In many mechanical engineering undergraduate curriculums, there are topics that are vital to the students' future careers in the manufacturing and design workforce that are not taught in-depth. As one of those topics, Geometric Dimensioning and Tolerancing, or GD&T, is vital to companies who develop and manufacture products because it allows…

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 article is based on the author's experiences as a second-year teacher at a small private school teaching all sections of Geometry and Algebra 2. Working with the same students in both courses, the author was aware of each one's levels of retention and execution of Algebra 1 concepts before the beginning of the year. The author often noticed…

During middle school years, students generally finalise their attitude toward mathematics and their perception of themselves as students of mathematics in terms of aptitude, motivation, interest, and competence. Therefore, giving them varied opportunities to foster a positive and successful approach to the study of mathematics is critical, and can…

Innovative education is a higher training requirement for education in the period of social transformation. It needs the education to cultivate talents with innovative consciousness and ability for the development of society. High school is critical for facilitating students' innovative consciousness, innovative thinking, and innovative ability…

The primary goal of this paper is to provide a commentary on the teaching and learning of geometry in the early years of schooling with the set of papers in this issue as a guiding factor. It is structured around issues about geometry education of young learners, such as: what should we teach in geometry and why; representation of geometrical…

As part of its proposal to the U.S. Department of Education, the Partnership for Assessment of Readiness for College and Careers (PARCC) committed to developing model content frameworks for mathematics to serve as a bridge between the Common Core State Standards and the PARCC assessments. The Model Content Framework for Mathematics for each grade…

Driven by faculty-based action research, redesigned residential and online courses, and changes to placement testing, Rasmussen College increased its developmental education pass rates by double digits while decreasing the number and percentage of students who require remedial coursework. Like many institutions of higher education, Rasmussen…

International calls have been made for reasoning-and-proving to permeate school mathematics. It is important that efforts to heed this call are grounded in an understanding of the opportunities to reason-and-prove that already exist, especially in secondary-level geometry where reasoning-and-proving opportunities are prevalent but not thoroughly…

In this article, I (a) illustrate how the K-2 CCSSM reflect the major findings from research studies carried out over the last 30 years on early mathematical abilities that indicate these standards are developmentally appropriate for young children, and (b) offer insights into some types of instructional strategies (e.g., student-centered…

Algebraic solving ability had been discussed by many educators and researchers. There exists no definite definition for algebraic solving ability as it can be viewed from different perspectives. In this paper, the nature of algebraic solving ability in terms of algebraic processes that demonstrate the ability in solving algebraic problem is…

This article was inspired by a set of 12 cylindrical cups, which are volumetrically indexed; that is to say, the volume of cup "n" is equal to "n" times the volume of cup 1. Various sets of volumetrically indexed cylindrical cups are explored. I demonstrate how this children's toy is ripe for mathematical investigation, with connections to…

An earlier paper discussed the case of a flexible but inextensible membrane filled to capacity with incompressible fluid. It was found that the resulting shape satisfies a set of three simultaneous partial differential equations. This article gives a more general derivation of these equations and shows their form in an interesting special case.

The wealth of assessment options that exists offers teachers and students a "menu" of selections. Just as matching appetite needs with appropriate food selection is fundamental to a successful dining experience, matching assessment options to targeted achievement needs is crucial to an effective assessment experience. The author uses a…

The article demonstrates that multiple solution tasks (MSTs) in the context of geometry can serve as a research instrument for evaluating geometry knowledge and creativity. Geometry knowledge is evaluated based on the correctness and connectedness of solutions, whereas creativity is evaluated based on a combination of fluency, flexibility, and…