker, Paul Drijvers, Monica Wijers, Frans van Galen
Computer games are part of many children’s daily life. Nowadays, children spend less hours of watching tv in favour of playing games (Pijpers & Marteijn, 2008). European research shows that more money is earned in computer gaming than in film industry. (Video gamers in Europe. Prepared for the Interactive Software Federation of Europe (ISFE), 2008). Playing computer games is done in leisure time. Nevertheless, there is also a growing interest in ‘serious games’ (also called casual games), games that are made to learn or to train a skill that is useful outside the game. A growing amount of games is available for educational use. An example is the success of the so-called braintrain programs (like Big Brain Academy1).
Several reviews on serious gaming have been carried out. Some of them focus on the area of educational games (Kirriemuir & McFarlane, 2003, 2004; Leemkuil, De Jong, & Ootes, 2000; Sefton-Green, 2003), others describe game characteristics and their implications for game design (Bjork & Holopainen, 2005; Overmars, 2003; Raessens & Goldstein, 2005; Salen & Zimmerman, 2004). Few studies focus on mathematical games (Alexopoulou et al., 2006; Jonker & Van Galen, 2004). From this review of game research it is possible to make a typology of actual game use in education (exercise; exploration; as an extra motivation; the role of the teacher; interaction). Also, game genres are distinguished, such as adventure, first-person shooter, sport, puzzle, role playing games (Overmars, 2003).
In this article we consider game characteristics of serious mini-games for mathematics education. A mini-game is a small online games that can be played within five to ten minutes. The mathematical mini-game triggers mathematical thinking and/or the use of mathematical skills, and can be used in the mathematics lesson as well as in the free space (during schooltime and in leisure time).
The goal of this paper is to investigate the relation between game characteristics and the experienced flow of the game. The flow of the game (Csikszentmihalyi, 1990) is the balance between skills (getting better and better) and challenge (getting more and more involved).
If the flow is optimal, the player will have a good time playing the game. The player will be motivated to play. The expectation of this research experiment is that games with a high score on game characteristics will lead to a better flow and thus the games will be played more frequently then games with a lower score on game characteristics.
First a selection is made from the reviewed literature for the focus of this research (mini-games for mathematics education). Based on this review a set of game characteristics that are central to the use mini-games will be characterized.
The next step is to give some background on the chosen set of mini-games, the so-called Th!nklets (mini-games for mathematics education, developed by the Freudenthal Institute, Utrecht University). The designers of this website (and its Th!nklets) start from the ideas of realistic mathematics education, where the mathematical activity is placed within a context that is meaningful to the player, and where it is possible to solve the problem in different ways. The frequent use of the Th!nklets website (measured on a 24 hours base) is neither a definite proof of the quality of the mini-games nor the assurance that they will give rise to the best mathematics education. The use of the website illustrates the enthousiam of the user to play with mini-games and the research tries to make a connection between the actual use of the game and the game characteristics.
2 What is a mini-game?
The research focuses on online mini-games. [Als je deze vraag stelt als kop van de sectie, verwacht ik ook snel een antwoord. Dus: A mini-game is…. Let ook op de verschillen / overeenkomsten mini-game, online mini-game, casual game, serious game, mathematical game, thinklet,…. Creeer duidelijkheid over de terminologie en houd je daaraan. ] The mini-games can be played on the internet instantly (with help of an internet browser like Internet Explorer, Firefox, etc. with appropriate plugins). This research is not about downloadable games or video games from DVD or Blu-ray discs. This research is definitely not about role playing games2, because the use of those games within an environmental context is complex (learning curve, duration, subsequent sessions, etc.). Still it is possible to learn about the principles that play a role within RPG, like the magic circle3 (Copier, 2007; Klabbers, 2006; Salen & Zimmerman, 2004) and semiotic domain4 (Gee, 2003).
