arXiv subjects

Olha Pelekhata

Publications and source records attributed to Olha Pelekhata.

3 recordsLinked to original sources

arXiv2026

A Psychometric and Practical Comparison of Standard Moodle-Based and STACK-Based Step-by-Step Tests in University Calculus

This paper compares two formats of online assessment in university Calculus: a standard Moodle-based step-by-step test and a STACK-based step-by-step test. Both tests assess integration by parts and divide the solution into consecutive response fields, but they differ in their validation mechanisms. The standard test relies on predefined scoring patterns, whereas the STACK-based test uses symbolic validation rules. The comparison is based on final manually verified scoring matrices from two student cohorts and follows a Classical Test Theory framework, including score distributions, reliability estimates, response-field-level indicators, and correlation-based measures. The results show high overall performance and ceiling effects in both formats. However, the STACK-based test required fewer manual corrections, showed higher internal consistency, and produced a more coherent relationship between solution steps and the total score.

math.HO↗

arXiv2020

Approximation properties of multipoint boundary-value problems

We consider a wide class of linear boundary-value problems for systems of $r$-th order ordinary differential equations whose solutions range over the normed complex space $(C^{(n)})^m$ of $n\geq r$ times continuously differentiable functions $y:[a,b]\to\mathbb{C}^{m}$. The boundary conditions for these problems are of the most general form $By=q$, where $B$ is an arbitrary continuous linear operator from $(C^{(n)})^{m}$ to $\mathbb{C}^{rm}$. We prove that the solutions to the considered problems can be approximated in $(C^{(n)})^m$ by solutions to some multipoint boundary-value problems. The latter problems do not depend on the right-hand sides of the considered problem and are built explicitly.

math.CA↗

arXiv2017

On Kiguradze theorem for linear boundary value problems

We investigate the limiting behavior of solutions of nonhomogeneous boundary value problems for the systems of linear ordinary differential equations. The generalization of Kiguradze theorem (1987) on passage to the limit is obtained.

math.CA↗