Learning with an educational mathematical game at a science center A case study exploring visitor interaction with a collaborative educational game illustrating the mathematical model of Voronoi diagrams Teresia Thilén Department of Communication and Learning in Science Chalmers University of Technology Gothenburg, Sweden 2024 ii iii MASTER’S THESIS 2024 Learning with an educational mathematical game at a science center A case study exploring visitor interaction with a collaborative educational game illustrating the mathematical model of Voronoi diagrams TERESIA THILÉN Department of Communication and Learning in Science Division of Engineering Education Research Chalmers University of Technology Gothenburg, Sweden 2024 iv v Learning with an educational mathematical game at a science center A case study exploring visitor interaction with a collaborative educational game illustrating the mathematical model of Voronoi diagrams © Teresia Thilén, 2024 This master’s thesis was executed in collaboration with Universeum Science Center in Gothenburg, Sweden Supervisor: Lena Pareto, Department of Education, Communication and Learning, University of Gothenburg Examiner: Philip Gerlee, Department of Mathematical Sciences, Chalmers University of Technology Master’s Thesis 2024 Department of Communication and Learning in Science Division of Engineering Education Research Chalmers University of Technology SE-412 96 Gothenburg Telephone +46 31 772 10 00 Photographs and illustrations: Teresia Thilén Gothenburg, Sweden 2024 vi Abstract Science centers are used as a way of creating easily relatable and authentic learning settings. The science center of Universeum in Gothenburg has developed their new mathematical exhibition Mathrix with the purpose of lowering visitor thresholds to mathematics. This study investigates one of the exhibits of Mathrix, the exhibit named Voronoi, which is designed as a collaborative and exploratory educational game based on the mathematical model describing the formation of Voronoi diagrams. The questions investigated are: What types of embodied conversations emerge when visitors are interacting with the exhibit? What learning opportunities can be identified during these conversations? And, do the identified learning opportunities align with the intentions of the exhibit designers? The results show that 73,0% of the utterances made by the studied visitors are connected to learning talk, either to explicit mathematical talk or to talk concerning the mechanics of the game. 11,8% of the utterances are connected to different kinds of problems in relation to the exhibit system, and 15,2% are connected to affective talk. The study concludes that the exhibit nurtured fruitful conversations and learning processes where the participants were given the opportunities to practice and assimilate the knowledge and the skills that the game was designed to foster. The study also concludes that the results align with the intentions of the exhibit designers, where the aim was to create a successful educational game where the mathematical content was well integrated into the game without interrupting the fun. Keywords: informal learning, exploratory learning, learning talk, science center, interactive exhibit, embodied learning conversations, illustrating mathematical models, educational games vii Acknowledgements First of all, I would like to thank my inspiring supervisor Lena Pareto for all her advice, support and creative ideas that were a crucial part of the formation and completion of this master’s thesis. I approached her with a total different idea and she answered by inviting me into her exciting world of games, mathematics and pedagogy. I would also like to express my gratitude to Universeum for letting me conduct my research at one of their exhibitions. I hope my findings will be useful for their future work. Furthermore, I would like to thank all the 57 participants of the case study that joyfully and without a doubt decided to take part in the data collection. Lastly, I would like to thank my husband Emil for undoubtedly taking care of our wonderful one year old daughter Liv during all the days and nights that I have been busy with my own thoughts and ideas. Your support is the ultimate reason as to why I am finally able to finish my studies. Teresia Thilén Gothenburg, May 2024 viii About the author Teresia Maria Louise Thilén, nee Forsman Master of Science Chalmers University of Technology Communication and Learning in Science Gothenburg, 2021-2024 Master of Science Chalmers University of Technology Architecture and Design for Sustainable Development Gothenburg, 2019-2021 Bachelor of Science Chalmers University of Technology Architecture and Engineering Gothenburg, 2015-2018 ix Thesis outline Chapter 1 presents the introduction to the study including relevant background information, purpose and aims, the three specific research questions and delimitations to the case study. Chapter 2 presents the theoretical framework used as the foundation of how learning may be described and understood in the empirical setting where the case study is executed. Chapter 3 presents previous research and related coding systems on learning talk in informal learning settings. The presented studies are used as inspiration for the methodology and the analysis used in the study. Chapter 4 describes the methodology of the study, including the research approach and strategy, the empirical setting of the case study, the data collection and the data analysis. Chapter 5 presents the results of the study, including the participant and session characteristics, the developed coding system, the utterances statistics and the design and learning objectives of the exhibit designers. Chapter 6 analyzes the findings in relation to the three research questions. This includes analyses of the participant and session characteristics, the conversation characteristics, the learning opportunities and the alignment with the intentions of the exhibit designers. Chapter 7 discusses the validity of the study, the limitations to the study, suggestions of future research and the applicability of the developed methodology. Chapter 8 is the final chapter and presents the conclusions of the study. x Table of contents 1. Introduction 1 1.1 Background 1 1.2 Purpose and aims 3 1.3 Research questions 3 1.4 Delimitations 3 2. Theoretical framework 5 2.1 Learning theories 5 2.1.1 Constructivism 5 2.1.1.1 Cognitive constructivism 6 2.1.1.2 Social constructivism 6 2.1.2 Experiential learning 7 2.2 Other approaches to learning 10 2.2.1 Game-based learning 10 2.2.2 Learning with interactive exhibitions in science 10 centers 3. Previous research 12 3.1 Previous research and related coding systems on learning 12 talk in informal learning settings 4. Methodology 16 4.1 Research approach 16 4.2 Research strategy 16 4.3 Empirical setting 17 4.4 Data collection 24 4.4.1 Use and conversations (audio-visual observations) 24 4.4.1.1 Recruitment of participants 24 4.4.1.2 Procedure 24 4.4.1.3 Chosen participants 25 4.4.1.4 Ethical considerations 25 4.4.2 Design and learning objectives (semi-structured 27 interviews) 4.4.2.1 Chosen interviewees 27 4.4.2.2 Procedure 28 4.5 Data analysis 28 4.5.1 Categorizing and classifying conversations 29 4.5.1.1 Categorizing conversations 29 4.5.1.1.1 Transcription 29 4.5.1.1.2 Addition of actions 31 4.5.1.1.3 Categorization 31 4.5.1.2 Classifying conversations 33 4.5.2 Identifying learning opportunities 34 4.5.3 Identifying and comparing design and learning 35 objectives xi 5. Results 36 5.1 Participant characteristics 36 5.2 Session characteristics 38 5.3 Coding system 40 5.3.1 Learning talk (mathematical talk) 41 5.3.2 Learning talk (game mechanics) 44 5.3.3 System talk 45 5.3.4 Affective talk 46 5.4 Utterance statistics 48 5.5 Design and learning objectives 52 6. Analysis 54 6.1 Participant and session characteristics 54 6.2 Conversations characteristics 55 6.3 Learning opportunities 60 6.3.1 Session 2 60 6.3.2 Session 7 62 6.3.3 Session 15 63 6.3.4 Session 19 64 6.3.5 Session 20 65 6.3.6 General conclusions 66 6.3.6.1 Learning trajectories 66 6.3.6.2 Success factors 69 6.4 Alignment with the intentions of the exhibit designers 73 7. Discussion 75 7.1 Validity of the study 75 7.2 Limitations to the study 77 7.3 Future research 78 8. Conclusions 79 References 80 xii Appendices I The full text of the information board i II Participation Form ii III Informationsformulär för deltagande iii IV Consent Form & Demographic Information iv V Samtyckesformulär & demografisk information vi VI Interview guide viii VII Interview transcripts ix VIII Learning talk (mathematical talk), utterance statistics xvii IX Learning talk (game mechanics), utterance statistics xviii X System talk, utterance statistics xix XI Affective talk, utterance statistics xx XII Misconceptions of the gameplay xxi XIII Extracts from session 2 xxiii XIV Extracts from session 7 xxvii XV Extracts from session 15 xxviii XVI Extracts from session 19 xxix XVII Extracts from session 20 xxxi xiii List of figures 2.1 An illustration of Kolb’s experiential learning process in a 9 four-step learning cycle 4.1 The setup of the exhibit Voronoi, including the digital display, 19 the three chairs and the information board 4.2 The information board presented to the visitors next to the 20 exhibit. The full text of the information board can be found in Appendix I 4.3 A close-up of the exhibit including the placements of the video 21 camera (1) and the microphone (2). This figure also shows an example of a complete Voronoi diagram at the end of a game round 4.4 The surroundings behind the exhibit 22 4.5 The surroundings behind the exhibit 23 5.1 Distribution of the ages of the participants of the study. The 37 figure presents both the percentage and the number of participants belonging to each age interval 5.2 The subcategories and subordinate groups of the main category 41 of Learning talk (mathematical talk) 5.3 The subcategories and subordinate groups of the main category 44 of Learning talk (game mechanics) 5.4 The subcategories and subordinate groups of the main category 45 of System talk 5.5 The subcategories and subordinate groups of the main category 46 of Affective talk 5.6 Percentage of the total amount of utterances belonging to each 49 main category and percentage of the total amount of utterances per session belonging to each main category. The numbers to the left of each column represent the corresponding session ID and the dots represent the five sessions that are analyzed more closely in chapter 6 5.7 A hierarchical chart presenting the frequencies and the 50 Percentages of the different subcategories, calculated from the total amount of utterances 6.1 The three levels of strategically placing the dots in the game in 58 relation to something 6.2 The different subcategories of Learning talk (mathematical talk) 58 mapped onto the five stages of the SOLO taxonomy. The second column shows a visual representation of the different stages xiv 6.3 The four identified stages of the learning trajectories mapped 68 Onto the experiential learning process defined by Kolb 6.4 The five identified success factors, where the purpose of the stair 72 is to demonstrate that the first step is the most frequently achieved and the fifth step is the least frequently achieved A.1 The full text of the information board i xv List of tables 4.1 Overview of the 20 sessions with a total of 57 different 26 participants. The columns represent the ages and nationalities of the participants as well as the number of participants in each session. The letters F and M represent whether the participants were female or male 5.1 Overview of the 20 sessions in relation to number of game rounds, 39 number of utterances and duration of the sessions. The first number in the utterances column represents the utterances from the participants and the