When learning about fractions, teaching usually follows certain topics -- e.g. part of the whole, fraction equivalence, and size comparison. Not yet answered is whether students' conceptual and procedural knowledge of fractions is coherent between those topics. To answer this question, we performed a latent profile analysis of data from N = 1005…

Fractions are a very important but difficult topic in elementary and secondary mathematics curricula around the world. The difficulty in teaching and learning fractions is usually caused by their various subconstructs. To facilitate learning of fractions, a test consisting of 20 items was developed to examine 310 sixth graders' hierarchical…

Many U.S. students possess only a weak knowledge of fraction arithmetic. I hypothesize that textbooks are a critical reason for students' poor performance on fraction arithmetic. This is not because of what textbooks contain but rather because of what they lack. Distributions of fraction arithmetic problems in textbooks are imbalanced, with…

The aim of this work is to study the knowledge that 11 to 12-year-old pupils have about the different meanings of fractions. For this purpose, an investigation about the ability that 11 to 12-year-old pupils have with fraction problems through problem posing is performed. In particular, we analyze if they pose different types of problems depending…

This article aims to show some activities based on non-routine problems with different levels of difficulty and from different classes that are integrated into the curriculum, additionally two spaces were opened for students to interact with recreational mathematics activities with the purpose of providing opportunities to all students access the…

This study explored whether initial skill moderated outcomes of Promoting Algebra Readiness, a Tier 2 sixth grade mathematics intervention targeting conceptual and procedural knowledge of fractions. The study analyzed data from a quasi-experimental pilot study in which at-risk students (n = 198) were assigned to the treatment or control condition…

This study explored whether initial skill moderated outcomes of Promoting Algebra Readiness, a Tier 2 sixth-grade mathematics intervention targeting conceptual and procedural knowledge of fractions. The study analyzed data from a quasi-experimental pilot study in which at-risk students (N = 198) from Oregon middle schools were assigned to the…

A one-on-one dialogue-based mathematics intelligent tutoring system (ITS) for learning multiplication and division of fractions was developed and evaluated in this study. This system could identify students' error types and misconceptions in real-time by using a block-based matching method. The adaptive dialogue-based instruction was supported by…

In this paper, we have tried to clearly explain the meaning of fractions and operations with fractions. Also, we have tried to illustrate with some examples how to apply the rules of operations with fractional numbers, giving different practical techniques through different figures, visualization methods, and concretizing problems. The paper…

Fraction arithmetic facility is fundamental to learning more advanced math topics. However, attaining the ability to add and subtract fractions is hard for many students. The present longitudinal study examined students' growth on simple addition and subtraction word problems between fourth and sixth grades (N = 536). Latent class growth analyses…

There is strong evidence from research conducted in the United States that fraction magnitude understanding supports mathematics achievement. Unfortunately, there has been little research that examines if this relation is present across educational contexts with different approaches to teaching fractions. The current study compared fourth and…

This paper describes the authors' journey in designing a linear representation that aligns mathematics and music to support fractional reasoning. The three authors, guided by the theoretical framing of realistic mathematics education, engaged in a task design process over a 12-month period to develop integrated resources. Data were collected in…

Mathematical knowledge for teaching (MKT) is a professional knowledge crucial for effective mathematics instruction, encompassing both content knowledge (CK) and pedagogical content knowledge (PCK). The purpose of this study is to investigate the hierarchical structure of PCK for fractions by seeking further evidence for the PCK-Fractions…

The current study assessed whether adding worked examples with self-explanation prompts focused on making connections between mathematical principles, procedures, and concepts of rational numbers to a curriculum focused on invented strategies improves pre-algebra students' fraction number line acuity, rational number concepts and procedures.…

Attending to the whole unit that a number refers to in a mathematical problem situation and showing flexibility in coordinating different units are foundational for mathematical understanding. In this study, we explored teachers' attention to and flexibility with referent units in situations involving fractions and fraction multiplication. Using…