Working memory capacity plays a major role in many applied contexts, and it is important to be able to accurately measure this construct. The current studies tested whether the modality of administration of the letter-number sequencing task affects performance on the task. The letter-number sequencing task is a working memory capacity measure…

In this article we discuss relationships between the cyclic group Z[subscript 12] and Western tonal music that is embedded in a 12-note division of the octave. We then offer several questions inviting students to explore extensions of these relationships to other "n"-note octave divisions. The answers to most questions require only basic…

Many children and adults have difficulty gaining a comprehensive understanding of rational numbers. Although fractions are taught before decimals and percentages in many countries, including the USA, a number of researchers have argued that decimals are easier to learn than fractions and therefore teaching them first might mitigate children's…

The purpose of the present study is to examine content knowledge (CK) and pedagogical content knowledge (PCK) of Greek teachers in number sense and specifically in mental calculations with rational numbers (fractions, decimals and percentages). Examined within the framework of CK were the type of strategies employed by teachers and the extent of…

Numerous studies have tried to identify the core deficit of developmental dyscalculia (DD), mainly by assessing a possible deficit of the mental representation of numerical magnitude. Research in healthy adults has shown that numerosity, duration, and space share a partly common system of magnitude processing and representation. However, in DD,…

How can we make sense of what we learned today?" This is a question the author commonly poses to her algebra students in an effort to have them think about the connections between the new concept they are learning and concepts they have previously learned. For students who have a strong, expansive understanding of previously learned topics,…

This article highlights four routines that use visual images and open questions to invite students to discuss, justify, make arguments, and question their own thinking as well as their classmates' thinking. The authors share specific classroom examples from each routine that highlight the meaningful discourse they can inspire. Teacher prompts and…

This study describes the way 14 pre-service teachers engaged in discourse about integers. The discourse being examined is framed by Sfard's view of a discourse as being composed of the four elements word use, visual mediators, routines, and narratives (Sfard, 2008). These elements combine to form a means for people to exchange and preserve ideas…

We share a subset of the 41 underlying strategies that comprise five ways of reasoning about integer addition and subtraction: formal, order-based, analogy-based, computational, and emergent. The examples of the strategies are designed to provide clear comparisons and contrasts to support both teachers and researchers in understanding specific…

Mathematics educators advocate for the use of models as an instructional practice that can potentially aid in building students' understanding of difficult topics. Integers and integer operations are historically problematic for students and are critically important in both arithmetic and the future study of algebra. In this chapter, I explore one…

Difficulties in mathematics have been described in very preterm children, but their origins are not well understood and may differ from other populations with specific learning disability. Very preterm children, children with learning disability, and typically developing children were compared in mathematics skills, using standardized tools,…

Pre-algebra mathematical competencies were assessed for a large and diverse sample of sixth graders (n = 1,926), including whole number and fractions arithmetic, conceptual understanding of equality and fractions magnitudes, and the fractions number line. The goal was to determine if there were clusters of students with similar patterns of…

Number Talks, created in the early 1990s by Ruth Parker and Kathy Richardson, have gained popularity in the mathematics education community over the past decade with the publication of the book series "Number Talks" (Parrish, 2010, 2014), and especially since the publication of "Making Number Talks Matter" (Humphreys &…

At the onset of the coronavirus disease (COVID-19) global pandemic, our interdisciplinary team hypothesized that a mathematical misconception--whole number bias (WNB)--contributed to beliefs that COVID-19 was less fatal than the flu. We created a brief online educational intervention for adults, leveraging evidence-based cognitive science…

Inflectional affixes expressing the same grammatical category (e.g., subject agreement) tend to appear in the same morphological position in the word. We hypothesize that this cross-linguistic tendency toward "category clustering" is at least partly the result of a learning bias, which facilitates the transmission of morphology from one…