Students, even as young as kindergarten, are natural problem solvers (Carpenter et al., 2017). Even before they learn to count, they can make sense of mathematical problems and real- world situations (National Council of Teachers of Mathematics, 2022). Kindergartners can make sense of complex story problems, including Separate Start Unknown…

Missing data are common with large scale assessments (LSAs). A typical approach to handling missing data with LSAs is the use of listwise deletion, despite decades of research showing that approach can be a suboptimal strategy resulting in biased estimates. In order to help researchers account for missing data, we provide a tutorial using R and…

Every educator knows the sinking feeling of a lesson gone wrong. As teachers look around the room and realize that many of their students are just not getting it, they often feel like failures. However, the struggle students experience as they persevere through high-quality challenging tasks is not a sign of failure, but rather a key aspect of…

The advancement of large language model-based generative artificial intelligence (LLM-based GenAI) has sparked significant interest in its potential to address challenges in computational thinking (CT) education. CT, a critical problem-solving approach in the digital age, encompasses elements such as abstraction, iteration, and generalisation.…

To provide practice and assessment of computational thinking, we need specific problems students can solve. There are many such problems, but they are hard to find. Learning environments and assessments often use only specific types of problems and thus do not cover computational thinking in its whole scope. We provide an extensive catalog of…

In the realm of K-12 Education, the growing significance of Computational Thinking has sparked extensive inquiry into its nature and instructional methodologies. Despite a wealth of literature on the subject, ongoing debates persist regarding its fundamental components. Across global educational landscapes, Computational Thinking is being…

Enrico Fermi is remembered for his many contributions to theoretical and experimental physics, but from an educational point of view he also popularized the use of the kind of questions we now call "Fermi problems" (or "Fermi questions"). Fermi problems (FPs) are back-of-envelope problems that arose from the need to make order…

Four variations of the Koch curve are presented. In each case, the similarity dimension, area bounded by the fractal and its initiator, and volume of revolution about the initiator are calculated. A range of classroom exercises are proved to allow students to investigate the fractals further.

Functions and formulas in spreadsheets provide an instructional opportunity to help students build their skills in identifying errors in their own work and identifying a path to go about correcting the errors. This paper provides examples of functions and equations used to create two approaches to calculating the solution to one problem, such as a…

In this paper we follow a hypothetical mathematician who is working on a problem that is eventually solved. We treat this problem as if it were difficult for the mathematician. In following the mathematician's work, we note both what she does and what she doesn't do in the process. By the latter, we consider the times when progress is not being…

This is a conceptual paper based on existing literature aiming to provide practical information on designing and implementing activities to promote children's computational thinking. Computational thinking is a relatively new term in early childhood education that refers to a specific problem-solving thinking process involving various logical and…

In a typical first physics class, homework consists of problems in which numerical values for physical quantities are given and the desired answer is a number with appropriate units. In contrast, most calculations in upper-division undergraduate physics are entirely symbolic. Despite the need to learn symbolic manipulation, students are often…

In this article we show that the electrostatic field intensity of a uniformly charged straight line equals that of the corresponding arc of a circle charged with the same linear density. This new method greatly simplifies the calculation of the electrostatic field of a system consisting of uniformly charged straight lines.

Quadratic functions are explained in the three equivalent formats: Standard (or Expanded), Vertex and Factorised. However, cubic functions are represented only in the two equivalent formats: Standard (or Expanded) and Factorised. In this article, the author shows how cubic functions can be expressed in three equivalent formats like quadratic…

Having students solve shape puzzles, such as with pattern blocks or tangrams, is a popular way to encourage students to compose shapes in different ways and talk about the effects of different compositions (Clements et al., 2004; Clements & Sarama, 2009; Sales, 1994), meeting Common Core geometry standards in kindergarten through second grade…