Mathematics Problem Solving Through Collaboration: Game Design and Adventure Reem Al Washmi, Matthew Baines, S. Organ, Gail Hopkins and Peter Blanchfield School of Computer Science, University of Nottingham, Nottingham, UK
[email protected] [email protected] [email protected] [email protected] [email protected] Abstract: Games designed for learning need to be enjoyable games with the learning content encoded in the game play mechanism. They also need to be designed in a user centric way. In this paper we describe the design of a game to teach maths to UK primary school children (age 7 9). Our work follows on from an earlier requirements gathering study where we observed collaborative game play in a commercial game to determine key game characteristics that promote collaboration. This paper reports on the subsequent design steps and how children have been included in the design process to ensure that the user interface is age appropriate and engaging. The pedagogy and the game mechanic for the game design come from the learning outcomes and approaches used in the classroom. However, on their own these can easily lead to a design that the players find boring. By integrating challenge which adapts with player achievement the idea of flow can be maintained and thus player engagement sustained. This paper outlines our approach to the game design showing why choices were made about the game levels and how they are designed to achieve engagement and maintain flow while at the same time providing a game mechanic that enshrines the learning outcomes. User input to the design process has been maintained through the use of pilot testing in local primary schools. This testing has shown the game to be effective in the main aims of the design being engaging and requiring the players to interact with the learning outcome and requiring the players to collaborate. Further longer term testing will be undertaken to evaluate the effect of the game in enhancing player learning of the game objectives. Keywords: games based learning, collaborative learning, mathematics, problem solving, game design
1. Introduction Mathematics is a fundamental skill that is taught to children in schools around the world and it forms the foundation to many aspects of life (Kaufman, 1979; Garnett, 1998; Aziz, 2002; Curriculum Development Centre, 2003; Nik Azis, 2008). De Corte et al. (2000) defined learning mathematics as a process of active construction where learners are assumed to control their learning and activities of problem solving; a process of thinking where students use their mathematical knowledge and attempt to obtain new information in order to solve problems (Lester and Kehle 2003). The importance of problem solving within the curriculum was recognised over 60 years ago (Suydam 1980) and development of problem solving skills has become a prominent instructional objective in mathematics education (Harskamp and Suhre 2007). However, evidence shows that some children find mathematical problem solving particularly difficult (Tay Lay Heong 2005). The role of collaboration within learning environments has been researched over a number of years and has been found to be particularly useful for children learning to problem solve (e.g, Johnson and Johnson 1989; Lohman and Finkelstein 2000). A number of studies have reported on the effectiveness of collaboration to promote learning and achievement (see, for example, Underwood et al. 2000; Webb et al., 2009) and research is ongoing into the use of tools to promote such collaboration (Cortez et al. 2009). One such tool that has been shown to promote collaboration and engagement is the game (Lenhart and Kahne 2008) and a number of studies have attempted to harness the power of gaming environments to enhance learning (Egenfeldt Nielsen 2005; Ke and Grabowski 2007; Coller and Scott 2009). However, doing so is challenging and measuring success is equally so. We report on our research into the design of a collaborative game to teach mathematics problem solving to children aged 7 11 years old (UK Key Stage 2). Our game design follows on from an initial study which aimed to gather requirements for such a collaborative game (Al Washmi, et al. 2013). This initial study was two fold; we observed existing practices for teaching mathematics, and maths problem solving in particular, within UK classrooms; and we observed children playing collaborative computer games in order to identify elements of the game which promoted collaboration. In this paper we briefly outline the requirements gathered from this
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Reem Al Washmi et al. study before moving on to describe the game designed based on these requirements and report initial observations of its use.
