Vince Wright makes a convincing argument for presenting children with a different "prototype" of a fraction to the typical one-half. Consider how the prototype that Wright mentions may be applied to a variety of fraction concepts. We are sure that you will never look at a doughnut in quite the same way.

Mathematical knowledge and skills are crucial to success in academics and the workplace. The Common Core State Standards emphasizes fraction teaching and learning in elementary school. This mixed-method study explores fraction concept understanding among 14 deaf and hard of hearing participants between the ages of 8 and 16, as quantitatively…

We present the results of an in-depth qualitative study that examined ninth graders' conceptual and procedural knowledge of fractions as well as their approach to mathematics learning, in particular fraction learning. We traced individual differences, even extreme, in the way that students combine the two kinds of knowledge. We also provide…

This study investigates the potential of Facebook as a medium and process for teachers' learning about mathematical and pedagogical knowledge. Participants' (N = 117) responses towards four inter-related posts regarding division-of-fractions were captured and systematically analysed to gain insight about the participants' engagement. The results…

The goal of the present article is to synthesize findings to date from the Delaware Longitudinal Study of Fraction Learning. The study followed a large cohort of children (N = 536) between Grades 3 and 6. The findings showed that many students, especially those with diagnosed learning disabilities, made minimal growth in fraction knowledge and…

In a previous study, Mix et al. (2016) reported that spatial skill and mathematics were composed of 2 highly correlated, domain-specific factors, with a few cross-domain loadings. The overall structure was consistent across grade (kindergarten, 3rd grade, 6th grade), but the cross-domain loadings varied with age. The present study sought to…

In a previous study, Mix et al. (2016) reported that spatial skill and mathematics were composed of 2 highly correlated, domain-specific factors, with a few cross-domain loadings. The overall structure was consistent across grade (kindergarten, 3rd grade, 6th grade), but the cross-domain loadings varied with age. The present study sought to…

This study analyzes the development of percentages knowledge by seventh graders given a sequence of activities starting with a realistic modeling task, in which students were expected to create a model that would facilitate the reinvention of percentages. In the first two activities, students constructed their own pricing model using fractions and…

Stephen Norton, Do Thi Phurong Thao and Mai The Duy provide an interesting insight into the teaching of fraction division in Vietnam. The article highlights one of the many teaching strategies available to teachers for building fraction concepts.

Tzur and Simon (2004) postulated two stages of concept development, participatory and anticipatory. The distinction between the two stages was exemplified by what they termed "the next-day phenomenon" in which learners who could solve a task one day in the context of the activity through which they made the abstraction, could not solve…

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…

The current study investigated college students' content knowledge and cognitive abilities as factors associated with their algebra performance, and examined how combinations of content knowledge and cognitive abilities related to their algebra performance. Specifically, the investigation examined the content knowledge factors of computational…

A number of studies have demonstrated links between linguistic knowledge and performance in math. Studies examining these links in first language speakers of English have traditionally relied on correlational analyses between linguistic knowledge tests and standardized math tests. For second language (L2) speakers, the majority of studies have…

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…

In a pretest-posttest cluster-randomized trial, one of the methods commonly used to detect an intervention effect involves controlling pre-test scores and other related covariates while estimating an intervention effect at post-test. In many applications in education, the total post-test and pre-test scores that ignores measurement error in the…