Felix Klein's Erlangen program classifies geometries based on the kinds of geometric transformations that preserve key properties of their figures, rather than focusing on the geometric figures themselves. This shift in perspective, from figurative to operative, fits Piaget's characterization of mathematical development. This paper considers how…

Undergraduate quantum mechanics (QM) uses a variety of notations, each with their own advantages and constraints, for representing quantum states and carrying out individual calculations. An example of this can be seen when calculating expectation values, which can be solved using several different methods. Analysis of written exam data given at…

This study investigates the impact of different modes and tailor-made response enhancing measures (TMREM)--such as bilingual interviewers with a shared ethnic background and translated questionnaires--on the measurement of substantive variables in surveys among minority ethnic groups in the Netherlands. It also provides insight into the ability to…

Whole Number Arithmetic (WNA) appears as the very first topic in school mathematics and establishes the foundation for later mathematical content. Without solid mastery of WNA, students may experience difficulties in learning fractions, ratio and proportion, and algebra. The challenge of students' learning and mastery of fractions, decimals, ratio…

This paper makes a proposal, from the perspective of a research mathematician interested in mathematics education, for broadening and deepening whole number arithmetic instruction, to make it more relevant for the twenty-first century, in particular, to enable students to deal with large numbers, arguably an essential skill for modern citizenship.…

Predictability of behavior is an important characteristic in many fields including biology, medicine, marketing, and education. When a sequence of actions performed by an individual can be modeled as a stationary time-homogeneous Markov chain the predictability of the individual's behavior can be quantified by the entropy rate of the process. This…

This paper develops the ideas of "The Pedagogical Power of Context: Iterative Calculus Methods and the Epidemiology of Eyam" (French "et al." 2018 "J. Phys. Educ."), where we considered the application of the Euler method to solve epidemiological problems. Our purpose was to convey some examples of school level work…

Since 2006, there has been an ever-increasing momentum in computational thinking educational policy initiatives (CTEPI) across the globe. In this paper, the representative CT educational policy initiatives viewed through the lens of international perspectives and cultural contexts were examined, compared and discussed. Reports, white papers, and…

A series of computational laboratory experiments aimed at teaching students principles of rational drug design are described and evaluated. These experiments range from an introduction to viewing protein-ligand complexes to optimizing geometries of potential drugs with quantum chemistry and automated docking. Student feedback indicates that such a…

All studies with randomized controlled experiments (scientific studies) on the effectiveness of SAT test preparation courses were analyzed to find SAT prep's true effectiveness (the average point change to average course hours ratio). The scientific studies complete with both known average point change and known average course length (complete…

Background and context: Historically underrepresented youth in computer science persistently experience barriers making it difficult to see themselves in the computer science field including computer science programs and curricula with consistent stereotypical references focused on competition, individualism, and male-associated topics…

Computational Thinking (CT) is essential for developing creativity, problem-solving, and digital competence in the 21st century. Coding tools like robotic toys and tablet apps have become popular in early childhood education to support CT development, but there is a debate on which tool is more effective. Little evidence exists on the effect of…

In the following research review, 57 articles were analysed to get an insight into research in the field of computational thinking and programming in K-12. The results show that empirical research regarding programming and computational thinking is prevalent in the USA and Greece. The articles were published in 43 different academic journals. A…

STEM experiences that capture students' curiosity have a unique role in inspiring awe in science, enculturing science engagement, and recruiting students to pursue STEM careers. Here, we present a unique interdisciplinary STEM experience for elementary school students that teaches them to write computer code to test primate intelligence at a zoo…

Computational thinking is acknowledged as an essential competency for everyone to learn. However, teachers find it challenging to implement the existing learning approaches in K-12 settings because the existing approaches often focus on teaching computing concepts and skills (i.e., programming skills) rather than on helping students develop their…