2. Literature review Educational games that combine collaborative work and technology can be one of the most valuable educational tools for teachers in the classroom (Alvarez, 2006). Playing collaborative games offers children the opportunity to share experiences and discuss information which can lead to interactive engagement and the reaching of personal goals. This process of explaining their ideas and thoughts is considered to be a significant element of peer to peer scaffolding (Quintana et al. 2004) which in turn promotes learning (ODonnel 2006). The process of scaffolding can give children the opportunity to achieve higher cognitive goals which they otherwise would not have been able to achieve without support from knowledgeable adults (Fretz et al. 2002).The quality of pupils learning can therefore be improved via scaffolding techniques in a collaborative learning environment either by teachers or peers (Pressley et al. 2001; Krajcik and Blumenfeld, 2006; Peery et al. 2006). This idea of peer interaction within learning environments allowing the exchange of views and the development of cognitive change is not new (Piaget 1965). The use of serious games, in other words games that have learning as their purpose (Stone 2005; Michael and Chen 2006), is widespread in the field of education (Egenfeldt Nielsen, 2005; Ke and Grabowski, 2007; Coller and Scott, 2009). Prensky (2003) highlighted that the importance of serious games lies in the understanding of the games abilities to change part of the way learning happens (Gee 2004). Educators believe that children learn best during play and that games give them that opportunity (Vygotsky 1978). Indeed, computer games can be effective motivational tools for children to learn mathematics and they can deliver good learning support (Malone, 1981; Quinn, 1994; Betz, 1995; Moreno, 2002; Liu and Chu, 2010; Charsky & Ressler, 2011) However, certain conditions are required for learning to take place. Designing an educational game requires a strong and flexible connection between the interface and instructional aspects of the game through actions and interaction. This connection must be present throughout the games duration to promote aspects such as attention, trust and satisfaction which in turn can increase learners motivation to achieve the instructional goals within the game (Cheng & Yeh, 2009). Many researchers believe that the bridge between educational games which incorporate the learning outcomes into the game mechanic and games which are fun to play has still to be achieved. (Squire 2003; Moreno Ger et al. 2008; Villalta et al. 2011). The game mechanic is at the heart of a games design (Villalta et al. 2011) and Kirriemuir & McFarlane (2004) pointed out several reasons explaining the failure of games design in the field of education. Firstly, many educational video games are not engaging for children because they do not incorporate any fun into learning. Secondly, the poor design of the games may involve tasks which are not useful for increasing the students' progress, and so they are centred on simple drill and practice models (Squire, 2003). Habgood et al. (2005) clarified that learning outcomes can only be successfully presented in a game if the actual game mechanic intrinsically integrates that learning outcome. They looked at the process of writing a maths game in which the player is required to understand maths operators in order to defeat enemy characters, ensuring the enjoyment of the game and that the learning requirements were supporting each other. It is this integration which is crucial to a successful educational game, to ensure that children learn what is intended (in this case, the maths) and not just game play techniques. The next section briefly details our previous observations which have produced the requirements for our collaborative game. Following this we describe the game design and our initial observations of its use. We then draw our conclusions and discuss the next stage of this work.
3. Game requirements Our earlier study involved observations of how mathematics was taught in a UK classroom (as reported in Al Washmi, et al. 2013) and revealed the use of collaboration and game play by teachers to build mathematical and problem solving skills. However, it was observed that some children struggled to build their knowledge in this area. In these observations children were seen to be less likely to collaborate in formal situations classroom activities set up to promote collaboration than when playing games. We suggest that this is because games are seen as less threatening and that there is less likelihood of being judged. We also suggest that the children
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Reem Al Washmi et al. may feel less awareness of the importance of competition with others when they are engaged with a game. Thus they are more likely to contribute their ideas without worrying that they are giving away their knowledge to others or revealing their ignorance. Subsequent to these observations we conducted an investigation into game elements that promote collaboration. Here we observed children playing a commercial game which had no deliberate learning outcome, with the aim of looking for evidence of collaboration and, if present, causes of that collaboration. We found two types of collaboration being used in the game, the situation where success in a game action was achieved more quickly when played collaboratively (that is, collaboration is really part of the game mechanic) and collaboration through discussion of game objectives (that is, where the advice from others is more spontaneous and will pass on game play ideas through encouragement of actions). We gathered a number of requirements from these observations. Challenge and complexity need to be incorporated in such a game to engage children, but children also need to understand each stage of the game and its goals and requirements and be able to progress through the game. Therefore, the presence of clear goals and well structured rules for playing the game are important requirements to allow progression through the game and the level of challenge needs to be such that children do not find the game too easy when collaborating with others. Additionally, instructional support should be available to help those who find the game too challenging. We proposed a fantasy genre for our game, which incorporates mystery and suspense and allows the players to take on the role of different characters to achieve their goals. To summarise, we proposed that our game should have a fantasy/adventure genre with role play elements, be multi player to allow for collaboration, have clear goals and rules with instructional support and sufficient challenge and complexity to promote engagement. As a result of the findings from this study we began the process of designing a game which deliberately encoded the learning outcomes of maths and number facts in the game play mechanism and also included intersections where deliberate collaboration would be required to achieve successful game outcome. In order to design the game a number of steps were taken. This involved game design input from teachers and children. The game was based around a fantasy theme that would allow the children to identify with the game characters whilst at the same time allowing the game mechanic to integrate the learning outcome. The original intention was to focus on children aged 7 11 but as the game was being developed it became clear that it would be easy to allow the teacher to tailor the game to suit the learning needs of any specific group. In doing so older or more able children could have more challenging exercises in order to win the game (for example multiplication and division) while younger children could engage with the more introductory ideas such as addition and number order. The next section describes the learning outcomes we aimed to achieve more specifically.
