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…

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…

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…

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…

This study aims to develop a conceptual framework regarding practitioner knowledge and describe how one mathematics teacher generates her practitioner knowledge based on the framework. The characteristic of this framework is a combination of static and dynamic aspects of knowledge based on the teacher's perception and interpretation. The research…

This study aims to understand individual differences between children in metacognitive monitoring and control processes and the developmental trajectories of metacognition over one year. Three indicators of procedural metacognition were used: monitoring accuracy (discrimination of confidence judgments between correct and incorrect test responses),…

We describe 24 third (8-9 years old) and 24 fifth (10-11 years old) graders' generalization working with the same problem involving a function. Generalizing and representing functional relationships are considered key elements in a functional approach to early algebra. Focusing on functional relationships can provide insights into how students…

Functional thinking is an established route into algebra. However, the learning mechanisms that support the transition from arithmetic to functional thinking remain unclear. In the current study we explored children's pre-instructional intuitive reactions to functional thinking content, relying on a conceptual change perspective and using mixed…

Jung and Won's (2018) review of elementary school ER found a lack of understanding of instructional practices for ER with young children. Other researchers have called for further studies into what effective classroom orchestration and interaction look like within ER classrooms (Ioannou & Makridou, 2018; Xia & Zhong, 2019). This study was…

The global COVID-19 pandemic has passed. This process required greater attention and care to the specifics of the organization of distance learning and the resolution of problems that arose for participants in the educational process. By late 2021 face-to-face teaching was returning but Russian aggression against Ukraine interrupted the…

Physical educators are often asked to promote whole-school physical activity programming beyond their scheduled class times. Previous research has supported that training in expanded roles would be beneficial during university-based physical education teacher education (PETE) training. In this qualitative study, 13 graduates from a single PETE…

Investigating symmetric dot patterns provides opportunities for foundational mathematical learning that is not restricted to multiplication alone. Students have opportunities to learn about the properties of symmetry, about the generalization of patterns, about writing and interpreting equations--all areas of study in grades 3-5. And symmetric dot…

First-grade mathematics curriculum has been typically constructed to emphasize the development of whole number and operations. Topics addressed to a lesser extent include algebraic thinking, measurement, and geometry. In this research study, we suggest an alternative to this balance of topics. We compared prior research and learning expectations…