Linear quantity models such as pre-tapes, tape diagrams, and number line diagrams have drawn increasing attention in mathematics education around the world. However, we still know relatively little about how teachers actually use these models in the classroom. This study explores how exemplary US and Chinese elementary teachers use linear quantity…

This paper is centred around a framework for studying teaching--Mediating Primary Mathematics (MPM)--developed in the context of the teaching of Whole Number Arithmetic (WNA) in South Africa. Findings from the analysis of four WNA lessons are used to illustrate how the application of the MPM framework can measure nuanced differences in the…

Computational thinking is a core skill in computer science that has become a focus of instruction in primary and secondary education worldwide. Since 2010, researchers have leveraged Evidence-Centered Design (ECD) methods to develop measures of students' Computational Thinking (CT) practices. This article describes how ECD was used to develop CT…

The effects of substitution on reaction rates are at the heart of both physical chemistry and organic chemistry. In this paper, we present a computational laboratory module to explore the effects of group substitution and isotopic substitution on reaction rates by using a readily accessible graphical interface, a computational engine, and…

In the field of physics teaching, the simple pendulum provides a very simple way to study the harmonic oscillator, the source of some fundamental concepts such as periodicity, relaxation time and anharmonicity. As such, its experimental study is frequently integrated into high school or first year university programs. With this in mind, in this…

The use of item responses from questionnaire data is ubiquitous in social science research. One side effect of using such data is that researchers must often account for item level missingness. Multiple imputation (Rubin, 1987) is one of the most widely used missing data handling techniques. The traditional multiple imputation approach in…

Background: The overarching goal of this study was to explore the underlying mechanism of solving statics or structural analysis problems by utilizing cognitive load theory to examine task characteristics (i.e., the characteristics of instructional materials) with a focus on working memory load (WML) and automaticity. Purpose/Hypothesis: According…

The maximal reliability of a congeneric measure is achieved by weighting item scores to form the optimal linear combination as the total score; it is never lower than the composite reliability of the measure when measurement errors are uncorrelated. The statistical method that renders maximal reliability would also lead to maximal criterion…

Estimation is such an important yet sometimes overlooked skill. Enhancing estimation skills through exposing students to enumeration ('how many') problems where they are required to estimate before calculating is a critical aspect of developing number sense (Reys et al., 2012). This article describes a 'how many' problem undertaken with a small…

This article distinguishes three measures of intergenerational economic mobility that emerge when the population is divided into groups: overall individual mobility, within-group mobility, and between-group mobility. We clarify their properties and the relationship between them. We then evaluate Clark's use of surname between-group persistence as…

Research indicates that understanding levels of abstraction (LOA) and being able to move between the levels is essential to programming success. For K-5 contexts LOA levels have been named: problem, design, code and running the code. In a qualitative exploratory study, five K-5 teachers were interviewed on their uses of LOA, particularly the…

Recently, researchers interested in the nature and origins of semantic representations have investigated an especially informative case study: The acquisition of the word "most"--a quantifier which by all accounts demands a sophisticated second-order logic, and which therefore poses an interesting challenge to theories of language…

In this paper, we propose that paper circuitry provides a productive space for exploring aspects of computational thinking, an increasingly critical 21st century skills for all students. We argue that the creation and operation of paper circuits involve learning about computational concepts such as rule-based constraints, operations, and defined…

Educational assessment data are often collected from a set of test centers across various geographic regions, and therefore the data samples contain clusters. Such cluster-based data may result in clustering effects in variance estimation. However, in many grouped jackknife variance estimation applications, jackknife groups are often formed by a…

This article describes the use of a spreadsheet to reinforce basic calculus that is expected of all university-level chemistry majors. The example provided shows a calculation using Excel to estimate, using a Riemann summation, the radiant exitance of a hot object using Planck's Law of Blackbody Radiation. The approach reinforces the elementary…