Children's understanding of fractions, including their symbols, concepts, and arithmetic procedures, is an important facet of both developmental research on mathematics cognition and mathematics education. Research on infants', children's, and adults' fraction and ratio reasoning allows us to test a range of proposals about the development of…

The standard technique taught in calculus courses for partial fraction expansions uses undetermined coefficients to generate a system of linear equations; we present a derivative-based technique that calculus and differential equations instructors can use to reinforce connections to calculus. Simple algebra shows that we can use the derivative to…

We draw on our work with designed instructional sequence on Fractions as Measures across three international contexts and explore the functions of the design features related to the stories embedded within the sequence. We discuss functions that relate to how stories support students' meaningful engagement in classroom mathematical activities,…

Mathematical and didactic knowledge presented in mathematics textbooks and other resources, like mathematics comics (MCs), needs to be evaluated from a lens of appropriate theoretical framework in mathematics education before it can be used as a medium for teaching and learning mathematics. Therefore, this study investigates mathematical and…

In this work we will analyze the relation between registers of representation and the construction of the fraction concept. Ninety-six students from first year of compulsory secondary education participated in the study, and performed equal share tasks in the context of Egyptian fractions (unit fractions with different denominators). The aim was…

Number lines and area models are both used pervasively in teaching fractions. Prior studies found that second and third graders demonstrated better magnitude knowledge of proper fractions after a 15-minute training using the number line as compared to using the area model. The current study aimed to extend these findings to improper fractions. We…

In this study, Turkish and Singaporean textbooks were compared in terms of teaching content for multiplying fractions, a subject that most students have difficulty in understanding. The study analyzed the 6th-grade mathematics textbook published by the Turkish Ministry of National Education and its Singaporean counterpart. While the Singaporean…

Teaching and learning fraction concepts continues to be increasingly challenging, especially for elementary and middle school mathematics teachers and students in intervention settings. It is critical for educators to implement instruction that proactively considers engagement, access, and conceptual growth for all students. Dream 2B, a web-based…

Microcredentials are a promising means for expanding teacher access to high quality professional development. This study examined the effectiveness of online, self-paced microcredential courses designed for teachers working in underserved rural communities. The content of these competency-based microcredentials centered on recommended…

Developing primary school students' interest in and getting them motivated to learn mathematics has been a perennial focus of educators. The use of comics for classroom instruction is an area gaining more attention from educators. In this paper, we review some existing education literature on the impact of comics on students' cognitive and…

This study aimed to enrich the learning environment of the 5th grade students with the interdisciplinary activities designed by connecting mathematics and music. The activities integrated the concepts of music such as note, beat, and measure with the concept of fractions in mathematics to ensure active participation of students and to promote…

National assessments suggest that many students do not display proficiency with fractions. Considering that time and materials are precious resources, many educators are looking to use technology to provide supplemental instruction with low demand on the instructor. The current study utilized a multiple-baseline design to examine the effects of…

One of the attributes of rational numbers that make them different from integers are the different symbolic modes (fraction, decimal and percentage) to which an identical number can be attributed (e.g. 1/4, 0.25 and 25%). Some research has identified students' difficulty in mental calculations with rational numbers as has also the switching to…

This study examined parent-child math talk within three contexts (formal learning; guided play; unguided play) in order to identify characteristics of activities supporting high-quality math engagement. Seventy-two dyads of parents and 4- and 5-year-olds were observed using a set of toy foods; instructions and materials varied across conditions.…

The aim of this study is to investigate Danish pre-service teachers' (PSTs) mathematical and didactical knowledge of operations with rational numbers. This knowledge is studied through their collaborative activities to certain tasks related to the teaching of operations with rational numbers. An explicit model of the teachers' mathematical and…