"Number sense" is "an intuition about numbers that is drawn from all varied meanings of number" (NCTM, 1989, p. 39). Students with number sense understand that numbers are representative of objects, magnitudes, relationships, and other attributes; that numbers can be operated on, compared, and used for communication. It is fundamental knowledge…

This article brings together two independent lines of research on numerally quantified expressions, e.g. two girls. One stems from work in linguistic theory and asks what truth conditional contributions such expressions make to the utterances in which they are used--in other words, what do numerals mean? The other comes from the study of language…

Patients with corticobasal degeneration (CBD) appear to have impaired number knowledge. We examined the nature of their number deficit while we tested the hypothesis that comprehension of larger numbers depends in part on verbal mediation. We evaluated magnitude judgments and performance on number conservation measures rooted in Piagetian theory…

The authors investigated how 2-digit Arabic numerals are named by looking at the effects of masked primes on the naming latencies. Target numerals were named faster when prime and target shared a digit at the same position (e.g., the target 28 primed by 18 and 21). In contrast, naming latencies were slower when prime and target shared 1 or 2…

The enumeration of small numbers of objects (approximately 4) proceeds rapidly, accurately, and with little effort via a process termed subitization. Four experiments examined whether it was possible to subitize the number of features rather than objects present in a display. Overall, the findings showed that when features are presented randomly…

Preschool children are often good at counting things but seem slow to learn that there is more to counting than simply finding out how many are in a single set. Counting is useful when comparing sets and when creating new sets to match existing ones. This is part of the numerical understanding that educators wish to foster in schools. In two…

This paper is written on a level accessible to college/university students of mathematics who are taking second-year, algebra based, mathematics courses beyond calculus I. This article combines material from geometry, trigonometry, and number theory. This integration of various techniques is an excellent experience for the serious student. The…

This investigation involves first assessing and then designing instruction to resolve student difficulties with addition facts. The ultimate goal was improving students' computational fluency.

In this study, we investigated patients with focal neurodegenerative diseases to examine a formal linguistic distinction between classes of generalized quantifiers, like "some X" and "less than half of X." Our model of quantifier comprehension proposes that number knowledge is required to understand both first-order and higher-order quantifiers.…

This paper reports the results of an exploratory study of the perceptions of and approaches to mathematical proof of undergraduates enrolled in lecture-based and problem-based "transition to proof" courses. While the students in the lecture-based course demonstrated conceptions of proof that reflect those reported in the research literature as…

In math classes, teachers often focus instruction on the formulas and processes needed to solve different types of problems, but neglect to teach the concepts on which these tools are based. In this article, the author argues that before they can do this, teachers themselves need to understand "understanding math." Teaching mathematics with…

This study is aimed at the mechanisms used by students with an intellectual disability in the counting process. The assessment of the counting process is carried out through experimental tests inspired by the basic principles of Gelman and Gallistel, namely one-to-one, stable order, cardinality, abstraction and order irrelevance. This is a…

Negative numbers extend our number line and greatly simplify our calculations, but sometimes students struggle with the concepts. These fun activities will help kids to make sense of the "other half" of our number system.

Translating numerals into number words is a tacit task requiring linguistic and mathematical knowledge. This project expanded on previous number production models by examining developmental differences in children's number naming errors. Ninety-six children from grades one, three, five, and seven translated a random set of numerals into number…

This volume is a teacher's edition in a series of books that contain open-ended exploration activities and experiments. These activities allow and encourage students to set their own goals, use their own creativity and ideas, investigate the wonders of nature, learn about the workings of real businesses, and draw conclusions from their…