In this paper, we describe how we integrated complex analysis into the second semester of a geometry course designed for preservice secondary mathematics teachers. As part of this inquiry-based course, the preservice teachers incorporated their geometric understanding of the arithmetic of complex numbers and complex-valued functions to create a…

The Common Core State Standards Initiative stresses the importance of developing a geometric and algebraic understanding of complex numbers in their different forms (i.e., Cartesian, polar and exponential). Unfortunately, most high school textbooks do not offer such explanations much less exercises that encourage students to bridge geometric and…

At grade 7, Common Core's content standards call for the use of long division to find the decimal representation of a rational number. With an eye to reconciling this requirement with Common Core's call for "a balanced combination of procedure and understanding," a more transparent form of long division is developed. This leads to the…

The use of difference and differential equations in the modelling is a topic usually studied by advanced students in mathematics. However difference and differential equations appear in the school curriculum in many direct or hidden ways. Difference equations first enter in the curriculum when studying arithmetic sequences. Moreover Newtonian…

Many students and adults feel that algebra is merely the shuffling of symbols. The three interrelated concepts of variable, expression, and equation are central to beginning algebra, and in recent years, helping students understand the idea of a variable has been emphasized. Although graphing calculators help students solve equations, it is also…

This work addresses the subject of mathematics education at secondary schools from a current and stimulating point of view intimately related to computational science. Cryptology is a captivating way of introducing into the classroom different mathematical subjects such as functions, matrices, modular arithmetic, combinatorics, equations,…

Describes a framework to help teachers decide when to use calculators with their students. (YDS)

Mathematics games are often used in the classroom as a reward or warm-up activity before the "real" learning takes place. Many teachers have witnessed how useful games are for tuning-in students to the impending mathematics lesson. However, have teachers considered playing games as the central part of the lesson? This article explores…

Calculators can be used in primary schools in a number of situations. They are most beneficial when working with large numbers, dealing with real data that leads to complex calculations, performing repetitive calculations, developing concepts, estimating and checking, problem solving, and looking for patterns and/or relationships. But what if the…

Examines the idea that the arithmetic calculator can act as a cognitive tool, supporting the amplification or reorganization of systems of thought. Examples were found in which use of the calculator helped pupils work with unusual problem representations and adapt solution strategies in which they focused on planning and monitoring computations…

Brownian motion is an important stochastic process used in modelling the random evolution of stock prices. In their 1973 seminal paper--which led to the awarding of the 1997 Nobel prize in Economic Sciences--Fischer Black and Myron Scholes assumed that the random stock price process is described (i.e., generated) by Brownian motion. Despite its…

Argues that the use of computer technologies in secondary schools should change the nature of mathematics education. Urges the rethinking of the uses of traditional paper-and-pencil computations. Suggests some computer applications for elementary algebra and for problem solving in arithmetic and calculus. (TW)