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 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…

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…

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…

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…

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…

Although school psychologists often comment on examinee motivation in their reports, systematic evaluation of effort is not common practice. Empirical assessment of performance effort provides critical evidence for the validity of evaluations and will likely lead to more valid assessments, recommendations, and placements. This article focuses on…

In this paper, a simple proof of the Morley's Trisector Theorem is presented which involves basic plane geometry only. The use of backward geometric approach, trigonometry or advanced mathematical techniques is not required. It is suitable for introducing to secondary or undergraduate students, as well as teachers or instructors for learning or…

The "k"-means clustering method, while widely embraced in college student typology research, is often misunderstood and misapplied. Many researchers regard "k"-means as a near-universal solution for uncovering homogeneous student groups, believing its success hinges primarily on the selection of an appropriate "k."…

The agreement between a wearable inertial sensor (GYKO, G) and the force platform (P) was assessed by evaluating "test-retest" and "inter-rater reliability." Thirty-eight subjects were enrolled; the selected indices of balance were investigated over foot positions and (un)stable conditions. Intraclass correlation coefficient…