skip to main content

This content will become publicly available on October 25, 2024

Title: Using Mathematizing Supports for Applied Problem Solving in a Game-Based Learning Environment

Students frequently struggled with the mathematizing process – forging connections between implicit and explicit mathematical thinking – when solving a context-rich applied problem. The current research investigated how students interact with and leverage purposively designed ‘mathematizing’ supports when solving applied math problems in a game-based, inquiry-oriented math learning environment. We conducted a naturalistic observation case study and a mixed-method study to investigate middle school students’ usage of mathematizing supports in relation to their math problem-solving performance. The findings indicated a positive and predictive impact of using mathematizing supports on the logged and observed practice of mathematization as well as the performance of applied math problem solving by the students during and after gaming. However, not all students leverage in-game mathematizing supports or engage in problem mathematizing processes. The grounds of students’ constructive interaction with a mathematizing support include their productive persistence in problem solving, their exercise of agency in gauging the utility of mathematizing, and their engagement with deductive reasoning from concrete to abstract. We also observed an interplay between internal and external mathematizing supports, which is moderated by the modality of learning settings.

more » « less
Author(s) / Creator(s):
 ;  ;  ;  ;  
Publisher / Repository:
SAGE Publications
Date Published:
Journal Name:
Journal of Educational Computing Research
Medium: X Size: p. 468-500
p. 468-500
Sponsoring Org:
National Science Foundation
More Like this
  1. Abstract Background

    Game‐based learning can frame problem‐solving as a sense‐making experience with domain‐specific tasks for school students. However, multiple challenges arise when trying to support learners in such a complex, problem‐oriented learning environment.

    Objectives and Methods

    With an architecture‐themed mathematics learning game, we conducted two mixed‐method studies to explore the impact and design of game‐based mathematical experience on the math problem‐solving performance of middle school students.

    Results and Conclusions

    The study findings suggested a positive impact of game‐based math experience on math problem‐solving for middle school students. Problematization‐oriented game‐based math tasks with structuring features enhanced students' reasoning with problems and channelled it to doing mathematics.


    The current research findings support the initiative to frame learning as a sense‐making experience with domain‐specific tasks and inform the design of game‐based mathematical experience and learning support.

    more » « less
  2. 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.

    more » « less
  3. null (Ed.)
    Worldwide, national initiatives have led to many school districts implementing computing curricula at the primary level. At that age, students are learning the foundational skills of reading and math. It is important to understand how computing can influence the development of these skills. While some argue that learning computing sharpens problem-solving skills that are applicable to other subjects, evidence supporting this belief is thin. In a quasi-experimental study of fourth-grade (ages 9-10) students, we compared state reading and math test scores of students receiving computing instruction with students who did not. Our findings demonstrated that a more open-ended, less scaffolded form of computing instruction was linked to performance gains in math, but not in reading (𝐹 (2, 232) = 11.08, 𝑝 < .01, 𝜂𝑝2 = .0625). When looking at students who face academic challenges that can impact reading and math, the same trend applied to students with economic disadvantages and students with limited English proficiency, but not for students with disabilities. These results suggest that moderately scaffolded computing instruction supports the development of skills applicable to math, a step towards better understanding the relationship between learning opportunities in computing and outcomes in other subjects. 
    more » « less
  4. Although prior research has highlighted the significance of representations for mathematical learning, there is still a lack of research on how students use multimodal external representations (MERs) to solve mathematical tasks in digital game-based learning (DGBL) environments. This exploratory study was to examine the salient patterns problem solvers demonstrated using MERs when they engaged in a single-player, three-dimensional architecture game that requires the acquisition and application of math knowledge and thinking in game-based context problem solving. We recorded and systematically coded the behaviors of using MERs demonstrated by 20 university students during 1.5 hours of gameplay. We conducted both cluster and sequential analyses with a total of 2654 encoded behaviors. The study indicated that the maneuverable visual-spatial representation was most frequently used in the selected architecture game. All of the participants performed a high level of representational transformations, including both treatment and conversion transformations. However, compared to the students in the second cluster who were mostly non-game players, students in the first cluster (composed of mainly experienced video game players) displayed a higher frequency of interacting with various MERs and a more cautious and optimized reflective problem-solving process. 
    more » « less
  5. Digital storytelling in combination with makerspace activities holds significant potential to engage students and support their learning. When students play, such as through makerspace activities, they engage in critical thinking and problem solving. In our work, we are joining storytelling with computational thinking (CT) practices, physical science exploration, and makerspace activities through a digital narrative-centered learning environment for elementary school. Learning within the environment is undergirded by makerspace play that centers on finding solutions to an open problem—how can stranded scientists on a remote island power up their village using found materials? The learning environment supports students’ CT practices and science content learning as they use and problem solve with physical energy conversion kits, culminating in their creation of an interactive story. We present here a brief case study of the ways students’ experiences with makerspace play support their problem solving and storytelling. 
    more » « less