Unravelling Tutors' Conceptions of Teaching Mathematics in Virtual School Using a Goal-Action Model.

This study explored the unique integration of mathematics tutors in teaching high school mathematics in a Virtual mathematics school (VMS). The tutors were three excelling STEM students who did not have any formal preparation for teaching before their work in the VMS. The goal of the study presented in this paper was to design a model of proficiency for these tutors. The model was designed using multiple case study methodology by tracking the learning through teaching of the tutors. Activity theory (Leontiev, 1978) framed the design of the study and led to a "goal-action" model of the tutors' proficiency in the VMS. The goals part of the model is rooted in the construct of students' mathematical potential (Leikin, 2021), and the action part was unraveled using the construct of a Teaching Triad (Jaworski in For the Learning of Mathematics, 12(1), 8-14, 1992). In this paper, we illustrate how our model can be used to analyze changes in the tutors' proficiency, and how it can be applied to descriptive, explanatory, and analytical power.

(Lack of) neural efficiency related to general giftedness and mathematical excellence: An EEG study.

Previous studies on intelligence have demonstrated that higher abilities are associated with lower brain activation, indicating a higher neural efficiency. In other words, more able individuals use fewer brain resources. However, it is unclear whether the neural efficiency phenomenon also appears for mathematical performance, which is influenced by both domain-general giftedness and domain-specific competencies. Therefore, this study examined the effects of general giftedness (G) and excellence in mathematics (EM) on performance and brain activation while solving learning-based mathematical tasks that required translation from graphical to symbolic representations of functions. Overall, 118 high school students (aged 16-18) participated in the present study and were divided according to G and EM using a 2 × 2 study design. Participants worked on a function task requiring translation between symbolic and graphical representations of functions. Analyses of the behavioral data revealed positive effects of both G and EM on the accuracy of solutions and an interaction effect of both factors on reaction times, reflecting a positive effect of EM only among the gifted individuals. EEG analyses focused on oscillatory activity in the theta and alpha frequency bands and showed a significant effect of EM in the upper alpha band (10-12 Hz) event-related desynchronization (ERD) for both graphical and symbolic representations. Specifically, higher (compared to lower) EM was associated with a larger alpha ERD, indicating a higher level of brain activity. This stands in contrast with the neural efficiency phenomenon. These findings suggest that the neural efficiency phenomenon cannot be generalized to higher-order mathematical demands in high-performing individuals. Several explanations for this limitation are offered.

When practice needs more research: the nature and nurture of mathematical giftedness.

The educational literature often includes debate over the nature and nurture of mathematical giftedness. The varied schools of thought reflect discrepancies between views, which are to a large extent functions of philosophical, political, and economic considerations. To address this debate, in the context of the current ZDM Special Issue, I attempt to analyze research and practices linked to mathematical giftedness in the Soviet Union in 1960-1980. I also look at the continuation of these Soviet-era practices, and to their influence on practices internationally. Particular attention is paid to the literature devoted to reaching a deeper understanding of the phenomenon of mathematical giftedness and of ways of nurturing this giftedness. The analysis starts with the discussion of domain-specific and domain-general characteristics of mathematical giftedness that have to be taken into account in educational environments for the mathematically gifted. It continues with a review of practices in special mathematical schools and classes in the Soviet Union, and a comparison to similar settings around the world in the twenty-first century. There is also an overview of enrichment mathematical activities, with a focus on mathematical circles, mathematical competitions and Olympiads, accompanied by a description of specificities of the mathematical content employed for the promotion of mathematical giftedness. Finally, the paper focuses on the question of what characterizes an excellent teacher of mathematically gifted students and on new educational technologies that are changing the education of these students worldwide. Following this analysis, I suggest some open questions for future research on the education of mathematically gifted students.

Brain activity associated with translation from a visual to a symbolic representation in algebra and geometry.

This paper presents a small part of a larger interdisciplinary study that investigates brain activity (using event related potential methodology) of male adolescents when solving mathematical problems of different types. The study design links mathematics education research with neurocognitive studies. In this paper we performed a comparative analysis of brain activity associated with the translation from visual to symbolic representations of mathematical objects in algebra and geometry. Algebraic tasks require translation from graphical to symbolic representation of a function, whereas tasks in geometry require translation from a drawing of a geometric figure to a symbolic representation of its property. The findings demonstrate that electrical activity associated with the performance of geometrical tasks is stronger than that associated with solving algebraic tasks. Additionally, we found different scalp topography of the brain activity associated with algebraic and geometric tasks. Based on these results, we argue that problem solving in algebra and geometry is associated with different patterns of brain activity.