numbers inside the parentheses the utterances from the researcher 5.2 Overview of the frequency and percentage of the eleven most 51 common utterances 6.1 A summary of the characteristics of each of the five participant 61 groups and their respective sessions 6.2 The five identified learning objectives 74 6.3 The eight identified design objectives 74 A.1 The most relevant quotes from the separate semi-structured ix interviews in relation to the intended learning objectives A.2 The most relevant quotes from the separate semi-structured xi interviews in relation to the intentions with the physical and digital design A.3 The most relevant quotes from the separate semi-structured xiv interviews in relation to the identified elements of improvement A.4 Overview of the frequencies and percentages of the utterances xvii belonging to the main category of Learning talk (mathematical talk). The frequencies and percentages are each presented per main category, per subcategory and per subordinate group A.5 Overview of the frequencies and percentages of the utterances xviii belonging to the main category of Learning talk (game mechanics). The frequencies and percentages are each presented per main category, per subcategory and per subordinate group A.6 Overview of the frequencies and percentages of the utterances xix belonging to the main category of System talk. The frequencies and percentages are each presented per main category, per subcategory and per subordinate group A.7 Overview of the frequencies and percentages of the utterances xx belonging to the main category of Affective talk. The frequencies and percentages are each presented per main category, per subcategory and per subordinate group xvi A.8 Overview of the frequencies of the different themes that had to be xxii brought up by the researcher, in relation to the different misconceptions of the gameplay 1 1. Introduction 1.1 Background Mathematics is by many considered to be the ‘mother of all sciences’ as it works as a tool to solve problems in every other field of science. It is the basic language of science, and all other fields of science would be hard to imagine without the presence and the use of mathematics (Shah et al., 2023). Research tend to indicate that students’ attitudes towards the subject of mathematics are predominantly negative, to the extent that many students sustain an aversion and an anxiety towards the subject (Fenyvesi, Koskimaa & Lavicza, 2015; Shah et al., 2023). These negative attitudes play a crucial role in students’ learning processes and accordingly in their learning success (Farooq & Shah, 2008). Research also shows that students generally have little knowledge of how deeply imbedded mathematics is in the everyday world around them. In our constantly developing digital society the importance of mathematically structured systems is increasing, affecting our daily lives more and more. However, the abstractness of the subject of mathematics makes it perceived as something very detached from reality. By using easily relatable and authentic learning methods, connecting mathematics to something the students have experience of and are interested in, their natural curiosities can be triggered and the education found more enjoyable (Fenyvesi, Koskimaa & Lavicza, 2015; Shah et al., 2023). One way of creating these easily relatable and authentic learning settings has been by using so called science centers. Science centers are impartial institutions with the aim of introducing individuals to science, triggering their scientific curiosity and offering them to learn about science in an experimental and practical environment. In comparison to museums, visitors are encouraged to touch, test and interact with the exhibitions (Gürsoy, 2020). Science centers should be open to visitors of all ages, learning styles and cultures, focus on the relationships between science, technology and society, work as lifelong learning centers and be able to provide an environment where current issues can be presented and discussed (Koster, 1999). During the past decades, there has been an increasing interest in teaching science and technology in informal settings such as science centers and by using cross-disciplinary methods to illustrate the wide range of uses and applications of the subjects (Sasson, 2014; Vainikainen, 2015). Sasson (2014) and Vainikainen (2015) also states that these out-of-school learning environments are thought to be particularly useful when it comes to creating engagement, interest and 2 motivation and thereby also having positive effects on learning. However, unlike traditional educational settings, there is much less guidance and no clearly defined curriculum and learning objectives in these informal settings, such as science centers. On the contrary, in science centers, the visitor herself usually bears the main responsibility of her learning process (Allen, 2004; Rogoff et al., 2016). This makes the design and implementation of interactive exhibits at science centers as well as the assessment of their success a difficult task. Universeum in Gothenburg is the national science center of Sweden and the following text explaining their focus can be found on their website: “Our mission is to offer a public arena for lifelong learning where children and adults can explore the world through science and technology. Our goal is to create experiences enhancing the creativity and innovation capacity, increasing the awareness and knowledge and activating the critical thinking. Using science as a foundation and engaging learning methods, Universeum aims at challenging people to enrichen their lives and act for a sustainable future” (Universeum, 2024a). In February 2023 a new exhibition was opened to the public, focusing solely on the subject of mathematics: Mathrix. The main target group of the exhibition is visitors between the ages of 13 and 18 years old, however, families of various ages are seen as the secondary target group. The exhibition introduces the visitors to mathematics in all kinds of ways with the aim of lowering the threshold to mathematics. With the help of more than 20 interactive exhibits, Mathrix challenges the view of mathematics as something too complicated and irrelevant. The visitors are shown the existence and usability of mathematics everywhere in their everyday life. For example, visitors can create their own music, explore the Gothenburg skyline, learn about myths about mathematics, compete against each other in different mind games and puzzles and discover some fields of application of artificial intelligence (Universeum, 2024b). This study will focus on one of these interactive exhibits; one that is named “Voronoi – Natural phenomena and mathematical model”. The purpose of this station is to introduce the visitors to something called the Voronoi diagram. This is a visual pattern that appear naturally in a wide range of contexts in nature, but the pattern can also be explained or created with a mathematical model. The visitors are invited to explore Voronoi diagrams by playing a game based on the creation of the diagrams. The station is hence designed as large display where the visitors are supposed to compete against each other in a game of four, trying to conquer as much display area as possible. A more elaborate 3 description of the chosen exhibit and how it works, including photographs from the exhibition, is presented in chapter 4.3. 1.2 Purpose and aims The overall aim of this study is to investigate what types of conversations that emerge during a typical gameplay and exploration of the exhibit by the general public. This includes the overall types of conversations as well as the content details. The aim is also to be able to draw conclusions about what learning opportunities arise and how these take place. The final aim is to investigate to what extent the presented findings align with the intentions and the learning objectives of the exhibit designers. This is to help Universeum understand how their exhibitions are used, what learning and exploration opportunities actually take place and if they align with their intentions. Furthermore, this might lead to useful insights for the creations of future exhibition designs. 1.3 Research questions RQ1: What types of embodied conversations emerge when visitors are interacting with the exhibit? RQ2: What learning opportunities can be identified during these conversations? RQ3: Do the identified learning opportunities align with the intentions of the exhibit designers? 1.4 Delimitations This study focuses on investigating what happens during the sessions where visitors are interacting with the chosen exhibit. This means recording and noting all embodied conversations and relevant actions of the visitors. However, the study does not include mapping what the visitors have learned or memorized after the session is over. The learning will be investigated solely based on analyses of the embodied conversations and drawing conclusions about possible learning opportunities. This is why the term ‘learning opportunities’, rather than actual learning outcomes, is used in the second research question. It would not be possible to determine any kinds of actual learning outcomes without testing the visitors prior to and after the sessions. This would have been too time consuming and also, more importantly, it would have affected the experience of the participants and thus would not have represented an authentic informal learning situation. Asking the visitors about their learning would instead only uncover the 4 perceived learning and not the actual learning outcomes. This difference is further explained by Bacon (2016), where he defines perceived learning as a self-report of knowledge gain done by the learner and generally based on reflection and introspection. This cannot be seen as the same thing as actual learning, which reflects a change in knowledge defined by a thorough measurement of learning. Therefore, the study focuses on the learning opportunities. The initial aim of this study was that it would only focus on completely authentic learning situations where visitors acted on their own initiatives and where the sessions were completely unguided. However, during the course of the study, it became evident that some instruction was needed in most of the sessions in order for the visitors to start interacting with the exhibit. These instructions only included the basics of the game and the interface to enable the visitors to start acting on their own. 5 2. Theoretical framework The theoretical framework that is presented in this chapter is focused on two learning theories and two other aspects of or approaches to learning that are used as the foundation of how learning may be described and understood in the empirical setting where the case study is executed. The analysis in chapter 6 will be based on and related to the theoretical framework that is presented here. Firstly, the extensive learning theory of constructivism is introduced and the two types of constructivism, cognitive and social constructivism, are further differentiated. Secondly, the learning theory of experiential learning is introduced. Thirdly, the more specific approach to learning related to game-based learning is introduced. The final part of the chapter presents a brief description of learning with interactive exhibitions in informal settings such as science centers, also mentioning the difficulty of creating and understanding these opportunities for learning. 