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|1||What is Logo?|
|2||A quick lesson in Logo|
|3||Why is Logo good for learning?|
|4||Who is using Logo and for what?|
|5||How does Logo fit into the curriculum?|
|6||What do students and teachers say about Logo?|
|7||What does Logo research tell us?|
|8||What is the role of the teacher?|
|9||How can parents get involved?|
|10||How does Logo compare with other educational software?|
|11||How does Logo compare with other languages?|
|12||How can I learn more about Logo?|
|Directory of Logo Resources|
1 What is Logo?
Logo is a unique piece of software. In the purest sense, Logo is a programming language; it is a full-featured computer language derived from LISP, the language of artificial intelligence. More important, however, Logo is a language for learning. It is the right tool to teach the process of learning and thinking. Logo provides an environment where students assume the role of teacher. As a teacher, they must:
MIT as a language for learning, Logo is by its nature:
|friendly||Logo is easily grasped; we can relate to the turtle and use it as an object to think with.|
|extensible||Logo can be taught new commands and other commands can be built thereon.|
|forgiving||Logo offers immediate feedback through helpful and informative messages.|
|flexible||Logo is as useful with preschoolers as it is with students of higher mathematics.|
|powerful||Logo is a programming language, providing all the tools needed to create programs of any degree of sophistication.|
So although Logo is a programming language, it is better thought of as a language for learning; a language that encourages students to explore, to learn, and to think.
2 A quick lesson in Logo
Logo's best known feature is the turtle, a triangular cursor used to create graphics. Even young children quickly learn to move and turn the turtle using easily-remembered, intuitive commands. For example, typing forward 50 moves the turtle forward 50 pixels (screen dots). Typing right 90 turns the turtle right (clockwise) 90 degrees.
these commands, it is easy to draw a square.
|forward 50 (You
can also abbreviate forward as
right 90 (You can also abbreviate right as rt.)
you can combine commands to form patterns. Here is the same square design
drawn using one instruction line:
|repeat 4 [forward 50 right 90]|
is an extensible language, you can add new commands by creating short programs
or sets of instructions called procedures. For example, here is the procedure
that will draw our familiar square:
repeat 4 [forward 50 right 90]
Now, to draw
a square, simply type square.
You can use the word square
as you would any other Logo command, even including it in other procedures.
Procedures are the building blocks of larger programs. For example, here
are some ways you can use the square
|You could draw
|You could make
a circle of squares:
repeat 12 [square right 30]
You could combine
a square and a triangle to build a house (typing
house to draw it).
can also use a name to represent the size of the square.
to sq :size
Now you can
draw squares of different sizes by typing
The design below
was created using two procedures that are more complex. They use procedure
inputs to represent the line lengths and turning angles, recursion to call
the same procedure again, and a conditional statement to make the procedure
stop. You would enter the name of the main procedure
design to run the
polyspi 5 120
to polyspi :size :angle
As you can see, just using turtle graphics, you can progress from drawing simple shapes with easy-to-learn commands to creating complex figures using quite sophisticated programming techniques. While turtle graphics are an excellent way to begin to learn Logo, you should view them as an introduction and building block, not as the end of a learning adventure. There is so much more that you can do with Logo!
3 Why is Logo good for learning?
Logo is a classic. Although it was one of the first pieces of educational software available, it is not outdated.
Papert, designer of the Logo language, tells us what is important about
Logo in his book, Mindstorms: Children, Computers and Powerful Ideas
|"Two fundamental ideas run through this book. The first is that it is possible to design computers so that learning to communicate with them can be a natural process, more like learning French by living in France than like trying to learn it through the unnatural process of American foreign-language instruction in classrooms. Second, learning to communicate with a computer may change the way other learning takes place....We are learning how to make computers with which children love to communicate. When this communication occurs, children learn mathematics as a living language. Moreover, mathematical communication and alphabetic communication are thereby both transformed from the alien and therefore difficult things they are for most children into natural and therefore easy ones. The idea of "talking mathematics" to a computer can be generalized to a view of learning mathematics in "Mathland" that is to say, in a context which is to learning mathematics what living in France is to learning French."|
beginnings in the mid-1960s, versions have evolved that take advantage
of newer hardware and software, but the Logo philosophy and the basics
of the language remain the same. Unlike other pieces of educational software,
Logo is not based on a period of time, a geographical place, or current
styles and trends. A timeless piece of software, Logo is as worthwhile
now as when it was introduced. After more than a decade of Logo use in
schools, a 1990 survey of past and current teachers of Logo showed that
an amazing 98% believed that Logo was still appropriate in the classroom.
