Problem solving is widely regarded as a fundamental feature within the school mathematics curriculum. However, there is considerable disagreement over what exactly problem solving is, and if and how it can be taught. In this article, I define problems as non-routine tasks and propose the explicit teaching of domain-specific problem-solving tactics…

On the surface, the number line may seem like a basic tool with obvious applications. However, using a number line is not always intuitive for students. Students may not recognize significant features such as the size of the unit, how units are represented by iterated equal lengths, or that the accumulation of iterated units is a magnitude of…

Capturing and measuring instructional patterns by using standardized observation manuals has become increasingly popular in classroom research. While researchers argue that a common vocabulary of teaching is necessary for the field of classroom research to move forward, instructional features vary across classrooms and contexts, which poses…

We introduce the concept of the "sequence of the ratios of convex quadrilaterals," identify some properties of these sequences and use them to provide new characterizations for some classic quadrilateral families. The research involves aspects of geometry, arithmetic and mathematical analysis, which converge to produce the results.

In this article, the authors explore how the 3C Model can be used to integrate other curriculum areas with mathematics, namely digital technologies. To illustrate the model, they provide a practical example of a teaching sequence. T he 3C Model is designed to create opportunities for applying reasoning and problem-solving skills and learning…

To help students acquire mathematics and science knowledge and competencies, educators typically use multiple external representations (MERs). There has been considerable interest in examining ways to present, sequence, and combine MERs. One prominent approach is the concreteness fading sequence, which posits that instruction should start with…

We define and describe how subitizing activity develops and relates to early quantifiers in mathematics. Subitizing is the direct perceptual apprehension and identification of the numerosity of a small group of items. Although subitizing is too often a neglected quantifier in educational practice, it has been extensively studied as a critical…

The use of video games as an educational tool initially causes a higher degree of motivation in students. However, the inclusion of educational activities throughout the game can cause this initial interest to be lost. A good way to maintain motivation is to use a good story that is used as guiding thread with which to contextualize the other…

Fractions are an essential foundational skill for future mathematics success (NMAP, 2008). The purpose of this article was to review current instructional practices for teaching fractions to struggling learners and to examine the quality and effectiveness of contemporary research with a view to indicating directions for future research. A…

In the process of experiential learning, students acquire skills and values as the consequence of a direct experience. Experiential learning draws on senses, emotions, and cognition and appeals to learners' entire being. Such learning, by nature, enables the development of a variety of capabilities, such as planning, teamwork, coping with…