2.1 Learning theories 2.1.1 Constructivism The first learning theory that may describe some of the learning processes taking place in the empirical setting where the case study is executed is the learning theory of constructivism. The fundamental idea of constructivism is that learners actively construct or build their own knowledge rather than just passively receive information as an entity from a source such as a teacher or a book (Amineh & Asl, 2015; Olusegun, 2015). This coincides with the fundamental idea of science centers as they are designed to engage visitors, encouraging them to touch, test and interact with the exhibitions (Gürsoy, 2020). In these active learning processes, learners use their previous knowledge as a foundation and continuously construct new knowledge from the new things that they learn. Hence the new knowledge is built upon the old knowledge (Amineh & Asl, 2015; Olusegun, 2015). Each learner takes pieces and puts them together in their own way, which means that no learner learns in the exact same manner but creates their own systems of meaning that works best for them. A part of this learning process is therefore also learning how to learn. Constructivism is also based on the idea that learning requires sensory input, which means that learners need to do something themselves in order to learn. Just listening or watching someone else is not enough to construct knowledge (Olusegun, 2015). This is another reason as to why the theories of constructivism are relevant when analyzing the learning opportunities that may arise in a science center. 6 2.1.1.1 Cognitive constructivism The cognitive constructivism is mainly based on the ideas of the Swiss theorist Jean Piaget (1896-1980). The cognitive constructivism is primarily highlighted in this context because of the four stages of cognitive development that were described by Piaget as they can be used as a tool to further understand when children of different ages may be receptive to different problems and learning situations. Piaget’s four stages are divided into the sensorimotor stage, from birth to 2 years old, the preoperational stage, from 3 to 7 years old, the concrete operational stage, from 8 to 11 years old, and the formal operational stage, from 12 years and up. The sensorimotor stage involves mastering physical activities such as grabbing things and bringing them to the mouth as well as understanding the world through movements and sensations. When children are in the preoperational stage they often struggle with understanding abstract situations, having a strong need for thinking in concrete terms. During the concrete operational stage, the understanding for abstract situations strengthens. For example, children in the preoperational stage usually have to learn to count by using specific objects, while children in the concrete operational stage begin to be able to simply use numbers. Piaget calls this the development of logic structures, where children’s thinking becomes more logical and organized. During the last stage, the formal operational stage, the logical structures of children start to become more and more equal to the logical structures of adults. They obtain the ability to solve abstract problems and to think in conceptual terms. The focus of cognitive constructivism is that learning should always be related to the learners’ stages of cognitive development, scaffolding the learners’ own building processes (Phillips & Soltis, 2020). 2.1.1.2 Social constructivism A common critique of the work of Piaget is that he underestimated the meaning of the societal and peer influences and that all descriptions of learning that do not address these influences cannot be defined as complete. The theory of cognitive constructivism focuses on how learning takes place among individuals and how their inner cognitive structures are built and constructed. The learner is hence described as a lone explorer, actively engaging with its environment but acting on its own (Amineh & Asl, 2015; Phillips & Soltis, 2020). To be able to better understand the learning opportunities that may arise in a science center, and particularly in relation to the chosen interactive exhibit as it is designed as a collaborative game, the importance of the social context has to be addressed. 7 The social constructivism was developed by the Soviet psychologist Lev Vygotskij (1896-1934). Vygotskij agreed on many of the ideas of the cognitive constructivism but not the assumption that it was possible to separate learning from its social context. He described learning as knowledge developing based on how people interact with each other, their culture and society at large. This means that learners rely on each other, and learning from others together with others helps them build their own cognitive structures (Amineh & Asl, 2015). Vygotskij was also critical to the different stages of cognitive development described by Piaget. According to him, the stages of cognitive development were quite statical, simply stating what kinds of intellectual activities children are able to conduct on their own. He was more interested in the learning potentials of children, meaning what kinds of intellectual activities children are able to conduct with the help of adults or older peers, also called ‘more knowledgeable others’. On the basis of these ideas he developed a theory called ‘the zone of proximal development’ (ZPD) (Phillips & Soltis, 2020). Vygotskij defines the zone of proximal development as “the distance between the actual developmental level as determined by independent problem solving and the level of potential development as determined through problem solving under adult guidance, or in collaboration with more capable peers” (Vygotskij, 1978, p. 86). What Vygotskij believed is that when a learner is in the zone of proximal development for a particular task and therefore tries to learn something new that they do not already have knowledge of, providing the learner with the suitable support will be the key to conquering the knowledge (Phillips & Soltis, 2020). Another theorist being critical to the works of Piaget is the American philosopher John Dewey (1859-1952). He claimed that the best way of learning a new concept is through ‘normal communication with others’ in a communication process where the learner interacts with others engaging in suitable activities or through exploration of common interests. Dewey was also critical to the common structuring of learning and teaching in school settings, where teachers mostly let students work separately with individual assignments rather than involving the students in activities which require collaboration to solve problems (Phillips & Soltis, 2020). 2.1.2 Experiential learning A learning aspect that also needs to be addressed in relation to the empirical setting where the case study is executed, is the fact that the learning takes place in an experiential setting where the learners use their own experiences as a foundation of their learning. Therefore, the learning theory of experiential learning is elaborated as it provides a 8 model of the learning process where the central role of experience is emphasized. The theory of experiential learning was developed by the American theorist David Kolb (1939-) and the term ‘experiential’ is used to differentiate the theory both from cognitive learning theories such as the constructivism and from behavioural learning theories such as the behaviourism. Kolb states that cognitive learning theories tend to focus on cognition rather than affect and that behavioural learning theories deny the role of the learner’s subjective experience in the learning process (Kolb, Boyatzis & Mainemelis, 1999). Kolb defines learning through the experiential learning theory as “the process whereby knowledge is created through the transformation of experience. Knowledge results from the combination of grasping and transforming experience” (Kolb, 1984, p. 41). Kolb described the experiential learning process with a four-step learning cycle. The first step is defined as experiencing, also called concrete experience (CE), and this is where the learner uses its senses and perceptions to engage in the current situation. The second step is defined as reflecting, also called reflective observation (RO), where the learner uses the experiences as the basis for observations and reflections. The third step is defined as thinking, also called abstract conceptualization (AC), where the observations and reflections from step two are assimilated and distilled into abstract concepts and theories that can be tested and acted on. The fourth and last step is then defined as acting, also called active experimentation (AE) where the concepts and theories from step three can be actively tested, the learners can get feedback and create new experiences. From the last step, where new experiences have been created, the cycle can begin from the first step once again (Kolb, Boyatzis & Mainemelis, 1999). Different people tend to prefer using different learning abilities, either obtaining knowledge by experiencing the concrete or by abstract conceptualization. Similarly, some people tend to prefer carefully watching others involved in experiencing and reflecting on what happens from afar, while others prefer to jump right in and actively take part. The fact is that the four-step learning cycle consists of two pairs of opposite ways of grasping information and transforming it into new knowledge. The pairs are experiencing-thinking (grasping) and reflecting-acting (transforming). However, even though different people may prefer using different learning abilities more or less or in different orders, Kolb emphasizes that the deepest kind of learning appears when all four steps of the learning cycle are used. They necessarily do not have to be used in the exact order presented in figure 2.1 on page 9, as long as they are all actively engaged at some point of the learning process (Kolb, Boyatzis & Mainemelis, 1999). 9 Figure 2.1: An illustration of Kolb’s experiential learning process in a four-step learning cycle. Concrete experience Abstract conceptualization A ct iv e ex pe ri m en ta tio n 1 2 3 4 Reflective observation T R A N S F O R M I N G G R A S P I N G 10 2.2 Other approaches to learning 2.2.1 Game-based learning Lastly, as the chosen interactive exhibit is designed as a game that the visitors are supposed to play, the learning approach of game-based learning is further elaborated. The definition of game-based learning can be summarized as taking advantage of and utilizing the power of different kinds of digital games to captivate and engage learners for a specific purpose. This purpose should include some clearly defined learning outcomes where learners are supposed to develop new knowledge and skills. In short, games are essentially recreated environments or systems where the users are supposed to solve a problem or a series of problems, which is what makes them the perfect setup for different learning situations (Corti, 2006; Felicia, 2014; Pan et al., 2021). By definition, game-based learning does not have the aspect of entertainment and fun as the primary purpose as the main objective is for the learners to learn something. However, if possible, the learners should also have fun while learning, and preferably the fun should be collaboratively shared (Michael & Chen, 2005). The ideas of game-based learning are not solely focused on collaborative gameplay, even though many argue that one of the strengths of game- based learning is the possibilities for collective learning. Games usually require some type of interaction, in most cases with the content of the game but often also with teammates or opponents. Collaborative gameplay where learners play in groups creates an effective learning environment where learners are allowed to help each other when playing, accommodating their talents and insights and learning from each other. Even when learners are not playing in teams together but rather against each other, the aspect of playing together in a group can foster learning through the communication with others (McCall, 2009). 