This study's purpose was to examine the effects of the concrete-representational-abstract integrated (CRA-I) sequence on the performance of students who struggled with rational number concepts. Three students in southeastern U.S. fifth grade class participated in the study. The CRA-I intervention was grounded in the principles of explicit…

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.…

In many schools across the world, students experience mathematical concepts as ideas empty of wisdom and possibility. In this paper the authors analyze a philosophical conversation in which fifth-grade students were caught up in the animacy of the concept of space. Challenging the common view of mathematics as dealing with absolute truths and…

After years of noticing the challenge our students have with fraction operations, we decided to implement a scaffold approach that focuses on using benchmarks to better develop both students' understanding of a fraction as a quantity and their ability to think about fraction operations meaningfully. While we found this approach supported students…

Mathematical coherence is a goal within the Common Core State Standards for Mathematics. One aspect of this coherence is how student mathematical thinking is developed across concepts. Unfortunately, mathematics is often taught as isolated ideas across grades. The multiplicative field is an area of study that needs to be examined as a space to…

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…

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…

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…

This pilot study examined the feasibility of using worked examples as a mechanism to improve verbal explanations of fractions concepts among Grade 5 students with mathematics difficulties in a small-scale randomized controlled trial (RCT) before scaling up to a large-scale RCT. Students (N = 49) were randomly assigned to a business-as-usual (BAU)…

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…

Understanding of the equal sign is associated with early algebraic competence in the elementary grades and equation-solving success in middle school. Thus, it is important to find ways to build foundational understanding of the equal sign as a relational symbol. Past work promoted a conception of the equal sign as meaning "the same as".…

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…

This research paper examines tasks related to mean, median, and mode in seven Swedish textbook series for students aged between 10-13 years. The tasks were analysed based on context, mathematical properties, input and output objects, and transformations. These categories allowed for a thorough analysis of the opportunities afforded to students to…

The authors describe a lesson--"You Decide"--which challenges students but also provides opportunities for success for those who may struggle. They show how this lesson has been helpful for teachers in revealing some misconceptions that often exist in primary students' thinking. In this article, they share data on the apparent relative…

An understanding of the equal sign is a fundamental concept for early algebra. While literature claimed that Chinese students commonly master the relational understanding of the equal sign in the elementary school, these claims are under-researched. This study used the Mathematics Equivalence Assessment with 237 Chinese Grade 5 students. The…