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"Mathematical problems"
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Comparison of Mathematics Problem-Solving Abilities in Autistic and Non-autistic Children: the Influence of Cognitive Profile
This study examines relationships between mathematical problem-solving performance (in terms of strategies used and accuracy) and the main cognitive domains associated with mathematical learning (i.e. executive functions, verbal comprehension and social perception) of children with and without autism spectrum disorder (ASD and non-ASD resp.). The study involved 26 ASD and 26 non-ASD children without intellectual disabilities, between 6 and 12 years old, matched by sex, age and school (grade and classroom). The results show a higher percentage of ASD children with problem solving difficulties than non-ASD (57% vs. 23% resp.). Poor performing ASD children showed comparatively lower scores in inhibition, theory of mind and verbal comprehension. Implications for the design of mathematical interventions for ASD students are discussed.
Journal Article
Valuing pedagogies: Parents’ affective, behavioral, and cognitive approaches to preschoolers’ mathematical gameplay in virtual reality
This study aims to identify parental valuing pedagogy (VP) that supports their children’s solving mathematical problems using a virtual reality application (app). To guide the development of this study and provide a framework for data analysis, this study proposes an initial gameplay model comprising three components: affect, behavior (social), and cognition (ABC). Three parent-child pairs solved 12 mathematical problems, and their interactions were fully recorded. Combining qualitative categories featuring rich descriptions with quantitative findings, this study identified detailed VPs within each of the ABC components. Quantitative analysis results reveal that the most significant VPs impacting child positive responses (PRs) are parental reasoning for knowledge and experimentation. The next two most significant VPs are in the behavioral aspect: parents’ description of mysterious experiences and their initiation of particular actions. Affective VP does not significantly impact child responses, but may play a pervasive, yet hidden role. The app and computer usage also appear to play a role in parental utilization of VPs. The findings suggest that higher-order parental VPs are critically related to child PR during serious gameplay using an app.
Journal Article
The contribution of critical thinking skills in rich mathematical problem completion: Insights from pre-service mathematics teachers
A narrow understanding of critical thinking challenges pre-service mathematics teachers to recognize situations that need critical thinking in problem-solving, remove errors in the formulation of mathematical problems due to unsupervised modification of data, and view content as a stimulus for critical thinking. This study aims to reveal how they perceive the extent to which rich mathematical problems require the contribution of critical thinking skills in their completion. We adopted grounded theory to locate the common trends of their perceptual following open, axial, and selective coding. Data saturation stemmed from the participation of 19 pre-service mathematics teachers through an in-depth interview session. Each pre-service mathematics teacher successfully recognized the application of at least two critical thinking skills in rich mathematical problem completion. The lack of understanding of critical thinking skills led them to focus on information as the catalyst for interpretation, while the question serves as the catalyst for evaluation and inference. They exhibited their involvement in critical thinking through questioning and discussion.
Journal Article
Teacher-student alignment to develop a valuing pedagogy: A case study of cultural dialogues for mathematical problem-solving
This study aims to develop effective pedagogies for addressing teacher and student values for mathematical problem-solving or valuing pedagogies (VPs) for mathematics. The aim is achieved by teacher-student alignment. The case study was conducted with a mathematician (the teacher) teaching an educational psychologist (the student) how to solve problems like a mathematician. The teacher taught the student by engaging in problem-solving activities like a one-to-one tutorial, immediately followed by their oral reflections. The formal teaching (including hand-writing) of teacher-student interaction was recorded. Follow-up oral and written dialogues continue between the teacher and the student in the later data analysis and paper process. Qualitative data analysis finds that the process generates three patterns of value alignment: teacher values transmission to students, teacher-student negotiations, and bridging teacher-student gaps by reform with teacher reflection and restructuring of pedagogies. The expert dialogues serve as an innovative methodology for identifying in-depth mechanisms for teacher-student value alignments and effective VPs.
Journal Article
Classification of radial solutions arising in the study of thermal structures with thermal equilibrium or no flux at the boundary
We provide a complete classification of the radial solutions to a class of reaction diffusion equations arising in the study of
thermal structures such as plasmas with thermal equilibrium or no flux at the boundary. In particular, our study includes
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