SCIDAR - A Digital Archive of the University of Kragujevac

PROMOTION OF MATHEMATICS THROUGH THE INTEGRATION OF THE MATHEMATICAL KANGAROO COMPETITION, A STUDENT JOURNAL, A WEB PLATFORM, AND A YOUTUBE CHANNEL

This paper presents an innovative approach to the promotion of mathematics based on the integration of the Mathematical Kangaroo competition, the student magazine "Matematički list", an educational web platform, and a YouTube channel featuring video solutions to mathematical problems. The primary objective of this approach is to increase students' interest in learning mathematics, encourage autonomous study, and develop mathematical literacy by combining formal and informal educational ...

INTEGRATING NOTEBOOKLM IN MATHEMATICS EDUCATION USING THE FLIPPED CLASSROOM APPROACH

The flipped classroom model integrates two complementary segments: computer-assisted independent instruction outside the school setting and collaborative learning within the classroom. This process can be examined through three distinct chronological stages: pre-class, in-class, and post-class activities. During the preparatory phase (prior to in-class instruction), students are provided with carefully designed or curated digital learning materials – such as video lectures, podcasts, or...

BEYOND RIGHT AND WRONG: A WEB PLATFORM FOR LEARNING MATHEMATICS THROUGH THE ANALYSIS OF CORRECT AND INCORRECT PROBLEM SOLUTIONS

This paper presents the web platform Beyond Right and Wrong, developed with the aim of supporting mathematics teaching and learning through the analysis of offered problem solutions. The platform is based on an approach according to which students are not only required to recognize the correct solution, but also to identify, analyze, and evaluate errors in incorrect procedures, which corresponds to higher cognitive levels of learning in Bloom’s taxonomy. In this way, students develop cr...

DYNAMIC VISUALIZATION OF MATHEMATICAL CONCEPTS USING THE MANIM TOOL

The development of educational technologies has opened up new possibilities for improving mathematics teaching, particularly in the visualization of abstract concepts and processes. This paper examines the use of Manim as a tool for creating mathematically precise animations that can play a significant didactic role in the teaching process. Special emphasis is placed on the possibility of dynamically presenting various types of content whose understanding often requires more than a stat...

Shift-invariant subspaces of Sobolev type

This paper has the characteristics of a review paper in which results of shift-invariant subspaces of Sobolev type are summarized without proofs. The structure of shift-invariant spaces $V_s$, $s\in\mathbb{R}$, generated by at most countable family of generators, which are subspaces of Sobolev spaces $H^s(\mathbb{R}^n)$, are announced in \cite{aap} and Bessel sequences, frames and Riesz families of such spaces are characterized. With the Fourier multiplier $\left(1-\fracΔ{4π^2}\right)^{s/2}f=...

Shift-Invariant Subspaces of Sobolev Spaces and Shift-Preserving Operators

Sensor fault estimation in Markov jump linear system: A Bayesian perspective

Existing fault estimation methods for Markov jump linear systems, particularly the interacting multiple model approaches, heavily rely on pre-defined fault model banks. This reliance renders them ineffective against faults with unknown or time-varying dynamics. Conversely, emerging Bayesian estimation approaches are typically confined to single-mode systems and fail to accommodate stochastic mode switching. To bridge this gap, this paper proposes a novel Bayesian framework for the real-time j...

APPLICATION OF ORTHOGONALITY ON THE SEMICIRCLE IN SIGNAL PROCESSING

In 1987, in Gautschi W., Landau H.J, Milovanović G.V. Polynomials orthogonal on the semicircle, II. Constr. Approx. 1987;3:389–404. the weighted orthogonality on the semicircle and the corresponding orthogonal polynomials were introduced.. Orthogonality is defined using an integral over the area of the upper unit semicircle centered at the origin, without conjugating the second component. Later, the Gaussian quadrature rule on the semicircle was considered. After a long period of time, the au...

COMPREHENSION OF INTERPOLATION AMONG THIRD-YEAR HIGH SCHOOL STUDENTS TALENTED IN COMPUTER SCIENCE AND INFORMATICS

This paper presents the outcomes of a five year study conducted with third grade students from class for talented students in computer science and informatics at grammar school, within the subject Application of Computers. The research addresses the pedagogical challenge of introducing advanced mathematical concepts, specifically interpolating polynomial, at an early stage of education. The aim was to evaluate both the effectiveness of instructional methods and the depth of student understand...