In this "Delving Deeper" article, the author introduces the slip-slide method for solving Algebra 1 mathematics problems. This article compares the traditional method approach of trial and error to the slip-slide method of factoring. Tools that used to be taken for granted now make it possible to investigate relationships visually,…

This paper deals with a brief history of the most remarkable Euler numbers "e,"?"i"?and?"?" in mathematical sciences. Included are many properties of the constants "e,"?"i"?and?"?" and their applications in algebra, geometry, physics, chemistry, ecology, business and industry. Special…

In this paper, lower-order mathematical thinking skills within finance were studied from the viewpoint of financial employees in the Iranian Bank of Industry and Mine. To conduct this research, a questionnaire was developed after reviewing lower-order mathematical thinking skills in finance. In accordance with the revised Bloom's taxonomy, the…

In recent years, artificial intelligence applications for understanding the human thinking process and transferring it to virtual environments come into prominence. The fuzzy logic which paves the way for modeling human behaviors and expressing even vague concepts mathematically, and is also regarded as an artificial intelligence technique has…

Mathematical conventions -- which account for the choices of mathematics community regarding definitions of concepts, their names and symbols -- are the focus of this paper. We introduce the task of unpacking, that is, offering plausible explanations and arguments for the choice of conventions. Using responses of four prospective teachers to the…

In this article, the author considers the merits of two classes of profit maximization problems: those involving perfectly competitive firms with quadratic and cubic cost functions. While relatively easy to develop and solve, problems based on quadratic cost functions are too simple to address a number of important issues, such as the use of…

Quantifier Elimination is a procedure that allows simplification of logical formulas that contain quantifiers. Many mathematical concepts are defined in terms of quantifiers and especially in calculus their use has been identified as an obstacle in the learning process. The automatic deduction provided by quantifier elimination thus allows…

A few years ago it was suggested that the distance to celestial bodies could be computed by tracking their position over about 24 hours and then solving a regression problem. One only needed to use inexpensive telescopes, cameras, and astrometry tools, and the experiment could be done from one's backyard. However, it is not obvious to an amateur…

We analyze the mathematical solutions of 7- to 8-year-old pupils while individually solving an arithmetic problem. The analysis was based on the "configuration of objects," an instrument derived from the onto-semiotic approach to mathematical knowledge. Results are illustrated through a number of cases. From the analysis of mathematical…

The starting point of this article is the question, "how might we inform an epistemology of numeracy from the point of view of better preparing young people for workplace competence?" To inform thinking illustrative data from two projects that researched into mathematics in workplace activity and the teaching and learning of modelling in…

In this thesis, I study some aspects of how students learn to use math to make sense of physical phenomena. Solving physics problems usually requires dealing with algebraic expressions. That can take the form of reading equations you're given, manipulating them, or creating them. It's possible to use equations simply according to formal rules of…

Double-entry bookkeeping (DEB) implicitly uses a specific mathematical construction, the group of differences using pairs of unsigned numbers ("T-accounts"). That construction was only formulated abstractly in mathematics in the nineteenth century, even though DEB had been used in the business world for over five centuries. Yet the…

The "Unsolved Problems in Number Theory" book by Richard Guy provides nice problems suitable for a typical math major. We give examples of problems that have worked well in our senior seminar course and some nice results that senior math majors can obtain.

In this paper I discuss the motivation behind using an introduction to Fourier series as a method to unify the topics of integration techniques and series calculations in a Calculus II course.

The analogical reasoning isn't used only in mathematics but also in everyday life. In this article we approach the analogical reasoning in Geometry Education. The novelty of this article is a classification of geometrical analogies by reasoning type and their exemplification. Our classification includes: analogies for understanding and setting a…