Mathematics educators and researchers have advocated for the use of manipulatives to teach mathematics for decades. The purpose of this article is to provide illustrative uses of a readily available manipulative rather than a complete list. From an Australian perspective, Pop-it fidget toys can be used across the mathematics curriculum. This paper…

Analogy is a powerful learning mechanism for children to learn novel, abstract concepts from only limited input, yet also requires cognitive supports. My dissertation sought to propose and examine number lines as a mathematical schema of the number system to facilitate both the development of rational number understanding and analogical reasoning.…

Background: While it has been widely demonstrated that children's and adolescents' understanding of rational number plays an important role in their mathematics achievement, we have limited knowledge about the cognitive correlates of this understanding. Aims: The current study aimed at examining whether children's non-symbolic ratio processing and…

Interventions are implemented with greater fidelity when their core intent is made explicit. The core intent of this intervention was to increase access to higher order learning opportunities for students with learning disabilities or difficulties in mathematics through use of research and practice from the fields of special education and…

The concept of fraction and the concepts related to the fraction have an important place in primary and secondary school education programs. In this respect, primary school teachers need to be careful about the concept and sub-meaning of the fraction. In this study, general survey model was used to determine the level of knowledge of the primary…

The purpose of this study is to analyze pre-service elementary teachers' problems in terms of the different meanings of the addition of fractions and to determine the types of errors made in these problems. Data were collected from 83 pre-service elementary teachers in the spring semester of the 2016-2017 academic year by means of a problem posing…

This study aimed at: (1) determining whether the Concrete-Pictorial-Abstract (CPA) strategy has a positive effect on students' mathematical conceptual understanding (MCU) and students' mathematical representation (MR) on fractions; (2) describing how CPA strategy can improve students' MCU and students' MR on fractions. This research used a mixed…

Through their work on the Fractions Project, Steffe and Olive (2010) identified a progression of fraction schemes that describes students' development toward more and more sophisticated ways of operating with fractions. Although several quantitative studies have affirmed this progression, the question has remained open as to whether it is specific…

Young children can quickly and intuitively represent the number of objects in a visual scene through the Approximate Number System (ANS). The precision of the ANS--indexed as the most difficult ratio of two numbers that children can reliably discriminate--is well known to improve with development: whereas infants require relatively large ratios to…

We introduce a methodology for diagramming the ways students use sequences of mental actions to solve mathematical tasks. We studied 12 pre-service teachers as they solved a set of fractions tasks, ranked by cognitive demand. We present the unit transformation graphs for one of those pre-service teachers, to illustrate how she experienced and met…

In this study, we explored teachers' attention to and flexibility with referent units as well as how teachers' understanding of referent units is related to their performance on other fraction concepts and their professional background. By using data collected from 246 U.S. mathematics teachers in Grades 3-7 where fractions are taught, we found…

Mathematics learning within the context of videogames is an increasingly important area of study that has not yet fulfilled its promise of powerfully contextualized and transformative learning. This research served to begin pushing the boundaries of the field by relying upon cutting edge mathematics education research on fractions and the best…

We present a method for finding partial fraction decompositions of rational functions with linear or quadratic factors in the denominators by means of repeated polynomial divisions. This method does not involve differentiation or solving linear equations for obtaining the unknown partial fraction coefficients, which is very suitable for either…

We analyzed the effects of a game-based, supplemental fraction curriculum on fourth and fifth grade students' fraction knowledge, engagement, and STEM interest. Students with and without disabilities with intersecting identities (e.g., race, disability status, gender) comprised the sample. Results indicate significant differences in fraction…

Rational number and fractions concepts are inherently difficult; and lack of mastery often holds students back from success in subsequent mathematics courses. This paper describes design characteristics of a software based, adaptive, rational number tutor with virtual manipulatives, realistic contexts, and procedural feedback. Then, the paper…