98% of teachers surveyed say Logo is still appropriate in today’s classroom.
But what's the point of Logo? Why is Logo so important to learning? Logo involves more than just moving a turtle or using mathematics. The essence of Logo involves thinking about processes; about how you are doing what you are doing. In Logo, the process of creating your product is more important than the finished product. It is more interesting and educational to look at how a design was created than to look at the design itself.
4 Who is using Logo and for what?
Although designed for children, Logo is now used from kindergarten to the university. Logo is easy to learn, yet offers power to the experienced user; it is said to have "no threshold and no ceiling." Thus, students who can barely read can learn with Logo, while experienced computer users find that Logo provides a powerful and flexible programming environment.
To give you an idea of who uses Logo,
Logo fits easily into the mathematics class, but it can also be used to explore other areas. The focus in most classrooms is not on programming, but on the thinking processes that Logo encourages.
|estimation||working with distances and angles|
|polygons||using REPEAT to create regular shapes|
|perimeter and area||investigating number relationships|
|symmetry||drawing with point and line symmetry|
|coordinates||plotting points and graphing lines|
|probability||using Logo's random number generator|
|functions||writing functions that output values|
|algebra||graphing linear and quadratic equations|
|geometry||drawing and measuring lines and angles|
|trigonometry||using Logo's sine and cosine functions|
|fractals||combining graphics and recursion|
|proper techniques||writing structured programs|
|program design||breaking down a problem into smaller tasks|
|flow of control||learning about branching and conditionals|
|variables and recursion||using the power of the language|
|data handling||manipulating numbers, words and lists|
|sentence structure||generating Logo sentences that follow the rules of grammar and parts of speech|
|creative writing||writing and illustrating poems|
|word structure||writing programs that rhyme words, pluralize nouns, and conjugate verbs|
|directions||translating the turtle's heading into compass points|
|cartography||making maps using Logo graphics|
|foreign languages||creating foreign language command names|
|robotics||controlling robotics devices through Logo|
|sensors||attaching light and touch sensors to the computer and reading the output|
|simulations||running physics experiments|
|computer art||using Logo's graphics capabilities|
|music||using Logo's sound-generating abilities|
|dance||choreographing the turtle|
|multi-media||capturing Logo graphics on videotape|
6 What do students and teachers say about Logo?
Teachers report that Logo offers students many measurable gains (understanding of angles, improved estimating skills, etc.). But Logo also helps students with personal development, attitudes toward learning, depth of understanding, creativity, and other long-term benefits. Teachers are enthusiastic about teaching with Logo, and students about learning with Logo.
Logo gives students:
|"Logo does everything you tell it, even if it's not what you really meant!"|
|"The turtle lets you know when you goofed."|
|"It is easy to say "what if..." in Logo and try different things."|
teacher know that if you make the turns twice as big
you get a star instead of a pentagon?"
|"Of course I know what a 45 degree angle is, Dad."|
|"I know I really understand a command when I can use it by myself and it works!"|
|"A program is like a recipe and you have to be really specific."|
|"It is like writing an outline that helps you organize your ideas."|
|"I never knew math could be so much fun!"|
|"What can I learn next?"|
is a blank slate upon which students build at their own pace and at their
own skill level."
"There is so much learning going on when kids use Logo. It's the kind of learning they can't get any other way. I see something magical happening when kids use Logo..."
