A visual proof that sin x/x is monotonically increasing on (0, pi/2). For tan x/x, see p. 420 (EJ1017686).

A visual proof that tan x/x is monotonically increasing on (0, pi/2). For sin x/x, see p. 408 (EJ1017684).

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…

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.

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…

This article discusses a writing project that offers students the opportunity to solve one of the most famous geometric problems of Greek antiquity; namely, the impossibility of trisecting the angle [pi]/3. Along the way, students study the history of Greek geometry problems as well as the life and achievements of Carl Friedrich Gauss. Included is…

This study aimed on the process of teaching taxicab geometry, a non-Euclidean geometry that is easy to understand and similar to Euclidean geometry with its axiomatic structure. In this regard, several teaching activities were designed such as measuring taxicab distance, defining a taxicab circle, finding a geometric locus in taxicab geometry, and…

A "k"-out-of-"n" system functions as long as at least "k" of its "n" components remain operational. Assuming that component failure times are independent and identically distributed exponential random variables, we find the distribution of system failure time. After some examples, we find the limiting…

In 1998 the National Science Foundation launched the Integrative Graduate Education and Research Traineeship (IGERT) program, a major initiative aimed at Science, Technology, Engineering, and Mathematics (STEM) graduate education. IGERT was developed to meet the challenges of educating U.S. Ph.D. scientists, engineers, and educators with…

Teaching teachers to become observers and inquirers into mathematics will help change how they teach math to students. Essential to all professional development in mathematics is the idea that making sense of mathematics is key to learning. Just as learning to read calls for bringing meaning to the printed page, learning math calls for bringing…

This report summarizes findings from an evaluation of the impacts of the National Science Foundation's (NSF) Integrative Graduate Education and Research Traineeships (IGERT) program. Through support of interdisciplinary graduate education programs in Science, Technology, Engineering, and Mathematics, the IGERT program aims to educate U.S.…

The objective of this research is to validate the algorithm of learning effort which is an indicator of a new real-time and non-interfering based diagnostic technique. IC3 Mentor, the adaptive e-learning platform fulfilling the requirements of intelligent tutor system, was applied to 165 university students. The learning records of the subjects…

This narrative considers how well equipped today's teacher education students and faculty are to meet the demands of the new Common Core State Standards. Data from the Teacher Education Accreditation Council's national evaluation of teacher education programs gives a mixed picture that, while mostly encouraging, also reveals that some…