Basis vectors e[subscript alpha] play a useful role in special and general relativity. In particular they allow an expansion of the vectorial spacetime interval dl along infinitesimal curvilinear coordinate differences dl = e[subscript alpha]d[Xi][superscript alpha]: (thus the definition e[subscript alpha] = dl/d[Xi][superscript alpha]). In this…

In this article we consider two triangles: one inscribed in another. We prove that the area of the central triangle is at least the harmonic mean of the areas of corner triangles. We give two proofs of this theorem. One is based on Rigby inequality and the other is based on the known algebraic inequality, to which we bring a new, geometric, proof.…

The goal of this note is to obtain the area enclosed between a parabola and two tangent lines using visual arguments. The first step that we have to follow, in order to do that, is noticing that the area between a parabola and a tangent line only depends on the leading coefficient of the quadratic function of the parabola. Finally, the…

Parents and caregivers can use the activities in this report to help youth learn to solve algebra problems using different strategies. Knowing different strategies for solving algebra problems may help your child approach algebra problems with confidence. Children could apply the most appropriate strategy for a particular problem or could try a…

In teacher education, enhancing pre-service teachers' higher-order thinking skills (HOTs) is very crucial. The effect of comprehensive professional development in assessment for learning (AfL) on pre-service teachers' HOTs in an algebra course was investigated using a nonequivalent group quasi-experimental design. A total of 129 pre-service…

Proportional reasoning has been greatly influencing the development of students' mathematical abilities. Along with the area conservation ability, it helps elementary students comprehend area measurement. This exploratory study aimed to produce qualitative-descriptive data on elementary students' proportional reasoning in solving the conservation…

This article makes a case for introducing moving averages into introductory statistics courses and contemporary modeling/data-based courses in college algebra and precalculus. The authors examine a variety of aspects of moving averages and draw parallels between them and similar topics in calculus, differential equations, and linear algebra. The…

This article aims to delve into the meaning of school mathematical concepts by their semantic analysis. Concretely, this paper aimed primarily to describe and characterize the meaning of derivative of a function at a point expressed by mathematics pre-service teachers. In order to achieve this goal, we use a semantic framework, in which the…

The understanding of the relationships between pattern recognition and mathematical abilities is important for students in their learning of mathematics and mathematics teachers in the design of their teaching pedagogies. This study examines the connections between pattern recognition and mathematical abilities of students from four Singapore…

This document contains a model policy for state departments of education to create a K-8 Math Act or policy. The intent of such Legislature is that each student is prepared for success in Algebra I starting with 60 minutes of daily math instruction to build math proficiency in grades Kindergarten through 8 using effective, standards aligned…

In a small rural school district in the southeast, two high schools have both seen a decline in their enrollment, so the two high schools are merging into one facility until a new school is built. Naturally students have concerns about the proposed organization, with students at one school already having concerns about the current lunch schedule,…

College algebra is regarded as a gatekeeper course for attaining degrees, higher paying jobs, and overall individual empowerment. Educational stakeholders have reconsidered alternative instructional approaches such as computer-assisted instruction (CAI) to curb high failure rates and increase retention rates among college algebra students. One…

In response to decreasing motivation in high school math classrooms, teachers are transforming classrooms with various instructional techniques. Traditional math instruction relies on direct instruction and memorization of content, processes, and skills. Teachers are transitioning to more constructivist student-led approaches. Utilizing multiple…

Evidence suggests females' mathematics skills and abilities are not as well developed as males resulting in females being underrepresented in science, technology, engineering, and mathematics (STEM) career fields. In addition, self-directed learning readiness (SDLR) plays a role in academic performance, giving those with greater SDLR and…

This quantitative study focused on the Algebra 1 End-Of-Course Exam Program (EOCEP) exam that students must complete if they are enrolled in beginning algebra classes. The research focused on one school, the high schools within this school's district, and South Carolina. The purpose of the study was to determine if there was a relationship between…