Although difficulties processing both symbolic and nonsymbolic proportion compared with absolute number are well established, the mechanisms involved remain unclear. We investigate four potential explanations to account for better number processing in adulthood: (a) number is more salient than proportion, (b) number is encoded more automatically…

To explain children's difficulties learning fraction arithmetic, Braithwaite et al. (2017) proposed FARRA, a theory of fraction arithmetic implemented as a computational model. The present study tested predictions of the theory in a new domain, decimal arithmetic, and investigated children's use of conceptual knowledge in that domain. Sixth and…

Many studies have used fraction magnitude comparison tasks to assess people's abilities to quickly assess fraction magnitudes. However, since there are multiple ways to compare fractions, it is not clear whether people actually reason about the holistic magnitudes of the fractions in this task and whether they use multiple strategies in a flexible…

Prior work exploring preschool-aged children's reasoning with repeating patterns has shown that patterning ability is an important predictor of math achievement; however, there is limited research exploring older children's growing pattern task performance. The current study tested whether presentation format impacts performance on growing pattern…

One of the attributes of rational numbers that make them different from integers are the different symbolic modes (fraction, decimal and percentage) to which an identical number can be attributed (e.g. 1/4, 0.25 and 25%). Some research has identified students' difficulty in mental calculations with rational numbers as has also the switching to…

Children and adults often have difficulties comparing decimal magnitudes. Although individuals attempt to reconcile decimals with prior whole-number and fraction knowledge, conceptual and procedural differences between decimals and prior knowledge of whole numbers and fractions can lead to incorrect strategies. The dynamic strategy choice account…

The fifth-grade curriculum presents many opportunities to use students' prior mathematical knowledge as a way to bridge new and more difficult mathematical ideas. In this article, the authors document an area tiling task given to fifth-grade students to connect aspects of area measurement covered in earlier grades to grade-level standards such as:…

Purpose: Most literature has focused solely on either knowledge about number sense or understanding of fractions. To fill the research gap, this study examined pupils' abilities in both number sense and fractions. In particular, it investigated Year 4 and Year 5 pupils' use of strategies in developing their fraction sense. Methodology: This study…

Transitioning from teaching whole number operations to teaching fraction operations can prove difficult, even for the seasoned mathematics teacher. However, with effective literacy practices, teachers can seamlessly shift their students to learning the rules for fractions. The implications can be a mastery of mathematical language used to describe…

The effectiveness of an experimental middle school fraction intervention was evaluated. The intervention was centered on the number line and incorporated key principles from the science of learning. Sixth graders (N = 51) who struggled with fraction concepts were randomly assigned at the student level to the experimental intervention (n = 28) or…

Rational number understanding is a critical building block for success in more advanced mathematics; however, how rational number magnitudes are conceptualized is not fully understood. In the current study, we used a dual-task working memory (WM) interference paradigm to investigate the dominant type of strategy (i.e., requiring verbal WM…

The present study investigated the development of fraction comparison strategies through a longitudinal analysis of children's responses to a fraction comparison task in 4th through 6th grades (N = 394). Participants were asked to choose the larger value for 24 fraction pairs blocked by fraction type. Latent class analysis of performance over item…

The effectiveness of an experimental middle school fraction intervention was evaluated. The intervention was centered on the number line and incorporated key principles from the science of learning. Sixth graders (N = 51) who struggled with fraction concepts were randomly assigned at the student level to the experimental intervention (n = 28) or…

Examines strategies used by preschool children to subdivide items and focuses on how counting and sharing relate to one another. Indicates that children exhibited alternative strategies--suggesting use of a recipient as a mental cycle-marker and an adjacent recipient strategy--with pauses between allocations suggesting a re-presentation of lots…

Discusses overall mental computation achievement and limits discussion to strategies middle school students used when computing with whole numbers, decimals, and fractions. Suggests that the development of conceptual knowledge of numbers is an important prerequisite for the understanding of mental computation procedures. (Contains 31 references.)…