Number relationships, which go far beyond counting skills, refer to the ability to represent a quantity in multiple, flexible ways. It is arguably among the most important mathematics concepts in number and quantity. The current study examined the effectiveness of number relationships instruction in preschool classrooms. Participants included 73…

The study was designed to probe students' thinking about which numerical values can be assigned to algebraic letters. The data from students in Year 7 (n = 533), Year 8 (n = 377) and Year 9 (n = 172) was analysed using response patterns. The data confirmed that each year contained students with two misconceptions; "Different Letter means…

How is number-concept acquisition related to overall language development? Experiments 1 and 2 measured number-word knowledge and general vocabulary in a total of 59 children, ages 30-60 months. A strong correlation was found between number-word knowledge and vocabulary, independent of the child's age, contrary to previous results (D. Ansari et…

In acquiring number words, children exhibit a qualitative leap in which they transition from understanding a few number words, to possessing a rich system of interrelated numerical concepts. We present a computational framework for understanding this inductive leap as the consequence of statistical inference over a sufficiently powerful…

By following learned rules rather than reasoning, students often fall into common error patterns, something every experienced teacher has observed in the classroom. In their effort to circumvent the developing common error patterns of their students, the authors decided to supplement their math text with two weeklong investigations. The first was…

Short term memory is famously limited in capacity to Miller's (1956) magic number 7 plus or minus 2--or, in many more recent studies, about 4 plus or minus 1 "chunks" of information. But the definition of "chunk" in this context has never been clear, referring only to a set of items that are treated collectively as a single unit. We propose a new…

Preservice Secondary Mathematics Teachers (PSMTs) were surveyed to identify if they could connect early-secondary mathematics content (Grades 7-9) in the Common Core State Standards for Mathematics (CCSSM) with mathematics content studied in content courses for certification in secondary teacher preparation programs. Respondents were asked to…

The purpose of this study was to test the promise of the NumberShire Level 1 Gaming Intervention (NS1) to accelerate math learning for first-grade students with or at risk for math difficulties. The NS1 intervention was developed through the Institute of Education Sciences, Small Business Innovation Research Program (Gause, Fien, Baker, &…

The purpose of this study was to test the promise of the NumberShire Level 1 Gaming Intervention (NS1) to accelerate math learning for first-grade students with or at risk for math difficulties. The NS1 intervention was developed through the Institute of Education Sciences, Small Business Innovation Research Program (Gause, Fien, Baker, &…

Formal algebras are among the most powerful and general mechanisms for expressing quantitative relational statements; yet, even university engineering students, who are relatively proficient with algebraic manipulation, struggle with and often fail to correctly deploy basic aspects of algebraic notation (Clement, 1982). In the cognitive tradition,…

External number representations are commonly used throughout the first years of instruction. The twenty-frame is a grid that contains two rows of 10 dots each, and within each row, dots are organized in two groups of five. The assumption is that children can make use of these structures for enumerating the dots, rather than relying on one-by-one…

This case study examines the salient features of two individuals' reasoning when confronted with a task concerning the cardinality and associated cardinal number of equinumerous infinite sets. The APOS Theory was used as a framework to interpret their efforts to resolve the "infinite balls paradox" and one of its variants. These cases…

This paper contributes to the theory and evidence that mathematical cognition is embodied. Drawing on the practices of primary teachers in South Africa engaged in a longitudinal research and development project -- Wits Maths Connect--Primary -- we report on aspects of lessons aimed at developing number sense through whole-class teacher-learner…

Mathematics is an important aspect of daily life. Basic numeracy skills are needed to accomplish everyday tasks. However, research regarding the relationship between cognitive ability, mental age, and basic numeracy skills for children with intellectual disability (ID) is scarce. This research study investigated the correlation between…

In this article, we provide an overview of current knowledge on the underlying cognitive deficits associated with mathematics learning disabilities (MLD). We highlight difficulties surrounding the identification of MLD that include inconsistency in defining MLD, comorbidity with other disabilities, problems associated with assessment tools and…