A series of course-specific MAP Growth Mathematics and Science subject tests were released successively starting in August 2017 to replace the older NWEA End-of-Course (EOC) tests. Different from the prior NWEA EOC tests taken only at the end of a course, these course-specific tests can be administered multiple times throughout the school year,…

The ACT College Readiness Benchmarks are the ACT scores associated with a 50% chance of earning a B or higher grade in selected first-year credit-bearing courses at a typical postsecondary institution. The Benchmarks were established by linking ACT test scores with grades in first-year college courses from the same subject area. Benchmarks were…

The Better Math Teaching Network offers a promising, practical model for teacher learning. Its practitioner members--who all teach at least one section of high school algebra and all joined voluntarily--are working with each other and a team of researchers to make their teaching more student-centered through an improvement science approach. With…

Montgomery County Public Schools (MCPS) is more than a school system, it is a community. It's a community of people working together to provide Montgomery County students with an education that prepares them for success today, tomorrow, and in the years to come. That is MCPS' core purpose: to prepare students to thrive in their future. The Annual…

To assess the raised expectations of college and career readiness for all students, a group of American Diploma Project (ADP) Network states formed the ADP Assessment Consortium in 2005. The Consortium created Algebra I and II end-of-course exams, based in large part on Achieve's ADP mathematics benchmarks, which would provide an honest assessment…

Define the centre of a parallelogram to be the intersection of its diagonals. It was shown in an earlier paper that the intersection of arbitrarily many parallelograms with the same centre is the unit disc about that centre in a metric defined using ideas from Linear Algebra. In this note, it is shown that this characterizes compact, convex sets,…

In the No Child Left Behind Act (NCLB), Congress called for the U.S. Department of Education (ED) to conduct a rigorous study of the conditions and practices under which educational technology is effective in increasing student academic achievement. A 2007 report presenting study findings for the 2004-2005 school year, indicated that, after one…

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…

An easy way to present the uniqueness of the square root of a positive semidefinite matrix is given.

If the point of suspension of a multiple pendulum is suitably oscillated then the pendulum can remain in motion in an upside-down position. Since such pendulums can model flexible materials, this inverted motion is sometimes referred to as an 'Indian rope trick'. Despite the complexity of the governing differential equations, this rope trick can…

A semigroup G is a group if it has a left identity and every element has a left inverse. The purpose of this note is to weaken this condition further in two different ways. A semigroup G with an identity e is a group if every element x in G has an inverse. It is well known that this statement can be weakened. A semigroup G with a left identity e…

In this article, an alternative multiplication method for rhotrices is proposed. The method establishes some relationships between rhotrices and matrices. This article has discussed a modified multiplication method for rhotrices. The method has a direct relationship with matrix multiplication, and so rhotrices under this multiplication procedure…

Similarities and differences in the univariate and multivariate analysis of repeated measures designs are discussed, using a hypothetical data set studying the effects of practice on the algebra performance of four students to illustrate both methods. When data are analyzed through the univariate approach and the homogeneity assumption is…

Many colleges and universities use a mathematics placement process to guide students to the appropriate entry-level mathematics course. The mathematics placement process presented here was developed over a four year period to make placement recommendations to Calculus I, Precalculus, and College Algebra. Placement recommendations are based on the…

The State of Florida Department of Education provides pre-and-post-graduation data for public high school graduates throughout Florida. These data were used for the present report to produce data sets for all M-DCPS regular high schools and charter high schools graduating students in 2009 and 2010. Summary data for the district are also provided.…