Valence shell electron pair repulsion theory (VSEPR) as explained in most textbooks predicts that substituents bonded to a central atom in AX[subscript n]E[subscript z][superscript c] species (A = main-group central atom, X = substituent, E = lone pair on central atom, c = charge) will change their X-A-X angles to bend away from the lone pairs.…

This article will provide a historical perspective on the use of technology in education by focusing on the field of mathematics education. It will focus specifically on two technologies - presentation tools and calculating tools - and will explore their history and evolution as an example of how technological change, while not dramatically…

In this paper we propose a universal curricular framework that is intended to aid K-6 schoolteachers holistically and humanistically developing their students' computational thinking (CT) skills (e.g. algorithmic thinking, abstraction, decomposition, generalization, patterns recognition, evaluation, and logical thinking). This framework, which can…

The results of this study revealed students' solution strategies progressed from inefficient strategies e.g., counting on fingers to more efficient strategies with mathematical connections. These findings should enable educators to gain more insight to use Number Talks to help student develop computational fluency with numbers.

Development of the cardinality principle, an understanding that the last number-word recited in counting a collection of items specifies the number of items in that collection, is a critical milestone in developing a concept of number. Researchers in early number development have endeavored to theorize its development. Here we critique two widely…

In the article 'How Long Is My Toilet Roll--A Simple Exercise in Mathematical Modelling' several models of increasing complexity are introduced and solved to calculate indirectly the length of paper on a toilet-roll. All these results are presented without errors. The authors of this comment believe the error analysis of measurements made in a…

This article explores the educational and philosophical contributions of Nikolai V. Bugaev, a prominent 19th-century Russian mathematician and founder of the Moscow philosophical-mathematical school. The study specifically focuses on Bugaev's textbook, "Arithmetic of Whole Numbers," analyzing Bugaev's pedagogical approaches within the…

Computational thinking is accepted today as a collection of cognitive and social skills required for functioning in the 21st century. The paper presents a conceptual view at computational thinking that encompass concepts, problem-solving skills, application skills, and social skills. To impart those perceptions and skills the paper proposes the…

Computing has become essential in modern-day problem-solving, making computational literacy necessary for practicing scientists and engineers. However, K-12 science education has not reflected this computational shift. Integrating computational thinking (CT) into core science courses is an avenue that can build computational literacies in all…

The pervasiveness of Computer Science (CS) in today's digital society and the extensive use of computational methods in other sciences call for its introduction in the school curriculum. Hence, Computer Science Education is becoming more and more relevant. In CS K-12 education, computational thinking (CT) is one of the abused buzzwords: different…

Recently, Robin claimed to introduce clever innovations ('wrinkles') into the mathematics education literature concerning the solutions, and methods of solution, to differential equations. In particular, Robin formulated an iterative scheme in the form of a single integral representation. These ideas were applied to a range of examples involving…

Integrating computational thinking (CT) and science education is complex, and assessing the resulting learning gains even more so. Arguments that assessment should match the learning (Biggs, "Assessment & Evaluation in Higher Education," 21(1), 5-16. 1996; Airasian and Miranda, "Theory into Practice," 41(4), 249-254. 2002;…

Students often look to the standard algorithm, which requires rewriting the task, regrouping tens to create enough ones to subtract, and other opportunities to make errors. However, when the authors apply structural thinking, the resultant strategy is an efficient and elegant shortcut and even brings a positive connotation to the word…

In this conceptual essay, the author argues that computational methods and computer science more broadly should be embedded into English education programs. Positing that computational methods can deepen and expand the way literature is already taught in many English education programs and secondary English classrooms, the author first makes a…

"Where Mathematics Comes From" (Lakoff & Núñez 2000) proposed that mathematical concepts such as arithmetic and counting are constructed cognitively from embodied metaphors of actions on physical objects, and four actions, or 'grounding metaphors' in particular: collecting, stepping, constructing and measuring. This article argues…