In this paper, some new results related to the integral mean value theorem are proven. This paper includes a discussion of Flett's Mean Value Theorem. (Contains 2 figures.)

Several proofs demonstrating that there are infinitely many primes, different types of primes, tests of primality, pseudo primes, prime number generators and open questions about primes are discussed in Section 1. Some of these notions are elaborated upon in Section 2, with discussions of the Riemann zeta function and how algorithmic complexity…

This short note demonstrates that even for smaller natural numbers, one can have some rule to follow when it comes to studying the divisibility by 4 and 8. One need not actually divide the number.

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"…

While research suggests that formative assessment can be a powerful tool to support teaching and learning, efforts to jump on the formative assessment bandwagon have been more widespread than those to assure the technical quality of the assessments. This report covers initial analyses of data bearing on the quality of formative assessments in…

Studies have shown that students' understanding is typically analytic and not visual. Two possible reasons for this are when the analytic mode, instead of the graphic mode, is most frequently used in instruction or, when students or teachers hold the belief that mathematics consists simply of skillful manipulation of symbols and numbers. The…

An activity providing practice with whole number addition and subtraction, as well as enlarging on the idea of numeration systems, is described. (DT)