An elementary proof of the "strong" version of Goldbach's Conjecture (GC) is presented, modifying a theorem previously derived by the author. (Contains 2 tables.)

Place-value is a central, powerful mathematical concept. From the earliest years of school, students focus on developing strong understanding of the ideas, notation and computational use. Many times, however, they get as far as thousands and then resort to waving their hands--at least until they start a far more advanced and abstract treatment of…

This article offers suggestions for teaching confidence intervals, a fundamental statistical tool often misinterpreted by beginning students. A historical perspective presenting the interpretation given by their inventor is supported with examples and the use of technology. A method for determining confidence intervals for the seldom-discussed…

Although variability and structure are often considered as antonyms in many everyday settings, a mathematically disciplined view contradicts this opposition. To initiate fifth- (10 years old) and sixth-grade (11 years old) students in this disciplinary view, we engaged students in practices of modeling data. These practices included inventing and…

I recently had the opportunity to teach a developmental mathematics class at a community college, something a little different from what I usually do as a mathematics teacher educator at a university. I welcomed the chance to examine the curriculum and try some new approaches. In particular, I wanted to explore the development of some fundamental…

This article uses photographs as a springboard for mathematical inquiry to encourage readers to see patterns and relationships that they can think about and extend in a mathematically playful way. Herein, two photographs are presented along with a discussion of the meaning of slopes and their relationship to gradient and pitch. (Contains 6…

Simulation is an important learning tool that allows students to grasp probability concepts, especially when the actual scenario does not need to be replicated entirely. In the cases of tossing coins and rolling dice, gathering the data before analyzing them can be laborious and might be a waste of precious class time--time that might be better…

The capital accumulation ratio (CAR) is commonly used in academic research as a measure of household portfolio quality. This study tested whether a higher initial CAR impacts change in wealth over a decade among households in the accumulation life cycle stage. Meeting the 25% CAR guideline resulted in a 28.1% increase in net worth between 1994 and…

We used a teaching experiment to evaluate the preparation of preservice teachers to teach early algebra concepts in the elementary school with the goal of improving their ability to generalize and justify algebraic rules when using pattern-finding tasks. Nearly all of the elementary preservice teachers generalized explicit rules using symbolic…

The mythology surrounding Hercules has been a part of human culture for over 2,500 years. In ancient Greek mythology, Eurystheus assigns various labors to Hercules, who has to perform them in order to cleanse his soul. This article treats one of the more famous labors, the fifth labor: The Augean Stables. The labor is provided verbatim from…

Interdisciplinary concepts and methodology are increasingly common in today's secondary schools. However, many interdisciplinary lessons combine courses in related areas (e.g., English with history or science with mathematics). This article examines the use of mathematical ideas in the teaching of literature and writing. Employing mathematical…

Promoting student understanding for transfer is an illusive hallmark of effective mathematics instruction. While much research has shown the necessity of promoting understanding for transfer, less attention has been paid to actual pedagogical strategies that can be used to promote transfer of mathematical ideas. Using Fogarty et al. (1992, "How to…

Early childhood teachers know that children arrive at school with an enormous range of mathematical capabilities, but this is not always reflected in mathematics curricula that are offered. The diverse nature of the experiences young children have encountered before commencing school and their differing abilities to articulate their thoughts…

Correlation is an essential concept in statistics; however, students may hold misconceptions about correlation, even after receiving instruction. This study aimed to elucidate (1) the misconceptions held by senior high school students about correlation, using the tool of concept mapping along with interviewing, (2) the possible causes of these…

The central ideas of postcalculus mathematics courses offered in college are difficult to introduce in middle and secondary schools, especially through the engineering and sciences examples traditionally used in algebra, geometry, and trigonometry textbooks. However, certain concepts in music theory can be used to expose students to interesting…