"It presents all students with the chance to succeed in a non-threatening environment. Kids see that there are many ways to solve a problem. They also learn to cooperate and honor others' skills."
"Students can create and express themselves."
"It can be an integral part of a good curriculum to teach kids how to think and discover."
7 What does Logo research tell us?
Classroom teachers experience the "magic" of using Logo, and believe that it helps them teach their students in many different ways. Researchers ask if this intuitive belief that Logo is an excellent teaching tool can be quantified. That is, do children using Logo exhibit statistical gains over non-Logo using students?
Studies have shown that students who use Logo:
|Logo's potential to develop geometric ideas will be fulfilled to the extent that teachers help shape their students' Logo experiences. Students do not automatically transfer knowledge gained in one situation to another. Repetition is not sufficient. Questions that cause students to reflect on what they were doing are instrumental.|
The teacher is critical to the students’ success.
The key to learning is the teacher. Logo is a good tool, but not one that most students will use to advantage on their own. Good teachers involve students in learning, give them choices, create a helpful environment, and turn mistakes into opportunities for exploration. Logo is the perfect tool for these teachers, as its very design makes it friendly, extensible, forgiving, flexible and powerful. These attributes are built into the language, making Logo an intrinsically powerful tool for learning.
8 What is the role of the teacher?
The teacher is most important to students' learning. There are many approaches to teaching Logo, or guiding or facilitating Logo learning.
Often, the student creates his or her own task, one that is personally motivating and challenging. The classroom teacher then serves as a facilitator, helping students understand new Logo commands that might be useful; suggesting approaches to the task; helping determine where and why things are not going as expected; and offering support, suggestions and encouragement, when needed. Logo is a participatory, hands-on environment where both student-teacher and student-student interactions are important.
and educator Donna Beardon explains what is needed:
teachers walk a fine line between free exploration and preplanned curricula:
Logo is powerful, but Logo is not magical. Insights are powerful, but insights
are not magical. Insights occur as a result of trial and thinking.
1. Steps toward
A teacher of Logo must know how much information to give, so that the student is able to discover important concepts. When students discover concepts, they "own" that knowledge. They have a much deeper understanding than if the teacher told them or even showed them.
Dan and Molly Watt, noted Logo specialists and authors of Teaching with Logo, note that individuals rarely complete projects alone, with no input, advice, or information from anyone else. Logo projects should be organized as real-life projects, where there is constant communicationówith peers and with advisors. Students working together learn Logo, encounter new problems to solve, and learn to work cooperatively. They are encouraged to share their knowledge, insights, discoveries, and strategies.
The Watts encourage students and teachers who are beginning with Logo to keep a journal of their project as part of the learning experience. In their journals, students record how they chose their project, new commands that they learned during the project, important discoveries that they made, problems that they ran into and how they solved them, and how they tested and debugged their program.
The final stage of a project is to publish it or put it in a form to share with others. This completes the project and gives the students pride in their work. Publication might mean sharing projects within the school or with students in a pen-pal school, creating bulletin board displays and library exhibits, writing articles for school or local newspapers, making a parent's night presentation, or sending projects to computer education magazines and journals for publication.
9 How can parents get involved?
Logo provides a wonderful opportunity for parents and children to work together. If your home computer is the same type as the school's computers, you should try to get the same version of Logo for home. Logo manufacturers usually have arrangements so that students can use Logo at home for a reasonable cost. If students can use the same version in both places, it will be easy to take a copy of a project home to work on.
If the computer at home is a different brand, there is most likely a similar version of Logo available. Most Logo languages use the same fundamental turtle graphics commands. Differences may occur in commands that involve color and disk functions, and the syntax of the commands may be different in some cases. Students are quite flexible, however, and usually have little difficulty using a version of Logo that differs slightly from the one with which they are familiar.
Parents can also get involved with Logo at their children's school. First, find out if your school has the Logo language and will welcome your volunteer help.
If your school already has Logo:
Logo is one of many pieces of software that schools use to teach. How does Logo compare with other types of software?
