We share a subset of the 41 underlying strategies that comprise five ways of reasoning about integer addition and subtraction: formal, order-based, analogy-based, computational, and emergent. The examples of the strategies are designed to provide clear comparisons and contrasts to support both teachers and researchers in understanding specific…

The aim of this study is to compare students' use of number sense strategies based on their mathematics success levels. Participants were 129 seventh graders from three elite secondary schools in Trabzon. Data were collected through a written examination with 10 problems and semi-structured interviews. Interview data were analyzed by considering…

The aim of the study is to examine whether classroom teachers' Pedagogical Content Knowledge (PCK) on numbers develops in the period from their university education to their active teaching profession. Cross-sectional comparative study method was used in this research in order to examine what kind of development classroom teachers? pedagogical…

The main aim of this article was to investigate the educational potential of a game-based math game competition to engage students in training rational numbers. Finnish fourth (n = 59; M[subscript age] = 10.36) and sixth graders (n = 105; M[subscript age] = 12.34) participated in a math game competition relying on intra-classroom cooperation and…

Algebraic notation has been bedazzling learners for generations, yet despite research, learned papers, comparative studies, and a great deal of hard work on the part of classroom practitioners the situation remains a stubborn constant. In this article some small-scale research has highlighted some issues that might find a resonance in many…

Looking for, recognizing, and using underlying mathematical structure is an important aspect of mathematical reasoning. We explore the use of mathematical structure in children's integer strategies by developing and exemplifying the construct of logical necessity. Students in our study used logical necessity to approach and use numbers in a…

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…

Research Findings: The present study involved using a questionnaire to investigate the mathematics teaching practices of 74 U.S. and 67 Chinese early childhood teachers. Quantitative and qualitative analyses yielded several key findings. First, U.S. teachers are less intentional in mathematics teaching than their Chinese counterparts.…

A majority of studies on learning disabilities have focused on elementary grades. Although problems with learning disabilities are life-affecting only a few studies focus on deficits in adults. In this study adults with isolated mathematical disabilities (n = 101) and adults with combined mathematical and reading disabilities (n = 130) solved…