Why Use Logo?
An Overview of Logo in Education
© 1990, 1992, 1997 Terrapin Software,
Permission is hereby granted to reproduce and distribute this
document for non-commercial use.
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:
the knowledge to be taught
- plan an approach
to impart this knowledge
- break the
knowledge into small, understandable chunks
- know how
to clearly communicate the knowledge
this new knowledge as the foundation for future learning
- be aware
of and build on knowledge that the learner already has
- be receptive
to exploring new ideas as they appear
- respond to
the learner's (computer's) misunderstandings and errors
this in Logo by:
with Logo commands to understand them and be confident in their
their task and organize it into its various components
- writing a
set of instructions to perform each small task
a program to perform all the tasks in the right order
their program to assess whether the task is performed correctly
their program by locating and correcting errors or restructuring
Logo is not
limited to any particular topic or subject area. However, it is
most useful for exploring mathematics, as Logo's turtle graphics
provides a natural mathematical environment. Since the turtle
moves in distances and turns in degrees, studying geometry by
constructing and investigating polygons and figures makes Logo
a powerful learning tool.
MIT as a language for learning, Logo is by its nature:
||Logo is easily grasped;
we can relate to the turtle and use it as an object to think
||Logo can be taught
new commands and other commands can be built thereon.
||Logo offers immediate
feedback through helpful and informative messages.
||Logo is as useful
with preschoolers as it is with students of higher mathematics.
||Logo is a programming
language, providing all the tools needed to create programs
of any degree of sophistication.
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.
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
right 90 (You can also abbreviate
right as rt.)
Using repeat, you can combine commands
to form patterns. Here is the same square design drawn using one
|repeat 4 [forward 50
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 procedure.
draw a flag:
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).
repeat 3 [forward 50 left 120]
|You can also use a name to represent the size of the
to sq :size
repeat 4 [forward :size right 90]
can draw squares of different sizes by typing
sq 10, sq 20, sq 30, etc.
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
polyspi 5 120
to polyspi :size :angle
if :size > 205 [stop]
polyspi :size+5 :angle+.12
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
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 (p. 6).
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.
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
To give you
an idea of who uses Logo,
- First graders
in New Hampshire use a single-keystroke version of Logo to move
the turtle and explore shapes and lines.
- Second and
third graders in Arizona learn about polygons using Logo.
- Fourth graders
in California program a miniature golf game in Logo.
- Fifth graders
in Massachusetts learn the geography of their state by drawing
a map in Logo.
- Middle school
students in Kentucky use Logo to control robotics.
- High school
girls conquer "mathphobia" in a summer program at Mount Holyoke
College in Massachusetts using Logo.
students in California use Logo to create scatter plots in their
students in Colorado learn to program using Logo.
students in Pennsylvania use a single-switch device with Logo
to move the turtle and create designs.
- A professor
at the Massachusetts Institute of Technology uses a special
version of Logo to teach music theory.
- An instructor
at the University of California at Berkeley teaches computer
science students how to program using Logo.
all around the world use Logo to learn.
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.
with distances and angles
to create regular shapes
|perimeter and area
||investigating number relationships
with point and line symmetry
points and graphing lines
random number generator
functions that output values
linear and quadratic equations
and measuring lines and angles
sine and cosine functions
graphics and recursion
down a problem into smaller tasks
|flow of control
about branching and conditionals
|variables and recursion
power of the language
||manipulating numbers, words and lists
||generating Logo sentences that follow the rules of grammar
and parts of speech
and illustrating poems
programs that rhyme words, pluralize nouns, and conjugate
||translating the turtle's heading into compass points
maps using Logo graphics
foreign language command names
||controlling robotics devices through Logo
light and touch sensors to the computer and reading the output
||choreographing the turtle
Logo graphics on videotape
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:
to be the teacher, not a passive learner, and to control the
visual, and nonjudgmental feedback
does everything you tell it, even if it's not what you
to explore and try their own ideas
turtle lets you know when you goofed."
to discover concepts on their own
is easy to say "what if..." in Logo and try different
to explore concepts normally taught much later
the teacher know that if you make the turns twice as big
you get a star instead of a pentagon?"
a means of
learning and understanding at their own pace
course I know what a 45 degree angle is, Dad."
to analyze a task and plan a set of instructions to solve it
know I really understand a command when I can use it by
myself and it works!"
a model for
solving problems by breaking them into smaller chunks
program is like a recipe and you have to be really specific."
to succeed in areas in which they may not feel comfortable
is like writing an outline that helps you organize your
never knew math could be so much fun!"
offer these comments about Logo:
||"It is a blank
slate upon which students build at their own pace and at their
own skill level."
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..."
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'
"Students can create and express themselves."
can be an integral part of a good curriculum to teach kids
how to think and discover."
