Investigated understanding of place value in 93 English-speaking and 50 Japanese-speaking children with cubes denoting units and tens for representation of multi-digit numbers. Found that differences between English and Japanese participants disappeared when use of tens cubes was demonstrated in practice trials. Results suggest that influence of…

Continues the theme developed in the first paper on this topic which was published in volume 10 of this journal. Carries the historical tale of pi from the late 16th century to the present. (ASK)

Compares a function to a mail carrier, with each letter, or domain value, placed in exactly one mailbox, or range value. Continues the mail carrier analogy for a constant function, a one-to-one function, and an onto function. (AIM)

Presents a dialog in question-and-answer form to explain the rationale behind using radians instead of degrees in calculus. (ASK)

This is the fifth in a series that examines the challenges that teachers in different domains face as they attempt to implement the pedagogical reform "Fostering a Community of Learners" (FCL). Here we focus on the relationship between FCL and the teaching of mathematics. We argue that it is possible to teach mathematics through the FCL pedagogy,…

Fuzzy logic programs for computers make them more human. Computers can then think through messy situations and make smart decisions. It makes computers able to control things the way people do. Fuzzy logic has been used to control subway trains, elevators, washing machines, microwave ovens, and cars. Pretty much all the human has to do is push one…

Direct sum decomposition of Abelian groups appears in almost all textbooks on algebra for undergraduate students. This concept plays an important role in group theory. One simple example of this decomposition is obtained by using the kernel and range of a projection map on an Abelian group. The aim in this pedagogical note is to establish a direct…

In this note, an integrated form of some significant means with two variables is provided, and some chains for mean value inequalities are obtained. At the same time, a concise family of algebraic functions appears, which satisfy Mitrinovic's requirements.