In an introductory physics course where students first learn about vectors, they oftentimes struggle with the concept of vector addition and decomposition. For example, the classic physics problem involving a mass on an inclined plane requires the decomposition of the force of gravity into two directions that are parallel and perpendicular to the…

This article describes a probability project used in an upper division, one-semester probability course with third-semester calculus and linear algebra prerequisites. The student learning outcome focused on developing the skills necessary for approaching project-sized math/stat application problems. These skills include appropriately defining…

Kaminski, Sloutsky, and Heckler (2008a) published in "Science" a study on "The advantage of abstract examples in learning math," in which they claim that students may benefit more from learning mathematics through a single abstract, symbolic representation than from multiple concrete examples. This publication elicited both enthusiastic and…

In this study, middle school students' abilities to translate mathematical texts into algebraic representations and vice versa were investigated. In addition, students' difficulties in making such translations and the potential sources for these difficulties were also explored. Both qualitative and quantitative methods were used to collect data…

A good-quality teacher may determines a good-quality learning, thus good-quality students will be the results. In order to have a good-quality learning, a lot of strategies and methods can be adopted. The objective of this research is to improve students' ability in determining the rules of a numeric sequence and analysing the effectiveness of the…

Background/Context: This opening article, like the other articles in this special issue, is situated in scholarship that attempts to understand the racialized nature of mathematics education in the United States and to examine the racial identities of students and teachers in the context of school mathematics. It is designed to respond to the…

This study was designed to forge stronger theoretical and empirical links between achievement goal theory and attribution theory. High school students ("N" = 224) completed a self-report survey that assessed 3 types of achievement goals, 7 types of attributions, and self-efficacy. Results indicated that students' adoption of achievement…

The ACT College Readiness Benchmarks are the ACT® College Readiness Assessment scores associated with a 50% chance of earning a B or higher grade in typical first-year credit-bearing college courses. The Benchmarks also correspond to an approximate 75% chance of earning a C or higher grade in these courses. There are four Benchmarks, corresponding…

There is a growing view that students who enroll in developmental courses are less successful in completing their programs than non-developmental students. Nevertheless, even though developmental students as a group ultimately might not be as academically successful as non-developmental students, many of them might still derive benefit from taking…

This study examined how preservice secondary mathematics teachers developed mathematical knowledge for teaching (MKT) around representations and big ideas through mathematics and mathematics education courses. The importance of big ideas and representations in mathematics has been emphasized in national standards as well as in literature. Yet,…

Beginning algebra is a gatekeeper course into the pipeline to higher mathematics courses required for respected professions in engineering, science, statistics, mathematics, education, and technology. Beginning algebra can also be a perfect storm if the necessary foundational skills are not within a student's grasp. What skills ensure beginning…

Background: American students have done poorly in algebra and that has generated policy concerns about preparing students for STEM careers. There has been growing recognition that the algebra problem may begin in earlier grades when students do not adequately master rational numbers. Purpose: The study provided a series of workshops organized…

A folded symplectic form on an even-dimensional manifold is a closed two-form that degenerates in a suitably controlled way along a smooth hypersurface. When a torus having half the dimension of the manifold acts in a way preserving the folded symplectic form and admitting a moment map, the manifold is called a folded symplectic toric manifold.…

In this thesis, our aim is the study the Vanishing of Maps of Tor Conjecture of Hochster and Huneke. We mainly focus on an equivalent characterization called the Strong Direct Summand Conjecture, due to N. Ranganathan. Our results are separated into three chapters. In Chapter 3, we prove special cases of the Strong Direct Summand Conjecture in…

Primary teachers play a key role in their students' future mathematical success in the early secondary years. While the word "algebra" may make some primary teachers feel uncomfortable or worried, the basic arithmetic ideas underlying algebra are vitally important for older primary students as they are increasingly required to use "algebraic…