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1. Structuring and Connecting 2D and 3D Space Using Linear Combinations

   Mauntel, Matthew ( January 2023 , Proceedings of the Annual Conference on Research in Undergraduate Mathematics Education)

   Cook, Samuel ; Katz, Brian ; Moore-Russo, Deborah (Ed.)

   Developing a rich understanding of linear combinations is key to understanding linear algebra. In this paper, I explore the rich connections students make between the geometric and numeric representations of linear combinations through playing and analyzing a video game. I look at population of students who have never taken linear algebra before and analyze how they structure space using the video game, Vector Unknown, as a realistic starting point. I detail and analyze this activity including the activities that transition them from 2D to 3D space. 

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2. Exploring the Relationships Among Middle School Students’ Peer Interactions, Task Efficiency, and Learning Engagement in Game-Based Learning

   https://doi.org/10.1177/1046878120907940  

   Moon, Jewoong ; Ke, Fengfeng ( March 2020 , Simulation & Gaming)

   Background. Middle school students’ math anxiety and low engagement have been major issues in math education. In order to reduce their anxiety and support their math learning, game-based learning (GBL) has been implemented. GBL research has underscored the role of social dynamics to facilitate a qualitative understanding of students’ knowledge. Whereas students’ peer interactions have been deemed a social dynamic, the relationships among peer interaction, task efficiency, and learning engagement were not well understood in previous empirical studies.

   Method. This mixed-method research implemented E-Rebuild, which is a 3D architecture game designed to promote students’ math problem-solving skills. We collected a total of 102 50-minutes gameplay sessions performed by 32 middle school students. Using video-captured and screen-recorded gameplaying sessions, we implemented behavior observations to measure students’ peer interaction efficiency, task efficiency, and learning engagement. We used association analyses, sequential analysis, and thematic analysis to explain how peer interaction promoted students’ task efficiency and learning engagement.

   Results. Students’ peer interactions were negatively related to task efficiency and learning engagement. There were also different gameplay patterns by students’ learning/task-relevant peer-interaction efficiency (PIE) level. Students in the low PIE group tended to progress through game tasks more efficiently than those in the high PIE group. The results of qualitative thematic analysis suggested that the students in the low PIE group showed more reflections on game-based mathematical problem solving, whereas those with high PIE experienced distractions during gameplay.

   Discussion. This study confirmed that students’ peer interactions without purposeful and knowledge-constructive collaborations led to their low task efficiency, as well as low learning engagement. The study finding shows further design implications: (1) providing in-game prompts to stimulate students’ math-related discussions and (2) developing collaboration contexts that legitimize students’ interpersonal knowledge exchanges with peers.

    

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3. Maximizing learning without sacrificing the fun: Stealth assessment, adaptivity and learning supports in educational games

   https://doi.org/10.1111/jcal.12473  

   Shute, Valerie ; Rahimi, Seyedahmad ; Smith, Ginny ; Ke, Fengfeng ; Almond, Russell ; Dai, Chih‐Pu ; Kuba, Renata ; Liu, Zhichun ; Yang, Xiaotong ; Sun, Chen ( July 2020 , Journal of Computer Assisted Learning)

   In this study, we investigated the validity of a stealth assessment of physics understanding in an educational game, as well as the effectiveness of different game‐level delivery methods and various in‐game supports on learning. Using a game calledPhysics Playground, we randomly assigned 263 ninth‐ to eleventh‐grade students into four groups: adaptive, linear, free choice and no‐treatment control. Each condition had access to the same in‐game learning supports during gameplay. Results showed that: (a) the stealth assessment estimates of physics understanding were valid—significantly correlating with the external physics test scores; (b) there was no significant effect of game‐level delivery method on students' learning; and (c) physics animations were the most effective (among eight supports tested) in predicting both learning outcome and in‐game performance (e.g. number of game levels solved). We included student enjoyment, gender and ethnicity in our analyses as moderators to further investigate the research questions.

