In this paper, we explore the following research questions: How do first-grade students define even and odd numbers? What types of justifications do they use to support their generalizations using these definitions? We report the ways in which first-grade students define even and odd numbers and how they justify generalizations that use their…

Identifying mathematically gifted students is an important objective in mathematics education. To describe skills typical of these students, researchers pose problems in several mathematical domains whose solutions require using different mathematical capacities, such as visualization, generalization, proof, creativity, etc. This paper presents an…

This paper is part of broader research being conducted in the area of algebraic thinking in primary education. Our general research objective was to identify and describe generalization of a 2nd grade student (aged 7-8). Specifically, we focused on the transition from arithmetic to algebraic generalization. The notion of structure and its…

The present study aims to examine 8th grade students' proof writing and justification skills. The research was conducted using the document analysis method. The participants of the study consisted of 16 voluntary 8th grade students. The participants were determined according to the convenience sampling method. Data were collected with the…

This study lies within the field of early-age algebraic thinking and focuses on describing the functional thinking exhibited by six sixth-graders (11- to 12-year-olds) enrolled in a curricular enhancement program. To accomplish the goals of this research, the structures the students established and the representations they used to express the…

Recent research has highlighted the role of functional relationships in introducing elementary school students to algebraic thinking. This functional approach is here considered to study essential components of algebraic thinking such as generalization and its representation, as well as the strategies used by students and their connection with…

Selecting and remembering the necessary information from rapidly increasing information requires summarization skills. Research on improving students' summarization skills has focused on deletion, generalization, and reconstruction strategies. However, direct teaching of these strategies does not yield successful results. For this reason,…

Many generalization studies in education are typically based on a sample of 30-70 schools while the inference population is at least twenty times larger. This small sample to population size ratio limits the precision of design-based estimators of the population average treatment effect. Prior work has shown the potential of small area estimation…

An important approach for developing children's algebraic thinking involves introducing them to generalized arithmetic at the time they are learning arithmetic. Our aim in this study was to investigate children's attention to and expression of generality with the subtraction-compensation property, as evidence of a type of algebraic thinking known…

The purpose of this study is to investigate the quality of class talk during episodes corresponding to different levels of generalization. A total of 10 sessions in two classrooms in grade 7 were videotaped. A mixed approach was adopted to analyze the videotaped sessions. The findings show that triadic dialog was the dominant mode of interaction…

This study investigated how three fifth-grade students' understanding of fraction and decimal magnitude evolved over the course of a five-week teaching experiment. Students participated in teaching and learning sessions focused on developing concepts of fraction and decimal magnitude. The following questions guided this study: (1) How do fifth…

Exercise is necessary for healthy living, yet individuals with intellectual disability (ID) remain strikingly inactive compared with nondisabled peers. To improve this outcome, individuals with ID can exercise independently by self-instructing. Self-instruction is considered a pivotal skill once it generalizes to untrained stimuli. This study used…

Purpose: This meta-analysis synthesizes published studies using "treatment of underlying forms" (TUF) for sentence-level deficits in people with aphasia (PWA). The study aims were to examine group-level evidence for TUF efficacy, to characterize the effects of treatment-related variables (sentence structural family and complexity;…

Given the relevance of graphs of functions, we consider their inclusion in primary education from the functional approach to early algebra. The purpose of this article is to shed some light on the students' production and reading of graphs when they solved generalization problems from a functional thinking approach. We aim to explore how 3rd and…

The aim of this study was to analyse preservice elementary mathematics teachers' concept definitions of circle, circular region, and sphere concepts in geometrical terms. The research was conducted during the 2016-2017 academic year with 56 preservice mathematics teachers enrolled within a teacher education programme at a state university in…