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…

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…

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…

This study aims to understand the instructional interactions that foster students' generalizing. By analysing video-recorded lessons from 13 different Grade 3 classrooms in which an early algebra intervention was implemented, activities related to generalizing and students' generalizing activities were identified, and the nature of the…

Due to their abstract nature, representation of mathematical concepts through different registers favors their understanding. In the case of ''sequences and regularities'', it becomes propitious the exploration of different registers of representation in the institution of topics, such as term, order, formation law, and generating expression.…

Little-to-no research examines the provision of targeted mathematical interventions to students struggling with mathematics in a virtual environment. And yet, the global pandemic of 2020--extending into 2021--found schools in such a scenario. This article reports two studies in which researchers explored the intervention package of explicit…

We share here results from a quasi-experimental study that examines growth in students' algebraic thinking practices of generalizing and representing generalizations, particularly with variable notation, as a result of an early algebra instructional sequence implemented across grades 3--5. Analyses showed that, while there were no significant…

Incremental rehearsal (IR) is a flashcard technique that has produced strong effects for a variety of outcomes including word recognition. We utilized theory-based modifications to IR to enhance maintenance and generalization of sight words. We utilized a within-subjects design in which 41 participants in 2nd and 3rd grade were taught seven…

According to a language-integrated view of spelling development, learning to spell involves the same language-learning skills across alphabetic systems. A prediction based on this view is that the same spelling training should be equally effective for learning to spell in a shallow (Italian, native language) or an opaque (English, additional…

Purpose: This retrospective study was intended to replicate findings from Sacks et al. (2013) regarding the efficacy of using the SATPAC (Systematic Articulation Training Program Accessing Computers) approach for remediating speech sound errors in a Tier 3 response to intervention (RTI) context. Method: Nine children aged 7;7 (years;months) to…

This paper focuses on pattern generalisation as a way to introduce young students to early algebra. We build on research on patterning activities that feature, in their work with algebraic thinking, both looking for sameness recursively in a pattern (especially figural patterns, but also numerical ones) and conjecturing about function-based…

This study examined whether 2 evidence-based intervention strategies resulted in maintenance and generalization of writing fluency gains. In this study, 115 third-grade students were randomly assigned to a performance feedback intervention condition, a goal setting intervention condition, or a control condition. Neither intervention strategy…

This study aimed to address two underexplored research questions regarding support for the separation between competence and affect self-perceptions due to differential relations to outcome criteria. First, it is tested whether higher relations between affect self-perceptions and effort than between competence self-perceptions and effort can also…

Research Findings: In 2 experiments, we tested whether children generalize psychological and biological properties to novel foods. We used an induction task in which a property (either biological or psychological) was associated with a target food. Children were then asked whether a taxonomically related and a script-related food would also have…