Elementary Mathematics

Reducing Abstraction: the Case of Elementary Mathematics

ion is a complex concept that has many faces. As such, in a general context it has attracted the attention of many psychologists and educators (e.g., Beth and Piaget, 1966). In the more particular context of mathematics education research, abstraction has been discussed from a variety of viewpoints (cf. Tall, 1991; Noss and Hoyles, 1996; Frorer, Hazzan and Manes, 1997). There is no consensus wi...

Prototyping Augmented Reality With Elementary Mathematics Teachers

In recent years, augmented reality (AR) applications for children’s entertainment have been gaining popularity, and educational organizations are increasingly interested in applying this technology to children’s educational games. In this paper we describe an effective process of collaboration between teachers and game designers, in order to explore educational game ideas for AR technology. Thi...

The Mathematics of Encryption: An Elementary Introduction

Elementary Mathematics from an Advanced Standpoint

In 1908, the German mathematician and mathematics educator Felix Klein published a series of three books (in German) under the title of Elementary Mathematics from an Advanced Standpoint, henceforth called EMAS for short. The first volume was subtitled Arithmetic, Algebra, Analysis, and the second volume was subtitled Geometry. Both of these volumes were translated into English in the1930s, and...

Linear syntax for communicating elementary mathematics

We consider computer aided assessment (CAA) of mathematics in which a student provides an answer in the form of a mathematical expression. A common approach is for CAA system implementors to adopt a linear syntax to allow students to communicate their answer to the machine. In this paper we consider the problems students encounter when mediating between (i) traditional mathematical notation and...