Introduction

Many students and teachers alike may not have experienced working with LOGO. In consequence a reminder of the versatility of this computer language would seem appropriate.

• LOGO was developed in the 1960's in America at the Artificial Intelligence Laboratory at MIT. It was created by Wallace Feurzei and Seymour Papert and was first used by them with children to write poetry!
• In the longer term LOGO has proved to be a powerful language that could be used by both young children and still challenge a post graduates at university when exploring mathematical ideas.
• LOGO is a Lisp (LISt processing) derived programming language. It works with single ideas and words i.e. primitives and commands. From these singular and simple ideas others of greater complexity can be built.
• Originally LOGO was used to make music, create poetry, control robotic toys - Pixies/ Pips and Roamers. But what has stood the test of time has been the ease with which children can engage with Turtle Geometry using single or multiple turtles (screen robots) and sprites.

This ease with which children can create graphics has not been lost.
Within a LOGO environment the opportunity is for mathematical students to engage in:

• investigating sophisticated aspects and ideas of mathematics;
• posing problems, amending problems and solving problems;
• doing practical tasks and working empirically.
• doing mathematics rather than being learners of other peoples mathematics!
• conjecturing and working systematically

The tele-visual output of turtle graphics is highly motivating. It provides instant feedback to the student on any errors made.
While the role of teacher is that of support, gently encouraging and nudging in fruitful directions the student in his/her development of a response.
Fundamentally you the user needs to understand and apply

• the primitives of LOGO i.e. the basic instructions,
• (when ready begin to develop) some procedures, that is lists of basic instructions brought together.

To help you in this task there are some diagrams to draw, to recreate and some questions to pursue. There will be ample opportunity for you to estimate, calculate, communicate and perhaps discover that measure has two distinct aspects.
i.e.it can be either continuous or discreet.

Along the way it is hoped that you will develop the necessary vocabulary, ideas, techniques and skills in variety of contexts.
Hopefully you will be learning to:

• give instructions
• contextualise ideas about movement
• perhaps work collaboratively with others
• record systematically what you have done and found out
• use and develop mathematics language in a context
• begin to communicate with others for a mathematical purpose.

But you will be controlling your own learning what you learn and the speed with which you learn.

On this trail we shall follow the tradition of recreating complex geometric figures and patterns as well as looking at some numerical applications.We shall assume that certain key ideas will also be developed en route. But we hope you will keep a valid record of all that you do and think in passing.
For example

• how impatient did you become?
• how did you get round the problems you met?
• did you share what you did with others?
• did other people help you solve the challenge? In what ways?
• what happened when the instructions you had worked on did not draw the shape required?

You will also be learning other aspects of mathematics by reading LOGO. But more of that later!

Throughout you will be encouraged to develop simple and elegant responses to the problems at hand.