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    A parameter-uniform hybrid method for singularly perturbed parabolic 2D convection-diffusion-reaction problems
    (Elsevier, 2025) Barman, Mrityunjoy; Natesan, Srinivasan; Sendur, Ali
    The solution of the singular perturbation problems (SPP) of convection-diffusion-reaction type may exhibit regular and corner layers in a rectangular domain. In this work, we construct and analyze a parameter-uniform operator-splitting alternating direction implicit (ADI) scheme to efficiently solve a two-dimensional parabolic singularly perturbed problem with two positive parameters. The proposed model is a combination of the backward-Euler method defined on a uniform mesh in time and a hybrid method in space defined on a special Shishkin mesh. The analysis is presented on a layer adapted piecewise-uniform Shishkin mesh. The developed numerical method is proved to be first-order convergent in time and almost second-order convergent in space. The numerical experiments are performed to validate the theoretical convergence results and illustrate the efficiency of the current strategy.
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    Development of TPACK with Web 2.0 tools: Design-based study
    (Bastas, 2023) Uygun, Tuğba; Sendur, Ali; Dere, Rahime; Özçakır, Bilal
    This mixed-method study, which aimed to examine the development of teacher candidates, was organized as a design-based study. During the 14-week instructional sequence, pre-service teachers were given training based on the designed hypothetical learning trajectory. The data collected through the lesson plans before and after the training and interviews were organized and analyzed by using the rubric prepared within the scope of Web 2.0 tools by the researchers. Moreover, the pre-training and post-training scores obtained using this performance rubric were analyzed with the related sample t-test. In addition, learning packages and interviews were analyzed using content analysis technique. The findings showed that there was an improvement in the technological pedagogical content knowledge of the pre-service mathematics teachers with the training provided for the use of Web 2.0 tools in mathematics education. In the study, an alternative educational content that can be used in lessons related to instructional technologies in undergraduate programs that train mathematics teachers has been prepared. © 2023, Bastas. All rights reserved.
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    Facilitating the development of preservice teachers' geometric thinking through artificial intelligence (AI) assisted augmented reality (AR) activities: The case of platonic solids
    (Springer, 2025) Uygun, Tugba; Sendur, Ali; Top, Beyza; Cosgun-Basegmez, Kadriye
    Although augmented reality has become one of the most commonly used materials that support learning, especially in learning geometric concepts, it is avoided to be used in the lessons due to its complex structure. At that point, artificial intelligence working as a personal assistant in many fields can help us learn to produce our own model with augmented reality by coping with its complexity. In this study, it is aimed to examine both the effectiveness of Artificial Intelligence (AI) assisted Augmented Reality (AR) activities on the development of the preservice teachers' (PSTs) geometric reasoning and their practicality in use. To this end, an interactive learning environment with AI assisted AR activities including Chat Generative Pre-Trained Transformer (ChatGPT), Blender and MyWebAR, and lasting five weeks have been designed. The participants in this case study were 15 preservice mathematics teachers selected by maximum variation and criterion sampling techniques. The data were collected through AI assisted AR activities, two semi-structured interview forms, focus group interviews, anecdotes, activity forms and test. The analysis results have been reported under three groups about the PSTs' test results, experiences on AI assisted AR activities and thoughts about the activities. To conclude, it has been observed that the PSTs' conceptualization and geometric thinking levels have been improved. Moreover, their thoughts have been illustrated with the themes of cognitive dimension, affective dimension, technological dimension and employability dimension.
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    Superconvergence error analysis of discontinuous Galerkin method with interior penalties for 2D elliptic convection - diffusion - reaction problems
    (Taylor & Francis Ltd, 2023) Singh, Gautam; Natesan, Srinivasan; Sendur, Ali
    This article focuses on constructing and analyzing a non-symmetric interior penalty Galerkin method (NIPG) on Shishkin mesh for solving singularly perturbed 2D elliptic boundary-value problems (BVPs). We use piecewise Lagrange interpolation at Gaussian points to improve the order of convergence of the interpolation error. We then study the superconvergence properties of the NIPG method and prove O(N-1 ln N)(k+1) order of convergence in the discrete energy-norm. Various numerical experiments are provided to validate the theoretical results.