This article discusses the challenges students face in making sense of zero as a number. A range of different student responses to a computation problem involving zero reveal students' different understandings of zero.

A Lattice Energy Spreadsheet by Christopher King, which can help instructors and students to easily calculate crystal lattice energies in many binary compounds, is introduced.

Using time series data, this study shows that domestic students' academic performance is generally better than international students' performance, but the gap is significantly narrowing as international students' performance is improving over time. The study also shows that there is no strong correlation between the percentage of international…

This paper examines the estimation of two-stage clustered RCT designs in education research using the Neyman causal inference framework that underlies experiments. The key distinction between the considered causal models is whether potential treatment and control group outcomes are considered to be fixed for the study population (the…

A widely recognized concern in elementary school mathematics education is that teachers' understanding of the mathematical curricular content generally appears quite fragmented, sparsely connected, and procedurally oriented. This pilot study applies methods of educational neuroscience to investigate and improve preservice teachers' learning and…

As a group, children from disadvantaged, low-income families perform substantially worse in mathematics than their counterparts from higher-income families. Minority children are disproportionately represented in low-income populations, resulting in significant racial and social-class disparities in mathematics learning linked to diminished…

Recognizing the need to implement standards-based instructional materials with school-wide coherence led some Philadelphia schools to adopt whole-school reform (WSR) models during the late 1990s. The authors report on the relation between mathematics achievement growth for middle-grade students on the Pennsylvania System of School Assessments and…

This article demonstrates an active learning technique for teaching the Central Limit Theorem (CLT) in an introductory undergraduate business statistics class. Groups of students carry out one of two experiments in the lab, tossing a die in sets of 5 rolls or tossing a die in sets of 10 rolls. They are asked to calculate the sample average of each…

Children's understanding of the cardinal significance of counting is often assessed by the "give x" task, in which they are categorized as "counters" or "grabbers". Previous research indicates a sudden stage-like shift, implying insight into a principle. Employing a microgenetic approach, the present study was…

This paper presents a derivation of all five Lagrange points by methods accessible to sixth-form students, and provides a further opportunity to match Newtonian gravity with centripetal force. The predictive powers of good scientific theories are also discussed with regard to the philosophy of science. Methods for calculating the positions of the…

A plausible factorial structure for many types of psychological and educational tests exhibits a general factor and one or more group or method factors. This structure can be represented by a bifactor model. The bifactor structure results from the constraint that each item has a nonzero loading on the primary dimension and, at most, one of the…

Public rates of return on higher education expenditures are calculated by state. Benefits accruing to states from their investments in higher education are measured by differential tax revenues collected from college-educated citizens versus high-school-educated citizens. For most states we find an adequate rate of return on such investments.…

A key question in early number development is how 4- and 5-year-olds learn the roles that counting and cardinal numbers play when comparing quantities. Children who wrongly used length to identify numerosity were assigned to five experimental groups and trained to judge whether a puppet--who sometimes miscounted--created equivalent sets. Over…

Patients with corticobasal degeneration (CBD) have calculation impairments. This study examined whether impaired number knowledge depends on verbal mediation. We focused particularly on knowledge of very small numbers, where there is a precise relationship between a cardinality and its number concept, but little hypothesized role for verbal…

This article describes a general item response theory model for personality items that allows the information provided by the item response times to be used to estimate the individual trait levels. The submodel describing the item response times is a modification of Thissen's log-linear model and is based on the distance-difficulty hypothesis in…