There has been a consensus that students' conceptual understanding of mathematical operations (such as multiplication) can be developed through communication about multiple representations. However, learning opportunities have often appeared to be limited to surface translations (in which only obvious similarities such as numbers have been…

Both professional and classroom-based scientific communities develop and test explanatory models of the natural world. For students to take up models as tools for sensemaking, practice must be agentive (where students use and revise models "for" specific purposes) and conceptually productive (where students make progress on their ideas).…

The paper presents findings from a study that examined, through the lens of the Image Having layer of the Pirie-Kieren model, the qualitative characteristics of the images that different children formed when engaging with eight, novel partitive quotient tasks. The Image Having layer is the first point of abstraction within the Pirie-Kieren model.…

This study sought to understand how students activate number sense in determining the position of fractions on a number line and identify how the natural number bias and number sense influences students' thinking processes. The study utilized the Cognitive Task Analysis (CTA), involving four fifth-grade elementary students as the research…

This study explores the metaphorical perceptions of gifted students towards basic science concepts. A total of 210 gifted students participated in the study, which utilized a phenomenology design to reveal the metaphors used by students to describe the concepts of 'universe, living thing, matter, light, sound, electricity and environment'. A…

Purpose: This paper aims to introduce a novel AI learning progression for upper-elementary students and aligns assessment items across levels of each construct to gather evidence of understanding. It also validates this quantitative measure by examining these items as two subscales for psychometric properties using the Rasch model.…

Contemporary conceptions of content learning that emphasize disciplinary practices offer opportunities to see and hear multilingual learners' (MLs') participation in new ways. However, research on disciplinary practices with MLs has primarily targeted those practices traditionally considered language intensive, such as explanation and…

The concept of fractions given in learning is the concept of part of whole and part of unit. The development of student's concepts of fractions can be built through fraction schemes. A partitive fraction scheme is a scheme that estimates the size of the fraction in the form of non-units to the whole that is not partitioned. The concept of…

In this article, we describe a case study that was conducted within a study aiming to diagnose grade 5 students' concept images of parallelograms. The theoretical framework that we adopted for this study was that of concept definition--concept image as reported by Tall and Vinner ("Educational Studies in Mathematics" 12:151-169, 1981), a…

In this study, we examine students' mathematical reasoning within a technological environment designed to support understanding of relationships between quantities with adjustable measuring units. In particular, we provide a cross-sectional snapshot of how 30 elementary students (Grades 3-5) engaged in a series of fraction-as-measurement tasks…

Ratios and proportions are new topics in the primary curriculum. Previous research shows that Year Five pupils have difficulty in learning ratio and proportion. This study aims to identify the conceptions of ratio and proportion of seven year five pupils. It is based on radical constructivism using qualitative case study. Data was collected…

This study examines the conceptual understanding of numbers and operations among 372 fifth-grade students, based on their responses to an online three-tier test designed to assess their number sense, declarative knowledge, explanatory knowledge, and confidence. The results showed that most students had low performance and low number sense, with…

This article describes a hands-on geometric tiling art activity used in two third-grade classes and four fifth-grade classes in a rural public elementary school with class sizes of around 20 students each. The lesson investigates concepts in geometry, number sense, and probability. Examples of student work and takeaways for other teachers…

Economic literacy is critical for success in one's career and life. Such literacy has never been more relevant than today due to supply-chain issues causing product shortages, surging inflation, and rising interest rates. Discovery learning through active learning materials discussed in this article were employed with fifth and sixth-grade…

This conceptual paper discusses two frameworks, developed independently by the lead author, that will provide the conceptual foundation for the identification and evaluation of mental computation strategies students demonstrate during an upcoming research project entitled Mental Computation in Year 5. These frameworks will be used by the lead…