Research has identified the essential proficiencies students should possess to be successful, but they are often not incorporated in the ESOL classroom. As a result, many teachers lack access to adequate instructional strategies to guide ELs to academic success. We argue in this article that, to provide a strong foundation and a bright future for…

Executive function (EF) refers to the set of core self-regulatory skills required for deliberate, goal-directed problem solving. These skills, which are exercised when children pause and reflect before reacting, provide a foundation for learning in a classroom context. They make it possible to pay attention, think flexibly, keep information in…

This article reviews the famous "matching problem," with a particular focus on the expected number of objects that are correctly placed. The author discusses the following topics: three versions suitable for teaching the matching problem in the classroom; the solution to the matching problem; the use of the strong form of mathematical…

In this article, Clay and Rhee use the mathematics topic of circles and the lines that intersect them to introduce the idea of looking at the single mathematical idea of relationships--in this case, between angles and arcs--across a group of problems. They introduce the mathematics that underlies these relationships, beginning with the questions…

Students with learning disabilities (LD) consistently struggle with word problem solving in mathematics classes. This difficulty has made curricular, state, and national tests particularly stressful, as word problem solving has become a predominant feature of such student performance assessments. Research suggests that students with LD perform…

The "Next Generation Science Standards" (NGSS Lead States 2013) urge science teachers to include engineering practices and ideas in their already full science curriculum, but many teachers do not know where to start. Only 7% of high school science teachers report feeling "very well prepared" to teach engineering. The…

Constructing viable arguments and reasoning abstractly is an essential part of the Common Core State Standards for Mathematics (CCSSI 2010). This article discusses the scenarios in which a mathematical task is impossible to accomplish, as well as how to approach impossible scenarios in the classroom. The concept of proof is introduced as the…

In this paper, I discuss one of the most distinguishing features of Jamshid al-Kashi's pedagogy from his "Key to Arithmetic", a well-known Arabic mathematics textbook from the fifteenth century. This feature is the multiple paths that he includes to find a desired result. In the first section light is shed on al-Kashi's life…

For students to be successful in algebra, they must have a truly conceptual understanding of key algebraic features as well as the procedural skills to complete a problem. One strategy to correct students' misconceptions combines the use of worked example problems in the classroom with student self-explanation. "Self-explanation" is the…

How do students think about an angle measure of ninety degrees? How do they think about ratios and values on the unit circle? How might angle measure be used to connect right-triangle trigonometry and circular functions? And why might asking these questions be important when introducing trigonometric functions to students? When teaching…

Providing students with an opportunity to explore mathematical content through games allows teachers to include tasks that: (1) present alternative representations of the content; (2) welcome various expressions of mathematical reasoning; and (3) incorporate variations that empower all students to engage in the problem solving process. Games not…

With regard to the growing interest in developing teacher education to match the twenty-first-century skills, while many assumptions have been made, there has been less theoretical elaboration and empirical research on this topic. The aim of this article is to present our pedagogical framework for the twenty-first-century learning practices in…

A strong and vibrant economy is reliant on a strong and vibrant workforce equipped with the necessary skills, competencies, and knowledge. Afterschool and summer learning programs play an integral role readying students for their career pathways; not only helping them develop the foundational skills that are critical across the different contexts…

When Martin Gardner first presented the Two-Children problem, he made a mistake in its solution. Later he corrected the error, but unfortunately the incorrect solution is more widely known than his correction. In fact, a Tuesday-Child variation of this problem went viral in 2010, and the same flaw keeps reappearing in proposed solutions of that…

This article describes what is often referred to as the dog, beetle, mice, ant, or turtle problem. Solutions to this problem exist, some being variations of each other, which involve mathematics of a wide range of complexity. Herein, the authors describe the intuitive solution and the calculus solution and then offer a completely new solution…