The note introduces sequences having M-bonacci property. Two summation formulas for sequences with M-bonacci property are derived. The formulas are generalizations of corresponding summation formulas for both M-bonacci numbers and Fibonacci numbers that have appeared previously in the literature. Applications to the Arithmetic series, "m"th "g -…

The number [pie] [approximately] 3.14159 is defined to be the ratio C/d of the circumference C to the diameter d of any given circle. In this article, the author looks at some surprising and unexpected places where [pie] occurs, and then thinks about some ways of remembering all those digits in the expansion of [pie].

In the teaching of calculus, the algebraic derivation of the derivative (gradient function) enables the student to obtain an analytic "global" gradient function. However, to the best of this author's knowledge, all current technology-based approaches require the student to obtain the derivative (gradient) at a single point by…

An attempt is made to analyze mathematical behavior from more general psychological perspectives. The mathematical language is a special case of the human language, which is a form of expression. Many people use common language in a meaningless way. The same is true about the mathematical language. Rituals are other forms of expression. Many…

In this paper, the author recommends that every teacher of mathematics should undertake an analysis using their own data. She further recommends that they reflect on the outcomes of their analysis and share it with colleagues. Teachers can look at an individual student's results, variations in results between student sub-groups in their classes,…

Nonlinear optics is generally first presented as an extension of conventional optics. Typically the subject is introduced with reference to a classical oscillatory electric polarization, accommodating correction terms that become significant at high intensities. The material parameters that quantify the extent of the nonlinear response are cast as…

University of Chicago School Mathematics Project (UCSMP) Algebra is a one-year course covering three primary topics: (1) linear and quadratic expressions, sentences, and functions; (2) exponential expressions and functions; and (3) linear systems. Topics from geometry, probability, and statistics are integrated with the appropriate algebra.…

The objective of this research was to better understand the transfer of learning between different variations of pre-algebra problems. While the authors could have addressed a specific variation that might address transfer, they were interested in developing a general model of transfer, so we gathered data from multiple problem types and their…

While teaching in New York City public schools, the author began planning collaboratively with a team of mathematics teachers. Collaborative planning enabled them to consider a range of issues that may not have emerged had they been planning independently. In this article, the author first describes their work through excerpts of conversations…

In this article, we investigate the construction of spirals on an equilateral triangle and prove that these spirals are geometric. In further analysing these spirals we show that both the male (straight line segments) and female (curves) forms of the spiral exhibit exactly the same growth ratios and that these growth ratios are constant…

The extreme interval values and statistics (expected value, median, mode, standard deviation, and coefficient of variation) for the smallest (min) and largest (max) values of exponentially distributed variables with parameter ? = 1 are examined for different observation (sample) sizes. An extreme interval value g[subscript a] is defined as a…

While linear programming is a common tool in business and industry, there have not been many applications in educational assessment and only a handful of individuals have been actively involved in conducting psychometric research in this area. Perhaps this is due, at least in part, to the complexity of existing software packages. This article…

Online discussion forums provide open workspace allowing learners to share information, exchange ideas, address problems and discuss on specific themes. But the substantial impediment to its promotion as effective e-learning facility lies in the continuously increasing messages but with discrete and incoherent structure as well as the loosely-tied…

With this paper, our main aim is to contribute to the realisation of the chemical reactivity concept, tracing the historical evolution of the concept of chemical affinity that eventually supported the concept of chemical equilibrium. We will concentrate on searching for the theoretical grounds of three key chemical equilibrium ideas: "incomplete…

Spatial reasoning is a skill that needs to be developed in students as it is important in geometry for determining total surface areas and volumes of 3-dimensional shapes (Liedtke, 1995). Simply teaching children the formulae, in this case for finding total surface areas, can limit them in understanding mathematics conceptually (Bonotto, 2003).…