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…

Rational numbers, such as fractions and decimals, are harder to understand than natural numbers. Moreover, individuals struggle with fractions more than with decimals. The present study sought to disentangle the extent to which two potential sources of difficulty affect secondary-school students' numerical magnitude understanding: number type…

Given that both children and adults struggle with fractions in mathematics education, we investigated the processing of nonsymbolic fractions in a continuous form of part-of-the-whole. Continuous features of nonsymbolic numbers (e.g., the size of dots in an array) were found to influence numerosity judgment, but it should be noted that the…

Mathematical definitions are central to learning and doing mathematics. Research has uncovered significant differences between how mathematicians and non-mathematicians construct, reason about, and refine mathematical definitions. Various strands of research provide insight into the development of definitional practices, yet an integrated approach…

One way to emphasize students' strengths when reasoning verbally is through number talks. During a number talk, a teacher facilitates a 5- to 15-minute conversation during which students have the opportunity to engage in mental mathematics and verbally explain and justify their reasoning regarding how they make sense of numerical computations.…

Three rational number notations--fractions, decimals, and percentages--have existed in their modern forms for over 300 years, suggesting that each notation serves a distinct function. However, it is unclear what these functions are and how people choose which notation to use in a given situation. In the present article, we propose quantification…

Although many researchers theorize that primitive numerosity processing abilities may lay the foundation for whole number concepts, other classes of numbers, like fractions, are sometimes assumed to be inaccessible to primitive architectures. This research presents evidence that the automatic processing of nonsymbolic magnitudes affects processing…

Research on cognitive obstacles related to fraction sense in preservice mathematics teachers is significant, because their success depends on their skills. The acquisition of fraction sense is a complicated problem requiring a strategy to solve it. This study presents cognitive obstacles with fraction sense tests in preservice who will teach in…

Many students face difficulties with fractions. Research in mathematics education and cognitive psychology aims at understanding where and why students struggle with fractions and how to make teaching of fractions more effective. Additionally, neuroscience research is beginning to explore how the human brain processes fractions. Yet, attempts to…

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…

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 chapter, I propose a stance on learning fractions as multiplicative relations through reorganizing knowledge of whole numbers as a viable alternative to the Natural Number Bias (NNB) stance. Such an alternative, rooted in the constructivist theory of knowing and learning, provides a way forward in thinking about and carrying out…

The overarching theme of this book can be simply stated: Building on a foundation of biologically based abilities, children construct number via sensorimotor and mental activity. In this chapter, we return to this theme, and we connect it to three additional themes that emerge across chapters: comparing competing models for conceptual change;…

Why might it be (at least sometimes) beneficial for adults to process fractions componentially? Recent research has shown that college-educated adults can capitalize on the bipartite structure of the fraction notation, performing more successfully with fractions than with decimals in relational tasks, notably analogical reasoning. This study…

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…