Mini-games5 are small online games. Small in this context means at least three things:
The mini-games fits within a browser window like Internet Explorer, Firefox, etc. The dimensions are less than 1500 pixels width and less than 1000 pixels height. Sometimes the whole screen is used for the mini-game. It is questionable if a fullscreen game must still be called a mini-game;
The mini-game is restricted to one episode, scene or image, with a restricted ‘rule-set’. This does not mean that there is no animation or that the game does not contain a certain amount of subscenes. Having one episode within the game means that the user knows quickly how to start and handle and this is important for mini-games and the motivation to play them;
Short period of playing.
The playing time is restricted to a maximum of about 5 to 10 minutes. This means that the player can switch from mini-game to mini-game within one playing session.
Mini-games are collected on game portals6 like Addicting Games, Big Fish Games, Coolmath Games (Jonker & Wijers, 2008; Prensky, 2005; Squire, 2003). A recent Dutch study on usability (Pijpers & Marteijn, 2008) shows that game portals are popular and which games are popular (e.g. Tetris7, Bejeweled8). European research shows the same type of games on the same type of game portals (Video gamers in Europe. Prepared for the Interactive Software Federation of Europe (ISFE), 2008).
The definition of mini-game is more or less similar to the definition of casual game9 (Juul, 2007). He uses the following definition: Casual games are small games that can be played online on portals. Wikipedia states:
The term casual game is used to refer to any computer game targeted at a mass audience of casual gamers. Casual games can have any type of gameplay, and fit in any genre. They are typically distinguished by their simple rules, in contrast to more complex hardcore games. The Casual Games Association10 (CGA), an organisation for game developers, investigated the use of PC games in 2007 (they promise to pay more attention to the different game consoles in the future). They state that the use of mini-games is widespread because the games work on nearly all platforms.
Figure 1 – Casual Games Market Report 2007
In general multimedia learning and playing objects have two main characteristics:
Interactivity11. A pdf document is an example in the growing family of formats for multimedia objects. It can be downloaded from internet. Current versions of pdf document provide interactive elements (embedded flash movies etcetera).
Appearance12. This is the combination of graphical user interface, the use of sound, text, images, animation etcetera.
These characteristics will be discussed in detail (see 3. Characteristics). Figure 2 gives an overview of the characteristics.
This part describes the subsequent characteristics: interactivity, appearance, goal, rules, narrative, game level and user-generated content. These are the characteristics of every game, but in this article we focus on mini-games. A mini-game is a game where the playing time is restricted to about 10 minutes (Jonker & Wijers, 2008).
Figure 2 – Characteristics of a mini-game for mathematics
In Figure 2 we see that the Th!nklet is the final object that inherits all surrounding characteristics and that it adds a mathematical character to it13. Within the game ontology project14 (Zagal & Bruckman, 2008) we see similar top level characteristics like Interface (a combination of appearance and interactivity) and Entity Manipulation (interactivity).
Interactivity is the possibility for the user to influence the sequence of events. In (Raessens, 2008) interactivity is described cultural-historically. From human-computer-interaction (HCI) research15 interactivity is interpreted as the way the user can act and interact with the phenomena on the screen (buttons, mouse, joystick). Raessens broadens the perspective and makes a comparison between software on the one hand and television and cinema on the other. He uses the concept of 'participatory culture' to underline the new possibilities of gaming to interact with the sequence of events, taking other roles, bring in new information etc. The possibility to participate in the construction (and not being restricted to play the role of the consumer) has an advantage and a disadvantage:
advantage: reconfiguration and construction. Interactivity gives the user free space to organize knowledge, reuse concepts and create new content (see ‘User-generated content’).
disadvantage: deconstruction. Raessens point at the subtile effect that the setting of the game (the narrative, gameplay, ruleset) leads to the [verdoezelend, disilluminating] effect that those environments sometimes seem to establish a new world with its own rules (for example Civilization III, World of Warcraft). The user could easily forget that 'outside' there is the real world with 'another rule-set' . The gamer isn't aware of it's own possibilities to construct and takes the restricted playing area for granted. This is what Raessens calls deconstruction.
For the mini-games research the definition from the HCI research will be used.
