As students have struggled to use the "chip model" (i.e., red and yellow chips representing positive and negative numbers) to model integer addition and subtraction and have found it confusing, the authors developed a series of activities based on adding and removing opposite objects to and from a boat to better help students in this…

Early mathematics plays an important role in introducing foundational concepts for number sense in children. One of the critical areas of learning is the establishment of a linear view of numbers. It is essential to create opportunities for young children to understand that numbers are equally spaced on the number line and that they increase in…

Reimagining elementary mathematics pedagogy using a three-step process--See It, Say It, Symbolize It--author Patrick L. Sullivan provides a guide for developing a dynamic and flexible understanding of numbers and operations. By helping students develop a language that is consistent across concepts and connecting it to what is seen and symbolized,…

According to National Council of Teachers of Mathematics (NCTM), students must develop a conceptual understanding of place value by second grade to understand that mathematics processes are more than a set of procedural steps. Yet, students with learning disabilities in mathematics typically struggle to understand place value in a deeper,…

The book synergizes research on number across two disciplines--mathematics education and psychology. The underlying problem the book addresses is how the brain constructs number. The opening chapter frames the problem in terms of children's activity, including mental and physical actions. Subsequent chapters are organized into sections that…

Research shows that frequent, high-quality mathematics talk that is shared between parents and children can increase mathematics achievement. This article describes ways in which teachers can support parents in increasing the frequency and quality of parent-child mathematics interactions, leading to better outcomes for students.

Students thrive when presented with tasks that are approachable, challenging, and interesting. Remembering to challenge all students is essential, not just those who excel in mathematics; teachers need to open the door to meaningful mathematics for every learner. In this exploration into subtraction patterns, teachers will see how curious young…

We are pleased to bring you this follow-up to Mairéad Hourigan and Aisling Leavy's article [EJ1289314] that was published in issue 1 this year. In this contribution, they demonstrate that embedding mathematics within a rich context and learning sequence assists with the consolidation of student understanding and makes more effective use of teacher…

This article examines the importance of developing the notion of place value as a rate of ten. In exploring how to nurture this concept, the author looks at the role of the language of value, the problem types of multistep multiplication and addition along with measurement division, each with ten as an organizing unit, as well as strategically…

When asked to determine the number of tens in twenty-five, most second graders who have had instruction on place value can quickly provide the correct answer of two. However, when asked to show how the numeral 2 is represented in a set of twenty-five objects, many children struggle to draw a connection between the digit 2 and twenty objects in the…

To become scientifically literate, students need to interpret science concepts using numbers, text, and visuals (Lemke 2004). Scientists use multiple modes to communicate their ideas to each other and the public, including images, text, mathematical notations, symbols, diagrams, charts, and graphs. Several of the science and engineering practices…

The author wants her students to see any new mathematics--fractions, negative numbers, algebra--as logical extensions of what they already know. This article describes two students' efforts to make sense of their conflicting interpretations of 1/2 × -6, both of which were compelling and logical to them. It describes how discussion, constructing…

Mathematics instruction in the United States has historically focused on procedures, facts, and algorithms. Because of that focus, mathematics instruction, in essence, becomes lessons in arithmetic and efficiency. While there are promising changes occurring in mathematics instruction, we still need to help both teachers and students develop a more…

Representations that create informative visual displays are powerful tools for communicating mathematical concepts. The National Council of Teachers of Mathematics encourages the use of manipulatives (NCTM 2000). Manipulative materials are often used to present initial representations of basic numerical principles to young children, and it is…

"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…