Part 2 considers the limit of a sequence and extends this to include ideas such as continuity, derivative, and integral. The discussion concludes with an example of a finite or "counted completely" set, the Fermat primes. (MK)

Learning activities are given for instruction in the skill of associating numbers with sets of dots, a skill intermediate between counting and higher number concepts. (MP)

Patterns generated by the set of natural or counting numbers are discussed. Included are quartic, odd, square, and triangular numbers. (MK)

Presents 12 problems for students to investigate the relationships involving properties of numbers by using BASIC language. (YP)

Discusses how to help children acquire mathematical concepts and teach for precise mathematical concepts. Describes four activities to reinforce the concepts introduced. (YP)

Discusses activities using base-10-block skits to teach number system concepts in first grade classrooms. Describes the students' responses to the activities. (YP)

Describes an activity in which students, grades 7-12, explore patterns and properties of repunits, an integer written as a string of ones. Includes extensions for exploring algebraic justifications. (MKR)

Discusses key areas in science that require students to have a well-developed sense of numeracy for full understanding. Suggests that some of the difficulties students have with numeracy arise from not distinguishing between the teaching of facts and skills and teaching through conceptual understanding. Makes some recommendations for correcting…

A study investigating the linguistic structure of Oneida and Lakota number systems found that base-10 numeracy is communicated more explicitly in these languages than in English. Further research is needed to determine whether teaching Oneida and Lakota students in their Native languages would help them to develop better number sense. A sample…

This brief report attempts to resolve the claim that infants preferentially attend to continuous variables over number [e.g. Psychol. Sci. 10 (1999) 408; Cognit. Psychol.44 (2002) 33] with the finding that when continuous variables are controlled, infants as young as 6-months of age discriminate large numerical values [e.g. Psychol. Sci. 14 (2003)…

Number sense, an integral part of the curriculum in primary school mathematics, has always been thought of as playing a major role in pupils' understanding and use of numbers in calculation. Research in number sense has been carried out in the West, as well as in Malaysia. That a study of such a nature be done to reflect on the abilities of…

This book is about playing with mathematics, teaching: (1) How to multiply and divide large numbers mentally; (2) Making addition and subtraction easy; (3) Tricks for understanding fractions and decimals; and (4) How to quickly check answers for each calculation. Described as a foolproof way to do multiplication, division, factoring estimating,…

This article, reprinted from "Arithmetic Teacher" in 1979, as part of the "MT" 100 celebration, discusses the importance of fractions.

Usiskin takes another look at fractions, years after writing the article "The Future of Fractions" for "Arithmetic Teacher."

Current neurocognitive theories of number processing [Dehaene, S., Piazza, M., Pinel, P., & Cohen, L. (2003). Three parietal circuits for number processing. "Cognitive Neuropsychology," 20, 487-506] state that mathematical performance is made possible by two functionally and anatomically distinct subsystems of number processing: a verbal system…