2.2.2 Learning with interactive exhibitions in science centers As mentioned in chapter 1.1, the interest in teaching science and technology in informal settings such as science centers has increased during the past decades (Sasson, 2014; Vainikainen, 2015). Designing these interactive experiences can be driven by many different objectives depending on the focus of the science center, however, visitor learning of some sort is usually the main priority (Barriault & Pearson, 2010). Falk (2001) describes the learning taking place at informal settings as ‘free-choice learning’. He argues that the degree of self-direction and self-selection involved when visitors choose to interact with exhibitions in these informal settings is very high. When visitors have chosen to interact with a specific exhibition, their learning tend to be non-linear and personally motivated where the learner herself chooses what to 11 learn and where and when to participate in the learning (Falk & Dierking, 2000). As science centers seldom offer clear guidance and learning objectives, in a way the direct result of them being informal which evidently is their intention, it is not easy to investigate and understand what kind of learning opportunities actually has taken place and how. The methods being used in formal settings to evaluate learning are not as applicable in these informal settings which means that other types of methods needs to be used (Allen, 2004; Barriault & Pearson, 2010; Rogoff et al., 2016). Barriault and Pearson (2010) argues that learning in science centers is multi-dimensional and that the understanding of the learning that takes place in these settings needs to include affective impacts as well as the understanding of how each experience is highly personal and contextualized. It is clear that getting an understanding of the learning in informal settings such as science centers is not as straight forward as in formal settings as the learning itself is a self-regulated and multi-dimensional process taking place in a partly unguided and unsupervised environment. It is also more difficult to express the actual learning objectives which leads to the expectations being unclear. In the next chapter, chapter 3, previous research on learning in informal settings will be presented which will then form the foundation for creating a coding system to further get an understanding of the conversations and the associated learning opportunities. 12 3. Previous research This chapter presents nine different case studies where learning talk has been investigated in different kinds of informal settings. The case studies were chosen based on the criteria that they were conducted from the year of 2000 and onwards, that they were investigating some kind of science-based learning in relation to conversations and utterances and that the learning settings were not strictly formal. During the process of finding these relevant studies, many case studies were found by looking at the references from another study as many of them are referring to each other. The nine case studies are used as inspiration, mainly in relation to the development of a coding system through which the participants’ utterances and actions will be categorized. Inspiration has also been taken in relation to the data collection, where most of the case studies presented below are using audio recordings or audio-visual recordings to collect the data as the participants are taking part in the different learning situations. Each case study is briefly presented and then the related coding system is described. The final part of the chapter discusses which coding system characteristics seen in the different case studies are most relevant as inspiration and why in relation to the research questions of this master’s thesis. 3.1 Previous research and related coding systems on learning talk in informal learning settings The first example of studying visitor conversations and learning talk is the study done by Scalfi et al. (2022) investigating what families visiting a zoo in Brazil are talking about in order to characterize the visitor experiences. The study develops and uses a bottom-up encoding system, meaning that a system of codes are created iteratively based on the analysis of the data itself. The final codes used in the study are: Superficial conversations about animals, Science-based conversations, Conversations about the exhibition, Conversations including associations with previous experiences, Conversations with emotional responses and Conversations involving reading. Another similar example is the study done by Tunnicliffe and Reiss (2000) where the conversations of children relating to three- dimensional representations of animals are investigated. The coding into categories is here done according to a systemic network developed from the work of Bliss, Monk and Ogborn (1983). The categories are structured in a hierarchical manner and the major categories of the 13 study are: Management and social comments, Exhibition-focused comments, Exhibit access comments and Animal-focused comments. The animal-focused comments are then divided into six subordinate groups according to: Interpretative comments, Affective comments, Environmental comments, Body part comments, Comments about the animals’ behaviours and Comments about the animals’ names. Allen (2003) has done a study looking for learning in visitor talk at an Exploratorium in San Francisco, focusing on a frog exhibition including elements typical for a science museum, a zoo and a natural history museum. Allen states that most of the methods used at that time to study visitors’ experiences rely on the responses of individuals rather than groups. She is also critical to using the visitors’ feedback after they have left the exhibitions rather than looking at their conversations and behaviours during the visits. The study thereby develops a system of categories and subcategories to analyze the visitors’ talk while experiencing the different elements of the exhibit. The five main categories are: Perceptual talk, Conceptual talk, Connecting talk, Strategic talk and Affective talk. Perceptual talk is divided into Identification, Naming, Feature and Quotation. Conceptual talk is divided into Simple inference, Complex inference, Prediction and Metacognition. Connecting talk is divided into Life-connection, Knowledge-connection and Inter-exhibit connection. Strategic talk is divided into Use and Meta performance and Affective talk into Pleasure, Displeasure and Intrigue/Surprise. Two other studies executed at about the same time as the study of Allen (2003) are the two connecting studies done by Ash (2002; 2003) exploring family conversations during museum visits in Santa Cruz. These studies focuses on collaborative scientific sense-making based on these family conversations. Ash (2002; 2003) does not use coding systems as straight forward as the previously mentioned studies as she is studying the conversations in terms of longer representative dialogic segments, meaning several sentences belonging together. However, some of the coding categories in relation to the visitor talk used that might be relevant to the scope of this master’s thesis are: Observing, Questioning, Interpreting, Comparing, Explaining, Hypothesizing, Identifying and Contrasting. In the study of DeWitt and Hohenstein (2010), they are investigating and comparing student discussions on different scientific topics being presented to the students in museums and then in classrooms. They are focusing on the discourses between only children, where no adults are taking part. Also, they are aiming at highlighting not only the content or the topics of the conversations, but also the nature of the interactions. Their coding system in relation to the nature of the discourses include the categories of Cumulative talk, Disputational talk, 14 Parallel talk and Exploratory talk. They also categorize the type of talk according to Content-related talk and Procedural talk, where the Content- related talk has been divided into the categories of Explanation, Fit, Description, Read, Description (visual), Content-superficial, Affective, Attention and Other. The following two studies are very different from the previous ones, however, they define and use coding systems that are of relevance. In the study done by Saraiya et al. (2005), several bioinformatic visualization tools are evaluated letting recruited subjects with no prior experience use the tools. The purpose of the visualization tools are to generate insight in relation to the data that they are visualizing, and the study is trying to determine whether this has occurred successfully or not. The categories used in the coding system of this study are: Observation, Time, Domain Value, Hypotheses, Directed/Unexpected insights, Correctness, Breadth/Depth and Category. Liu and Heer (2014) uses the categories from the study by Saraiya et al. (2005) to further develop a coding system to be used when evaluating the performance of another exploratory visual analysis tool. In their coding system, they are using the categories Observation, Generalization, Hypothesis, Question, Recall, Interface and Simulation (Mental visualization). The final study presented here is the study conducted by Isaksson and Söderberg (2022), also at the science center of Universeum in Gothenburg but focusing on another exhibition called the OpenSpace exhibit were visitors can explore open research data from space that requires visualizations to be accessible. In this study, Isaksson and Söderberg took inspiration from Saraiya et al. (2015) and Liu and Heer (2014) when they created their own coding system. Their coding system consisted of three main categories related to Learning, The visualization system and Experience. Learning included the subcategories of Observation, Comparison, Shallow question and answer, Deep question and answer, Recall, Mental visualization, Quotation, Interpretation of written information, Interpretation of visual information and Exploration. The visualization system included the subcategories of Interface, Instruction, Orientation and Planning and Experience included the subcategory of Indication of experience. The findings from this study has later been summarized and published together with Pareto (Pareto et al., 2023). The nine above presented studies are different in their nature. Some focusing more on the specific content and topics of the conversations rather than the conversation processes and the interactions between the participants, wherein this category some studies focused more on the child-child relations and others on the child-adult relations. Some differentiating units or segments based on single words or sentences 15 rather than complete conversations or several sentences. Also, they are different in how they choose to summarize the findings. Some count frequencies in numbers, other by total absence or presence. Some do not even present the findings in a quantitative way at all, instead focusing on figures and maps illustrating the analyses and the results. Reflecting back to the research questions of this master’s thesis in relation to what kind of coding system would fit best, a coding system focused on revealing the specific content and topics of the conversations would be most relevant as this is what will be the foundation of the analyses. This coding system should preferably also categorize this conversational content according to larger categories to be able to determine what parts of the conversations are related to learning and not. The process of developing the coding system, with the inspiration from these previous studies, is further elaborated in chapter 4.5.1.1.3. The final coding system is presented in chapter 5.3. 