In this paper we present results relating undergraduate student retention in science, technology, engineering, and mathematics (STEM) majors to the use of Peer Instruction (PI) in an introductory physics course at a highly selective research institution. We compare the percentages of students who switch out of a STEM major after taking a physics…

"Lord Brouncker's continued fraction for pi" is a well-known result. In this article, we show that Brouncker found not only this one continued fraction, but an entire infinite sequence of related continued fractions for pi. These were recorded in the "Arithmetica Infinitorum" by John Wallis, but appear to have been ignored and forgotten by modern…

In my Calculus classes I encourage my students to actively reflect on course material, to work collaboratively, and to generate diverse solutions to questions. To facilitate this I use peer instruction (PI), a structured questioning process, and i-clickers, a radio frequency classroom response system enabling students to vote anonymously. This…

The celebrated Basel Problem, that of finding the infinite sum 1 + 1/ 4 + 1/9 + 1/16 + ..., was open for 91 years. In 1735 Euler showed that the sum is pi[superscript 2]/6. Dozens of other solutions have been found. We give one that is short and elementary.

Using continued fraction expansions, we can approximate constants, such as pi and e, using an appropriate integer n raised to the power x[superscript 1/x], x a suitable rational. We review continued fractions and give an algorithm for producing these approximations.

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…

This chapter discusses the impact that four multisite National Science Foundation (NSF) evaluations had on the broader field of science, technology, engineering, and mathematics education and evaluation. Three approaches were used to investigate the broader impact of these evaluations on the field: (a) a citation analysis, (b) an on-line survey,…

Differences in the perception of the difficulty level of integrating specific educational objectives into Mathematics teaching between beginner and experienced secondary school Mathematics teachers was examined. One hundred and seventeen Mathematics teachers from State Secondary Schools in Anambra, Nigeria were included in the investigation. A…

In 1997, Bailey and Bannister showed that a + b greater than c + h holds for all triangles with [gamma] less than arctan (22/7)where a, b, and c are the sides of the triangle, "h" is the altitude to side "c", and [gamma] is the angle opposite c. In this paper, we show that a + b greater than c + h holds approximately 92% of the time for all…

The Integrative Graduate Education and Research Traineeship (IGERT) program represents a substantial investment by the National Science Foundation (NSF) to improve the quality of graduate education, and ultimately, to increase the number of graduates better prepared to address our nation's 21st century scientific and technological needs. The…

The researcher employed two designs to address the research question for this particular study. This quasi-experimental non-equivalent control group study compared the math achievement of 92 eighth grade students who received Classroom Performance System (CPS)-based instruction using Peer Instruction (PI) to 76 eighth grade students who received…

This paper is a whimsical survey of the various explanations which might account for the biblical passage in I Kings 7:23 that describes a round object--a bronze basin called Solomon's Sea--as having diameter ten cubits and circumference thirty cubits. Can the biblical pi be any number other than 3? We offer seven different perspectives on this…

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…

The activities suggested in this article are intended for use with lower secondary school students. The "Australian Curriculum: Mathematics" states that students in lower secondary school should "investigate the relationship between features of circles such as circumference, area, radius and diameter" and "use formulas to solve problems involving…

If students are in an advanced mathematics class, then at some point they enjoyed mathematics and looked forward to learning and practicing it. There is no reason that this passion and enjoyment should ever be lost because the subject becomes more difficult or rigorous. This author, who teaches advanced precalculus to high school juniors,…