The purpose of the study was to establish perceptions and attitudes of student teachers and their cognitive-metacognitive awareness in mathematics in colleges of education in Zambia. Although there has been abundant research into perceptions, attitudes and cognitive-metacognitive awareness in teacher education, relatively little research has…

This article describes various courses designed to incorporate mathematical proofs into courses for non-math and non-science majors. These courses, nicknamed "math beauty" courses, are designed to discuss one topic in-depth rather than to introduce many topics at a superficial level. A variety of courses, each requiring students to…

This paper describes and assesses the implementation of online homework in a first-semester calculus course. Comparing sections of the course before implementation to those after, we find statistically significant improvements in retention rates, measures of student engagement, and participation on homework. We do not, however, find statistically…

The purpose of this study was to investigate how a set of physical and digital instructional activities can serve as an example space to help further develop a concept image that is aligned with the formal concept definition for the limit of a sequence. In addition, the unique affordances and constraints allowed by using either a physical or…

This research is a sequential explanatory mixed methods study seeking to understand the influences of mathematics self-efficacy (math SE) on the behavior and attitudes of engineering students with poor math preparation behavior and attitudes in their first college math courses. The quantitative phase of this research assessed the math SE of…

The purpose of this study is to examine how knowledge of astronomy can enhance college-level learning situations involving mathematics. The fundamental symbiosis between mathematics and astronomy was established early in the 17th century when Johannes Kepler deduced the 3 basic laws of planetary motion. This mutually harmonious relationship…

A pair of 6-sided dice cannot be relabeled to make the sums 2, 3,...., 12 equally likely. It is possible to label seven, 10-sided dice so that the sums 7. 8,..., 70 occur equally often. We investigate such relabelings for "pq"-sided dice, where "p" and "q" are distinct primes, and show that these relabelings usually…

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).

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…

A number of papers find the velocity that minimizes the wetness of a traveler caught in the rain. In this capsule we determine, in addition, the necessary amount of forward bend (slouching) so that the traveler stays as dry as possible.

We count the number of group homomorphisms between any two dihedral groups using elementary group theory only.

We give an elementary solution to the famous Basel Problem, originally solved by Euler in 1735. We square the well-known series for arctan(1) due to Leibniz, and use a surprising relation among the re-arranged terms of this squared series.

Combining D'Alembert's ratio test and Cauchy's condensation test, we present a new ratio test for any positive monotone series.

In the popular television show "Survivor", the winner of a million-dollar prize is determined in a final election, where the votes are read aloud as the winner is announced. We hypothesize that the show's producers purposely alter the order of the ballots in order to build audience suspense. We test our hypothesis using the Poisson binomial…