16 4. Methodology 4.1 Research approach This study was executed on the basis of an inductive research approach. Thomas (2006) states that “the primary purpose of the inductive research approach is to allow research findings to emerge from the frequent, dominant, or significant themes inherent in raw data, without the restraints imposed by structured methodologies”. Inductive research represents the reverse procedure of deductive research, where key themes and categories are usually based on the preconceptions imposed by the researchers meaning that some findings might be overlooked or left invisible. Thomas (2006) also explains that “the inductive approach is intended to clarify the data reduction process by describing a set of procedures for creating meaning in complex data through the development of summary themes or categories from the raw data”. The inductive research approach was chosen based on the nature of the research questions. To be able to fully explore what types of conversations, actions and learning opportunities emerged, the analyses had to be unhindered by any preconceptions. At the beginning of the process of the study, there were no expected ideas of what the results might turn out to be. 4.2 Research strategy The main aim of this study was to investigate authentic informal learning situations in a science center, where participants were using an interactive mathematical exhibit. To ensure the validity of the study, the authentic experiences of the participants had to be preserved. This resulted in the research strategy of a case study being the natural choice. A case study can be defined as an empirical investigation of any phenomenon in its natural setting. Multiple methods of data collection can be used depending on what type of phenomena is to be studied. The definition of a case study also includes the fact that it is bound by time and activity, where the researcher executes the data collection over a sustained period of time (Creswell, 2014; Priya, 2020; Yin, 2009). Case studies are usually divided into three different categories: descriptive, explanatory and exploratory case studies. This case study belongs to the category of exploratory case studies, meaning that the aim is to gain a deeper understanding of a particular phenomenon or topic. Exploratory case studies involve detailed investigations of specific cases to explore and generate new insights, theories or hypotheses (Yin, 2014). 17 In the case study, the methods of audio-visual observations and semi- structured interviews were used. The audio-visual observations were done through recordings executed at the interactive mathematical exhibit at the science center to be able to capture the embodied conversations and the learning opportunities of the participants. The semi-structured interviews were used to be able to understand the intentions of the exhibit designers and to compare those to the findings from the audio- visual observations. A semi-structured interview is defined as a qualitative data collection method where the investigator asks the interviewees a number of predetermined but also open-ended questions. Semi-structured interviews are the middle ground between unstructured interviews, mainly general verbal communication, and structured interviews, where template questions are used and asked in a specific order (Ayres, 2008). Semi-structured interviews are suitable when the goal is to better understand the unique perspectives and opinions of the interviewees (Adeoye-Olatunde & Olenik, 2021). Adeoye-Olatunde & Olenik (2021) also argues that “a primary benefit of the semi-structured interview is that it permits interviews to be focused while still giving the investigator the autonomy to explore pertinent ideas that may come up in the course of the interview”. 4.3 Empirical setting The audio-visual observations were conducted at the mathematical exhibition Mathrix at the science center Universeum in the city of Gothenburg. The exhibition consists of 23 interactive exhibits that are divided into four different zones: ‘The self”, “The world”, “The creation” and “The nature”. Each of the themes are meant to describe how mathematics are related to things that the visitors encounter in their everyday lives. The case study focuses on one of these interactive exhibits which belongs to the theme related to nature. The station is called “Voronoi – Natural phenomena and mathematical model” and at this station the visitors are introduced to something called a Voronoi diagram. As explained in chapter 1.1, a Voronoi diagram is a visual pattern that appears naturally in a wide range of contexts in nature, but the pattern can also be explained mathematically. A Voronoi diagram is constituted by a plane with a given number of dots in the plane, called seeds or generators. For each seed there is a corresponding region, consisting of all points of the plane that are closer to that seed than to any other seed on the plane. Voronoi diagrams are, among other things, used to help understand the proximity and distance of different features (Wolfram MathWorld, 2024). See figure 4.2 on page 20 and figure A.1 in Appendix 18 I for the full information text that can be found at the station, explaining the mathematical model as well as several areas of application. The station is designed as large horizonal digital display surrounded by a green pattern influenced by the Voronoi diagram and accompanied by three chairs, see figure 4.1 on page 19. Directly in front of the display there are four separate buttons in the colours of yellow, green, red and blue. The visitors are invited to explore the Voronoi diagram by playing a game based on the formations of different Voronoi diagrams. Before any participants have started the game, the display shows the text “Can you capture the largest area?”. The goal of the game is hence to try and conquer as much display area as possible. This is done by placing three different dots for each player, each participant in its turn, on the display. These dots will, when all dots are placed, be the originating points, or seeds, of a Voronoi diagram, filling the whole display area with regions of the four different colours. When the whole display is filled with the different colours, the game tells the players which player has conquered the largest area and how many percent that area conquers. See figure 4.3 on page 21 for an example of the display after the completion of a game round. The game can only be played with four different players. If the participants choose to play with fewer than four players, the computer will act as the remaining player or players. As far as the gameplay is concerned, the game interface itself does not offer any instructions on how the formation of the pattern works. The instructions from the game interface are: “Press the button to play”, which means that the visitors need to press the different coloured buttons to enter the game, and “Press the yellow/green/red/blue button” and “Press anywhere on the screen to place your dot” which means that the visitors always have to press the physical coloured button first and then the display to place their dots. These last two hints are repeated during the course of the whole game round. To be able to understand how the formation of the pattern works, the visitors need to read the information that is provided on the information board, next to the horizontal digital display. 19 Figure 4.1: The setup of the exhibit Voronoi, including the digital display, the three chairs and the information board. 20 Figure 4.2: The information board presented to the visitors next to the exhibit. The full text of the information board can be found in Appendix I. 21 Figure 4.3: Close-up of the exhibit including the placements of the video camera (1) and the microphone (2). This figure also shows an example of a complete Voronoi diagram at the end of a game round. 1 2 22 Figure 4.4: The surroundings behind the exhibit. 23 Figure 4.5: The surroundings behind the exhibit. 24 4.4 Data collection The data collection was based on two empirical sources: use and conversations (audio-visual observations) and design and learning objectives (semi-structured interviews). In order to produce reliable results, the interviews with the exhibit designers were conducted after the completion of the data collection and the analysis of the data. In that way, there would be no preconceptions that might affect the findings from the case study, in accordance with the inductive research approach. 4.4.1 Use and conversations (audio-visual observations) The main empirical source of the data collection was the audio-visual observations executed on site at the exhibition Mathrix at the science center of Universeum in Gothenburg. The observations were executed during two days of a week of school holiday when the exhibition was more crowded than usual with visitors between approximately the ages of 1 and 70 years old. This was an intentional choice to be able to have multiple visitors to choose from. 4.4.1.1 Recruitment of participants As the main target group of the exhibition is children of the ages between 13 and 18 years old, the main focus was to find participants in that particular age range. Groups of two participants or more were aimed for as a crucial part of the study includes the verbal conversations between the participants when using and exploring the interactive exhibit. Also, only pairs or groups of participants speaking the languages of Swedish, English or Danish were selected so that the transcription process would be as easy as possible. 4.4.1.2 Procedure The randomly chosen visitors of the science center was observed with the help of audio-visual recordings from a GoPro Hero8 Black camera discretely placed on top of the interactive exhibit, only capturing the display area and the four coloured buttons (see figure 4.3 on page 21). As the audio recordings provided by the camera itself were insufficient, a Zoom H1n microphone was placed just above the display area to be able to better capture the sound and conversations coming from multiple directions at once (see figure 4.3 on page 21). In order to maintain a natural visit experience for the participants and to influence the result as little as possible, the initial aim was that the participants would be given no specific instructions. They were also not asked to communicate more than usual or to explain what they were 25 doing or thinking. However, as the interface, the rules and the purpose of the game turned out to be quite tricky for the participants to understand, some instructions had to be given to most of the participants before or during the different sessions to encourage them to interact with the station. The aim was then that these instructions would affect the results of the study as little as possible. 4.4.1.3 Chosen participants In total 20 sessions with 57 different participants were recorded and they were all included in the analysis. The different sessions were given the anonymous numbers from 1 to 20. Table 4.1 on page 26 summarizes the ages, genders and nationalities of each participant belonging to each session. It also presents the number of actively talking or playing participants in each session. 