The rules of indices, e.g. a[superscript n] b[superscript n] = (ab)[superscript n], are a particularly important part of elementary algebra. This paper reports results from a textbook analysis which examined how the shift from integer to rational exponents in the rules of indices is discussed in school textbooks. The analysis also considered…

Adding Digital Technologies curriculum content into primary classrooms may feel, to many primary teachers, like a new burden and more work--but many aspects of computational thinking can be explored in the context of our existing mathematics programmes. This article highlights the connection between computational thinking and mathematics, and…

The aim of this study was to develop a scale which can be used to measure the computational thinking skills (CTS) of high school students. Validity and reliability testing of the scale was performed with the participation of 785 students. Exploratory and confirmatory factor analysis showed that the five-point Likert scale had a construct…

Combination problems are a cornerstone of combinatorics courses, but little research has been done examining the ways that students perceive and differentiate among different combination problems. In this article, we investigate how mathematics education students (n = 18) in a discrete mathematics course view two categorically different…

As computing has become an integral part of our world, demand for teaching computational thinking in K-12 has increased. One of its basic competences is programming, often taught by learning activities without a predefined solution using block-based visual programming languages. Automatic assessment tools can support teachers with their assessment…

Students studying statistics often misunderstand what statistics represent. Some of the most well-known misunderstandings of statistics revolve around null hypothesis significance testing. One pervasive misunderstanding is that the calculated p-value represents the probability that the null hypothesis is true, and that if p < 0.05, there is…

In recent years, there have been calls for researchers to report and interpret confidence intervals (CIs) rather than relying solely on p-values. Such reforms, however, may be hindered by a general lack of understanding of CIs and how to interpret them. In this study, we assessed conceptual knowledge of CIs in undergraduate and graduate psychology…

Longitudinal data analysis has received widespread interest throughout educational, behavioral, and social science research, with latent growth curve modeling currently being one of the most popular methods of analysis. Despite the popularity of latent growth curve modeling, limited attention has been directed toward understanding the issues of…

A striking characteristic of human thought is that we form representations about abstract kinds (Giraffes have purple tongues), despite experiencing only particular individuals (This giraffe has a purple tongue). These generic generalizations have been hypothesized to be a cognitive default, that is, more basic and automatic than other forms of…

The aim of this article is to present a set of simple exercises that help the students of a second course in quantum chemistry to understand that some molecular properties do not improve even when the molecular energy improves with an increasing number of basis functions in the expansion of the wavefunction. The essential idea is to create a…

Numerical competencies acquired in preschool are foundational and predictive for children's later mathematical development. It remains to be determined whether there are gender differences in these early numerical competencies which could explain the often-reported gender differences in later mathematics and STEM-related abilities. Using a…

Applying single-level statistical models to multilevel data typically produces underestimated standard errors, which may result in misleading conclusions. This study examined the impact of ignoring multilevel data structure on the estimation of item parameters and their standard errors of the Rasch, two-, and three-parameter logistic models in…

Memory for numbers improves with age. One source of this improvement may be learning linear spatial-numeric associations, but previous evidence for this hypothesis likely confounded memory span with quality of numerical magnitude representations and failed to distinguish spatial-numeric mappings from other numeric abilities, such as counting or…

Psychological studies of early numerical development fill a void in mathematics education research. However, conflations between magnitude awareness and number, and over-attributions of researcher conceptions to children, have led to psychological models that are at odds with findings from mathematics educators on later numerical development. In…

Each year, policymakers, educators, and the general public engage in debates around the statewide average teacher pay figure that the North Carolina Department of Public Instruction (DPI) publishes on its website and reports to the National Education Association. These debates take up the important consideration of whether or not teachers are…