Perceptions of instrumentality (PI) are the connections one sees between a current activity and a future goal. With high PI, one is motivated to persist with quality effort because the current activity, even when difficult, is perceived as aligned with, and progress toward, the goal. Conversely, with low PI, one is motivated to relinquish effort…

Using modern technology to examine classical mathematics problems at the high school level can reduce difficult computations and encourage generalizations. When teachers combine historical context with access to technology, they challenge advanced students to think deeply, spark interest in students whose primary interest is not mathematics, and…

For at least 2000 years people have been trying to calculate the value of [pi], the ratio of the circumference to the diameter of a circle. People know that [pi] is an irrational number; its decimal representation goes on forever. Early methods were geometric, involving the use of inscribed and circumscribed polygons of a circle. However, real…

Celebrating mathematics should be a yearlong event in which students in mathematics classes of all levels engage in mathematics activities and competitions that will encourage growth in mathematical knowledge, enthusiasm for the subject, and collaboration among students of different abilities and backgrounds. Pi Day and Pi Week festivities--a good…

This study investigates pre-service mathematics teachers' concept images of radian and possible sources of such images. A multiple-case study was conducted for this study. Forty-two pre-service mathematics teachers completed a questionnaire, which aims to assess their understanding of radian. Six of them were selected for individual interviews on…

Vieta's famous product using factors that are nested radicals is the oldest infinite product as well as the first non-iterative method for finding [pi]. In this paper a simple geometric construction intimately related to this product is described. The construction provides the same approximations to [pi] as are given by partial products from…

This paper describes the analysis of the National Science Foundation (NSF) Math and Science Partnership (MSP) program's January 2008 Learning Network Conference (LNC). This study focuses on the methodologies used by the MSP community to generate evidence and seeks to understand topics of interest to the 320 LNC participants. The data set for this…

An anharmonic solution to the differential equation describing the oscillations of a simple pendulum at large angles is discussed. The solution is expressed in terms of functions not involving the Jacobi elliptic functions. In the derivation, a sinusoidal expression, including a linear and a Fourier sine series in the argument, has been applied.…

Employs statistical tools to determine whether the digits of Pi are pseudorandom. Discusses the difficulties in answering this question. (Author/NB)

Describes an activity in which students develop a conceptual understanding of the formulas of the circumference and area of a circle by exploring pi. (YDS)

This third volume of the 31st annual proceedings of the International Group for the Psychology of Mathematics Education conference presents research reports for author surnames beginning Han- through Miy-. Reports include: (1) Elementary Education Students' Memories of Mathematics in Family Context (Markku S. Hannula, Raimo Kaasila, Erkki…

Argues that by celebrating the number pi with special mathematical activities we may be teaching the fundamental concept of the place-value structure of our decimal place system. Includes several examples to illustrate the argument. (MM)

Euler gave a simple method for showing that [zeta](2)=1/1[superscript 2] + 1/2[superscript 2] + 1/3[superscript 2] + ... = [pi][superscript 2]/6. He generalized his method so as to find [zeta](4), [zeta](6), [zeta](8),.... His computations became increasingly more complex as the arguments increased. In this note we show a different generalization…

Illustrates a way in which students can estimate the ratio of an area of a circle using the radius square. Discusses why the same value of pi appears in both the formulas for the circumference and the area of the circle. (YDS)

This volume of the 27th International Group for the Psychology of Mathematics Education Conference includes the following research reports: (1) The Affective Views of Primary School Children (Peter Grootenboer); (2) Theoretical Model of Analysis of Rate Problems in Algebra (Jose Guzman, Nadine Bednarz and Fernando Hitt); (3) Locating Fractions on…