In a previous gaze-contingent boundary experiment, Angele and Rayner (2013) found that readers are likely to skip a word that appears to be the definite article "the" even when syntactic constraints do not allow for articles to occur in that position. In the present study, we investigated whether the word frequency of the preview of a…

The heterogeneous equilibrium of the solubility of calcium hydroxide in water is used to predict both its solubility product from solubility and solubility values from solubility product when inert salts, in any concentration, are present. Accepting the necessity of including activity coefficients to treat the saturated solution of calcium…

We propose an articulated computational experiment in which both quantum mechanics (QM) and molecular mechanics (MM) methods are employed to investigate environment effects on the free energy surface for the backbone dihedral angles rotation of the small dipeptide N-Acetyl-N'-methyl-L-alanylamide. This computation exercise is appropriate for an…

This article describes how "curriculum-based measurement--computation" (CBM-C) mathematics probes can be used in combination with "error pattern analysis" (EPA) to pinpoint difficulties in basic computation skills for students who struggle with learning mathematics. Both assessment procedures provide ongoing assessment data…

Large-scale assessment programs such as the National Assessment of Educational Progress (NAEP), Trends in International Mathematics and Science Study (TIMSS), and Programme for International Student Assessment (PISA) use a sophisticated assessment administration design called matrix sampling that minimizes the testing burden on individual…

This paper explores sixty-six students' personal meaning and interpretation of the vertex of a quadratic function in relation to their understanding of quadratic functions in two different representations, algebraic and word problem. Several categories emerged from students' personal meaning of the vertex including vertex as maximum or minimum…

Chess is a game of minds, bodies, and emotions. Most players recognize each of these as essential to playful competition, and all three are embedded in social relations. Thus chess, despite its reputation as a game of the mind, is not only a deeply thoughtful exercise, but also a test of physical endurance and strong emotions in its joys and…

This study focuses on teachers' engagement with tasks based on the income tax tables issued by the South African tax authorities. The participants in the study are a group of 37 teachers who were enrolled in an in-service programme for Mathematical Literacy teachers. The purpose of the study is to explore the teachers' interpretation and use of…

A valuable extension of the single-rating regression discontinuity design (RDD) is a multiple-rating RDD (MRRDD). To date, four main methods have been used to estimate average treatment effects at the multiple treatment frontiers of an MRRDD: the "surface" method, the "frontier" method, the "binding-score" method, and…

Regression discontinuity (RD), an "as good as randomized," research design is increasingly prominent in education research in recent years; the design gets eligible quasi-experimental designs as close as possible to experimental designs by using a stated threshold on a continuous baseline variable to assign individuals to a…

We explore the use of instrumental variables (IV) analysis with a multisite randomized trial to estimate the effect of a mediating variable on an outcome in cases where it can be assumed that the observed mediator is the only mechanism linking treatment assignment to outcomes, an assumption known in the IV literature as the exclusion restriction.…

Many view mathematics as a rich and wonderfully elaborate game. In turn, games can be used to illustrate mathematical ideas. Fibber's Dice, an adaptation of the game Liar's Dice, is a fast-paced game that rewards gutsy moves and favors the underdog. It also brings to life concepts arising in the study of probability. In particular, Fibber's Dice…

Test scores are commonly reported in a small number of ordered categories. Examples of such reporting include state accountability testing, Advanced Placement tests, and English proficiency tests. This paper introduces and evaluates methods for estimating achievement gaps on a familiar standard-deviation-unit metric using data from these ordered…

In 1923, Weyl published a (not widely known) protocol for the calculation of redshifts. It is completely independent of the origin of the shift and treats it as a pure Doppler shift. The method is comprehensive and depends solely on the relation between the world lines of source and observer. It has the merit of simplicity of statement and…

Pedagogical reform in Australia over the last few decades has resulted in a reduced emphasis on the teaching of computational algorithms and a diversity of alternative mechanisms to teach students whole number computations. The effect of these changes upon student recording of whole number computations has had little empirical investigation. As…