This paper explores the usefulness of understanding quotients as measures of relative size in mathematics. The paper characterizes the types of thinking displayed by high school mathematics teachers on two novel tasks designed to reveal teachers' meanings in contexts where making comparisons of relative size is productive. [For the complete…

This case study presents an example of using a generalized linear model with a log-linear link to calculate an adjusted risk ratio to be able to assess the association between educational attainment and obesity in a cohort study of American adults. Both risk ratios and odds ratios can be calculated based on cohort study data, and risk ratios are…

Within the last 10 years, new tools for assisting in the teaching and learning of academic skills and content within the context of science have arisen. These new tools include multiple types of computer software and hardware to include (video) games. The purpose of this study was to examine and compare the effect of computer learning games in the…

Advances in software and hardware have promoted the use of computational chemistry in all branches of chemical research to probe important chemical concepts and to support experimentation. Consequently, it has become imperative that students in the modern undergraduate curriculum become adept at performing simple calculations using computational…

Problems concerning carbon dioxide emissions and other climate change-related issues are on the global political agenda and constantly debated in media. Such issues are important for individuals to enable active participation in society. This study has a particular interest in the use of carbon footprint calculators (tools for calculating carbon…

Counting skills are foundational for young children to build number concepts in mathematics. Multitiered instruction that involves core instruction as well as supplemental interventions is implemented to support young children in the learning process and promote early intervention of basic skills. Researchers show that explicit instruction is…

The Reduced Reparameterized Unified Model (Reduced RUM) is a diagnostic classification model for educational assessment that has received considerable attention among psychometricians. However, the computational options for researchers and practitioners who wish to use the Reduced RUM in their work, but do not feel comfortable writing their own…

Mathematical word problems are the most common form of mathematics problem solving implemented in K-12 schools. Identifying key words is a frequent strategy taught in classrooms in which students struggle with problem solving and show low success rates in mathematics. Researchers show that using the concrete-representational-abstract (CRA)…

This study aims to explain the thinking process of students in solving combination problems considered from assimilation and accommodation frameworks. This research used a case study approach by classifying students into three categories of capabilities namely high, medium and low capabilities. From each of the ability categories, one student was…

Lesotho's educational system and development are largely influenced by missionaries and colonisers who taught the three 'Rs' (reading, writing and numeracy skills) to the Basotho. Most of those enlightened Basotho were to carry on the duties of either educating others or as missionary workers. Some became clerks, interpreters, police officers,…

Today, most young people in the United States (U.S.) live technology-saturated lives. Their educational, entertainment, and career options originate from and demand incredible technological innovations. However, this extensive ownership of and access to technology does not indicate that today's youth know how technology works or how to control and…

This guide is subject to WWC version 2.0 standards. The Fractions practice guide will provide evidence-based guidance on the teaching and learning of fractions among students in the elementary and middle grades. The guide will offer concrete recommendations for practices that improve students' conceptual understanding of fractions, operational…

Background: There is an increased focus on randomized trials for proximal behavioral outcomes in early childhood research. However, planning sample sizes for such designs requires extant information on the size of effect, variance decomposition, and effectiveness of covariates. Objectives: The purpose of this article is to employ a recent large…

We present mentally efficient algorithms for mentally squaring and cubing 2-digit and 3-digit numbers and for finding cube roots of numbers with 2-digit or 3-digit answers.

This article studies the convergence of the infinite series of the reciprocals of the Catalan numbers. We extract the sum of the series as well as some related ones, illustrating the power of the calculus in the study of the Catalan numbers.