Mathematics educators and researchers have advocated for the use of manipulatives to teach mathematics for decades. The purpose of this article is to provide illustrative uses of a readily available manipulative rather than a complete list. From an Australian perspective, Pop-it fidget toys can be used across the mathematics curriculum. This paper…

Algorithms and representations have been an important aspect of the work of mathematics, especially for understanding concepts and communicating ideas about concepts and mathematical relationships. They have played a key role in various mathematics standards documents, including the Common Core State Standards for Mathematics. However, there have…

Experts think in patterns and structures using the specific "language" of their domains. For mathematicians, these patterns and structures are represented by numbers, symbols and their relationships (Stokes, 2014a). To determine whether elementary students in the United States could learn to think in mathematical patterns to solve…