Integer operations are typically introduced in sixth grade, but they are a consistent area of struggle among these students. This struggle also inhibits their understanding of algebraic computations involving positive and negative terms. In this article, the author provides introductory tasks and models for adding and subtracting integers that can…

Understanding fraction magnitudes is foundational for later math achievement. To represent a fraction "x/y," children are often taught to use "partitioning": break the whole into "y" parts, and shade in "x" parts. Past research has shown that partitioning on number lines supports children's fraction…

Understanding fraction magnitudes is foundational for later math achievement. To represent a fraction x/y, children are often taught to use "partitioning": Break the whole into y parts and shade in x parts. Past research has shown that partitioning on number lines supports children's fraction magnitude knowledge more than partitioning on…

Visualising positive and negative numbers on a number line is helpful for exploring problems involving operations with positive and negative numbers. This is because number lines lend themselves to exploring problems involving continuous linear contexts such as travelling distances and temperature. Teachers in a professional development program…

Recent studies show that English learning students are a growing population within the United States school system. Language barriers have been shown to negatively influence reading scores as well as math scores, and math scores are a predictor of future academic success in many subject areas. This qualitative action research study demonstrates…

Number system knowledge (NSK) is broadly defined as the understanding of number relationships and is an essential mathematics skill for young elementary school-aged students. NSK instruction that emphasizes connections between number sense and spatial reasoning could be a critical anchor for second-grade students to stay rooted in their conceptual…

This paper reports on exploratory research into visual imagery in the learning of early mathematics. It aims to present a theoretical position in relation to perceptual perspectives of visual imagery. Students' visual imagery is explored in one example of a teacher's use of a protocol to encourage students to replicate dot patterns. This example…

The purpose of this study was to examine patterns of mathematical practices evident during children's interactions with touchscreen mathematics virtual manipulatives. Researchers analyzed 33 Kindergarten children's interactions during activities involving apps featuring mathematical content of early number sense or quantity in base ten, recorded…

Research indicates that parental involvement in children's education is positively related to academic achievement in mathematics; however, there are few studies on the role of parental involvement in the context of developing countries. The purpose of this paper is to document the iterative development using design-based research (DBR) of a…

The purpose of this study was to investigate the preservice secondary mathematics teachers' development of pedagogical understanding in the teaching of modular arithmetic problems. Data sources included, written assignments, interview transcripts and filed notes. Using case study and action research approaches cases of three preservice teachers…

Describes three activities of imaging, including constructing an image, representation-presenting the image, and transforming the image. Discusses a link between imaging and number sense, teaching students to image, and assessing imaging. Contains 25 references. (ASK)

Provides opportunities for children to develop visual images of the number situations they are exploring in order to develop powerful number sense. Illustrates two visual teaching aids to help young children develop number images. (ASK)

Six- to eight-year-old children (N=42) who were identified by their teachers as within the average range of ability in mathematics were individually tested on three different mathematics tasks. On the flashcard task and the nonverbal task where children replicated the number of buttons placed under a box, the same 14 addition problems with sums up…

Presents examples of visual representations helpful in understanding number relationships and the algebraic statements of these relationships. Suggests that these representations can be used by teachers to aid students in discovering number relationships and in acquiring meaning for given mathematical statements. (PK)

Sample materials from a primary training packet are included. The packets were developed as a part of a teacher development program aimed at improving elementary mathematics by giving teachers practical ideas. The sample student materials are drawn from the areas of geometry and oral mathematics. (PK)