This paper is concerned with developing a new class of generalized numbers. The main advantage of this class is that it generalizes the two classes of generalized Fibonacci numbers and generalized Pell numbers. Some new identities involving these generalized numbers are obtained. In addition, the two well-known identities of Sury and Marques which…

By the time they reach middle school, all students have been taught to add fractions. However, not all have "learned" to add fractions. The common mistake in adding fractions is to report that a/b + c/d is equal to (a + c)/(b + d). It is certainly necessary to correct this mistake when a student makes it. However, this occasion also…

Comparing datasets, that is, sets of numbers in context, is a critical skill in higher order cognition. Although much is known about how people compare single numbers, little is known about how number sets are represented and compared. We investigated how subjects compared datasets that varied in their statistical properties, including ratio of…

In two experiments, participants judged the average numerosity between two sequentially presented dot patterns to perform an approximate arithmetic task. In Experiment 1, the response was given on a 0-20 numerical scale (categorical scaling), and in Experiment 2, the response was given by the production of a dot pattern of the desired numerosity…

The aim of this paper is to investigate the role that auxiliary means (manipulatives such as cubes and representations such as number line) play for kindergartners in working out mathematical tasks. Our assumption was that manipulatives such as cubes would be used by kindergartners easily and successfully whereas the number line would be used by…

This article deals with a brief history of Fibonacci's life and career. It includes Fibonacci's major mathematical discoveries to establish that he was undoubtedly one of the most brilliant mathematicians of the Medieval Period. Special attention is given to the Fibonacci numbers, the golden number and the Lucas numbers and their fundamental…