Representations are key to mathematical activities and meaning-making processes as they are part of modeling, connecting, communicating, and understanding mathematical ideas and concepts. The current study sought to examine a group of novice algebra learners' interactions with different representations from an onto-semiotic approach. A case study…

While numerous studies have investigated teachers' professional learning through their interaction with resources, the question of how teachers' knowledge evolves at different stages of the instructional process remains underexplored. To address this gap, this article builds on the documentational approach to didactics (DAD) and the theory of…

The paper presents an analysis of elementary grade mathematics teaching in India focusing on mathematical reasoning. Mathematical reasoning is an important tool to make sense of mathematical ideas, which in turn makes mathematics more accessible to learners and promotes social equality. The paper analyzes 112 lessons from Grades 1 to 8 by 21…

Rational number knowledge is a crucial feature of primary school mathematics that predicts students' later mathematics achievement. Many students struggle with the transition from natural number to rational number reasoning, so novel pedagogical approaches to support the development of rational number knowledge are valuable to mathematics…

Self-efficacy in mathematics is related to engagement, persistence, and academic performance. Prior research focused mostly on examining changes to students' self-efficacy across large time intervals (months or years), and paid less attention to changes at the level of lesson sequences. Knowledge of how self-efficacy changes during a sequence of…

The aim of this study is to better understand the notion of early algebraic thinking by describing differences in grade 4-7 students' thinking about basic algebraic concepts. To achieve this goal, one test that involved generalized arithmetic, functional thinking, and modeling tasks, was administered to 684 students from these grades. Quantitative…

According to the design principle of progressive schematization, learning trajectories towards procedural rules can be organized as independent discoveries when the learning arrangement invites the students first to develop models for mathematical concepts and model-based informal strategies; then to explore the strategies and to discover pattern…

The aim of this study was to explore the beliefs of elementary school students about mathematics and about themselves as mathematics learners. The participants, Israeli grade 4 and grade 6 students, completed questionnaires. Using an "animal metaphor" to tap beliefs, some students perceived mathematics as difficult and complicated, while…

Early experiences with theoretical thinking and generalization in measurement are hypothesized to develop constructs we name here as logical reasoning and preparedness for algebra. Based on work of V. V. Davydov (1975), the Measure Up (MU) elementary grades experimental mathematics curriculum uses quantities of area, length, volume, and mass to…

Although according to the Finnish curriculum the learning environment in mathematics lessons should promote supportive interaction, Finnish pupils' attitudes toward and self-beliefs regarding mathematics deteriorate during basic education. This article investigates emotion work in teacher-student interaction in Finnish mathematics classrooms; the…

The expanding use of data in modern society for prediction and decision-making makes it a priority for mathematics instruction to help students build sound foundations of inferential reasoning at a young age. This study contributes to the emerging research literature on the early development of informal inferential reasoning through the conduct of…

This paper examines the contribution of quality mathematics teaching to student achievement gains. Quality of mathematics teaching is assessed through teacher demonstration of the five strands of mathematical proficiency, the level of cognitive task demands, and teacher mathematical knowledge. Data is based on 1907 grade 6 students who sat for the…

This study describes the types of explanations one student, Sharon, gives and prefers at different ages. Sharon is interviewed in the second grade regarding multiplication of one-digit numbers, in the fifth grade regarding even and odd numbers, and in the sixth grade regarding equivalent fractions. In the tenth grade, she revisits each of these…

This study examined 361 Chinese and 345 Singaporean sixth-grade students' performance and problem-solving strategies for solving 14 problems about speed. By focusing on students from two distinct high-performing countries in East Asia, we provide a useful perspective on the differences that exist in the preparation and problem-solving strategies…

Subtractions of the type M - S = ? can be solved by various strategies, including subtraction by addition. In this study, we investigated children's use of subtraction by addition by means of reaction time analyses. We presented 106 third to sixth graders with 32 large non-tie single-digit problems in both subtraction (12 - 9 = .) and addition…