Working Mathematically in a Graphics Environment

Written by: Garry Clark

Hi All

Welcome to Working Mathematically in a Graphics Environment.

I hope you enjoy this course and use it to learn a little about programming and to develop your mathematical thinking in ways that are not usually available in schools.
  

Introduction

Logo is an interactive programming language for adventurers of all ages. It has been designed for young children to use. You may begin by controlling the actions of a cybernetic turtle in a graphic environment that provides immediate feedback. These immediate actions let you see how you are thinking. When your sequence of thoughts does not make the turtle do what you want, the descriptive nature of Logo lets you easily trace your thoughts to debug your thinking.

Logo involves the manipulation of words and ideas combined with other powerful ideas such as the use of procedures, variables and recursion to provide a unique interactive programming environment. You will experience some of these powerful ideas in this course as you create interesting geometrical designs. In the process of creating geometrical designs, you will focus on applying many mathematical concepts, such as number, angle, variable, algorithm, etc. in order to solve the problems encountered.

One of the main objectives of this course is for you to realise that thinking and (more precisely) thinking ABOUT thinking is a very important skill. You will probably be fascinated by Turtle graphics and will probably be excited when they produce something interesting, either by intention or accident, and you will find it hard to get back to attacking the ideas or problems in the course. You will want to experiment and investigate ideas that occur to you as you work through the material set. I suggest that you print your 'best' designs and the programs (set of procedures) that created them. You should annotate your designs with comments on how they were achieved. That is, I AM EXPECTING YOU TO COMMENT ON THE THINKING THAT WAS INVOLVED IN THEIR CREATION, THE INITIAL THINKING THAT WAS INCORRECT, HOW PROBLEMS WERE OVERCOME, etc. Please do NOT think that this course is about drawing pretty designs - it is about encouraging you to learn to think, and to both enjoy it and see it as a worthwhile activity.

Creating the designs that are set is a lot of work. You will have to think hard. You will need to practice skills and understand the ideas presented. Be patient, work systematically and with perserverence in applying the ideas to the creative designs. When you encounter a problem that you or your teacher/parent cannot solve it often helps to explain the problem clearly to someone else and to explain your thoughts on solving it.

You will be presented with a number of activities and extension activities. Some of these activities will involve secondary school mathematics so if you are a primary school student it is unlikely that you will find the most efficient way to create the design, but that does not stop you from attempting the activity and researching (books, Internet, teacher, parent, etc.) the mathematics involved in the problem. Some problems may take days or even months to solve. Keep trying! I hope you also set yourself some interesting challenges.

NOTE: It is not necessary to complete all activities but to work at a pace with which you are comfortable.

Let's Get Started

You will need one of the many versions of Logo that are available to complete this course.

If you have a copy of Logo, for example, LogoWriter, Microworlds EX, UCBLogo, MSWLogo, etc on your computer, then find the manual and start reading.

If you do NOT have a copy of Logo on your computer, then you will either have to buy a copy or you can download free software from the Internet. While this software may not have as nice an interface as the commercial software it is adequate for this course.

For Windows users surf to http://www.softronix.com/logo.html and click on the Setup.Kit link. You might also download 'Release Notes'. If you have any problems in doing this, email mills@softronix.com and explain the problem.

For Mac users surf to http://www.cs.berkeley.edu/~bh/ and download UCBLogo by clicking on the 'Mac' link. This software is available for DOS/Windows users by clicking on the 'DOS/Windows' link. If you have any problems in doing this, email bh@cs.berkeley.edu and explain the problem. UCBLogo comes with a user manual which you should read at some stage and you might want to printout (not essential).

For a commercial version of Logo surf to http://www.microworlds.com/ and download a demo version suitable for your computer operating system. The demo version will not save or print projects. You can also purchase a complete version of the software if you are so inclined.

Your Timetable: Only the link to the Group 1 activities is active. You are advised to start with the notes for Group One and then move on to the Introductory activities. Once you are confident with the ideas, move to the Notes for the next group, etc.

Group 1:

  • Now that you have the software on your computer, you need to know how to use it. A good start is to read the manual that comes with the software, but if that is gobbledegook then I suggest you read The Fundamentals of Logo notes that I have written.
  • Having worked through 'The Fundamentals of Logo' notes you are now ready to start on the Introductory Activities for Group One.
  • You might like to look at this Web site. It has quite a lot of information on Logo programming.

Group 2:

  • Read the Logo notes for this group of activities.
  • Having worked through the notes you are now ready to start on the Activities for Group Two.
  • You might like to look at this Web site. It has information on programming by students.

Group 3:

  • Read the Logo notes for this group of activities.
  • Having worked through the notes you are now ready to start on the Activities for Group Three.
  • You might like to look at this Web site. It has general information on Logo that teachers and students should know.

Group 4:

  • Read the Logo notes for this group of activities.
  • Having worked through the notes you are now ready to start on the Activities for Group Four.
  • You might like to look at this Web site. It has, among other things, ideas on Logo projects.

Week 5:

  • Read the Logo notes for this group of activities.
  • Having worked through the notes you are now ready to start on the Activities for Group Five.
  • You might like to look at this Web site. It has information on a Logo and lots of other educational material.

Group 6:

  • Read the Logo notes for this group of activities.
  • Having worked through the notes you are now ready to start on the Activities for Group Six.
  • You might like to look at this Web site. It is one of the major Internet sites with information on Logo. You might like to join in discussions on Logo from this site.

Group 7:

  • Read the Logo notes for this group of activities.
  • Having worked through the notes you are now ready to start on the Activities for Group Seven.
  • If you are interested in geometrical designs, you might like to have a look at some Recursive Graphic Designs on the World Wide Web. One day you may be able to create designs like these!

Group 8:

  • Read the Logo notes for this group of activities.
  • Having worked through the notes you are now ready to start on the Activities for Group Eight.
  • You might like to continue writing computer programs. This site could be useful if you want to write computer games.
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