The current study investigated the effects of the concrete-representational-abstract integrated sequence (CRA-I) for teaching fifth grade students receiving tier two interventions within a multi-tiered system of support (MTSS). The research questions addressed the following: the extent to which students' rational number skills changed as a result…

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…

Understanding negative numbers can be challenging for many students, as these concepts may seem less tangible than counting objects, which are commonly represented by positive numbers. In addition, the multiplication of two negative numbers resulting in a positive might appear inconsistent and puzzling to young learners who are used to seeing the…

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…

Background: Foundation phase teachers are encouraged to develop learners' number sense skills in their teaching and learning activities. Despite the significance of teaching number skills in mental mathematics activities, there are inadequate guidelines that could assist teachers in developing number sense skills through technology-enhanced mental…

This paper reports on an experiment involving 108 sixth-grade French students in which the history of Chinese numeration was used in mathematics education. The aim of this study is to evaluate the relevance of using ancient number systems in mathematics education, which is common in French textbooks. In the experiment a pre-test with usual…

Identifying and addressing the knowledge gap in early numeracy is crucial, given the strong associations between early numeracy skills and later school success. The purpose of this study is to establish current viewpoints and ideas on children's numeracy development via three forms of representation: manipulative, symbolic, and static. The…

Solving problems involving absolute value is one of the hardest topics for students learning in elementary algebra course. This is an important topic in student's mathematics life since absolute value functions are important example of a function which is continuous on the real line but not differentiable at the origin. A deep understanding of…

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 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)…

Developing a positive relationship with mathematics in early elementary is vital for success in future mathematics education. Students who do not develop an understanding of mathematical number sense in early grade levels struggle to make connections in later courses. Mathematical discourse sessions, specifically Number Talks, encourage students…

This article is dedicated to the topic of discovering effective ways of developing students' programming abilities with the means of non-programming disciplines and activities. The authors argue that the process of educating students in programming becomes effective if students participates not only in programming lessons themselves, but also…