There are many geometrical approaches to the solution of the quadratic equation with real coefficients. In this article it is shown that the monic quadratic equation with complex coefficients can also be solved graphically, by the intersection of two hyperbolas; one hyperbola being derived from the real part of the quadratic equation and one from…

In this article, we present investigative tasks that concern loci, which integrate the use of dynamic geometry software (DGS) with mathematics for proving the obtained figures. Additional conditions were added to the loci: ellipse, parabola and circle, which result in the emergence of new loci, similar in form to the original loci. The…

This article describes a project inspired by Liping Ma's "Exploring New Knowledge" in which future 7-12 grade mathematics teachers enrolled in a fall 2013 capstone course at a typical regional state university were assigned fictitious student conjectures. These future teachers (all current high school mathematics teachers) were…

In Years 9 and 10 of secondary schooling students are typically introduced to quadratic expressions and functions and related modelling, algebra, and graphing. This includes work on the expansion and factorisation of quadratic expressions (typically with integer values of coefficients), graphing quadratic functions, finding the roots of quadratic…

This paper presents an investigation by pre-service secondary school teachers in a geometry class of the relationship between the perpendicular distance from the eyeball to the wall (x) and the viewable vertical distance on the wall (y) using a view tube of constant length and diameter. In undertaking the investigation, students used tabular and…

This article presents a guided investigation into the spacial relationships between the centres of the squares in a Fibonacci tiling. It is essentially a lesson in number pattern, but includes work with surds, coordinate geometry, and some elementary use of complex numbers. The investigation could be presented to students in a number of ways…

The possibilities for using graphic calculators to enhance the teaching and learning of mathematics are great. However, the boundaries explode when these powerful tools for learning are connected to data logging devices: a whole new approach to mathematics learning becomes possible. Using real world data to introduce the main functions (which are…

The activity "First One Home" in the Shell Centre's "Problems with Patterns and Numbers" Blue Box gives rise to a number of interesting patterns for those looking beyond the basic solution given in the book. The game is for two players, each taking turn and turn about to move a single counter on the grid down and/or to the left…

Introduces the Sharp EL-9600 graphing calculator and its capabilities, and discusses its possible uses in mathematics classrooms. (ASK)

This article discusses Pythagoras' theorem, typically, it is introduce to students in the junior years of secondary school. Students consolidate their understanding of the theorem by using it for finding missing sides of triangles and for checking whether a given triangle has a right angle. But the topic often seems to dry up rapidly once these…

Describes a personal problem solving-inquiry journey, working on a problem suggested by an activity on probability observed in a junior primary classroom. Presents reflective thoughts about the mathematical and pedagogical lessons to be learned from this journey. (ASK)

Presents interesting investigations and activities for inscribed and escribed circles of right-angled triangles. (ASK)

Presents an activity carried out by aboriginal students that addresses solving a real-life problem that could be linked to number sequence, graph theory, and combinations. Contains 14 references. (ASK)

Argues that the calculator is fallible as a repository of mathematical knowledge. Suggests that the calculator should be considered not only a labor-saving device but a learning device. Provides examples of the use of calculators as a learning device. Contains 16 references. (ASK)

One way to assist students in developing correct intuitive ideas about the effect of sample size is to allow students to simulate similar problems. Describes experiences with classes performing simulation using graphing calculators. (ASK)