4. Learning outcomes The learning of maths concepts in early years education (throughout the primary years) is reinforced by practice of different maths facts. In conventional settings these are often exercised through a sequence of sheets of maths problems. The student is given a set of computations that will require the given process to be applied. Challenge is usually added by requiring this to be done in as short a time as possible. Often this is so the number facts (like the set of numbers that add up to 10 or the multiplication tables) will gradually be memorised. For typical children this process though it can be hard and often boring can be achieved. For others it is less easy particularly for those with learning differences that affect this process or those with attention deficit disorder. For most children the opportunity to practice these can potentially be stimulated through the use of a suitable game. As mentioned earlier, problem solving can be more intrinsically interesting but is also often found to be more challenging. The use of collaboration can benefit learning as it allows children to verbalise the way in which mathematical problems can be solved. In collaboration with a junior school (UK year 3) teacher it was decided that problem solving with a focus on the combination of operators was a suitable topic to incorporate in the design of a game. The aim was to enhance pupil willingness to engage with practice at the same time as using collaboration to encourage verbalising and explaining the problem solving process. One of the problems the teacher was keen to use was that of the number square, an example of which can be seen in figure 1. Appropriate numbers must be added
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Reem Al Washmi et al. to the empty locations to enable the calculation in each of the horizontal and vertical rows to give the correct outcome. 1 2 1
1 5 2
3 4 1
Figure 1: Number square requiring pupils to fill in blanks, in this case, each line adds up to 10 A second maths problem solving idea was presented which consisted of combining sets of numbers to make a larger target. The idea in both cases is that the children not only try to solve the problem but also discuss their strategy and its validity. The teacher involved often used collaborative exercises to present these sorts of problems.
5. Game theme The game design is based around a fantasy theme. The theme has similarities in content style to those commonly encountered by children of this age group in CBBC games (BBC, 2014). The characterisation uses a common visual theme based on the idea of a school trip to a forest. The player characters are dressed in the way that is common for the children with whom the pilot designs have been worked out. The character designs were approved by the class teacher also as being appropriate. In the game a pair of students get cut off from the rest of the children and do not realise their teachers have been kidnapped. They encounter a witch who has kidnapped the teachers and will only show the children the way out of the forest and allow their teachers to be released if the children can collect the witchs tools (her cat, broomstick, cauldron etc.) and return them to her. In order to collect the tools they have to undertake a set of tasks which will involve them solving mathematical problems. To date, two levels have been designed and initial testing has been undertaken. Both levels are based around the fantasy world into which the children have entered. The first shown in Figure 2 is based around the children collecting bugs from a spider web. The children have to collect the correct bugs to make a target number in the time a spider spends descending to try and recapture the treasures.
Figure 2: Bug collecting game The number to be achieved and the operator to be used by the player are displayed. Each bug on the web carries a number and the players take it in turns to move around the web and gather the right numbers. The games are linked through a common server so individual players use their own computer but collaborate by talking to each other and discussing the best move. Each player can see the others actions and thus give advice.
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Reem Al Washmi et al. The second game level is based around the number square activity shown in Figure 1. The game theme is retained and so the style of layout is adapted. The level setup is shown in Figure 3 below.
Figure 3: Game screen for second level The number square has now been replaced by stepping stones over a pool. The children must choose the correct numbers to complete the number square. Each child takes it in turns to select a number and they must take it from either the odd or even set. Incorrect stones will fall into the water once all the stones have been placed. While this does allow for the possibility of solution by trial and error it also reduces the level of frustration. The player chooses a number using the handle and selects and places the number when they have chosen what they think is the correct one. Again collaboration is from the children discussing the process. Target objects will be won through correct solutions and may be exchanged for a larger prize. This is true in level one also.
6. Pilot study 6.1 Method The initial game design was tested in a daylong session at a local primary school. Short sessions were engaged in by pupils in classes ranging from Reception (4 years old) to Year 6 (aged 11). Thus the testing involved seven groups of approximately 30 children in each session, with children working in teams, two to a computer. At the opening of the game the children chose their game character from a predetermined set. This was felt to aid identification. The level of the challenge of the game was set as stage appropriate where possible though it was obvious that there was a lot of variability in attainment level for each age group and the children played through both stages of the game. Observations were made of the game play and hand written notes taken.
