The ubiquity of the subject of percentages in our everyday life demands that math teachers and pre-service math teachers demonstrate a profound knowledge and thorough understanding of the concept of percentages. This work, which originated from one specific lesson in an 8th grade math class, studies the conceptual understanding and problem-solving…

Augmented reality (AR) is one of the emerging technologies that has demonstrated to be an efficient technological tool to enhance learning techniques. In this paper, we describe the development and evaluation of an AR system for teaching Euclidean vectors in physics and mathematics. The goal of this pedagogical tool is to facilitate user's…

This article aims to describe the transition process from procedural understanding to conceptual understanding in solving mathematical problems. Subjects in this study were three students from 20 fifth grade students of SDN 01 Sumberberas Banyuwangi selected based on the results of the students' answers. The transition process from procedural to…

The paper proposes a new interdisciplinary approach to helping low attaining learners in basic mathematics. It reports on the research-informed design and user testing of an adaptive digital game based on constructionist tasks with intrinsic feedback. The approach uses findings from the neuroscience of dyscalculia, cognitive science research on…

A "repeating pattern" is a cyclical repetition of an identifiable core. Children in the primary grades usually begin pattern work with fairly simple patterns, such as AB, ABC, or ABB patterns. The unique letters represent unique elements, whereas the sequence of letters represents the core that is repeated. Based on color, shape,…

In light of the recent growing interest in conceptual learning and teaching of calculus, and especially with the focus on using technological environments, our study was designed to explore the learning processes and the role played by multiple-linked representations and by interactive technological environment in objectifying the accumulation…

American schools and districts shift from teaching previously adopted math standards to the Common Core State Standards for Mathematics. Previous researchers have addressed aspects of exemplary pedagogy for Common Core math standards, but much of the research to this point has lacked descriptions of specific teacher language and actions that…

The purpose of this guide is to provide brief explanations of practices that can be implemented when working with students in need of intensive intervention in mathematics. Special education instructors, math interventionists, and others working with students who struggle with mathematics may find this guide helpful. Specific topics covered…

This paper presents a hypothesised learning trajectory for a Year 3 Indigenous student en route to generalising growing patterns. The trajectory emerged from data collected across a teaching experiment (students n = 18; including a pre-test and three 45-minute mathematics lessons) and clinical interviews (n = 3). A case study of one student is…

Every three years, the Programme for International Student Assessment, better known as PISA, evaluates 15-year-old students around the world to determine how well their education system has prepared them for life after compulsory schooling. Once the results are published, the media rush to compare their countries' positions in the international…

This study tried to explore the degree of representation of math textbooks for grades (4-8) in the Kingdom of Saudi Arabia concerning the key concepts, shape, and levels of questions used in the TIMSS test. The study population of this study includes both students and teachers from fourth grade to eighth grade. The goal of this study was…

In this paper we outline the main tenets of the commognitive approach and we exemplify its application in studies that investigate the learning and teaching of mathematics at university level. Following an overview of such applications, we focus on three studies that explore fundamental discursive shifts often occurring in the early stages of…

Scotland's Curriculum for Excellence (CfE), constitutes the demands that teachers are supposed to meet. Its intentions for the mathematics curriculum are similar to those in many countries: that learners be sufficiently mathematically literate to use mathematics in the personal, professional and societal dimensions of their lives. But like many…

In this article, John West explores student misconceptions relating to division. A range of activities that promote the understanding of divisibility rules are provided.

This paper reports on two students' work on geometry tasks in a dynamic geometry system. It augments prior work on students' instrumental geneses via a consideration of emergent goals that arise in students' work. It offers a way to interpret students' (working with new software) awareness of what software can and cannot do and students'…