An interesting geometric conservation problem is presented. Here proof is presented in a 'proof without words' style, with the aim of developing the reader's visual proof ability. The study of the task and its expansion is accompanied by a dynamic sketch to highlight the conservation property.

Combinatorial proofs of binomial identities involve establishing an identity by arguing that each side enumerates a certain set of outcomes. In this paper, we share results from interviews with experienced provers (mathematicians and upper-division undergraduate mathematics students) and examine one particular aspect of combinatorial proof, namely…

Rapid guessing (RG) is a form of non-effortful responding that is characterized by short response latencies. This construct-irrelevant behavior has been shown in previous research to bias inferences concerning measurement properties and scores. To mitigate these deleterious effects, a number of response time threshold scoring procedures have been…

Considerations related to generalization of a study's findings are often interconnected to researchers' judgements regarding the 'quality' of the methodology and methodological pluralism. Too often, researchers consider generalization as only possible with respect to quantitative studies with large numbers of randomly selected participants…

Eye gaze tracking has recently become indispensable for domains like virtual reality, augmented reality, human-computer interaction and advertisement. The commercial eye gaze tracking equipment is too expensive to be used by the masses. In this manuscript, a non-invasive, low-resolution ordinary camera-based system has been proposed for tracking…

The current study reviewed the practice and application of social validity assessments in single-case design (SCD) studies within the field of school psychology. Social validity refers to the acceptability of intervention or program goals, procedures, and outcomes to educators, families, and students. Understanding the ways social validity is…

This paper introduces the concept of logical consistency in students' thinking in mathematical contexts. We present the Logical in-Consistency (LinC) instrument as a valuable assessment tool designed to examine the prevalence and types of logical inconsistencies among undergraduate students' evaluation of mathematical statements and accompanying…

This article presents an inquiry-oriented lesson for teaching Lagrange's theorem in abstract algebra. This lesson was developed and refined as part of a larger grant project focused on how to "Orchestrate Discussions Around Proof" (ODAP, the name of the project). The lesson components were developed and refined with attention to how well…

This study aimed to develop and validate the Evaluator Competencies Assessment Tool (ECAT) Cultural Competencies Subscale, which measures cultural competence among evaluators. By addressing the scarcity of validated tools in this area, the study offers professionals a valuable resource to assess their strengths and areas for improvement. The…

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."…

This study aims to (1) produce an instrument for measuring college student entrepreneurial skills; (2) describe the quality of the measurement instrument for college students' entrepreneurial skills; (3) describe the practicality of the measurement instrument for college students' entrepreneurial skills. The method used in this study is the…

The Motivated Strategies for Learning Questionnaire (MSLQ) is one of the most widely used instruments to measure students' motivation and self-regulated learning. However, the MSLQ was developed and has been predominantly used in the Western context, is a domain-general measure, and is quite lengthy. Hence, adapting the MSLQ to the Chinese…

The Cognitive Test Anxiety Scale (CTAS) is a unidimensional scale designed to measure the cognitive aspect of test anxiety. The instrument has been adapted in several countries, and convincing psychometric properties have been found; however, uncertainties remain regarding its factor structure. Therefore, the aim of this study is twofold: to…