In classical calculus textbooks, the existence of primitive functions of continuous functions is proved by using Riemann integrals. Recently, Patrik Lundström gave a proof via polynomials, based on the Weierstrass approximation theorem. In this note, it is shown that the proof will be easy by using continuous piecewise linear functions.

A fascinating and catchy method for proving that a number of special lines concur is using the concept of locus. This is now the classical method for proving the concurrency of the internal angle bisectors and perpendicular side bisectors of a triangle. In this paper, we prove the concurrency of the altitudes and the medians by showing that they…

The present study explores the sources of validity evidence of the mathematics self-concept construct in Programme for International Student Assessment (PISA) 2022 with a focus on concurrent, discriminant, and predictive evidence. Mathematics self-concept was provided with a single index variable in PISA 2022. Using only the U.S. students who…

The orthogonality of eigenfunctions in problems of unsteady heat conduction in an infinite slab with symmetric and nonsymmetric convective boundary conditions are demonstrated by performing actual integration of the products of the derived forms of eigenfunctions and by implementing the corresponding eigenvalue conditions. The analysis also…

Between limb strength, asymmetry is a leading risk factor for hamstring strain re-injury. However, few accurate testing methodologies are available in clinical settings. This study examined the validity and reliability of eccentric knee flexor torque measured with a novel Nordic Hamstring Device. Twenty-seven healthy participants were assessed in…

Using the basic properties of the base-b representation of rational numbers, we will give an elementary proof of Gauss's lemma: "Every real root of a monic polynomial with integer coefficients is either an integer or irrational." The paper offers a new perspective in understanding the meaning of 'irrational numbers' from a deeper…

Purpose: The primary objective of this research paper was to examine the objectivity of the preselected items evaluation (PIE) method, a prevalent translation scoring method deployed by international institutions such as UAntwerpen, UGent and the University of Granada. Design/methodology/approach: This research critically analyzed the scientific…

In this article, we state an interesting geometric conservation property between the three angle bisectors of three similar right triangles and provide a proof without words for its justification. A GeoGebra applet is also presented to help with the understanding of the progression of the proof from inductive to deductive stage.

In this paper, we provide a conceptual framework of the central aspects of mathematical definitions discussed in the mathematics education literature. Based on a systematic literature review, we found that characterizations of definitions in the mathematics education literature can be classified into five main themes: requirements, preferred…

Intra-organizational relationships have become common in higher education. Scholars have offered limited knowledge about the ways in which ancillary organizations pursue and maintain intra-organizational relationships in higher education. Notably, the literature provides no examination of their legitimacy-seeking efforts. Based on data collected…

Computational thinking (CT) assessment is crucial for testing the effectiveness of CT skills development. However, the exploration of CT assessment in the context of text-based programming is in its initial stages. The intrinsic relationship between the core skills of text-based programming and the core elements of CT isn't analyzed in depth in…

This study aimed to assess the agreement in physical activity (PA) estimates from Garmin Vivofit Jr. 3 (VFJ 3) and Fitbit Ace 3 (Ace 3) with a research-grade accelerometer (wGT3X-BT) in children under free-living conditions. Twenty-five children (Girls: 56%, Age: 10.1 ± 2.5 years, BMI: 17.1 ± 2.4 kg/m2) performed daily activities for 7 consecutive…

Background: Existing literature failed to explore the parental expectations and experiences from physiotherapy for children with Down syndrome. Hence, we aimed to validate a semi-structured interview guide to explore parental experiences and expectations from physiotherapy for children with Down syndrome. Methods: A 28-item interview guide was…

This is the second article in a series of three in this special issue on establishing a boundary object to foster network health and development. The first article laid out the theoretical rationale for an Improvement Network Health and Development Framework. This article details the efforts to develop a set of practical measures tied to this…

Studies have shown that raising L2 learners' metaphor awareness contributes to the acquisition of figurative language, which fosters students' development of language skills. However, the instruments measuring metaphor awareness, in the majority of relevant research, did not seem to have undergone proper methodological procedures for checking…