This article uses "fibbin" (Fibonacci poems) as an instructional strategy to teaching reading and writing across the curriculum. It describes fibbin from a historical and mathematical perspective and discusses it as an adaptation of the famous Fibonacci sequence to teaching content area material (e.g. science, math, and social studies). This…

According to one theory about how children learn the concept of natural numbers, they first determine that "one", "two", and "three" denote the size of sets containing the relevant number of items. They then make the following inductive inference (the Bootstrap): The next number word in the counting series denotes the size of the sets you get by…

In this article, the author presents his tales of very large numbers. He discusses the concept of infinity and extremely large numbers such as "googol" and "googolplex". "Googol" which could be written as 1, followed by one hundred zeros, was popularized by Edward Kasner and James Newman. Moreover, "googol"…

Flexible knowledge, knowing multiple approaches for solving problems, is a hallmark of expertise in mathematics. Frequently, the author writes, students memorize only one method of solving a certain kind of problem, without understanding what they are doing, why a given strategy works, and whether there are alternative solution methods. Comparison…

In this article, I present an updated account that attempts to explain, in cognitive processing and neural terms, the nonverbal intellectual impairments experienced by most children with deletions of chromosome 22q11.2. Specifically, I propose that this genetic syndrome leads to early developmental changes in the structure and function of clearly…

Adults can represent approximate numbers of items independently of language. This approximate number system can discriminate and compare entities as varied as dots, sounds, or actions. But can multiple different types of entities be enumerated in parallel and stored as independent numerosities? Subjects who were prevented from verbally counting…

After experiencing a Developing Mathematical Ideas (DMI) class on the construction of algebraic concepts surrounding zero and negative numbers, the author conducted an interview with a first grader to determine the youngster's existing level of understanding about these topics. Uncovering young students' existing understanding can provide focus…

In this article, we consider some generalizations of Fibonacci numbers. We consider k-Fibonacci numbers (that follow the recurrence rule F[subscript k,n + 2] = kF[subscript k,n + 1] + F[subscript k,n]), the (k, l)-Fibonacci numbers (that follow the recurrence rule F[subscript k,n + 2] = kF[subscript k,n + 1] + lF[subscript k,n]), and the Fibonacci…

Four proofs, designed for classroom use in varying levels of courses on abstract algebra, are given for the converse of the classical Chinese Remainder Theorem over the integers. In other words, it is proved that if m and n are integers greater than 1 such that the abelian groups [double-struck z][subscript m] [direct sum] [double-struck…