In this article we present an activity theory based framework that can capture the complex situations that arise when modern technology like multi-touch devices are introduced in classroom situations. As these devices are able to cover more activities than traditional technologies, even computerbased, media, we have to accept that they now take a…

This paper presents guided classroom activities that showcase two classic problems in which a finite limit exists and where there is a certain charm to engage liberal arts majors. The two scenarios build solely on students' existing knowledge of number systems and harness potential misconceptions about limits and infinity to guide their thinking.…

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…

How can children's natural perceptuo-motor skills be harnessed for teaching and learning mathematical structure? We address this question in the case of the integers. Existing research suggests that adult mental representations of integers recruit perceptuo-motor functionalities involving symmetry. Building on these findings, we designed a…

When a child understands number relationships, he or she comprehends the meaning of numbers by developing multiple, flexible ways of representing them. The importance of developing number relationships in the early years has been highlighted because it helps children build a good foundation for developing a more sophisticated understanding of…

The authors compared the performance of students who received integration of number sense activities in instruction with students who received instruction using regular mathematics textbooks. Two classes of third-grade students (N = 60) were randomly assigned to experimental and control groups. Students in each group were given a pretest, post I…

Fluency with basic number facts is vital for students' progress in mathematics. Not only does it contribute to students' facility with mental computation and algorithms, but an understanding of numbers and their properties builds a foundation for future mathematical work including algebra. There are many activities that can help students…

How do teachers teach students to count rhythms? Teachers can choose from various techniques. Younger students may learn themed words (such as "pea," "carrot," or "avocado"), specific rhythm syllables (such as "ta" and "ti-ti"), or some other counting method to learn notation and internalize rhythms. As students grow musically, and especially when…

Considerable evidence shows that the number line is a powerful learning tool for children in elementary school. Diezmann and Lowrie (2006) noted several cognitive advantages for users, including opportunities to demonstrate the continuity aspect of numbers as well as the provision of a useful tool for representing and solving problems. However,…

The aversion that many girls and boys experience towards mathematics has been one of the author's major concerns since he started teaching. In this article, he describes a project called "Numbers Day" that was designed to improve students' attitudes toward mathematics. There are many features of Numbers Day that teachers might…

A good-quality teacher may determines a good-quality learning, thus good-quality students will be the results. In order to have a good-quality learning, a lot of strategies and methods can be adopted. The objective of this research is to improve students' ability in determining the rules of a numeric sequence and analysing the effectiveness of the…

Prime numbers are often described as the "building blocks" of natural numbers. This article shows how the author and his students took this idea literally by using prime factorizations to build numbers with blocks. In this activity, students explore many concepts of number theory, including the relationship between greatest common factors and…

This document presents a review of evidence commissioned by the Education Endowment Foundation to inform the guidance document "Improving Mathematics in Key Stages Two and Three" (Education Endowment Foundation, 2017). The review draws on a substantial parallel study by the same research team, funded by the Nuffield Foundation, which…

Subtraction has two meanings and each meaning leads to the different strategies. The meaning of "taking away something" suggests a direct subtraction, while the meaning of "determining the difference between two numbers" is more likely to be modeled as indirect addition. Many prior researches found that the second meaning and…

Starting with an interesting number game sometimes used by school teachers to demonstrate the factorization of integers, "sum-difference numbers" are defined. A positive integer n is a "sum-difference number" if there exist positive integers "x, y, w, z" such that n = xy = wz and x ? y = w + z. This paper characterizes all sum-difference numbers…