Uses base-ten manipulative pieces to illustrate divisibility tests with single-digit divisors. (YDS)

Suggests ways to increase students' computational fluency using concrete materials, engaging tasks, and reflection time to increase number automaticity, flexibility in thinking about numbers, and use of efficient problem-solving strategies to find sums and differences. (Author/NB)

Investigates the way native Chinese speakers process Chinese and Western numerals. Finds they process the numerals differently and that they processed Western numerals differently than native English speakers do. Concludes that Chinese and Western numerals are not a homogeneous set of stimuli. (RS)

Contrasts nominal, cardinal, and ordinal uses of numbers with linguistic and historical examples. (MKR)

The repeating cyclic fraction, 1/7, provides a plausible explanation for use of the number 71.428571 (71 and 3/7) in cosmology; for 22/7 as a value for pi; and for concepts of time and circle division related to breaths per minute. (Author/MKR)

Demonstrates some of the usefulness of number theory to students on the high school setting in four areas: Fibonacci numbers, Diophantine equations, continued fractions, and algorithms for computing pi. (ASK)

Presents an integrated mathematics and science activity in which students explore the concept of sampling on a soccer field. (ASK)

Discusses some surprising properties of the natural numbers set such as axioms for natural numbers and mathematical induction. (ASK)

Explores secondary school students' conceptions of division by zero. A substantial number of the participating secondary school students argued that division by zero results in a number, and concrete arguments were generally regarded as valid for justifying the impossibility of division by zero. (Contains 30 references.) (Author/ASK)

Presents an activity that engages children in thinking about the results of combining numbers. (ASK)

Reconsiders the article 'The .999999 Controversy' by Ronald Selby featured in the Spring 1999 issue which tracks the responses of high school classes to a sequence of six arguments offered to them that .999999=1. Discusses mathematical proofs and the proof of this particular question. (ASK)

Children's number sequence progress through several developmental changes that are brought about through adaptations in the children's counting activities. Introduces key psychological aspects of number sequences, pre-numerical counting schemes, an initial number sequence, a tacitly-nested number sequence, explicitly-nested number sequence, and…

Examines three strands of elementary mathematics--numerals and counting, recording and calculating, and mathematics exploration and play--and provides ways to integrate culture and mathematics experiences in each area. Specific topics include Egyptian methods for multiplication, the abacus, and the words for the numbers 1-10 in seven different…

Benjamin Banneker, a self-taught mathematician, surveyor and astronomer published annual almanacs containing his astronomical observations and predictions. Banneker who also used logarithms to apply the Law of Sines believed that the method used to solve a mathematical problem depends on the tools available.

The problem considered in this paper demonstrates that quite profound and inherently fascinating mathematics is accessible to students who have a sound number sense and deep conceptual understanding of very basic mathematics. This is one of many reasons why we should teach mathematics in ways that promote these attributes in students.