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…

In spite of the growing interest in cross-cultural research and assessment, there is little research on statistical procedures that can be used to simultaneously assess the differential item functioning (DIF) across multiple groups. The chief objective of this work is to show a unified framework for the analysis of DIF in multiple groups using one…

Behavior analysis as a discipline currently is doing relatively well. How it will do in the future is unclear and depends on how the field, and the world at large, changes. Five current characteristics of the discipline that appear to reduce the probability that it will survive and prosper are discussed and suggestions for improvement are offered.…

Woollams, Lambon Ralph, Plaut, and Patterson (see record 2007-05396-004) reported detailed data on reading in 51 cases of semantic dementia. They simulated some aspects of these data using a connectionist parallel distributed processing (PDP) triangle model of reading. We argue here that a different model of reading, the dual route cascaded (DRC)…

Latent class analysis (LCA) is a statistical method used to identify subtypes of related cases using a set of categorical or continuous observed variables. Traditional LCA assumes that observations are independent. However, multilevel data structures are common in social and behavioral research and alternative strategies are needed. In this…

Previous research has shown that young children make a perseverative, gravity-oriented, error when asked to predict the final location of a ball dropped down an S-shaped opaque tube (Hood, 1995). We asked if providing children with verbal information concerning the role that the tubes play, in determining the ball's trajectory would improve their…

Chance, randomness and probability constitute statistical notions that are interrelated and characterize the logicomathematical thinking of children. Traditional theories support that probabilistic thinking evolves after the age of 7. However, recent research has underlined that children, as young as 4, may possess and develop basic notions,…

Various studies have demonstrated enhanced visual processing when information is presented across both visual hemifields rather than in a single hemifield (the "bilateral advantage"). For example, Alvarez and Cavanagh (2005) reported that observers were able to track twice as many moving visual stimuli when the tracked items were presented…

The field of the learning sciences appears to favor cognitive and social approaches to the study of human learning. In this article, the author proposes that a deep cognizance of cultural influences on learning is vital if formal and informal learning are to make vital connections to learners' lives and their personal need for meaning making in…

There is much to be learned and pondered by reading "Proofs and Refutations," by Imre Lakatos. It highlights the importance of mathematical definitions, and how definitions evolve to capture the essence of the object they are defining. It also provides an exhilarating encounter with the ups and downs of the mathematical reasoning process, where…

Multiple cue probability learning studies have typically focused on stationary environments. We present 3 experiments investigating learning in changing environments. A fine-grained analysis of the learning dynamics shows that participants were responsive to both abrupt and gradual changes in cue-outcome relations. We found no evidence that…

Quilt investigations, such as the Barn quilt problem in the December 2008/January 2009 issue of "Teaching Children Mathematics" and its solutions in last month's issue, can spark interdisciplinary pursuits for teachers and exciting connections for the full range of elementary school students. This month, North Dakota's centennial quilt…

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…

This study presents an efficient approach to personalized mispronunciation detection of Taiwanese-accented English. The main goal of this study was to detect frequently occurring mispronunciation patterns of Taiwanese-accented English instead of scoring English pronunciations directly. The proposed approach quickly identifies personalized…