This article illustrates how teachers can use number lines to support students with or at risk for learning disabilities (LD) in mathematics. Number lines can be strategically used to help students understand relations among numbers, approach number combinations (i.e., basic facts), as well as represent and solve addition and subtraction problems.…

Development of the cardinality principle, an understanding that the last number-word recited in counting a collection of items specifies the number of items in that collection, is a critical milestone in developing a concept of number. Researchers in early number development have endeavored to theorize its development. Here we critique two widely…

This paper describes a study for teaching number system in a computer arithmetic course and addresses the existing gap in the current course by focusing on the characteristics of applications. A redundant residue number system (RRNS) is an efficient and innovative number system that inherits the interesting properties of both residue number system…

Building proficiency with fraction arithmetic poses a consistent challenge for students with learning difficulties or disabilities in mathematics. This article illustrates how teachers can use the number line model to support struggling learners in making sense of fraction arithmetic. Number lines are a powerful tool that can be used to help…

Young children need to be taught using effective interventions. A good teaching method is one that will increase children's motivation to learn, keep them aware of their understanding and encourage them to reflect on what they learn, if this teaching is based on relevant and visible training. Otherwise, they may suffer from delays in mathematics.…

This report delineates the outcomes of an intervention conducted with in-service high school educators, focusing on elucidating three distinct scenarios within geometric and arithmetic domains: the infinitely large, infinitely numerous, and infinitesimally close. Grounded in the theoretical framework of conceptual change, it is posited that when…

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…

To explain children's difficulties learning fraction arithmetic, Braithwaite et al. (2017) proposed FARRA, a theory of fraction arithmetic implemented as a computational model. The present study tested predictions of the theory in a new domain, decimal arithmetic, and investigated children's use of conceptual knowledge in that domain. Sixth and…

In this paper, we report how 5-year-olds' arithmetic skills developed through participation in an 8-month-long intervention. The intervention program aimed to enhance the children's ways of experiencing numbers' part-part-whole relations as a basis for arithmetic skills and was built on principles from the variation theory of learning. The report…

This practical book draws on Ronit Bird's teaching experience to create detailed strategies and teaching plans for students aged 9-16 who have difficulties with number. Activities and games are used to teach numeracy skills in these key areas: number components, bridging, multiplication, division and reasoning strategies. New to this edition: (1)…

Although the complexity of children's number learning is recognized, trade books about number have been treated as a simple, undifferentiated set. This analysis of 186 children's books, however, categorized a distinct subset of books about number as "counting books." These counting books were complex with regard to portrayal of counting…

This document includes instructional tips on: (1) Building on students' informal understanding of sharing and proportionality to develop initial fraction concepts; (2) Helping students recognize that fractions are numbers that expand the number system beyond whole numbers, and using number lines to teach this and other fraction concepts; (3)…

This paper makes a proposal, from the perspective of a research mathematician interested in mathematics education, for broadening and deepening whole number arithmetic instruction, to make it more relevant for the twenty-first century, in particular, to enable students to deal with large numbers, arguably an essential skill for modern citizenship.…

"Where Mathematics Comes From" (Lakoff & Núñez 2000) proposed that mathematical concepts such as arithmetic and counting are constructed cognitively from embodied metaphors of actions on physical objects, and four actions, or 'grounding metaphors' in particular: collecting, stepping, constructing and measuring. This article argues…