New nationwide data collected by the U.S. Department of Education's civil rights office reveal stark racial and ethnic disparities in student retentions, with black and Hispanic students far more likely than white students to repeat a grade, especially in elementary and middle school. The contrast is especially strong for African-Americans. In the…

Background: Exposure to mathematical pattern tasks is often deemed important for developing children's algebraic thinking skills. Yet, there is a dearth of evidence on the cognitive underpinnings of pattern tasks and how early competencies on these tasks are related to later development. Aims: We examined the domain-specific and domain-general…

This study examined prospective middle grade mathematics teachers' knowledge of algebra for teaching with a focus on knowledge for teaching the concept of function. 115 prospective teachers from an interdisciplinary program for mathematics and science middle teacher preparation at a large public university in the USA participated in a survey. It…

In this paper we compare how three teachers, one from each of Finland, Flanders and Hungary, introduce linear equations to grade 8 students. Five successive lessons were videotaped and analysed qualitatively to determine how teachers, each of whom was defined against local criteria as effective, addressed various literature-derived…

This qualitative case study explored how students learning Maths at an Irish institute of higher education benefited from their instructor's use of self-developed screencasts. The screencasts (47 in total) were posted on the institute's Maths Moodle site for students to access. One hundred and thirty-eight (n = 138) students participated in an…

National attention is focused on the persistent high failure rates for students enrolled in math courses, and the search for strategies to change these outcomes is on. This study used a mixed-method research design to assess the effectiveness of a learning community course designed to improve the math performance levels of firstyear students.…

This research examined differences in causal attributions and an exam score in a developmental mathematics course based on student classification: traditional, minimally nontraditional, moderately nontraditional, and highly nontraditional as well as grade and gender among nontraditional students. Statistical analysis revealed significant…

The Rhode Island Department of Education determined that 56% of high school juniors in public schools are not meeting mathematics performance standards. If a student is not proficient in school, then his or her ability and desire to continue education are diminished, raising the chances of drop out. Hispanic students have the highest dropout rate…

Automobile sunshades always fold into an "odd" number of loops. The explanation why involves elementary topology (braid theory and linking number, both explained in detail here with definitions and examples), and an elementary fact from algebra about symmetric group.

Even in the highest-level mathematics courses at undergraduate institutions, most students do not read mathematical research from professional journals. Such depth of content is often reserved for "independent studies" or summer REU's. In this article I describe a course that required students to read research papers, all of which centered on a…

Rayleigh's criterion states that a pair of point sources are barely resolved by an optical instrument when the central maximum of the diffraction pattern due to one source coincides with the first minimum of the pattern of the other source. As derived in standard introductory physics textbooks, the first minimum for a rectangular slit of width "a"…

Following an introduction to the diagonalization of matrices, one of the more difficult topics for students to grasp in linear algebra is the concept of Jordan normal form. In this note, we show how the important notions of diagonalization and Jordan normal form can be introduced and developed through the use of the computer algebra package…

We will prove a well-known theorem in Linear Algebra, that is, for any "m x n" matrix the dimension of row space and column space are the same. The proof is based on the subject of "elementary matrices" and "reduced row-echelon" form of a matrix.

Local influence analysis is an important statistical method for studying the sensitivity of a proposed model to model inputs. One of its important issues is related to the appropriate choice of a perturbation vector. In this paper, we develop a general method to select an appropriate perturbation vector and a second-order local influence measure…

Commencing in 2011, the Mathematics Academies Initiative is a series of professional development academies (lasting 1 to 2 years, depending on cohort) with the primary objectives of (a) providing educators with a high quality professional development experience that enhances their mathematical content knowledge and pedagogical skills, and (b)…