This is the set of characteristics that constitute the appearance of learning and playing objects:
A good game will use clear - and often not too long - text segments. From several research publications (Elliott & Bruckman, 2002; Nielsen, 2000; Squires & Preece, 1999) it is known how to make optimal use of text in game design.
Good multimedia use is essential to a good game experience. A problem for this characteristic is that playing in a room with other people will give some inconvenience. A good game design gives the opportunity to play with the sound muted.
From research (Veen & Jacobs, 2005) it is known that visual information (images/drawings) are often better understood ('read') then the simple use of text.
When pictures are binded together in a subsequence of images the constructed animation can show dynamical information that plays an important role in understanding.
Every game will make use of a mix of the characteristics above. The question what mix will lead to a goo game design. From usability research (Nielsen, 2000); (Van Nimwegen, 2008) it is known that making the appearance (and interaction) too smooth will lead to less understanding of the actual game/tool because all the thinking already has been done by the designer.
The goal16 is defined as the final aim of playing a game: to win something, to gain rewards, to achieve a desired result, etc. This is a crucial ingredient in a game. The goal can be a price or the top position of the highscore (Overmars, 2003):
"A game needs a goal
This is a crucial ingredient in a game. People want to win a game and, hence, there must be a goal to reach. For long games there should also be sub-goals, like finishing a particular level, defeating a certain monster, or acquiring a new spell. Reaching a goal or sub-goal should result in a reward. Such a reward can consist of a score or some nice movie, but it is better if the reward is actually part of the game play itself, for example a new weapon, some additional useful information, etc."
A goal is a crucial part of a game (Leemkuil et al., 2000; Raessens & Goldstein, 2005; Salen & Zimmerman, 2004, 2005). The question is of course whose goal will be reached when playing the game? The goal of the user or the goal of the designer?
A rule17 gives the boundaries of what is the possible and accepted behavior of the player. A game needs rules to get a interesting game play. Between the boundaries of what is accepted by the game rules the player needs to be inventive to get the maximum out of the play. If it is a good game, the restrictions set by the rules will lead to motivation to deal with the given rule-set and find the optimal solutions. In a sense this is similar to mathematics. The world of mathematics will be experienced (by many users/'players') as a set of difficult rules. By playing (exercising is a better word in this context) the user will become familiar with the set of mathematical.
A narrative18 is a construct created in a suitable medium (speech, writing, images) that describes a sequence of real or unreal events. The word "story" may be used as a synonym of "narrative", but can also be used to refer to the sequence of events described in a narrative. A narrative can also be told by a character within a larger narrative. Narratives may play an important role in mathematical games for motivational purposes;
A game can have a narrative. This is not necessarily for all games (in contrary with Goal and Rules). A narrative will have a strong influence on how the game is experienced (Juul, 2005a, 2005b).
In a sense the narrative plays the same role as the context19 in realistic mathematics education (Drijvers, 2006; Van Oers, 1998). It is of no use to put all learning of mathematical knowledge in context, it is even impossible. At the other hand it is motivating for users to get an idea what all knowledge is about and where it can be used in situations in daily life. Do (mathematical) mini-games need context/narrative to function as game? This is not necessarily so for all games, but it definitely plays an important role in the greater subset of games (Fuit, 2004; Hoefakker, 2004; Kerstens, 2002; Van Galen & Jonker, 2003, 2004; Verbeek, 2004).
A level20 is a section or part of a game. Most games are so large that they are broken up into levels, so only one portion of the game needs to load at one time. To complete a game level, a gamer usually needs to meet specific goals or perform a specific task to advance to the next level. In puzzle games, levels may be similar but more difficult as you progress through the game. By builiding the perfect sequence of levels players can experience ‘flow’21 (Csikszentmihalyi, 1990, 1997; Mitchell & Savill-Smith, 2004) going from level to level.
The concept of level is a core characteristic for games (Copier, 2007; Egenfeldt-Nielsen, 2005; Klawe, 1998). One of the roots of Level in games is the Role Playing Game22 (the player takes a role within the rules and narrative of the play), where the Levels are used to go from one state/context in the game (for example a room, walking through the wood) to another (going outside, entering the sky). The Level marks the steps taken in the game.