4.4.1.4 Ethical considerations As the data collection was executed in the form of audio-visual recordings, naturally there were ethical issues that had to be considered beforehand. Research ethics are not static nor straight forward, however the guidelines provided by the Swedish Research Council (2017) were used as foundation when designing the setup of the data collection. During the data collection, all groups of participants were informed of their participation and what the collected data was going to be used for, in other words the main purpose of the overall study. They were informed that their participation was voluntary and anonymous and that they were always able to withdraw their participation after the collection of the data. Also, the participants were informed of how the data was going to be collected, who was going to have access to it and for how long it was going to be stored and where. Time was allocated for any kinds of questions from the participants prior to and after the data collection. The demographic information of age, gender and nationality was collected from the participants. All aspects of the data collection were presented in the Participation form and Consent form & demographic information (see Appendix II, III, IV and V) which was written in simple language to enable all participants to understand what they were agreeing to. All participants younger than 15 years old were required to be accompanied by a parent or legal guardian who could fill in the Participation form and the Consent form & demographic information. However, the parent or the legal guardian did not have to take part in the data collection. Participants of age 15 or older were allowed to fill in the forms 26 ID <13 13-15 16-18 19-21 22-25 26-35 >35 N P 1 FF M SWE 3 2 MM F SWE 3 3 F M SWE 2 4 MM F SWE 3 5 FFF SWE 3 6 FM FM GER 4 7 FM F SWE 3 8 FFM F SWE 4 9 M M DEN 2 10 FM SWE 2 11 F M SWE 2 12 MM F SWE 3 13 F SWE 1 14 F M SWE 2 15 FMM F SWE 4 16 FM FM DEN 4 17 F M M SWE 3 18 M F SWE 2 19 M MM NED 3 20 M M FM SWE 4 Table 4.1: Overview of the 20 sessions with a total of 57 different participants. The columns represent the ages and nationalities of the participants as well as the number of participants in each session. The letters F and M represent whether the participants were female or male. 27 themselves. The contact details of the researchers were included in the form to enable participants to retrieve from the case study or to ask questions risen long after the visit to the science center. The most problematic ethical aspect was the fact that the data collection was made through audio-visual recordings. However, both the audio and the visual parts of the recordings were crucial to be able to fully conduct the data collection. The video recorder was placed so that only the display area of the exhibit was visible which means that only the hands of the participants were recorded. Even though hands might be enough to identify a person, the hands were not blurred as the video recordings were never used visually in the final report of the study. Whenever the participants used personal identification information in their conversations, such as the participants’ own names, these parts were removed from the transcripts and replaced with the unique number of each participant (see chapter 4.5.1.1.1). Each group or pair of participants was given a number and the same number was used on their matching participation and consent forms, recordings and transcriptions. 4.4.2 Design and learning objectives (semi-structured interviews) The second empirical source of the data collection was the semi- structured interviews with the exhibit designers. They were interviewed to identify and categorize their design and learning objectives. 4.4.2.1 Chosen interviewees In total four people who were involved in the developing of the exhibit were interviewed and they were chosen based on the suggestion of the supervisor. These were Håkan Sigurdsson, Philip Gerlee, Mats Blysing and Lena Pareto. Håkan Sigurdsson works as a scientific director at the science center of Universeum. He describes his role as being responsible for the bigger decisions in relation to the exhibition rather than focusing on individual exhibits. Together with a group of other colleagues, he developed the story and the concept of the exhibition as a whole. In the case of the exhibition of Mathrix, he was also further involved in the details of some of the exhibits where Voronoi was one of them. Philip Gerlee works as a professor in applied mathematics and statistics at Chalmers University of Technology. He describes his main research interest as mathematical biology but he is also interested in applications of game theory to biology. In terms of the development of 28 the exhibition Mathrix, he was involved in the beginning phases where he and another colleague was invited to brainstorm different ideas of possible exhibits, including the idea of the exhibit Voronoi. His main role was to act as a so called ‘external expert’, providing Universeum with useful insights and knowledge on specific topics. Mats Blysing works as a UX-designer and creative director and his role in the project of Mathrix mainly included the responsibility for the overall user experience of the exhibition. He made sure that all exhibits were connected, in relation to both graphics and tonality, to maintain the feeling of a unified exhibition even though the exhibits contain very different topics. He also describes his role as making sure that the experiences are similar and dissimilar enough, to stimulate movement through the exhibition space. He was specifically involved in the development of some of the exhibits where Voronoi was one of them. The last interviewee, Lena Pareto, is also the supervisor of this master’s thesis. She works as a professor in pedagogy with a special mission for Universeum and is based at the University of Gothenburg. She describes her main research interest as digital design for learning including game design. Similar to the rest of the interviewees, she has been involved in the process of the development of the exhibition Mathrix from the very beginning. She describes that she took the responsibility of keeping the level of mathematical content sufficiently high based on the chosen main target group. She also made sure that external experts were involved and that prototypes were created and tested throughout the process. She has also been further involved in the details of the exhibit Voronoi and that is the main reason as to why she has been included in the interviews. When the Voronoi interactive exhibit was chosen to be the focus of this master’s thesis, it had not been revealed that it was one of the exhibits that she had been specifically involved in. 4.4.2.2 Procedure The semi-structured interviews were conducted separately due to logistic reasons. The audio from the interviews was recorded. The interviews were based on an interview guide containing three sections: 1. The interviewees’ roles in the project 2. The intended learning objectives associated with the exhibit 3. The intentions with the physical and digital design of the exhibit to support the intended learning objectives See Appendix VI for the complete interview guide including all questions and themes that were asked and discussed. 29 The initial idea was to interview all four interviewees after the completion of the data collection. However, during the course of the study, it became evident that as one of the designers of the exhibit was the supervisor of the master’s thesis, that interview had to be conducted in a way so that neither the supervisor nor the researcher would be coloured by one another. This was solved by not having an oral interview but rather a written one, where the questions from the interview guide were sent to the supervisor before any discussions of the data and the analysis were begun. The answers to these questions were not read and analyzed by the researcher until after the completion of the analysis of the data. This way the analysis would not be based on any preconceptions, neither from the supervisor nor the researcher, in accordance with the inductive research approach. 4.5 Data analysis The data analysis consisted of three different parts. The categorization and classifying of the conversations, the identification of learning opportunities and the identification and comparing of design and learning objectives. The classifying of the conversations was only done to the subcategories belonging to the main category of Learning talk (mathematical talk). 4.5.1 Categorizing and classifying conversations The categorization of the conversations was done by developing a coding system through which the participants’ utterances and related actions were categorized. The creation of the coding system was done in three different steps where each session was thoroughly transcribed, relevant actions were added and lastly a categorization was done which then resulted in the final coding system. 4.5.1.1 Categorizing conversations 4.5.1.1.1 Transcription Firstly, each session was transcribed by hand by only using the audio recordings. This means that all conversations that were possible to pick up were written down in the order that they were spoken. Any utterances from the researcher were removed as the details of these utterances were assessed as irrelevant to the scope of the study. However, the nature of the utterance was noted which, at the end of the transcription process, resulted in four different themes of utterances from the researcher. These utterances were all related to different kinds of instructions to the participants. As mentioned in chapter 1.4, these instructions were only allowed to include the basics of the game and the 30 interface to enable the visitors to start acting on their own. This means that in the transcriptions, these utterances are presented as “The researcher gives the instructions of theme 1/2/3/4”. Any comments from the participants only being reactions to these instructions were also removed. If any of the comments from the participants in relation to the instructions were evaluated as relevant, they were included in the transcriptions. All other utterances were linked to each participant by using the names from P1 to P57, meaning participant 1 to participant 57. As many of the participants had voices that sounded similar to each other, especially the youngest participants, and as the video recordings only showed the display and the hands of the participants, linking all quotes to the correct participant was not always a simple task. It was a process of listening to the sessions several times to try and understand the dynamics of the conversations and making sense of who must have said what. For example, trying to understand when a participant was answering herself or himself or when a participant was talking to another participant. Also, many of the participants used each other’s names and nicknames, which worked as a support in identifying who was talking and who was answering. During the transcription, a segmentation process was developed to determine the appropriate level of granularity. This means that many of the utterances were divided into parts where each part only had one specific focus. This segmentation process was not straight forward, however, during the course of the work it was quite evident which utterances had different characteristics or not. The segmentation process was mainly inspired by those of Liu and Heer (2014), Scalfi et al. (2022) and DeWitt and Hohenstein (2010), where the segments consisted of single sentences instead of words or longer conversations. The following utterance is expressed by the same participant but was segmented into three different parts as they were assessed to have different foci: Original utterance P5 Yes, look at red! Yes, but look, it looks pretty good for yellow! I could have... I won! I thought I would try to do it very tight, it was just a test Segmented utterance P5 Yes, look at red! Yes, but look, it looks pretty good for yellow! P5 I could have... I won! P5 I thought I would try to do it very tight, it was just a test 31 Choosing a level of granularity that singles out each word would have made the utterances lose their contextual meaning and would also have been too time consuming, whereas analyzing the data as continuous conversations would have been off-topic as the scope of this study is to focus on the content and topics of the conversations. 