Modelling physical phenomena and acquiring mathematical formalisation can be challenging in physics and math education at all grades. It is recommended that interpretative and mathematical models be developed gradually from an early age, starting from kindergarten. Although innate visuospatial representation and numeracy skills are present in individuals from an early age, numerous socio-cultural factors encountered during the educational journey impede the realisation of an individual's full potential. This study explored how to harness the transformative power of transduction and measurement in mathematics education. The key connection between these activities is the shift from using the entire body for large macro movements to manipulating small objects at a micro level. This progression from bodily transformations to fine motor skills helps students link significant movements with precise tasks.
Our object is the Poisson integral for the upper half-space ℝ^n × (0,+∞ ) such that its boundary datum is integrable, non-negative, non-trivial and compactly supported. We show that the function is strictly -1/(n+1) -concave in the variable of ℝ^n if the variable of (0,+∞ ) is large enough compared with the diameter of the support of the boundary datum. For each α∈ (-1/(n+1),+∞ ) , we give a region in which the function is strictly α -concave in the variable of ℝ^n if the variable of (0,+∞ ) is large enough. For each α∈ (-1/(n+1),1] , we also give a region in which the function is not α -concave in the variable of ℝ^n .
The purpose of this paper is to prove the global L^∞ -boundedness of solutions for a Dirichlet nonlinear anisotropic elliptic systems with non standard growth conditions. The functional requirements involves anisotropic Lebesgue–Sobolev spaces in the scalar case and their ℝ^m -valued versions.
This paper presents a model for studying the processes involved in mathematics teacher professional development. Specifically, it focuses on professional development programs in which researchers in mathematics education act as teacher educators and collaborate with teachers in designing classroom activities and mathematical tasks for students. The model is constructed by combining the meta-didactical transposition framework, the documentational approach to didactics, and the construct of beliefs. Its evolution is described through an account of the subsequent developments and refinements. A general methodology for data collection and analysis is proposed, aimed at providing a nuanced understanding of the complex processes characterizing teacher professional development. This includes the examination of teachers’ and researchers’ meta-didactical praxeologies, documentation work, and beliefs, as well as the interrelations among these elements. For each version of the model, an example of application is provided to illustrate its modularity and the possibility of partial use. Finally, the application of the complete model in its final version is presented, showing how it can be fruitfully adopted to shed light on different yet complementary aspects of the processes under investigation.
