In high school geometry, students are expected to deepen their understanding of geometric shapes and their properties, as well as construct formal mathematical proofs of theorems and geometric relationships. The process of helping students learn to construct a geometric proof can be challenging given the multiple competencies involved (Cirillo…

Constructing mathematical proofs is a fundamental yet challenging skill in secondary school geometry. While technology has been used to scaffold different aspects of the proving process, existing approaches often separate inquiry and conjecturing from formal proof or focus on structural and technical assistance without addressing students' initial…

Proof, as a central and integral part of mathematics, is an essential component of mathematical education and is considered as the basic procedure for revealing the truth of mathematical propositions and for teaching productive reasoning as part of human civilization. Is there therefore room for conjectures in mathematics? In this paper after…

The EdSurvey package helps users download, explore variables in, extract data from, and run analyses on large-scale assessment data. The analysis functions in EdSurvey account for the use of plausible values for test scores, survey sampling weights, and their associated variance estimator. We describe the capabilities of the package in the context…

We present action research of a problem posed as part of a multi-participant national (Israeli) test checking the mathematical knowledge of high school students at the ages of 16-17, where some of those who solved this problem made an error by using the converse to a well-known theorem, where the converse is not true. In order to examine the…

This technical manual provides an overview of the Mosaic™ by ACT®: Social Emotional Learning Screener. The Mosaic by ACT: Social Emotional Learning Screener (hereafter referred to as the Screener) assesses the social emotional skills of students in elementary school (Grades 3-5), middle school (Grades 6-8), and high school (Grades 9-12). Each…

Mathematics in its nature is exploratory, giving learners a chance to view it from different perspectives. However, during most of their schooling, South African learners are rarely exposed to mathematical explorations, either because of the lack of resources or the nature of the curriculum in use. Perhaps, this is due to teachers' inability to…

The worldwide consequences of the COVID-19 pandemic affected virtually every domain of human life. The pandemic's impact on the education and development of children and adolescents was particularly severe given the closure of schools, shifts to online learning, and cancelation of college entrance exam administrations early in the pandemic. These…

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…

In this paper, we propose an elementary proof of Niven's Theorem in which the tangent function will have a primary role.

Proof plays many important roles in mathematics. Proofs should do more than simply verify that a statement is true; instead, a proof should also explain why a statement is true and enrich both the author's and the readers' understanding of the statement and important mathematical ideas within it. Common practice in high school geometry classrooms…

Educational institutions around the world have been integrating AI into their educational practices. Many studies and reports highlight both the advantages and disadvantages of this integration. This paper focuses on the positive aspects of AI in education, specifically through the lens of a high school geometry project at a technology-focused…

Inside the discipline, mathematical work consists of the interplay between stating and refining conjectures and attempting to prove those conjectures. However, the mathematical practices of conjecturing and proving are traditionally separated in high school geometry classrooms, despite some research showing that students can successfully navigate…

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…

We perform dynamic investigation of two surprising geometrical properties, each of which involves additional properties. In the first task the property belongs to two regular polygons with the same number of sides and with one common vertex. It is found that all the straight lines that connect corresponding vertices of the two polygons intersect…