Productive engagement in fractional reasoning is essential for abstracting fundamental algebraic concepts vital to college and career success. Yet, data suggest students with learning disabilities (LDs), in particular, display pervasive shortfalls in learning and mastering fraction content. We argue that shortfalls in understanding are in fact…

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 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.…

This study investigates the use of manipulatives by elementary students working on a fraction task. Extending previous work on the role played by the manipulatives in students' activity, we aim at describing how the choices made for the task design disrupt students' activity, creating opportunities to learn. The theoretical underpinnings allow…

Generative activities have been shown to support students to engage in space-creating play and exercise their conceptual agency to generate a mathematical space (e.g. Stroup et al. 2004), yet these studies implement generative activities only with their resonating counterpart, classroom networks, technological infrastructures that connect…

Existing studies have quantitatively evidenced the relatedness between problem posing and problem solving, as well as the magnitude of this relationship. However, the nature and features of this relationship need further qualitative exploration. This paper focuses on exploring the interactions, i.e., mutual effects and supports, between problem…

Background: Fractions continue to pose a critical challenge for students and their teachers alike. Mathematics education research indicates that the challenge with fractions may stem from the limitations of part-whole concepts of fractions, which is the central focus of fractions curriculum and instruction in the USA. Students' development of more…

In this paper characterizations of mental objects for fractions of middle school students (from 12 to 14 years old) with absenteeism problems and low academic performance, are described. A test was designed as part of a research whose general purpose is to contribute in the building up of better mental objects for fractions through a teaching…

How should a wide variety of educational activities be sequenced to maximize student learning? Although some experimental studies have addressed this question, educational data mining methods may be able to evaluate a wider range of possibilities and better handle many simultaneous sequencing constraints. We introduce Sequencing Constraint…

Prior research shows that representational competencies that enable students to use graphical representations to reason and solve tasks is key to learning in many science, technology, engineering, and mathematics domains. We focus on two types of representational competencies: (1) "sense making" of connections by verbally explaining how…

Prior research shows that representational competencies that enable students to use graphical representations to reason and solve tasks is key to learning in many science, technology, engineering, and mathematics (STEM) domains. We focus on two types of representational competencies: (1) "sense making" of connections by verbally…

Debates on transfer of learning in mathematics are not new. Claims of situatedness of learning within tasks and non-transferability of knowledge between tasks are widely contested. Direct Application (DA) of learning is a common paradigm for characterising transfer which led to many instances of transfer failure (Bransford & Schwartz, 2001).…

Dual eye-tracking measures enable novel ways to test predictions about collaborative learning. For example, the research project we are engaging in uses measures of gaze recurrence to help understand how collaboration may differ when students are completing various learning activities focused on different learning objectives. Specifically, we…

Presents transcripts of interviews with two children to illustrate their understanding of traditional fraction notation. Suggests an activity to help children construct schemes to coordinate units. (MKR)

Describes a case study of a first-grade class in fractions, presents preliminary findings suggesting that students in others grades can learn fractions in similar ways, and offers ideas for action research. (MKR)