We present a logistic function of a monotonic polynomial with a lower asymptote, allowing additional flexibility beyond the three-parameter logistic model. We develop a maximum marginal likelihood based approach to estimate the item parameters. The new item response model is demonstrated on math assessment data from a state, and a computationally…

In recent years, the integration of computation with crafting has garnered increased attention. Partly spurred by the growth of the "maker movement" and also by recognition of the importance of broadening computational interest and proficiency, computational crafts have become more familiar to educational technologists and designers. For…

The recent surge of interests in cognitive assessment has led to developments of novel statistical models for diagnostic classification. Central to many such models is the well-known "Q"-matrix, which specifies the item-attribute relationships. This article proposes a data-driven approach to identification of the "Q"-matrix and…

The numerical range, easy to understand but often tedious to compute, provides useful information about a matrix. Here we describe the numerical range of a 3 x 3 magic square. Applying our results to one of the most famous of those squares, the Luoshu, it turns out that its numerical range is a piece of cake--almost.

In this article, we describe results of a reanalysis of two randomized studies that tested the effects of enhanced anchored instruction (EAI) on the fractions computation performance of students in special education resource rooms and inclusive mathematics classrooms. Latent class analysis and latent transition analysis classified students…

A high comorbidity between reading and arithmetic disabilities has already been reported. The present study aims at identifying more precisely patterns of arithmetic performance in children with developmental dyslexia, defined with severe and specific criteria. By means of a standardized test of achievement in mathematics ("Calculation and…

This paper evaluates the influence of the classmates' age on individual academic achievement. The identification strategy explores a mechanism for the division of classes based on age homogeneity, with cutoff value determined by the Brazilian law of age at school entry. Fuzzy regression discontinuity estimates a local average treatment effect of…

Approximately half of students who are deaf or hard of hearing (DHH) have a co-occurring disability. Although assessing as well as diagnosing learning disabilities (LDs) is particularly difficult in this population, it is important to properly identify students who may be eligible for academic interventions or accommodations. This study analyzed…

The major purpose of this study was to investigate the prevalence of learning difficulties (LDs) among primary school students (Grade 1 to Grade 3) in Jordan. A total of 306 students were randomly selected and tested using the Arabic version of the Woodcock-Johnson Basic Achievement Tests that measure reading, spelling, and calculation skills. The…

Understanding spoken words involves a rapid mapping from speech to conceptual representations. One distributed feature-based conceptual account assumes that the statistical characteristics of concepts' features--the number of concepts they occur in ("distinctiveness/sharedness") and likelihood of co-occurrence ("correlational…

Sprego is programming with spreadsheet functions. The present paper provides introductory Sprego examples which have so far only been available in Hungarian. Spreadsheet environments offer both a programming tool which best serves beginner and end-user programmers' interest, and an approach which lightens the burden of coding and language details.…

The purposes of this study were to (a) investigate the efficacy of a core fraction intervention program on understanding and calculation skill and (b) isolate the effects of different forms of fraction word-problem (WP) intervention. At-risk fourth graders (n = 213) were randomly assigned to the school's business-as-usual program, or one of two…

In this article we present an integrative framework of knowledge for teaching the standard algorithms of the four basic arithmetic operations. The framework is based on a mathematical analysis of the algorithms, a connectionist perspective on teaching mathematics and an analogy with previous frameworks of knowledge for teaching arithmetic…

This article presents a case study that examines the level of integration of mathematical knowledge in physics problem solving among first grade students of upper secondary school. We explore the ways in which two specific students utilize their knowledge and we attempt to identify the epistemological framings they refer to while solving a physics…

Using a dog's paw as a basis for numerical representation, sixth grade students explored how to count and regroup using the dog's four digital pads. Teachers can connect these base-4 explorations to the conceptual meaning of place value and regrouping using base-10.