When students are working collaboratively and communicating verbally in a technology-enhanced environment, the system cannot track what collaboration is happening outside of the technology, making it difficult to fully assess the collaboration of the students and adapt accordingly. In this article, we propose using gaze measures as a proxy for…

Fraction knowledge and algebraic skill are closely linked. Algebra is a gatekeeper for advanced courses (Booth & Newton, 2012; Brown & Quinn, 2007). This study uses the person-centered approach of latent profile analysis to examine individual differences in middle schoolers' (N = 350) algebra performance at the end of the year (EOY). The…

Fractions and the understanding of fraction concepts affect later conceptualization of advanced mathematics and affect how people live their everyday lives. Research shows that many deaf or hard of hearing (DHH) students have not mastered fraction skills even by the time they enter college. In the present article, the author looks at literature…

Through a search executed on Web of Science database with general keywords pertaining to 'teaching fractions' or 'understanding fractions' and 'representation', this study utilized PRISMA's procedure in analysing previously published articles. This review reveals seven articles in inclusion criteria and seventeenth articles in exclusion criteria…

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…

This article investigates the interplay of time words with how children position hands on an analog clock. Using a mathematics discourse framework (Sfard, 2008), we analyzed how students interpreted precise (e.g., 2:30) and relative (e.g., half past 11) times, finding that particular words are dynamically interwoven with activity. Interviews with…

Fostering conceptual understanding in mathematics classrooms is an important goal in mathematics education. To support this goal, we need to be able to diagnose and assess the extent to which students have conceptual understanding. In this study we employed a problem-posing task and a problem-solving task in order to diagnose and assess preservice…

Fraction proficiency continues to be a challenge for many learners of mathematics. Valid and reliable methods for assessing fraction understanding are critical tools in the pursuit of meeting this challenge. Written assessments have been widely used with K-12 students to assess fraction understanding, including units coordination. However, using…

Fraction proficiency is a critical milestone for students to reach, as fraction knowledge strongly predicts later math achievement. However, fractions are notoriously difficult for students to learn. The first study in this dissertation reviewed commonly used math curricula to determine if their fraction lessons used evidence-based instructional…

One of the most persistent areas of difficulty in mathematics for children with learning disabilities (LDs) and difficulties is fractions. We report the development and initial testing of an intervention designed to increase access to and advancement in conceptual understanding. Our asset-based theory of change--a tested and confirmed learning…

This study examined the role of student generated drawings to offload cognitive demands of a mathematical problem. We used Unit Transformation Graphs to compare students' thought processes when they had to solve the problem mentally, and when they were allowed to use pen and paper. The results indicated that the possibility to rely on drawings…

Peter Sullivan and colleagues present a report on an initiative at a Victorian primary school which embraced opportunities offered by purposeful collaborative professional learning communities. They utilised a form of Japanese Lesson Study as part of their approach. There are three parts to the story of this initiative: (1) a description of the…

How dyslexia students solve number operations is still challenging to unravel. This study aimed at revealing the types of errors conveyed by a dyslexic student in performing fractional operations on mathematical tasks that combined non-verbal text (symbols and pictures) and verbal text. The data were collected using a task-based interview with a…

Fractions are a challenging mathematics topic for many elementary and middle school students, and even for adults. However, a growing body of developmental research suggests that young children can reason about visually presented proportions, well before fraction instruction, providing insight into how fractions might be introduced to improve…

Fraction arithmetic facility is fundamental to learning more advanced math topics. However, attaining the ability to add and subtract fractions is hard for many students. The present longitudinal study examined students' growth on simple addition and subtraction word problems between fourth and sixth grades (N = 536). Latent class growth analyses…