We discuss the evolution of an instructional unit for supporting prospective elementary and middle grades' teachers' conceptions of fractions as measures. We first studied prospective teachers' conceptions of fractions using a task-based written assessment with discrete, linear, and circle representations. We designed an instructional unit that…

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…

A multidisciplinary origami activity that could be used in middle school mathematics and science lessons was designed and implemented. Mathematical purpose of the origami activity is to support students' conceptual understanding and procedural skills related to the concept of fraction. Regarding science, the activity aims to visualize Solar system…

Teachers' understanding of the concepts they teach affects the quality of instruction and students' learning. This study used a sample of 303 teachers from across the USA to examine elementary school mathematics teachers' knowledge of key concepts underlying fraction arithmetic. Teachers' explanations were coded based on the accuracy of their…

Primary school students have trouble understanding concepts related to fractions. On the other hand, technology constantly provides interesting tools that stimulate students' interest and foster learning. Among these, tangible user interfaces allow users to interact with digital applications through the manipulation of everyday objects. Given that…

Three iterative, 18-episode design experiments were conducted after school with groups of 6-9 middle school students to understand how to differentiate mathematics instruction. Prior research on differentiating instruction (DI) and hypothetical learning trajectories guided the instruction. As the experiments proceeded, this definition of DI…

In this article we present an overview of four studies investigating Greek secondary students' conceptual and procedural knowledge of fractions. We discuss the problem of defining conceptual and procedural knowledge, and the implications of adopting one particular definition over others. We draw on the studies and their results to discuss the…

The current study aims to show the transition skills of sixth grade students between the representations (numerical, model, number line and verbal) given in addition-subtraction operations in fractions and to analyse the ability of the students to construct each representation type. In this research, case study method was used in terms of the…

This study reports an analysis of how pre-service teachers (n=34) made sense of fraction division with remainders using pictorial modeling strategies, and how small-group and whole-class discussion helped them develop conceptual understanding. One and a half class sessions were video recorded, and 12 interviews were conducted. Results indicate…

Making math more engaging for students is a challenge that every teacher faces on a daily basis. These authors write that they are constantly searching for rich problem-solving tasks that cover the necessary content, develop critical-thinking skills, and engage student interest. The Mystery Fraction activity provided here focuses on a key number…

This research aims to analyze ways of understanding of students with mathematics learning disabilities when learning fraction. The research was conducted in an Inclusive Junior High School in the West Java Province, Indonesia. This study is qualitative, with the single-case (holistic) designs. The case will focus on three students who suspected of…