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…

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…

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…

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…

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…

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…

Background: Being skillful is a prerequisite for lifelong participation in physical activity (WHO 2022). Hence, investigating the quality of children's skill performance is important. If physical education wants to contribute to the development of a physically active lifestyle, demonstrating whether children apply skills learned in physical…

Early algebraic thinking is the reasoning engaged in by 5- to 12-year-olds as they build meaning for the objects and ways of thinking to be encountered within the later study of secondary school algebra. Ever since the 1990s when interest in developing algebraic thinking in the earlier grades began to emerge, there has been a steady growth in the…

Purpose: Our purpose was to investigate the effect of generalization of participation in parkour from physical education classes to organized parkour recess. Methods: A total of 143 (64 girls and 79 boys) third-grade elementary school children received a 12-lesson parkour sport education season in physical education. Voluntary participation in…

By design, randomized experiments (XPs) rule out bias from confounded selection of participants into conditions. Quasi-experiments (QEs) are often considered second-best because they do not share this benefit. However, when results from XPs are used to generalize causal impacts, the benefit from unconfounded selection into conditions may be offset…

Engaging students in comparing and contrasting, forming conjectures, generalising and justifying is critical to develop their mathematical reasoning, but there are untapped opportunities for primary school students to improve these reasoning processes in mathematics lessons. Through a case study of one task, this paper reports on levels of…

There is a burgeoning body of evidence on the average impacts of educational programs. Yet, for many local decision makers, because impacts can vary across sites, the question of whether a certain program will work in their particular district or school remains. This article addresses the question of the generalizability of large-scale average…

Visualizations are commonly used in educational materials, however not all visualizations are equally effective at promoting learning. Prior research has supported the idea that both perceptually rich and bland visualizations are beneficial for learning and generalization. We investigated whether the perceptual richness of a life cycle diagram…

The ACTFL Assessment of Performance Toward Proficiency in Languages (AAPPL, https://www.actfl.n.d.org/assessments/k-12-assessments/aappl) assesses proficiency in 11 languages for students in grades 3 to 12 and is often used to award the Seal of Biliteracy. While arguments for the valid interpretation and uses of the AAPPL have previously been…