For a given rational number r, a classical theorem of Niven asserts that if cos(rp) is rational, then cos(rp) [element-of] {0,±1,±1/2}. In this note, we extend Niven's theorem to quadratic irrationalities and present an elementary proof of that.

Literary discussions are widely utilized in education, yet their profound impact on students' comprehension requires in-depth exploration. This paper delves into the influence of literary discussions on student comprehension and examines how these discussions can enhance students' understanding and analytical skills. Through literature reviews and…

Teaching leadership in today's world requires a combination of introducing theory and best practices, as well as allowing moments that are happening in real-time, both current events and interactions from the "laboratory" of the classroom, to affect the teaching agenda. Instructors can lean into the model of Intentional Emergence (IE) to…

Regression discontinuity (RD) designs are increasingly used for causal evaluations. For example, if a student's need for a literacy intervention is determined by a low score on a past performance indicator and that intervention is provided to all students who fall below a cutoff on that indicator, an RD study can determine the intervention's main…

The assessment of instructional quality has been and continues to be a desirable, yet difficult endeavor in higher education. The development of new teaching evaluation frameworks along with instruments to measure various aspects of teaching practices holds promise. The challenge rests in the implementation of these frameworks and measures in…

A majority of American adults value the role that art plays in education at the K-12 level. However, the potential benefits of arts-based, kinesthetic learning activities have not been well-documented at the college level. Twenty-three undergraduate students participated in passive learning, traditional active learning activities and arts-based…

The evaluation of teacher's work has traditionally been a cornerstone of educational systems worldwide, driven by the need to maintain educational standards and ensure teacher accountability. Recognizing the limitations of conventional evaluation practices, a growing movement advocates for a more sustainable and inclusive approach that values the…

Mathematics is often taught by lecturing students on how to perform procedures, but it could be taught in ways that promote active student engagement and develop deep conceptual understanding. Research supports the latter approach as better for students' retention, engagement, and success with learning mathematics. An important time to influence…

Numerous studies indicate that new nursing graduates lack the ability to respond quickly in situations with deteriorating patients and are struggling with competency and clinical judgment. As healthcare increases in complexity and the nursing workforce declines, new and innovative teaching methods are needed for clinical experiences to produce…

Despite the increasing number of coding initiatives to promote computational thinking (CT), their main focus on in-service teachers in large school districts of the big cities far from exemplifies opportunities for preservice teachers (PSTs) to learn how to promote it in rural elementary school settings. As a preliminary step, this research…

Teacher evaluation systems have evolved over centuries based on how cultures view the profession. Currently, one of the most used evaluation tools is Danielson's framework for teaching (FFT), which has been in use for over 20 years. In this qualitative study, 12 teachers across different high schools shared their experiences of the framework's…

The "Building Your Research Data Management Toolkit" was developed to provide introductory research data management skills training to liaisons in academic libraries. This paper assesses the participants' perceived change in knowledge, behaviors and attitudes as a result of participation in the RoadShow program. Long term changes in…

The American Speech-Language-Hearing Association (ASHA) Code of Ethics (2023) requires all practitioners to uphold the welfare of others without discrimination. Graduate programs in communication sciences and disorders, therefore, must guide future clinicians to apply theoretical knowledge to clinical practice equitably and inclusively. This…

The rapid growth of culturally and linguistically diverse populations in K-12 schools has increased the need for preparing culturally responsive teachers. Yet, many pre-service teachers feel unprepared to work with diverse students. With the urgent need to connect educational theory to classroom practice, teacher preparation programs have turned…

Mathematical modeling is crucial in the field of education, particularly in mathematics, as it enhances students' mathematical skills and prepares them for solving real-world problems. The study focuses on the challenges of teaching mathematical modeling, specifically in the Malaysian education system. We utilized a case study approach, involving…