To find population proficiency distributions, a two-level hierarchical linear model may be applied to large-scale survey assessments such as the National Assessment of Educational Progress (NAEP). The model and parameter estimation are developed and a simulation was carried out to evaluate parameter recovery. Subsequently, both a hierarchical and…

Since 2001, the authors have been working with groups of teachers to investigate students' early algebraic thinking--learning representations, connections, and generalizations in the elementary school grades. They began paying attention to students' explicit remarks about regularities in the number system or what students imply by their…

The performance of parameter estimates and standard errors in estimating F. Samejima's graded response model was examined across 324 conditions. Full information maximum likelihood (FIML) was compared with a 3-stage estimator for categorical item factor analysis (CIFA) when the unweighted least squares method was used in CIFA's third stage. CIFA…

Probability theory has long been taken as the self-evident norm against which to evaluate inductive reasoning, and classical demonstrations of violations of this norm include the conjunction error and base-rate neglect. Many of these phenomena require multiplicative probability integration, whereas people seem more inclined to linear additive…

African American students are overrepresented in special education and underrepresented in gifted education. This is in large part due to students' poor performance in core academic areas such as reading, math, and writing. Differentiating instruction in early grades could assist in closing the writing performance gap between African American and…

Children's understanding of the inversion concept in multiplication and division problems (i.e., that on problems of the form "d multiplied by e/e" no calculations are required) was investigated. Children in Grades 6, 7, and 8 completed an inversion problem-solving task, an assessment of procedures task, and a factual knowledge task of simple…

This article describes how to make an origami paper box and explores the algebra, geometry, and other mathematics that unfolds. A set of origami steps that transforms the paper into an open box can hold mathematical surprises for both students and teachers. An origami lesson can engage students in an open-ended exploration of the relationship…

This article proposes procedures for simultaneously assessing and controlling acquiescence and social desirability in questionnaire items. The procedures are based on a semi-restricted factor-analytic tridimensional model, and can be used with binary, graded-response, or more continuous items. We discuss procedures for fitting the model (item…

Quality control (QC) measures are less prevalent in teaching laboratories than commercial settings possibly owing to a lack of commercial incentives or teaching resources. This article focuses on the use of QC assessment in the analytical techniques of high performance liquid chromatography (HPLC) and ultraviolet-visible spectroscopy (UV-vis) at…

As part of individual interviews incorporating whole number and rational number tasks, 323 grade 6 children in Victoria, Australia were asked to nominate the larger of two fractions for eight pairs, giving reasons for their choice. All tasks were expected to be undertaken mentally. The relative difficulty of the pairs was found to be close to that…

Within increasing pressure on young people to perform successfully in work, there is a growing concern regarding their levels of numeracy (and literacy). Whether such concerns are founded is the basis of this paper. This paper reports on the numeracy practices undertaken by three young boatbuilders who were nearing the completion of their 4-year…

"Enthalpy Costs" is a simple card game created to assist students in developing proper Lewis structure drawing skills. Score keeping is accomplished by tracking the enthalpy changes associated with bond-making and bond-breaking processes during formation of molecules represented by proper Lewis structures. Playing the game requires the student to…

The authors examined the effectiveness of strategy instruction taught by general educators in mixed-ability classrooms. Specifically, the authors compared the mathematical word problem-solving performance and computational skills of students who received schema-based instruction (SBI) with students who received general strategy instruction (GSI).…

The "Foundations" (English/language arts, mathematics, social emotional skills, approaches to play and learning, science, social studies, creative arts, and physical health and growth) are Indiana's early learning development framework and are aligned to the 2014 Indiana Academic Standards. This framework provides core elements that…

The ability to do arithmetic calculations is essential to school-based learning and skill development in an information rich society. Arithmetic is a basic academic skill that is needed for learning which includes the skills such as counting, calculating, reasoning etc. that are used for performing mathematical calculations. Unfortunately, many…