The tradition of studies involving the combinatorial approach to recurring numerical sequences has accumulated a few decades of tradition, and several problems continue to attract the interest of mathematicians in several countries. This work specifically discusses the Fibonacci, Pell, and Jacobsthal sequences, focusing on Mersenne sequences. The…

Even though there is a great temptation as teachers to share what is known, many are aware of an idea called "rules that expire" (RTE) and have realized the importance of avoiding them. There is evidence that students need to understand mathematical concepts and that merely presenting rules to carry out in a procedural and disconnected…

Early algebraic thinking is the reasoning engaged in by 5- to 12-year-olds as they build meaning for the objects and ways of thinking to be encountered within the later study of secondary school algebra. Ever since the 1990s when interest in developing algebraic thinking in the earlier grades began to emerge, there has been a steady growth in the…

It's often useful extending students beyond the limiting geometry of triangles and quadrilaterals to regularly consider generalizations of results for triangles and quadrilaterals to higher order polygons. A brief heuristic description is given here of the author applying this strategy, and which led to an interesting result related to the…

This article examines whether geography can provide the powerful knowledge that is a key element of a Future 3 curriculum, and an important component of the GeoCapabilities Project's proposals for the teaching of geography. Powerful knowledge is knowledge that gives students the intellectual ability to analyse, explain, predict, evaluate and think…

There is limited research using small-scale simulation in applied behavior analysis. We used small-scale simulation to train firearm safety skills to 3- to 5-year-old children and assessed whether the skills generalized to the natural environment through in situ assessment. Three participants completed the training, and all participants learned…

According to Bryan Warwick, policy can cause tragedy. A famous example is the tragedy described in Sophocles' play "Antigone." In this play, Creon, the political leader of ancient Thebes, causes tragedy in his quest to educate his people about civic loyalty. The conflict engendered by his educational policy eventually brings death and…

Educational materials focused on spatial data analysis often feature mathematical descriptions of methods and step-by-step instructions of software tools, but infrequently discuss the set of decisions involved in specifying a statistical model. Failing to consider model specification may lead to specification searching, or the process of repeating…

This paper explored the following: (1) teachers' ways of attending to students' written responses in pattern generalization tasks and (2) differences in the ways of attending to students' responses associated with different factors. A questionnaire was developed to classify teachers' ways of attending to students' written responses. The…

This article presents a checklist of 10 evidence-based practices for educators to apply in mathematics instruction for students with learning disabilities. The checklist is "actionable," meaning the items on the checklist can be put into action immediately. It provides practical strategies teachers can adopt to fit their lessons…

Studies of lexical coverage are valuable because they reveal the importance of vocabulary knowledge to comprehension. Lexical profiling research is also extremely useful because it indicates the vocabulary knowledge necessary to understand different text types such as novels, newspapers, academic lectures, television programs, and movies.…

In this article, David Lewin examines the processes of educational representation, simplification, and selection, proposing the term "pedagogical reduction" in order to clarify the role these processes play within pedagogy. Although this term is virtually unknown among Anglo-American educational theorists, it reflects a substantial…

The work describes an analogy-based small oscillations analysis of a standard static equilibrium lab problem. In addition to force analysis, a potential energy function for the system is developed, and by drawing out mathematical similarities to the simple harmonic oscillator, we are able to describe (and experimentally verify) the period of small…

The paper focuses on the comparative analysis of professional competences development in public management and administration university programmes and the possibilities of implementation of international experience in Ukraine. Using the methods of comparative and system-functional analysis, synthesis and generalisation, the authors concentrate on…

The United States of America is currently experiencing some socio-political problems. These problems stem from myriad mythologies and assumptions that have created labels, categories, stereotypes, and generalizations. While they are not uncommon in many communities and societies all over the world, in the United States, they have exposed intense…