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…

As a component of the ongoing development of the mathematics curriculum in China, we compare the country's high school mathematics textbooks with those of several other countries. We base our analysis on the assumption that textbooks, as primary printed teaching resources, are key tools for interpreting educational policy. In this paper, we…

In this work we examined the content of approximately 950 mathematics questions used in measuring achievement among 4th, 5th and 6th graders in the US in an attempt to determine how the current standardized examinations, which were developed to reflect new national curricular mandates, compared to the old measures used for the same purpose. Using…

In recent years, the usefulness of affect detection for educational software has become clear. Accurate detection of student affect can support a wide range of interventions with the potential to improve student affect, increase engagement, and improve learning. In addition, accurate detection of student affect could play an essential role in…

Since the introduction of the Common Core State Standards for Mathematics (CCSSM) in 2010, stakeholders in adopting states have engaged in a variety of activities to understand CCSSM standards and transition from previous state standards. These efforts include research, professional development, assessment and modification of curriculum resources,…

A long-standing challenge for knowledge tracing is how to update estimates of multiple subskills that underlie a single observable step. We characterize approaches to this problem by how they model knowledge tracing, fit its parameters, predict performance, and update subskill estimates. Previous methods allocated blame or credit among subskills…

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…

We apply collaborative filtering (CF) to dichotomously scored student response data (right, wrong, or no interaction), finding optimal parameters for each student and item based on cross-validated prediction accuracy. The approach is naturally suited to comparing different models, both unidimensional and multidimensional in ability, including a…

This paper presents a comparison of Virginia's mathematics performance expectations with the common core state standards for mathematics. The comparison focuses on number and quantity, algebra, functions, geometry, and statistics and probability. (Contains 1 footnote.)

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 community colleges in the state of New Jersey went through a process of establishing statewide cut-off scores for English and mathematics placement tests. The colleges wanted to communicate to secondary schools a consistent preparation that would be necessary for enrolling in Freshman Composition and College Algebra at the community college…

2009 was the final year of parallel implementation for Mathematical Methods Units 3 and 4 and Mathematical Methods (CAS) Units 3 and 4. From 2006-2009 there was a common technology-free short answer examination that covered the same function, algebra, calculus and probability content for both studies with corresponding expectations for key…

The purpose of this study is to describe how the attribute hierarchy method (AHM) can be used to evaluate differential group performance at the cognitive attribute level. The AHM is a psychometric method for classifying examinees' test item responses into a set of attribute-mastery patterns associated with different components in a cognitive model…

Differential gender performance in standardized mathematics assessment has long been a heated topic. Gender gaps of varied magnitude have been identified on large-scale assessments in the United States. To continue the investigation, this study examined male and female performance on the Programme for International Student Assessment (PISA) 2003…

University of Chicago School Mathematics Project (UCSMP) Algebra is a one-year course covering three primary topics: (1) linear and quadratic expressions, sentences, and functions; (2) exponential expressions and functions; and (3) linear systems. Topics from geometry, probability, and statistics are integrated with the appropriate algebra.…