Problem solving and proofs have always played a major role in mathematics. They are, in fact, the heart and soul of the discipline. The using of a number of different proof techniques for one specific problem can display the beauty, and elegance of mathematics. In this paper, we present one specific, interesting geometry problem, and present four…

This technical report provides an authoritative bibliographic resource of all the studies conducted on "easyCBM"® and published on the main website for Behavioral Research and Teaching under Publications (https://brtprojects.org). The "easyCBM"© software is a direct descendent of "Curriculum-based Measurement" (CBM)…

This paper highlights as issues of concern the rapid changes in technology and the tendency to report on partial validation efforts where the work is not identified as forming part of a larger validation project. With close human supervision emerging technologies can have a significant and positive impact on language testing. While technology…

Nurse educators at the undergraduate level spend significant time developing and revising exam questions. Following the exam administration, course faculty have the opportunity to complete an item analysis and question revision to improve reliability and validity. A challenge faculty face is tracking these exam changes when teaching as part of a…

The cutting-edge technology, namely Cloud of Things (CoT) has shaped the existing business process into a new orientation in terms of performance, usability, and reliability. Among different business processes, online education is one of the prime areas where CoT can be used to make it more agile in the context of performance and usability. In…

This paper discusses strategies that two high school geometry teachers employed to solve a challenging geometry problem with the aid of dynamic geometry software (The Geometer's Sketchpad (GSP). The teachers were part of a group of teachers who participated in a summer professional institute funded by the National Science Foundation. The paper…

This short note presents and discusses an interesting area partition result related to a parallelogram. It is, then, shown how proving the result, and understanding why the result is true based on the principle of conservation of the area of triangles with the same base and between the same parallel lines, leads to further generalizations to…

The article presents some examples of plane geometric variance of an area with the use of computer technology. These tools can offer teachers opportunities for adaptation and preparation of pedagogical presentations which will help students along the process of fruitful conjectures formation and eventually construction of formal deductive proofs.…

Valid proofs need not be in the traditional two-column format. This classroom activity allows students to explore, discuss, and use specialized facts to create a general statement of truth.

The emergence of 21st-century skills convinced educational institutions in modifying teaching styles, which lead to the introduction of blended, flipped, and personalized learning. Studies demonstrated present-day best practices, but none provided a practical assessment procedure. Thus, this study aimed to develop a tool in evaluating learning…

As teachers of mathematics we encourage our students to ask good questions, and we strive to help our students find and understand answers to these questions. This journey can be made more meaningful if students conclude by reflecting on their learning process. If we find careful questioning and reflection important, we should include such…

A summary of an experimental course on algebraic curves is given that was held for young learners at age 11. The course was a part of Epsilon camp. a program designed for very gifted students who have already demonstrated high interest in studying mathematics. Prerequisites for the course were mastery of Algebra I and at least one preliminary year…

In a study about pre-service secondary mathematics teachers' (PSMTs) understanding about the nature of theorems in geometry, the researcher noticed that it was challenging for the PSMTs to visualize and draw counterexamples to disprove the given mathematical statements. Meanwhile, the use of the dragging feature of dynamic geometry environments…

Students use GeoGebra to explore the mathematical relations among different radii of circles in a triangle (circumcircle, incircle, excircles) and the sides and other segments in the triangle. The more formal mathematical development of the relations that follows the explorations is based on known geometrical properties, different formulas…

The purpose of this paper is to provide examples of "non-traditional" proof-related activities that can explored in a dynamic geometry environment by university and high school students of mathematics. These propositions were encountered in the dynamic geometry environment. The author believes that teachers can ask their students to…