Search results for "mathematics"
showing 10 items of 22031 documents
Case study on teachers’ contribution to children’s participation in Finnish preschool classrooms during structured learning sessions
2013
The main aim of this study was to identify different teaching practices and explore the types of opportunities that they provide for children’s participation in four different Finnish preschool classrooms for 6-year olds during structured learning sessions. Observational data of four preschool teachers were analyzed according to the principles of qualitative content analysis. Three themes of teachers’ practices were identified, which described the key practices through which teachers influence children’s participation, namely, through discussion and conversations; by referring to shared rules and managing the classroom; and through demonstrating pedagogical sensitivity and understanding tow…
Sur la dynamique des acquisitions à l'école élémentaire
1987
On the dynamics of learning in elementary schools. - The statistical results presented in this paper are based on data from a longitudinal survey of elementary school children in the Dijon area. They provide strong support for the hypothesis — which stresses the cumulative aspect of learning, predicting that better mastery of concepts and higher levels of initial learning are inputs which aid in further acquisition of learning — indicating that differences in learning in grade 1 that are attributable to pedagogical inputs exert a large and statistically significant effect on learning in grades 2 and 3.
“You really brought all your feelings out” – Scaffolding students to identify the socio-emotional and socio-cognitive challenges in collaborative lea…
2021
Abstract The aim of this study is to explore how students experience and describe socio-cognitive and socio-emotional challenges in collaborative learning. The participants (N = 20) were teacher education students whose collaborative learning was supported with a designed regulation macro script during a six-week mathematics course. The purpose of the script was to provide structured phases during the collaborative learning tasks for the group members to plan, monitor, and evaluate their workings. The video data of groups' face-to-face work was collected and analysed by focusing on the different types of challenges the groups experienced and the types of challenges they described during the…
On the Almost Everywhere Convergence of Multiple Fourier-Haar Series
2019
The paper deals with the question of convergence of multiple Fourier-Haar series with partial sums taken over homothetic copies of a given convex bounded set $$W\subset\mathbb{R}_+^n$$ containing the intersection of some neighborhood of the origin with $$\mathbb{R}_+^n$$ . It is proved that for this type sets W with symmetric structure it is guaranteed almost everywhere convergence of Fourier-Haar series of any function from the class L(ln+L)n−1.
Better numerical approximation by Durrmeyer type operators
2018
The main object of this paper is to construct new Durrmeyer type operators which have better features than the classical one. Some results concerning the rate of convergence and asymptotic formulas of the new operator are given. Finally, the theoretical results are analyzed by numerical examples.
Estimates for the differences of positive linear operators and their derivatives
2019
The present paper deals with the estimate of the differences of certain positive linear operators and their derivatives. Oxur approach involves operators defined on bounded intervals, as Bernstein operators, Kantorovich operators, genuine Bernstein-Durrmeyer operators, and Durrmeyer operators with Jacobi weights. The estimates in quantitative form are given in terms of the first modulus of continuity. In order to analyze the theoretical results in the last section, we consider some numerical examples.
Better approximation of functions by genuine Bernstein-Durrmeyer type operators
2018
The main object of this paper is to construct a new genuine Bernstein-Durrmeyer type operators which have better features than the classical one. Some direct estimates for the modified genuine Bernstein-Durrmeyer operator by means of the first and second modulus of continuity are given. An asymptotic formula for the new operator is proved. Finally, some numerical examples with illustrative graphics have been added to validate the theoretical results and also compare the rate of convergence.
Exact Fourier expansion in cylindrical coordinates for the three-dimensional Helmholtz Green function
2009
A new method is presented for Fourier decomposition of the Helmholtz Green Function in cylindrical coordinates, which is equivalent to obtaining the solution of the Helmholtz equation for a general ring source. The Fourier coefficients of the Helmholtz Green function are split into their half advanced+half retarded and half advanced-half retarded components. Closed form solutions are given for these components in terms of a Horn function and a Kampe de Feriet function, respectively. The systems of partial differential equations associated with these two-dimensional hypergeometric functions are used to construct a fourth-order ordinary differential equation which both components satisfy. A s…
Frame-related Sequences in Chains and Scales of Hilbert Spaces
2022
Frames for Hilbert spaces are interesting for mathematicians but also important for applications in, e.g., signal analysis and physics. In both mathematics and physics, it is natural to consider a full scale of spaces, and not only a single one. In this paper, we study how certain frame-related properties of a certain sequence in one of the spaces, such as completeness or the property of being a (semi-) frame, propagate to the other ones in a scale of Hilbert spaces. We link that to the properties of the respective frame-related operators, such as analysis or synthesis. We start with a detailed survey of the theory of Hilbert chains. Using a canonical isomorphism, the properties of frame se…
Frames and weak frames for unbounded operators
2020
In 2012 G\u{a}vru\c{t}a introduced the notions of $K$-frame and of atomic system for a linear bounded operator $K$ in a Hilbert space $\mathcal{H}$, in order to decompose its range $\mathcal{R}(K)$ with a frame-like expansion. In this article we revisit these concepts for an unbounded and densely defined operator $A:\mathcal{D}(A)\to\mathcal{H}$ in two different ways. In one case we consider a non-Bessel sequence where the coefficient sequence depends continuously on $f\in\mathcal{D}(A)$ with respect to the norm of $\mathcal{H}$. In the other case we consider a Bessel sequence and the coefficient sequence depends continuously on $f\in\mathcal{D}(A)$ with respect to the graph norm of $A$.