This article makes a case for introducing moving averages into introductory statistics courses and contemporary modeling/data-based courses in college algebra and precalculus. The authors examine a variety of aspects of moving averages and draw parallels between them and similar topics in calculus, differential equations, and linear algebra. The…

This paper reports changes in the extent to which a group of Year 11 students used a Computer Algebra System (CAS), pen-and-paper (P&P), or a combination of both, when solving routine problems across seven months in four different topics. Comparing the frequency of CAS use across topics shows students made greater use of CAS in the topics of…

Selection bias is a persistent, and often hidden, problem in educational research. It is the primary obstacle standing in between increasingly available large education datasets and the ability to make valid causal inferences to inform policymaking, research, and practice (Stuart, 2010). This article provides an accessible discussion on the…

Computer technologies and especially computer algebra systems (CAS) allow students to overcome some of the difficulties they encounter in the study of real numbers. The teaching of calculus can be considerably more effective with the use of CAS provided the didactics of the discipline makes it possible to reveal the full computational potential of…

Galileo dropped cannonballs from the leaning tower of Pisa to demonstrate something about falling bodies. Gauss was a giant of mathematics and physics who made unparalleled contributions to both fields. More contemporary (and not a person), the Green Monster is the left-field wall at the home of the Boston Red Sox, Fenway Park. Measuring 37 feet…

An experiment was conducted over three recent semesters of an introductory calculus course to test whether it was possible to quantify the effect that difficulty with basic algebraic and arithmetic computation had on individual performance. Points lost during the term were classified as being due to either algebraic and arithmetic mistakes…

In this article, the authors begin by considering symbolic literacy in mathematics. Next, they examine the origins of misuse of the equals sign by primary and junior secondary students, where "=" has taken on an operational meaning. They explain that in algebra, students need both the operational and relational meanings of the equals…

In computing real-valued functions, it is ordinarily assumed that the input to the function is known, and it is the output that we need to approximate. In this work, we take the opposite approach: we show how to compute the values of some transcendental functions by approximating the input to these functions, and obtaining exact answers for their…

In this article we examine 2 x 2 first-order systems of ordinary differential equations and show how to identify separatrices for phase plane portraits when the system has a saddle point critical value. We describe how to use a computer algebra system to generate trajectories from contour plots, when possible, and determine the equation of the…

We introduce a new open source (free) software package that provides a simple, highly interactive interface for carrying out certain mathematical tasks that are commonly encountered in physics. These tasks include plotting and animating functions, solving systems of coupled algebraic equations, and basic calculus (differentiating and integrating…

National Council of Teachers of Mathematics' (NCTM's) (2000) Connections Standard states that students should "recognize and use connections among mathematical ideas; understand how mathematical ideas interconnect ...; [and] recognize and apply mathematics in contexts outside of mathematics" (p. 354). This article presents an in-depth…

The long-running debate over whether students should be allowed to wield calculators during mathematics exams may soon seem quaint. The latest dilemma facing professors is whether to let students turn to a Web site called WolframAlpha, which not only solves complex math problems, but also can spell out the steps leading to those solutions. In…

This paper presents a prototype of a computer learning assistant ILMEV (Interactive Learning-Mathematica Enhanced Vector calculus) package with the purpose of helping students to understand the theory and applications of integration in vector calculus. The main problem for students using Mathematica is to convert a textbook description of a…

Visualizing complex roots of a quadratic equation has been a quest since the inception of the Argand plane in the 1800s. Many algebraic and numerical methods exist for calculating complex roots of an equation, but few visual methods exist. Following on from papers by Harding and Engelbrecht (A. Harding and J. Engelbrecht, "Sibling curves and…

The concept of definite integral is almost always introduced as the Riemann integral, which is defined in terms of the Riemann sum, and its geometric interpretation. This definition is hard to understand for high school students. With the aid of mathematical software for visualisation and computation of approximate integrals, the notion of…