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…

In this paper, we examine the concept definitions a group of South African upper secondary school mathematics teachers (N = 47) express and how their understanding of the truth value, the role of variable and the syntax of expression appear in the participants' explanations for their assessment of examples and non-examples of equations. We use…

This causal-comparative study was designed to address an increasing educational trend: providing interventions to students who passed a No Child Left Behind tested course but who failed the accompanying high school assessment in one Maryland public school system. The purpose of the study was to determine which of three intervention types…

This Capstone project studied a pilot of the web-based homework system "Hawkes" in developmental mathematics classes at a mid-sized community college. The purpose of the study was to investigate how three instructors of developmental mathematics courses incorporated "Hawkes" in their classes, what obstacles they encountered,…

The importance of understanding the various uses of the literal symbol in algebra, and in particular the idea of generalised number, is well documented in the literature. Many research findings have also reported student difficulties with this vital and central concept. This research study examines the use of a combination of historical and…

New laws in California have set the state on a course for some potentially significant changes to the curriculum, including a measure that revisits the matter of teaching Algebra 1 in 8th grade and another that revamps the state's textbook-adoption process and hands districts greater leeway in choosing instructional materials. The algebra-related…