    

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4. A learning analytics approach towards understanding collaborative inquiry in a problem‐based learning environment

   https://doi.org/10.1111/bjet.13198  

   Saleh, Asmalina ; Phillips, Tanner M. ; Hmelo‐Silver, Cindy E. ; Glazewski, Krista D. ; Mott, Bradford W. ; Lester, James C. ( February 2022 , British Journal of Educational Technology)

   This exploratory paper highlights how problem‐based learning (PBL) provided the pedagogical framework used to design and interpret learning analytics from Crystal Island: EcoJourneys, a collaborative game‐based learning environment centred on supporting science inquiry. In Crystal Island: EcoJourneys, students work in teams of four, investigate the problem individually and then utilize a brainstorming board, an in‐game PBL whiteboard that structured the collaborative inquiry process. The paper addresses a central question: how can PBL support the interpretation of the observed patterns in individual actions and collaborative interactions in the collaborative game‐based learning environment? Drawing on a mixed method approach, we first analyzed students' pre‐ and post‐test results to determine if there were learning gains. We then used principal component analysis (PCA) to describe the patterns in game interaction data and clustered students based on the PCA. Based on the pre‐ and post‐test results and PCA clusters, we used interaction analysis to understand how collaborative interactions unfolded across selected groups. Results showed that students learned the targeted content after engaging with the game‐based learning environment. Clusters based on the PCA revealed four main ways of engaging in the game‐based learning environment: students engaged in low to moderate self‐directed actions with (1) high and (2) moderate collaborative sense‐making actions, (3) low self‐directed with low collaborative sense‐making actions and (4) high self‐directed actions with low collaborative sense‐making actions. Qualitative interaction analysis revealed that a key difference among four groups in each cluster was the nature of verbal student discourse: students in the low to moderate self‐directed and high collaborative sense‐making cluster actively initiated discussions and integrated information they learned to the problem, whereas students in the other clusters required more support. These findings have implications for designing adaptive support that responds to students' interactions with in‐game activities.

   What is already known about this topic

   Learning analytic methods have been effective for understanding student learning interactions for the purposes of assessment, profiling student behaviour and the effectiveness of interventions.

   However, the interpretation of analytics from these diverse data sets are not always grounded in theory and challenges of interpreting student data are further compounded in collaborative inquiry settings, where students work in groups to solve a problem.

   What this paper adds

   Problem‐based learning as a pedagogical framework allowed for the design to focus on individual and collaborative actions in a game‐based learning environment and, in turn, informed the interpretation of game‐based analytics as it relates to student's self‐directed learning in their individual investigations and collaborative inquiry discussions.

   The combination of principal component analysis and qualitative interaction analysis was critical in understanding the nuances of student collaborative inquiry.

   Implications for practice and/or policy

   Self‐directed actions in individual investigations are critical steps to collaborative inquiry. However, students may need to be encouraged to engage in these actions.

   Clustering student data can inform which scaffolds can be delivered to support both self‐directed learning and collaborative inquiry interactions.

   All students can engage in knowledge‐integration discourse, but some students may need more direct support from teachers to achieve this.

    

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5. Grade 5 Students’ Elective Replay After Experiencing Failures in Learning Fractions in an Educational Game: When Does Replay After Failures Benefit Learning?

   https://doi.org/10.1145/3506860.3506873  

   Zhang, Qian ; Rutherford, Teomara ( March 2022 , LAK22: LAK22: 12th International Learning Analytics and Knowledge Conference)

   Despite theoretical benefits of replayability in educational games, empirical studies have found mixed evidence about the effects of replaying a previously passed game (i.e., elective replay) on students’ learning. Particularly, we know little about behavioral features of students’ elective replay process after experiencing failures (i.e., interruptive elective replay) and the relationships between these features and learning outcomes. In this study, we analyzed 5th graders’ log data from an educational game, ST Math, when they studied fractions—one of the most important but challenging math topics. We systematically constructed interruptive elective replay features by following students’ sequential behaviors after failing a game and investigated the relationships between these features and students’ post-test performance, after taking into account pretest performance and in-game performance. Descriptive statistics of the features we constructed revealed individual differences in the elective replay process after failures in terms of when to start replaying, what to replay, and how to replay. Moreover, a Bayesian multi-model linear regression showed that interruptive elective replay after failures might be beneficial for students if they chose to replay previously passed games when failing at a higher, more difficult level in the current game and if they passed the replayed games. 

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