4.5.1.1.2 Addition of actions Secondly, the video recordings were used to better understand the utterances and what the participants were referring to when they were talking. For example, many of the participants talked about or commented on actions of their co-participants or on things that happened on the display without actually saying what it was. These components would be impossible to analyze and understand without also being able to see what the participants themselves saw. Whenever an action of this sort was conducted, this was noted as an addition to the utterance by using brackets and explaining what the participant did or what they meant. However, the video recordings were not used to make notes of exactly everything that the participants did. As long as the utterances themselves were enough to understand the context and meaning of the utterances, no actions were added. 4.5.1.1.3 Categorization Lastly, the written transcripts consisting of clearly segmented utterances together with the notes of the relevant actions of the participants were used to categorize and structure the data. This was done by using the MaxQDA software for Mac, a qualitative research tool that can be used to easily code and analyze different source materials (MaxQDA, 2024). During the process of categorizing the data and developing a well-fitted coding system, the thematic analysis method of Braun and Clarke (2006) was used. This method is an iterative process consisting of six steps explained in the following paragraphs. The first step (1) was to become familiar with the data, which was done by reading through all transcriptions several times to get a initial feel for the sense of the conversations. The second step (2) was to generate codes, which was done as a linear process from beginning to end were all sessions were coded until all utterances were matched to a code. A code in this case study was a description of the content of the utterance on a very specific level, which means that during this step the number of codes was very high, close to 100. Whenever an utterance could be fitted into several codes, which happened seldom but a few times, the utterance was matched to 32 the code that fitted best with the assessed core meaning of the utterance. During this step, none of the coding systems of the previous research studies were reviewed yet. Up to this point, the code generation was only based on the conceptions of the researcher with no aim of trying to fit the codes into an already existing coding system. During the third step (3), more general themes were generated from the set of codes. This means that the set of codes were reviewed with the purpose of finding similarities so that the number of codes could be narrowed down and combined into bigger themes. During this step, the coding systems of the previous case studies were used as inspiration. The set of codes were matched to different categories or themes that could be found in other coding systems. New categories were also created when there was no category that seemed to fit. At this point, the number of codes were narrowing down to about 50-60, and the categories to about 20-25. All nine example case studies were used as inspiration, however, as none of them are investigating the exact same thing with the exact same focus, no coding system could be used as a whole. Bits and pieces from the different coding systems were used to develop a new coding system. As these kinds of case studies are very specific, it is quite evident that most of them also need a specific coding system. In this case study, the coding system was supposed to investigate the actual content of the conversations, as well as the overall types or themes of the conversations, which means that different case studies with different foci could be used as inspiration. For example, the coding systems used to categorize what families visiting the zoo in Brazil (Scalfi et al., 2022) and what children seeing representations of three-dimensional animals (Tunnicliffe & Reiss, 2000) are talking about are more focused on the specific content of the conversations. The coding systems used to categorize what visitors of the frogs exhibition in San Francisco (Allen, 2002) and visitors at the museum in Santa Cruz (Ash, 2002; Ash, 2003) talk about, on the other hand, are much more focused simply on the type of conversation. The fourth step (4) was then to start reviewing the themes, checking if they made sense in relation to the codes and to the data set as a whole. The fifth step (5) was to ultimately define and name the codes and the themes. At this stage in the process, during step 4 and 5, the codes and the categories were reviewed several times together with the supervisor to find possible overlaps, additions and general improvements. The purpose was to ensure that no code or theme was mentioned twice, was missing or was described in an unclear manner. This then resulted in several codes being combined, redefined and renamed. Quite early in the process, already during the second step, the aim was to distinguish which utterances were related to the process of learning and which were not. This means that some main themes or categories were already in 33 mind, where Learning talk was one of them. However, it was not until the fourth step of the process that all of these main categories were ultimately distinguished. The final main categories were also inspired by some of the previous case studies, mainly the case study conducted by Isaksson and Söderberg (2022) and Pareto et al. (2023). The three main categories that were defined in the end of the process were Learning talk, System talk and Affective talk. However, during the finalization of the main categories, it became evident that the category of Learning talk consisted of two types of talk that were not fully related to each other. On the one hand, the participants explicitly talked about the mathematical content of the game. On the other hand, they talked about the game by commenting on the game rules and the actions that they were taking. This second type of talk is defined as game mechanics (Fe, 2016). The main category of Learning talk was therefore divided into mathematical talk and game mechanics, to distinguish these different characteristics from each other. The characteristics of these two types of Learning talk, and why they are both considered to be Learning talk, are further elaborated in chapter 5.3. The sixth and final step (6) was to locate exemplars which essentially meant finishing off the coding system and presenting it in a clear arrangement. The final coding system is presented in chapter 5.3 and the result is a hierarchical coding system containing three main categories, 16 subcategories and 37 subordinate groups. Examples from the data from the different main categories and subcategories are presented, together with a description of the characteristics of each main category. The final analysis of the conversations is done in chapter 6.2, where the data is viewed from the perspective of the utterance statistics based on the final coding system. 4.5.1.2 Classifying conversations The subcategories belonging to the main category of Learning talk (mathematical talk) were further analyzed by using the SOLO taxonomy as defined by Briggs and Collis (1982). The SOLO taxonomy, where SOLO is a shortening for The Structure of the Observed Learning Outcome, is used as a means of classifying different levels of understanding in terms of complexity, focusing on the quality of the learning outcome rather than quantitative measures. Five different stages of cognitive development are defined as Prestructural, Unistructural, Multistrucutral, Relational and Extended abstract. At the prestructural stage, the learner has not yet reached an understanding of the point of the task. At the unistructural stage, the learner has understood one relevant aspect of the task, while at the multistructural 34 stage, the learner has understood several but unconnected aspects of the task. When the learner reaches the relational stage, he or she can start to connect different ideas and aspects of the task. The final stage, the extended abstract stage, is reached when the learner is able to make connections beyond the original task (Biggs & Collis, 1982). The analysis of the mathematical talk in relation to these different levels of complexity is also done in chapter 6.2. 4.5.2 Identifying learning opportunities The identification process of the learning opportunities of the participants was made in four different steps. Firstly, five of the 20 sessions were chosen to look further into where opportunities for learning were thought to be the most possible. The developed coding system and the analyses of the conversations were used as a tool to find these five sessions. The criteria for the selection was mainly based on the extent to which utterances belonging to the subcategories of game strategies, game management, connection and interpretation were present as these subcategories were classified as the parts of the mathematical talk that were the most complex. Session 2, 7, 15, 19 and 20 were chosen mainly based on these criteria but also based on the fact that they were some of the longest sessions with the most utterances. This decision was made so that there would be enough utterances to analyze. This means that these five sessions were the only ones being more closely analyzed. The analysis therefore does not represent the learning opportunities in a typical session, but rather the learning opportunities of some of the most ‘successful’ sessions. The method of interaction analysis was then used to be able to draw conclusions about what learning opportunities actually arose. Jordan and Henderson (1995) defines the method of interaction analysis as “a method for the empirical investigation of the interaction of human beings with each other and with objects in their environment. It investigates human activities, such as talk, nonverbal interaction, and the use of artifacts and technologies, identifying routine practices and problems and the resources for their solution”. Here, specific utterances and actions of each session were chronologically highlighted and described to get an understanding of what was said and what happened during these sessions. The third and the fourth step involved generalizing the findings from the previous steps. The goal of the third step was to identify common patterns in the so called ‘learning trajectories’ of the participants. A learning trajectory can be explained as “ordered tendencies developed 35 through empirical research designed to identify highly probable steps students follow as they develop their initial ideas into formal concepts” (Maloney & Confrey, 2010). Simon (1995) expressed it more concisely as “the paths by which learning might proceed”. This is presented as the different identified stages of the learning processes that the participants were engaging in during the course of the gameplays, and the mathematical abilities that were practiced during these stages. The four-step experiential learning process defined by Kolb (Kolb, Boyatzis & Mainemelis, 1999) was then used as a foundation onto which the identified stages were mapped. The fourth step involved identifying possible success factors that could be found in all five sessions. The five identified success factors were used as a tool to understand and explain why the learning opportunities took place and why the sessions seemed to turn out so fruitful. During step three and four, the analyses and findings were closely linked to the theoretical framework presented in chapter 2. The interaction analyses of the five chosen sessions, the identified learning trajectories and success factors are presented in chapter 6.3. 