An alternative approach for introducing instrumental variables in econometrics courses is presented in this article. The method is based on the ordinary least squares omitted variable bias formula. The intuition for the approach capitalizes on students' understanding and intuition of omitted variables. Thus, if students understand omitted variable…

Even at the primary level, computational thinking (CT) can support young students to prepare for participating in futures that are immersed in data. In mathematics classrooms, there are few explanations of the ways CT can support students in formulating and solving complex problems. This paper presents an example of a primary classroom…

One model of numeric perception is a density-area mechanism: a process that estimates both density and area of an array, then multiplies them to create an estimate of number. One line of evidence that supports this is the surprising numeric Ebbinghaus illusion: smaller context circles lead to greater perceived number than larger context circles,…

Ben Zunica describes a lesson in which computational thinking has been successful in assisting students to understand the process of simplifying surds. The strengths and limitations of this approach are discussed. The author concludes that computational thinking can assist in solidifying understanding of a range of mathematical processes for…

The application of decomposition strategies (i.e., associative or distributive strategies) in two-digit multiplication problem solving supports algebraic thinking skills essential for later complex mathematical skills like solving algebra problems. Use of such strategies is also associated with improved accuracy and speed in mathematical problem…

Math performance is negatively related to math anxiety (MA), though MA may impact certain math skills more than others. We investigated whether the relation between MA and math performance is affected by task features, such as number type (e.g., fractions, whole numbers, percentages), number format (symbolic vs. nonsymbolic), and ratio component…

The close relationship between working memory and maths problem solving is generally accepted, but the specifics of how working memory and its subcomponents contribute to maths problem solving remain poorly understood. Tests of working memory, maths problem problem solving, calculation, and intelligence were administered to 246 university…

Recent developments have enabled the modeling of longitudinal assessment data in a diagnostic classification model (DCM) framework. These longitudinal DCMs were developed to provide measures of student growth on a discrete scale in the form of attribute mastery transitions, thereby supporting categorical and criterion-referenced interpretations of…

Computational models of reading have tended to focus on the cognitive requirements of mapping among written, spoken, and meaning representations of individual words in adult readers. Consequently, the alignment of these computational models with behavioural studies of reading development has to date been limited. Models of reading have provided us…

Since Wing "Communications of the ACM," 49, 33-35, (2006) popularized computational thinking (CT) as a skill for every student, it has gained significant traction as an approach to bring computer science tools and practices into K-12 classrooms. At the same time, teachers often see the relevance of CT as a tool to introduce problem…

As smartphones have become a part of our everyday life, their sensors have successfully been used to allow data acquisition with these readily available devices in a variety of different smartphone-based school experiments. Such experiments most commonly take advantage of the accelerometer and gyroscope. A less frequently used sensor in…

Electrophilic aromatic substitution (EAS) represents an important class of reactions taught in the undergraduate organic chemistry curriculum. The EAS reaction of benzene and its substituted derivatives is generally described as proceeding through a carbocation (arenium cation) intermediate, and the regiochemistry of the product is heavily…

Although Cattaneo et al. (2019) provided a data-driven framework for power computations for Regression Discontinuity Designs in line with rdrobust Stata and R commands, which allows higher-order functional forms for the score variable when using the non-parametric local polynomial estimation, analogous advancements in their parametric estimation…

Early mathematics plays an important role in introducing foundational concepts for number sense in children. One of the critical areas of learning is the establishment of a linear view of numbers. It is essential to create opportunities for young children to understand that numbers are equally spaced on the number line and that they increase in…

Computers and computer algorithms have contributed to important scientific advances by allowing scientists and engineers to create and use sophisticated models to explain and predict phenomena. Yet, of the eight "Next Generation Science Standards" ("NGSS") science and engineering practices, computational thinking may be the…