Finite Mathematics has become an enormously rich and productive area of contemporary mathematical biology. Fortunately, educators have developed educational modules based upon many of the models that have used Finite Mathematics in mathematical biology research. A sufficient variety of computer modules that employ graph theory (phylogenetic trees,…

We study here an aspect of an infinite set "P" of multivariate polynomials, the elements of which are associated with the arithmetic-geometric-mean inequality. In particular, we show in this article that there exist infinite subsets of probability "P" for which every element may be expressed as a finite sum of squares of real…

We explore the transition from school to university through a commognitive (Sfard 2008) analysis of twenty-two students' examination scripts from the end of year examination of a first year, year-long module on Sets, Numbers, Proofs and Probability in a UK mathematics department. Our analysis of the scripts relies on a preliminary analysis of the…

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…

This article reports on a study designed to estimate the effect of high school coursetaking in the algebra-calculus pipeline on the likelihood of placing out of postsecondary remedial mathematics. A nonparametric variant of propensity score analysis was used on a nationally representative data set to remove selection bias and test for an effect…

Since its establishment in 1996, the North Carolina Early Mathematics Placement Testing (NC EMPT) Program has provided a low stakes reality check of readiness for college-level mathematics to more than 600,000 high school students statewide. The program strives to help reduce the percentage of incoming college freshmen requiring mathematics…

This article describes how a Brier score analysis can be used as an evaluative tool to estimate the predictive accuracy of a course placement policy that was established based on professional or subjective judgment. The policy being evaluated uses the score received on the mathematics portion of the SAT examination as the primary mechanism to…

The goal of this work is to provide instructors with detailed information about their classes at each assignment during the term. The information is both on an individual level and at the aggregate level. We used the large number of grades, which are available online these days, along with data-mining techniques to build our models. This enabled…

Augustus De Morgan (1806-1871) was a significant Victorian Mathematician who made contributions to mathematics history, mathematical recreations, mathematical logic, calculus, and probability and statistics. He was an inspiring mathematics professor who influenced many of his students to join the profession. One of De Morgan's significant books…

The theme of the 39th proceedings of the North American Chapter of the International Group for the Psychology of Mathematics Education (PME-NA) conference was "Synergy at the Crossroads: Future Directions for Theory, Research, and Practice." The metaphor of crossroads was inspired by the conference venue--the historic Indianapolis Union…

In 2007, the Virginia Board of Education directed the Virginia Department of Education (VDOE) to study academic indicators that are associated with high school students' successful preparation for college and careers. VDOE then embarked on a multi-year effort to identify available data sources and conduct research on high school indicators that…

This paper surveys the fascinating mathematics of fair division, and provides a suite of examples using basic ideas from algebra, calculus, and probability which can be used to examine and test new and sometimes complex mathematical theories and claims involving fair division. Conversely, the classical cut-and-choose and moving-knife algorithms…

The material in this module introduces students to some of the mathematical tools used to examine molecular evolution. This topic is standard fare in many mathematical biology or bioinformatics classes, but could also be suitable for classes in linear algebra or probability. While coursework in matrix algebra, Markov processes, Monte Carlo…

We describe an ongoing collaborative curriculum materials development project between Sweet Briar College and Western Michigan University, with support from the National Science Foundation. We present a collection of modules under development that can be used in existing mathematics and biology courses, and we address a critical national need to…

This volume, a comprehensive survey and critical analysis of today's issues in mathematics education, distills research to build knowledge and capacity in the field. The compendium is a valuable new resource that provides the most comprehensive evidence about what is known about research in mathematics education. The 38 chapters present five…