Also known as CAI (computer assisted instruction), drill and practice programs provide practice in specific skills, such as multiplication or spelling. These programs may be appropriate for some students at times, but unlike Logo, they typically:
Teachers find that tool programs such as word processing, database, and spreadsheet programs provide excellent opportunities for learning. In a sense, Logo is also a tool program, useful by both students and teachers. When students use a tool program, either a word processor or Logo, they are provided with an environment
11 How does Logo compare with other languages?
Although Logo is most frequently used by children who only explore a small portion of the language, Logo is a full-featured programming language. Almost any program can be written as well in Logo as in any other language, and frequently more quickly and elegantly. Logo is the ideal first language to learn because:
Logo is an easy language to learn.
12 How can I learn more about Logo?
If you would like to learn more about Logo, find ways of using it in the classroom, improve your programming skills, and meet other Logo-using educators, here are some ideas for resources you might find in your area. Details about specific resources to contact are included in the directory that follows.
Directory of Logo Resources
Books: (Some books may be out-of print, but are worth looking for.)
Logo (or that contain major sections about Logo)
Bork, Alfred. Personal Computers for Education. Harper & Row, Publishers; New York, NY, 1985.
Harper, Dennis. Logo Theory and Practice. Brooks-Cole Publishing Company; Pacific Grove, CA, 1989.
Maddax, C. D. Logo in the Schools. Haworth Pr.; Redding, CA, 1985.
Muir, Michael. Fantastic Journey Through Minds and Machines. ISTE; Eugene, OR, 1991.
Papert, Seymour. Mindstorms: Children, Computers and Powerful Ideas. Basic Books, Inc.; New York, NY, 1980.
Papert, Seymour. Children's Machine: Rethinking School in the Age of the Computer. Basic Books, Inc.; New York, NY, 1993.
Papert, Seymour. The Connected Family: Bridging the Digital Generation Gap. Longstreet Press; New York, NY, 1996.
Solomon, Cynthia. Computer Environments for Children, The MIT Press; Cambridge, MA, 1986.
Turkle, Sherry. The Second Self: Computers and the Human Spirit. Simon and Schuester; New York, NY, 1984.
Weir, Sylvia. Cultivating Minds: A Logo Casebook. Harper & Row, Publishers; New York, NY, 1987.
and teaching Logo
Beardon, D., Martin, K., and Muller, J. The Turtle's Sourcebook. Reston Publishing Company, Inc.; Reston, VA, 1983.
Bull, G., Tipps, S., and Riordon, T. R. Nudges: Apple Logo Projects. Holt, Rinehart and Winston; New York, NY, 1985.
Charishak, Ihor. Creating Dynamic Stories with LogoWriter. Dynamic Classroom Press; White Plains, NY, 1988.
Goldenberg, E. P. and Feurzeig, W. Exploring Language with Logo. The MIT Press; 1987.
Shimabukuro, Gina. Thinking in Logo: A Sourcebook for Teachers of Primary Students. Addison-Wesley; Menlo Park, CA, 1987.
Tipps, S. and Bull, G. Beginning with Logo: Terrapin Version. Prentice-Hall; Englewood Cliffs, NJ, 1987.
Watt, Daniel. Learning with Logo. McGraw-Hill Book Company; New York, NY, 1983.
Watt, M. and Watt, D. Teaching with Logo: Building Blocks for Learning. Addison-Wesley Publishing Co.; Menlo Park, CA, 1986.
Yoder, S. and Moursund, D. Logo PLUS (or LogoWriter) for Educators: A Problem Solving Approach. ISTE; Eugene, OR, 1990.
a programming language
Abelson, H. Logo for the Apple II. Byte/McGraw Hill; Peterborough, NH, 1982.
Anderson-Freed, S. and Brown, L. The Well-Tempered Turtle. Harvard Associates, Inc.; Cambridge, MA, 1995.
Friendly, Michael. Advanced Logo. Lawrence Erlbaum Associates, Publishers; Hillsdale, NJ, 1988.
