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…

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 mathematics curricula of Australia (ACARA, 2019), Scotland, England and America all require an understanding of proof by contradiction. Specifically, proof by contradiction is included as a Geometry topic in Specialist Mathematics (Version 8.4). In Specialist Mathematics, it is expected that students construct proofs in a variety of contexts…

A group of eighth-graders was presented with a two-day lab exploring graph theory as an enrichment experience. With the school's winter break looming, students were weary of solving linear equations, and this topic was intended to inject some new life into the classroom. In addition to learning about a completely new topic, they would be exposed…

Assessments are one of the most important--and often misunderstood--elements of education. In most cases, tests are administered by the state as well as by districts and schools. Assessments at each of these levels have distinct purposes, yield different information, and are part of a powerful, coordinated approach to improving student outcomes.…

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…

The Comprehensive Assessment System (CAS) Framework presents a vision for a system of assessments for English Learners in secondary grades that brings assessment closer to the classroom and fully involves teachers in assessment development and validation. The CAS Framework is intended to signal a new and equitable direction and to provoke…

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 article provides a detailed review of the Computer-based English Listening Speaking Test (CELST) used in Guangdong, China, as part of the National Matriculation English Test (NMET) to assess students' English proficiency. The CELST measures listening and speaking skills as outlined in the "English Curriculum for Senior Middle…

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…

Undergraduate mathematics instructors are called by many current standards to promote prospective teachers' learning of geometry from a transformation perspective, marking a change from previous standards. The novelty of this situation means it is unclear what is involved in undergraduate learning and teaching of geometry from a transformation…

While participating as a mentor teacher in a professional development project, Alison Vickery, a middle school teacher, developed a strategy: claim-rule-connection (CRC). The "claim" was the answer or response to the question; the "rule" was the theorem, fact, or proof; and the "connection" was an explanation of how…

The population of young language minority (LM) students is rapidly growing worldwide due to global migration and immigration trends. The increasing representation of young LM students in school settings creates high demand for the language assessment of LM students in order to meet the needs of stakeholders, such as governments and language…

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…