In educational effectiveness research, multilevel data analyses are often used because research units (most frequently, pupils or teachers) are studied that are nested in groups (schools and classes). This hierarchical data structure complicates designing the study because the structure has to be taken into account when approximating the accuracy…

The aim of this single-case intervention study was to examine whether a conceptual knowledge-based strategy training would improve the accuracy of single-digit arithmetical calculation in a child with specific language impairment. The intervention concerned an 11-year-old Finnish-speaking child with specific language impairment. He was trained…

For more than three decades now, sociologists, politicians and economists have used a wide range of statistical and econometric techniques to analyse and measure the quality of life of individuals with the aim of obtaining useful instruments for social, political and economic decision making. The aim of this paper is to analyse the advantages and…

Generalizability theory is used to examine the impact of scaling gradients on a single-item Direct Behavior Rating (DBR). A DBR refers to a type of rating scale used to efficiently record target behavior(s) following an observation occasion. Variance components associated with scale gradients are estimated using a random effects design for persons…

In Singapore, 6-12 year-old students are taught to solve algebra word problems with a mix of arithmetic and pre-algebraic strategies; 13-17 year-olds are typically encouraged to replace these strategies with letter-symbolic algebra. We examined whether algebra problem-solving proficiency amongst beginning learners of letter-symbolic algebra is…

The formation constant of iron(III) complex with glycine (Gly) ligand in aqueous acidic medium (0.2 M HNO[subscript 3], I = 0.2 M at 28 plus or minus 1 degree C) was determined spectrophotometrically in which a competing color reaction between Fe(III) and SCN[superscript -] was used as an indicator reaction. Under the specified conditions Fe(III)…

This research examines students' ability to integrate algebraic variables with arithmetic operations and symbols as a result of the type of instruction they received, and places their work on scales that illustrate its location on the continuum from arithmetic to algebraic reasoning. It presents data from pre- and post-instruction clinical…

Cantor's diagonal proof that the set of real numbers is uncountable is one of the most famous arguments in modern mathematics. Mathematics students usually see this proof somewhere in their undergraduate experience, but it is rarely a part of the mathematical curriculum of students of the fine arts or humanities. This note describes contexts that…

Understanding conceptual relationships is an important aspect of learning arithmetic. Most studies of arithmetic, however, do not distinguish between children's understanding of a concept and their ability to identify situations in which it might be relevant. We compared 8- to 9-year-old children's use of a computational shortcut based on the…

The circle of Apollonius is named after the ancient geometrician Apollonius of Perga. This beautiful geometric construct can be helpful when solving some general problems of geometry and mathematical physics, optics, and electricity. Here we discuss two of its applications: localizing an object in space and calculating electric fields. First, we…

Perhaps no topic has as thoroughly vexed officials who oversee the nation's leading test of academic progress as the wide variation among states and cities in the proportion of students with disabilities and limited English proficiency whom they exclude from taking the exam or provide with special accommodations for it. The board that sets policy…

In earlier columns, the celestial coordinate system of hour circles of right ascension and degrees of declination was introduced along with the use of an equatorial star chart (see SFA Star Charts in Resources). This system shows the planets' motion relative to the ecliptic, the apparent path the Sun follows during the year. An alternate system,…

A simplified version of a volumetric apparatus for gas/liquid solubility measurements is proposed. The procedure familiarizes undergraduate students with the experimental study of the solubility of a gas in a liquid and contributes to the understanding of this important phase equilibrium concept. The experimental results report the determination…

The purpose of this article is to propose a new design for the presentation of the periodic system of the elements. It is a system that highlights the fundamental importance of elements as basic substances rather than elements as simple substances, a distinction that is explained in the article. The proposed table is a variant of the Janet or…

Computational experiment is proposed in which a linear algebra method is applied to the solution of the Schrodinger equation for a diatomic oscillator. Calculations of the vibration-rotation spectrum for the HCl molecule are presented and the results show excellent agreement with experimental data. (Contains 1 table and 1 figure.)