4.5.3 Identifying and comparing design and learning objectives The data collected from the four semi-structured interviews were summarized based on the same six steps of the thematic analysis method of Braun and Clarke (2006), described in chapter 4.5.1.1.3. This analysis was, however, much more brief and executed without the support from the supervisor as she was one of the four interviewees. The aim was to find a few general themes that could be used to categorize the design and learning objectives of the exhibit designers. These objectives were then compared to the analyses in relation to the categorizing and classifying of the conversations and the identifying of the learning opportunities. The summary of the design and learning objectives of the exhibit designers is presented in chapter 5.5 and the comparison of the intentions of the designers and the analyses is done in chapter 6.4. 36 5. Results This chapter presents the results from the audio-visual observations conducted at the science center of Universeum and the semi-structured interviews with the four chosen exhibit designers. Chapter 5.1 and 5.2 presents the participant and session characteristics. Chapter 5.3 presents the final coding system where each main category is presented separately, followed by example utterances from the data belonging to the different subcategories of each main category, to further explain the characteristics of the different parts of the coding system. Chapter 5.4 presents a summary of the overall utterance statistics, in relation to all utterances and in relation to each session. The final chapter, chapter 5.5, consists of the results from the semi-structured interviews presenting the design and learning objectives from the exhibit designers. It also includes elements of improvement that were highlighted in the interviews. The first four chapters were completed before chapter 5.5 was started. In Appendix XII, a summary of the most common misconceptions of the gameplay is also presented. 5.1 Participant characteristics In total, 57 different participants were actively playing or talking during the sessions. The vast majority of the participants were actively playing, however, there were a few participants that did not play but still took part in the discussions. These have also been included in the results. The most represented age group was the participants under the age of 13. 27 out of 57 participants belonged to this age group, which corresponds to 47,4% of the participants belonged to this age group. The second most represented age group was the participants over the age of 35. 19 out of 57 participants belonged to this age group, which corresponds to 33,3% of the participants. The remaining age groups only corresponded to a total of 19,3% of the participants, where the participants between the ages of 13 and 15 represented 8,8% (5 participants), the participants between the ages of 16 and 18 represented 1,8% (1 participant), the participants between the ages of 19 and 21 represented 1,8% (1 participant), the participants between the ages of 22 and 25 represented 3,5% (2 participants) and the participants between the ages of 26 and 35 represented 3,5% (2 participants). Figure 5.1 on page 37 summarizes the distribution of the ages of the participants of the case study. 27 out of 57 participants were female, which corresponded to 47,4% of the participants. The remaining 30 participants were male, which 37 Figure 5.1: Distribution of the ages of the participants of the study. The figure presents both the percentage and the number of participants belonging to each age interval. 27 5 1 1 2 2 19 38 corresponded to 52,6% of the participants. The most common nationality which corresponded to 77,2% of the participants (44 participants) was Swedish. Apart from the Swedish participants, 10,5% were Danish (6 participants), 7,0% were German (4 participants) and 5,3% were Dutch (3 participants). The most common number of participants taking part in the session was three. 40,0% of the sessions (8 sessions) consisted of three actively playing or talking participants. 30,0% of the sessions (6 sessions) consisted of two participants, 25,0% of the sessions (5 sessions) consisted of four participants and 5,0% of the sessions (1 session) consisted of only one participant. 5.2 Session characteristics In total, 20 different sessions were recorded. Table 5.1 on page 39 presents the number of game rounds, the number of utterances and the duration of each session. Both the number of utterances from the participants and from the researcher has been calculated, however summarized separately. This differentiation has been done so that the results from the conversations of the participants can be presented separately, without being affected by the number of utterances from the researcher. A total of 86 different game rounds were played, which represented a mean of 4,3 game rounds per session. The participants made a total of 901 different utterances, while the researcher made 66. This represented a mean of 45,1 participant utterances and 3,3 researcher utterances per session. The total session time was 117 minutes and 42 seconds, which represented a mean of 5 minutes and 53 seconds per session. 39 ID Game rounds Utterances, participants (researcher) Session duration 1 3 30 (7) 04:51 2 12 195 (6) 16:12 3 4 15 (3) 04:36 4 3 9 (3) 03:01 5 9 80 (9) 11:06 6 3 35 (3) 04:49 7 4 85 (4) 07:37 8 7 41 (7) 07:34 9 3 6 (2) 03:22 10 3 67 (1) 06:01 11 2 7 (1) 02:17 12 2 17 (2) 02:58 13 2 9 (3) 02:39 14 1 12 (1) 01:31 15 8 87 (6) 08:16 16 2 15 (2) 02:46 17 3 34 (3) 03:14 18 4 47 (2) 07:17 19 5 51 (0) 08:13 20 6 59 (1) 09:22 Total 86 901 (66) 117:42 Mean 4,3 45,1 (3,3) 05:53 Table 5.1: Overview of the 20 sessions in relation to number of game rounds, number of utterances and duration of the sessions. The first number in the utterances column represents the utterances from the participants and the numbers inside the parentheses the utterances from the researcher. 40 5.3 Coding system The coding system is a hierarchical system containing three main categories, 16 subcategories and 37 subordinate groups. The first main category is named Learning talk and, as mentioned in chapter 4.5.1.1.3, the Learning talk is divided into mathematical talk and game mechanics. The mathematical talk consists of all the utterances from the participants that are explicitly connected to the mathematical content of the exhibit. The game mechanics consists of all the utterances where the participants are commenting on the rules of the game and the actions that they are taking, as defined by Fe (2016). In the most successful educational games, the educational content is placed at the heart of the gameplay which means that the participants of the game are engaging directly in the targeted thinking as they play the game (Fe, 2016; Fisch, 2005). The game presented in the exhibit of Voronoi can be seen as one of these successful educational games, as the participants’ playing of the game draws directly on the mathematical knowledge and skills that the game is designed to foster. The educational content is not presented alongside the gameplay, but is rather integrated into the very game mechanics. Based on these arguments, both the mathematical talk and the game mechanics have been included in the main category of Learning talk as they are both related to the fundamental mathematical content of the game. The following chapter presents each of these main categories, with their corresponding subcategories and subordinate groups. As the main category of Learning talk has been divided into Learning talk (mathematical talk) and Learning talk (game mechanics), these two are presented separately. Three typical utterances from each of the 16 subcategories used in the coding system is presented to demonstrate what kinds of utterances belong to the different subcategories. The 37 different subordinate groups are not demonstrated separately. The examples are taken from most of the different subordinate groups belonging to each subcategory. 41 Learning talk (mathematical talk) Observation Observing the formation of the pattern Observing the placements of the dots Inquiry Wondering how the pattern will be formed Wondering why the winner wins Prediction Predicting how the pattern will be formed Interpretation Interpreting the pattern to understand the outcome of the game Connection Making connections between the winner and the seating positions of the participants during the game Strategy management Realizing the need for a strategy Reflecting on what strategy to use Realizing a strategy is successful Realizing a strategy is not successful Strategy types Using the strategy of placing the dots far from other participants’ dots Using the strategy of placing the dots close to other participants’ dots Using the strategy of placing the dots far from each other Using the strategy of placing the dots close to each other Using the strategy of placing the dots in the middle of the display Using the strategy of placing the dots on the edges of the display Figure 5.2: The subcategories and subordinate groups of the main category of Learning talk (mathematical talk). 42 5.3.1 Learning talk (mathematical talk) The utterances belonging to the main category of Learning talk (mathematical talk) includes all utterances in relation to observing, predicting and interpreting the mathematical pattern on the display, making inquiries about how the pattern will be formed and why, identifying mathematical connections and identifying and using different mathematical strategies. These types of utterances corresponded to 34,4% of the total amount of utterances. Example utterances from the data Observation P6 Mine, look now, it grows [name of P4] [P6 points at a big blue area at the corner of the display] P41 Oh wait, now it’s mostly green... or blue P52 Looks like I just won Inquiry P51 Who wins now? P2 What will this become? P38 Let’s see if I will win one more time Interpretation P19 Okay, so that’s how you were thinking, that you would get all of that, but I stole a bit from you there I think P4 Look, if I hadn’t placed my dot there, you would have come and taken all of this [P4 points at his blue areas next to the yellow areas of P5] P53 I think we tried to go against each other too much here Connection P53 I think being in your spot is the best, I think the last dot is the best, you have... like in the last place you can just look at what dots give you the most area P56 It was easiest for [name of P55] because he was the last one, your spot was the most difficult P29 Yes, now I get to be the last one, that’s great, that’s really great [P29 thinks of what to do for a longer while] 43 Prediction P47 I think it is the red one P14 I bet yellow will win again, no, red? P43 There will be very little of this colour, I’m completely sure Strategy management P54 I need to know if it’s a good strategy to surround someone P51 To like if the good spots... that’s a really good strategy. Good spots go together P53 I guess you have to consider who has got the most space currently Strategy types P54 But it is obviously a good thing to stay at the edges of the display P56 I placed them where no one else was because then I get a bigger area P29 So then you should be farthest away, kind of? So that you get a big area 44 Learning talk (game mechanics) Gameplay comments Making comments about the rules of the game Making comments about the playing of the game Making comments about the outcomes of previous games Gameplay organization Organizing the start and the end of the gameplay Choosing and allocating colours Organizing taking turns Figure 5.3: The subcategories and subordinate groups of the main category of Learning talk (game mechanics). 5.3.2 Learning talk (game mechanics) The utterances belonging to the main category of Learning talk (game mechanics) includes all utterances in relation to commenting on the rules of the game, the playing of the game, recalling earlier events and outcomes and organizing and structuring the course of the gameplay. These types of utterances corresponded to 38,6% of the total amount of utterances. Example utterances from the data Gameplay com