In 2024, the National Center for Education Statistics (NCES) administered the National Assessment of Educational Progress (NAEP) mathematics assessment to representative samples of fourth- and eighth-grade students in the nation, states, the District of Columbia, Puerto Rico, Department of Defense schools, and 26 participating large urban…

The Programme for International Student Assessment (PISA) is an international comparative study that assesses how well 15-year-olds, who have nearly completed compulsory schooling in most participating educational systems, can use their knowledge and skills to meet real-world opportunities and challenges. In each cycle of PISA, students are…

The current project, Exploring Math Education Relations by Analyzing Large Data Sets (EMERALDS) II, is an attempt to identify specific Common Core State Standards procedural, conceptual, and problem-solving competencies in earlier grades that best predict success in algebraic areas in later grades. The data for this study include two cohorts of…

This report describes efforts to measure teachers' knowledge of their own students' abilities in mathematics and offers preliminary findings. It provides a description of the sample, a description of the study design and its realization, and descriptive statistics for teacher judgment accuracy. The work described here was completed as part of a…

Socio-economically advantaged and disadvantaged students are not equally exposed to mathematics problems and concepts at school. Exposure to mathematics at school has an impact on performance, and disadvantaged students' relative lack of familiarity with mathematics partly explains their lower performance. Widening access to mathematics content…

Poisson integral formula is revisited. The kernel in the Poisson integral formula can be derived in a series form through the direct BEM free of the concept of image point by using the null-field integral equation in conjunction with the degenerate kernels. The degenerate kernels for the closed-form Green's function and the series form of Poisson…

This classroom note presents a final solution for the functional equation: f(xy)=xf(y) + yf(x). The functional equation if formally similar to the familiar product rule of elementary calculus and this similarity prompted its study by Ren et al., who derived some results concerning it. The purpose of this present note is to extend these results and…

Eigenvalue is an important concept in Linear Algebra. It is well known that the eigenvectors corresponding to different eigenvalues of a square matrix are linear independent. In most of the existing textbooks, this result is proven using mathematical induction. In this note, a new proof using Vandermonde determinant is given. It is shown that this…

A method for the numerical evaluation of the error term in Gaussian quadrature rules is derived by means of Chebyshev polynomials of the first kind.

The analysis of tautochrone problems involves the solution of integral equations. The paper shows how a reasonable assumption, based on experience with simple harmonic motion, allows one to greatly simplify such problems. Proposed solutions involve only mathematics available to students from first year calculus.

This paper focuses on the representation of a proper fraction "a"/"b" by a decimal number base "n" where "n" is any integer greater than 1. The scope is narrowed to look at only fractions where "a","b" are positive integers with "a" less than "b" and "b" not equal to 0 nor equal to 1. Some relationships were found between "b" and "n", which…

The Bernoulli numbers are among the most interesting and important number sequences in mathematics. They first appeared in the posthumous work "Ars Conjectandi" (1713) by Jacob Bernoulli (1654-1705) in connection with sums of powers of consecutive integers (Bernoulli, 1713; or Smith, 1959). Bernoulli numbers are particularly important in number…

A simple problem relating to birds chasing each other gives rise to a homogeneous differential equation. The solution draws on student skills in differential equations and basic co-ordinate geometry.

In this work, the authors present a commonly used example in electrostatics that could be solved exactly in a conventional manner, yet expressed in a compact form, and simultaneously work out special cases using the method of images. Then, by plotting the potentials and electric fields obtained from these two methods, the authors demonstrate that…

This document presents the executive summary of the National Assessment of Educational Progress (NAEP) 1992 mathematics assessment. It included nearly 250,000 fourth, eighth, and twelfth grade students attending approximately 10,000 schools across the United States. The results from the assessment indicate that student performance is improving…