User-generated content23 is content that can be added to a game as fill-in within the restrictions of goal and rules. An increasing amount of games provide possibilities to choose the own Avatar, to add a self made level, or to create content that is added to the game (e.g., see Spore24). The construction abilities of games are as important as playing the gameplay. This is closely related to constructivist ideas (Cobb, Yackel, & Wood, 1992; Kafai & Resnick, 1996) where is stressed that learners will perform better when learning is transformed from reproduction to (re)construction.
If the user thinks it's a game, then it is a game
From research (Lenhart et al., 2008; Pijpers & Marteijn, 2008) about teenage behavior in relation to new media (television, internet, games, social software) we see children choosing their own set of tools to have fun. When interviewed, they easily mention Messenger, Skype or highly interactive websites as games they enjoy. In our methodology to describe the attractiveness of a game by scoring the seven characteristics above we also have to take into account that the user will have another interpretation.
For this research experiment we take 5 steps into account:
Development of an operationalization of the game characteristics, resulting in a questionnaire for an international group of 15 game experts
The results of the questionnaire will lead to an adjusted operationalization. It is even possible that the proposed set of seven game characteristics will be adjusted.
The adjusted set of game characteristics (and their operationalization) will be used to score a set of 20 Th!nklets. Every scored Th!nklet will thus get a GameLike Score.
The next step is to log the actual use of each Th!nklet by the group of online users25. For each Th!nklet the actual use score during three months (july-september 2008) is used (this is the number of unique visitors to the webpage where the game is displayed). This leads to the ActualUse Score.
Finally a comparison is made between the GameLike Score and the ActualUse Score and the hypothesis can be analyzed. This will lead to the final conclusions of this experiment.
Game Characteristics operationalized
To make an operationalization of each game characteristic described above we make an operationalization question and a scoring system.
Is it possible to interact with the game?
1 – 2 – 3 – 4– 5
Is the graphical/auditive and dynamical interface ‘rich’ or ‘poor’?
1 – 2 – 3 – 4 – 5
Is the goal attractive?
1 – 2 – 3
Is the rule-set restricted to one rule (simple) or more rules (complex)
Is it possible to change elements/content of the game?
The 15 game experts will receive an instruction how to comment on the set of 7 game characteristics and their operationalization.
We need a context of ‘similar’ well-known and popular games (like Tetris and Bejeweled) in order to make a kind of ‘Richter Magnitude Scale’ for mini-games. In this way the GameLike Score means a relative position of the game to other mini-games.
See the Instruction as Attachment.
[dat kan nog niet]
[dat kan ook nog niet]
Example Hit the Balloon
vincent, 23 oktober 2008
Laten we eens proberen een voorbeeld te maken. Het gaat dan om Plofsommen, een spel dat gaat over het plaatsen van getallen op een getallenlijn. De getallenlijn kan leeg zijn (met alleen getallen bij het begin- en eindpunt) of er kunnen hulpstreepjes in staan, zodat het makkelijker te zien is hoe de getallenlijn is ingedeeld. De speler moet een ballon verslepen naar de gevraagde plek op de getallenlijn.
Bijv.: er is een getallenlijn van 0 tot 100 en de vraag is om de ballon te verslepen naar '36'. Als de gebruiker dit gedaan heeft kan er op een knop gedrukt wordt en zal er een pijl vallen op positie 36. Als de ballon goed geplaatst is zal de ballon knappen en krijgt de speler een punt.
Uit observaties is bekend dat dit speler met enthousiasme gespeeld wordt (leeftijd 7-12 jaar). We gaan nu de GameLike-score bepalen.
Is it possible to interact with the game?
Het aantal interactiemogelijkheden is beperkt. Je kunt alleen de ballon op een bepaalde plek hangen en op een knop drukken
1 – 2 – 3 – 4 – 5
2-not very present
Is the graphical and dynamical interface ‘rich’ or ‘poor’?