Harvey, Brian. Computer Science Logo Style (in three volumes), The MIT Press; Cambridge, MA, 1985-87, 1996.
Spezeski, William. Logo: Models and Methods for Problem Solving. Harvard Associates, Inc.; Cambridge, MA, 1996.
Yoder, Sharon. An Introduction to Programming in Logo (Logo PLUS, Terrapin Logo/Macintosh). ISTE; Eugene, OR, 1988-1990.
also Logo curriculum materials at end of Logo Directory)
Abelson, H. and diSessa, A. Turtle Geometry. The MIT Press; 1980.
Baker, J. and Hulme, D. The Expert Mathematician. New Directions Computer Mathematics Curriculum Development; 2018 James Ave. N., Minneapolis, MN, 55411, 1992.
Clayson, James. Visual Modeling with Logo. The MIT Press; 1988.
Cuoco, Al. Investigations in Algebra. The MIT Press; 1990.
Feurzeig, W. The Logo Language: Learning Mathematics Through Programming. Entelek, Inc.; Portsmouth, NH, 1977.
Hoyles, C. and Sutherland, R. Logo Mathematics in the Classroom. Routledge, Chapman and Hall, New York, NY, 1989.
Lewis, Phil. Approaching PreCalculus Discreetly. MIT Press; 1990.
Neufeld, Rudy. Learning Math with Logo, 1986. Learning Math with LogoWriter, 1990. Logo Publications; London, Ontario.
Billstein, Libeskind and Lott. Mathematics for Elementary School Teachers, 3rd edition. The Benjamin/Cummings Publishing Co., Inc.; Menlo Park, CA, 1987.
Clements, Doug. Computers in Elementary Mathematics Education. Prentice-Hall; Englewood Cliffs, NJ, 1989.
Cummins, J. J., Kenney, M., and Kanold, T. D. Informal Geometry. Merrill Publishing Company; Columbus, OH, 1988.
Serra, Michael. Discovering Geometry. Key Curriculum Press; Berkeley, CA, 1989.
journals, and magazines:
Logo journals or journals with a regular Logo section
The Computing Teacher, journal of the International Society for Technology in Education; 1787 Agate Street, Eugene, OR, 97403.
Logo Exchange, journal of the Special Interest Group for Logo-Using Educators, published 4 times a year by ISTE (see address above).
Computer education magazines with occasional Logo articles
Technology and Learning, 2169 Francisco Blvd. East, Suite A4, San Rafael, CA 94901.
Teaching and Computers, contact P.O. Box 2040, Mahopac, NY 10541.
Listing of available Logo Memos (pre-1986) and E&L Memos (since 1986). Epistemology and Learning Group, MIT, 20 Ames St. Room E15-309, Cambridge, MA 02139.
See also Logo Foundation (address below).
organizations and Logo user groups:
CLIME (Council for Logo In Mathematics Education), 10 Bogert Avenue, White Plains, NY 10606
ISTE (International Society for Technology in Education), 1787 Agate Street, Eugene, OR 97403;
Logo Foundation, 250 West 85th St., Suite 4D, New York, NY 10024 (212-579-8028)
SIG Logo, the Logo User's Group of ISTE (see address above).
Independent Study Course offered by ISTE (see Journals for address): Introduction to Programming in Logo.
Graduate Logo courses offered by Lesley College, Cambridge, MA. Call 1-800-832-4808 for course offerings or to arrange a course.
International Computer Problem Solving Contest. For information, contact: ICPSC, P.O. Box 085664, Racine, WI 53408.
curriculum materials from Terrapin (see also our complete on-line catalog):
Birch, Alison. Logo Probability, 1988.
Birch, Alison. The Logo Project Book, 1986.
Cory, S. and Walker, M. Logo Works: Lessons in Logo, 1985.
Fitch, Dorothy. 101 Ideas for Logo, 1993.
Fitch, D. and Flanagan, P. Kinderlogo, 1984-95.
Picciotto, Henri. Logo Math: Tools and Games, 1990.