Attending to the whole unit that a number refers to in a mathematical problem situation and showing flexibility in coordinating different units are foundational for mathematical understanding. In this study, we explored teachers' attention to and flexibility with referent units in situations involving fractions and fraction multiplication. Using…

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…

Mathematics teacher professional-development (PD) programs based on Cognitively Guided Instruction (CGI) have been developed and implemented with tens of thousands of elementary mathematics teachers worldwide since the 1980s. Starting with a focus on addition and subtraction on whole numbers in the first CGI PD program, the content of these…

This study examined preservice elementary teachers' change in their understanding of fraction operations while taking a mathematics methods course focused on grades 3-5. The preservice teachers (n = 48) completed an assessment before and after the course's unit on the teaching and learning of fractions. Specifically, the preservice teachers were…

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…

Simple experiences with probability can extend third graders' understanding of the need for fractions. Three activities are given which build on language-arts experiences and incorporate concepts in multiplication, graphs, and fractions. (MNS)

The National Science Foundation funded Calculators and Mathematics Project, Los Angeles (CAMP-LA) developed curriculum materials focused solely on the use of calculators. The project was developed in three stages. The first stage studied the mathematics curriculums from different states and identified topics that are not included but should be if…