Early mathematics plays an important role in introducing foundational concepts for number sense in children. One of the critical areas of learning is the establishment of a linear view of numbers. It is essential to create opportunities for young children to understand that numbers are equally spaced on the number line and that they increase in…

The approximate number system (ANS) is foundational to numerical cognition. Whereas some studies hint at intact ANS skills in individuals with Down syndrome (DS), others report impaired ANS abilities. To reconcile these discrepant findings, we investigated ANS skills of children with DS and typically developing (TD) children in a non-symbolic…

It is difficult for an instructor to just make up valid numbers for B[subscript x], B[subscript y], B[subscript z], E[subscript x], E[subscript y], and E[subscript z] in the creation of homework problems and test questions calculating the Poynting vector. In this paper, 25 examples are given of the electric and magnetic fields of electromagnetic…

The give-"n" task is widely used in developmental psychology to indicate young children's knowledge or use of the cardinality principle (CP): the last number word used in the counting process indicates the total number of items in a collection. Fuson (1988) distinguished between the CP, which she called the count-cardinal concept, and…

This study concerns the cognitive process of mathematical problem posing, conceptualized in three stages: understanding the task, constructing the problem, and expressing the problem. We used the eye tracker and think-aloud methods to deeply explore students' behavior in these three stages of problem posing, especially focusing on investigating…

Numbers (i.e. 45) are symbols that are common in reading texts in various forms such as dates, percentages, and quantity expressions. Each digit corresponds to a word, unlike words in which each letter represents a phoneme. Despite their high frequency in reading texts, eye movement research on numeral processing is still rare. Numerals are easy…

This study's purpose was to examine the effects of the concrete-representational-abstract integrated (CRA-I) sequence on the performance of students who struggled with rational number concepts. Three students in southeastern U.S. fifth grade class participated in the study. The CRA-I intervention was grounded in the principles of explicit…

There are three main types of number used in modern, industrialized societies. Cardinals count sets (e.g., people, objects) and quantify elements of conventional scales (e.g., money, distance), ordinals index positions in ordered sequences (e.g., years, pages), and nominals serve as unique identifiers (e.g., telephone numbers, player numbers).…

When the new programming language Pascal was developed in the 1970's, Walter Gander did not like it because because many features which he appreciated in prior programming languages were missing in Pascal. For example the block structure was gone, there were no dynamical arrays, no functions or procedures were allowed as parameters of a procedure,…

This study aimed to describe students' semantic representation obstacles in solving geometric problems. There are three types of obstacles, that are ontogeny, epistemology, and didactics obstacles. This study was carried out on three subjects with different obstacles and focused on math semantic representations in solving geometry problems. The…

In this article, we review research literature concerning number sense from several related fields. Whereas other authors have pointed to difficulty defining number sense or to some degree of inconsistency in the literature, we argue instead that this is a case of polysemy: three constructs given the same name. Our purpose is to clarify the…

Are there some differences so small that we cannot detect them? Are some quantities so similar (e.g., the number of spots on two speckled hens) that they simply look the same to us? Although modern psychophysical theories such as Signal Detection Theory would predict that, with enough trials, even minute differences would be perceptible at an…

Reading numbers aloud involves visual processes that analyze the digit string and verbal processes that produce the number words. Cognitive models of number reading assume that information flows from the visual input to the verbal production processes--a feed-forward processing mode in which the verbal production depends on the visual input but…

The current longitudinal study measured 279 kindergartners' (M[subscript age] = 5.76 years; SD = 0.55; 135 females) place value understanding using both approximate and syntactic measures based on previous evidence that early variation in performance on approximate measures was associated with subsequent syntactic place value understanding. In the…

To understand misconceptions with rational numbers (i.e., fractions, decimals, and percentages), we administered an assessment of rational numbers to 331 undergraduate students from a 4-year university. The assessment included 41 items categorized as measuring foundational understanding, calculations, or word problems. We coded each student's…