As students develop understanding and fluency in single-digit operations such as addition, they develop sophisticated strategies and number sense (magnitude, number order, and composition). Deficits in number sense and reliance on inefficient approaches can lead to struggle in mathematics. Intervention research in this area reported effects on…

The teacher displayed counting cards that included both dots and numerals in order from one to five, as she counted them with her students. She then turned the cards facedown, keeping them in order, and began an identify-a-hidden-card activity with the class. This class was engaged in the third of three card activities that develop number sense…

To understand the concepts or principles in mathematics, children who have a concrete operational stage need physical objects that can bridge abstract concepts in mathematics. This research aims to evaluate the influence of coastal contextual learning media on a child's understanding concept in the material of numbers counting operation. This…

"Improving Mathematics in the Early Years and Key Stage 1" reviews the best available evidence to offer five recommendations for developing the maths skills of 3-7-year olds. Recommendations include integrating maths into different activities throughout the day -- for example, at registration and snack time -- to familiarise children…

Teachers in early childhood and elementary classrooms (grades K-5) have been using ten-frames as an instructional tool to support students' mathematics skill development for many years. Use of the similar five-frame has been limited, however, despite its apparent potential as an instructional scaffold in the early elementary grades. Due to scant…

Do concrete learning materials promote strong learning outcomes, or do they simply make learning tasks more initially accessible? Although concrete materials may offer an intuitive foothold on a topic, research on desirable difficulties suggests that more challenging tasks facilitate greater retention and transfer. In the approach introduced here,…

How do children use physical and virtual tools to develop new numerical knowledge? While concrete instructional materials may support the delivery of novel information to learners, they may also over-simplify the task, unintentionally reducing learners' performance in recall and transfer tasks. This reduction in testing performance may be…

"The Zeroing in on Number and Operations" series, which aligns with the Common Core State Standards and the NCTM Standards on Focal Points, features easy-to-use tools for teaching key concepts in number and operations and for addressing common misconceptions. Sharing the insights they've gained through decades of mathematics teaching and research,…

This paper examines the contribution of mathematical knowledge for teaching (MKT) and curriculum materials to the implementation of lessons on integer subtraction. In particular, it investigates the instruction of three teachers with differing MKT levels using two editions of the same set of curriculum materials that provided different levels of…

"The Zeroing in on Number and Operations" series, which aligns with the Common Core State Standards and the NCTM Standards and Focal Points, features easy-to-use tools for teaching key concepts in number and operations and for addressing common misconceptions. Sharing the insights they've gained in decades of mathematics teaching and research,…

"The Zeroing in on Number and Operations" series, which aligns with the Common Core State Standards and the NCTM Sandards and Focal Points, features easy-to-use tools for teaching key concepts in number and operations and for addressing common misconceptions. Sharing the insights they've gained through decades of mathematics teaching and research,…

"The Zeroing in on Number and Operations" series, which aligns with the Common Core State Standards and the NCTM Standards and Focal Points, features easy-to-use tools for teaching key concepts in number and operations and for addressing common misconceptions. Sharing the insights they've gained in decades of mathematics teaching and research,…

Projects that involve counting real things either from 1 to 100 or from 1 to 1000 are presented. The projects encourage children's guessing, ordering numbers, recording results in a variety of ways, counting elements of a subset as well as the entire set, and some problem solving. (MN)

This article introduces a framework for the remediation of number combination (NC) deficits. Research on the remediation of NC deficits is summarized, and research program studies are used to illustrate the 3 approaches to remediation. The Framework comprises a 2-stage system of remediation. The less intensive stage implementing 1 of 3…

Not all children are made the same. Learning disabilities like dyslexia, dysgraphia or dyscalculia are either not understood or ignored in schools. As a result, the schoolchildren suffer for no fault of theirs and they lag behind in their course of learning. They may find it difficult to achieve the basic skills of learning such as reading,…