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Creators/Authors contains: "Pan, Yanjun"

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  1. 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.

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  2. 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. 
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  3. The increasingly sophisticated at-home screening systems for obstructive sleep apnea (OSA), integrated with both contactless and contact-based sensing modalities, bring convenience and reliability to remote chronic disease management. However, the device pairing processes between system components are vulnerable to wireless exploitation from a noncompliant user wishing to manipulate the test results. This work presents SIENNA, an insider-resistant context-based pairing protocol. SIENNA leverages JADE-ICA to uniquely identify a user’s respiration pattern within a multi-person environment and fuzzy commitment for automatic device pairing, while using friendly jamming technique to prevent an insider with knowledge of respiration patterns from acquiring the pairing key. Our analysis and test results show that SIENNA can achieve reliable (> 90% success rate) device pairing under a noisy environment and is robust against the attacker with full knowledge of the context information. 
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