6.2 Observations The children expressed interest in the storyline and characters of the game and several reported that they enjoyed choosing their game character. During game play we observed a lot of collaboration within pairs sharing computers but also between the pairs of pairs. Initially, the younger children (5 7 years) found level 1 too challenging because they were required to use different operators to perform the calculations. They were, however, very interested in the game storyline and some showed interest in the mathematics once they got help from an adult or an older child. It was observed that some children needed help to understand the rules of the game. Some of these children also took some time adapting to the need for collaboration. The children who were slightly older (8 10 years) found that the time allowed for them to complete the maths was too short. They reported finding it hard to think of what they needed to do in the time allowed. It was
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Reem Al Washmi et al. thus realised that having the ability to increase the time allowed and/or limit the required operators would have benefitted them. The oldest children, aged 10 11, demonstrated a difference in approach between boys and girls. The girls loved the idea of cooperation to complete the tasks. The boys, however, found the task really easy and so initially didnt show much interest. However, once they were encouraged to start playing the game they engaged well with the levels and showed lots of motivation to play (e.g. discussing the task and collaborating). For this age range it would have been useful to have made the tasks more challenging. Some of the children who played the game were deaf and very much enjoyed playing the game, collaborating using sign language. As they were integrated into the school other children are able to use sign language and thus the deaf children were able to collaborate fully in the game. Feedback from the teachers showed that they were impressed with the game and were particularly impressed by the collaborative approach to learning that was encouraged by the game.
6.3 Discussion The children responded well to the game, collaborating with each other, and that collaboration was observed to help their progression through the game. Due to the difficulties which had been experienced by some children, the research team made lots of changes to the game during the play session so that it was more adaptable in terms of challenge. At this point, it had become clear that the teacher should be able to adapt the difficulty level of the game. In order for the game to be adaptable to the player attainment level and the required learning outcome the teacher was given access to a control menu see Figure 3 before the game was started. The teacher could therefore choose stereotype game parameters for an age group but could also modify this depending on a specific outcome. For example the operators used can be limited to multiplication and division at one point or for the early stage learners could be limited to addition only. The range of the target numbers is also definable by the teacher, so that for older children more extensive requests can be made.
Figure 4: Teacher control interface As with the first level, the detail of the second level can now be pre set by the teacher from a menu. Thus for beginner learners (Reception and Year 1 in the UK system) the square could be made of two rows by two columns and only addition used. For older groups a bigger array might be used combining any operator the teacher is interested in.
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Reem Al Washmi et al. The role play element of the game proved very successful in engaging the children as was evidenced by their excitement in playing the game. Role play is one of the most effective ways of learning to think in new ways and learning new subject matter (Gee, 2003; Turkle, 1995; Vygotsky, 1978). The games storyline was entertaining and appealed to both genders.
7. Conclusion and future work Mathematics is a particularly important subject which is core to childrens education and stimulates children intellectually on a number of levels. However, difficulties in mathematics are not uncommon and, in particular, some children find problem solving in mathematics challenging. Games based learning has been suggested in the research literature as a potentially useful approach in teaching mathematical skills. However, there is little or no literature which addresses the teaching of mathematical problem solving in primary school children through the use of computer games. Educational games that enhance communication, collaboration and problem solving skills are required in the environment of learning (Pivec and Pivec, 2008). Using technological devices such as computers in the classroom has also proven to be effective in achieving motivation (Ke, 2008), collaboration (Cortez et al., 2009) and learning results (Zurita et al., 2003; Carbonaro et al., 2008; Plass et al., 2010a). The initial trial of the game has proved successful, with children throughout the intended age range engaging with both the storyline and the problem solving. It has presented academic subjects in a more learner centred, more accessible manner, more enjoyable, more interesting, and, thus, more effective (Malone, 1980; Kafai, 2001; Prensky, 2003) without ignoring educational objectives which should be included within the game in an interesting manner. Learners were able to increase their knowledge within the collaborative learning environments where they could share that knowledge and discuss experiences with other learners. The difficulties which were experienced by some children alerted us to the fact that it is important to have a facility for teachers to reduce the complexity as well as make it harder. This has been done by providing a teacher control interface to reduce the number of operators required to solve the problems, the range of numbers involved, or increase the time allowed. It would also be useful to include a facility for providing hints to help children learn how to solve the problems presented. Games that involve some hints or supplementary information can be helpful for any player who is struggling to solve a task (Lowe et al, 2005). Our initial observations show that the game designed will allow the teacher to get the pupils to work on specific learning objectives. The game will now be tested more fully over a longer period of time with the intended age range and a comparison made with traditional problem solving teaching methods to determine whether the game offers higher levels of engagement and motivation to play and enhanced ability to problem solve through interaction with the learning outcomes.
Acknowledgements The researchers would like to thank the staff and children of Firbeck Academy and Southwold Primary School for their help and input.
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