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?
shown that students who use Logo:
- plan more
planning tasks differently
- have an increased
understanding of geometry
in solving problems
- are better
at resolving conflict
- are more
- exhibit desirable
have had mixed or inconclusive results. Why? Possibilities include:
lack of familiarity with an appropriate teaching style
critical variables, such as instruction method used, and "cultural
climate" in the classroom
- the fact
that gains may not be measurable within the timeframe of the
- the individual
- the level
of instructional support provided
- the fact
that skills acquired using Logo may not transfer to particular
mathematical insights or cognitive gains without instructional
summarizes Logo research results (Logo Exchange, January
||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.
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
and educator Donna Beardon explains what is needed:
"Effective Logo 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.
Insights are what Logo is so good at promoting if the ingredients
are all there. These ingredients include:
1. Steps toward understanding;
2. Significant problems that challenge and entice students
to think hard;
3. Time to get in tune with the activity."
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
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.
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:
- find out
if your child's class is using it
- get Logo
to use at home, if you have a computer
- help the
parent-teacher organization arrange for teacher training
- suggest a
session for parents and children to introduce them to Logo
in the classroom to give teachers extra time to plan for and
- help prepare
displays of student Logo projects
If your school
doesn't have Logo, or isn't using it:
- share this
information with the teachers and administration
- suggest that
they use Logo to teach problem solving and math
- arrange for
a Logo-using teacher in the area to make a presentation
10 How does Logo compare with other educational
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:
- control the
- present problems
with a single correct answer
- get predictable,
causing students to become easily bored
- provide inappropriate
feedback to students
- allow for
minimal customization by the teacher
- make unnecessary
and distracting use of sound and graphics
Simulations and problem solving software set
up an experiment or situation that the student can control and
explore. Well-designed programs in this category offer a valuable
experience similar to that offered by Logo. Unlike simulations
that could be written in Logo, however, these programs may restrict
the user's ability to make changes to the content, the conditions
of the experiment, or the algorithms used to determine results.
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
- that they
can control completely
- that allows
them to begin, revise, refine and complete a project
- that is useful
for students in any grade and at any level
- that has
a minimal amount of knowledge necessary to begin
- offers appropriate
and nonjudgmental feedback
- can be used
in any subject area
If your goal
is to teach the process of thinking, give your students a hands-on
environment for mathematics explorations, or combine the capabilities
of several types of tools, then Logo offers the power and flexibility
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.
- the commands
are English-like and easy to remember
- there are
friendly and helpful error messages
- it is interactive,
so the user gets immediate feedback
good programming habits.
- it encourages
the development of short programs (procedures)
are then used as building blocks by other procedures
- there are
no line numbers that encourage jumping around the code
you to create and reuse procedures.
- as an extensible
language, Logo allows you to add new commands
- you can run
and test procedures independently
- it is easy
to use procedures from one program in another
- it encourages
the creation of a library of often-used procedures
are easy to write and maintain.
are easy to debug with tracing and pausing tools
- you can use
long and descriptive variable and procedure names
- error messages
are detailed and helpful
programmers should be aware that:
- Logo is derived
from LISP, the language of artificial intelligence
- Logo is a
- Logo offers
dynamic variable scoping
- Logo offers
a full range of disk and file handling commands
Logo is structured
similarly to Pascal. Program development is done in the same way:
you create a main program, which calls other procedures and functions,
passing them variables as needed. Both languages are recursive.
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.
- Attend in-service
training provided by your school district.
courses or summer seminars at colleges in your area.
- Inquire about
Logo training from your Logo manufacturer.
- Look for
privately run workshops for educators.
to computer education and Logo journals.
- Attend local,
regional, and national computer education conferences.
- Sign up for
a distance learning course in Logo.
- Locate area
user groups, especially those that focus on Logo.
- Meet with
other teachers in your district who are using Logo.
- Start your
own Logo user's group.
If you have
a modem, get online and seek out other Logo users. The Logo Foundation,
in cooperation with the Global SchoolNet Foundation, manages a
Logo discussion group available to anyone with access to Internet
E-mail. The objectives of this Logo discussion group are to:
- Promote active
sharing of ideas among Logo-using educators.
- Provide a
forum for questions to be asked about using Logo in the classroom.
This could be of service to both experienced and novice Logo
- Provide a
meeting place for Logo educators interested in collaborating
on telecomputing projects involving their students sharing Logo
- Provide a
forum for discussion of educational philosophy on the user of
technology in education and how Logo fits into that philosophy.
To join this
Logo listserv discussion group, send an E-mail message to:
with the only line in the
message: subscribe Logo-L
(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,
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.
Learning 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,
as a programming language
Abelson, H. Logo for the Apple II. Byte/McGraw Hill; Peterborough,
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.
and Mathematics (see also Logo curriculum
materials at end of Logo Directory)
Abelson, H. and diSessa, A. Turtle Geometry. The MIT Press;
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;
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;
Neufeld, Rudy. Learning Math with Logo, 1986. Learning
Math with LogoWriter, 1990. Logo Publications; London, Ontario.
Textbooks featuring Logo
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.
Periodicals, journals, and magazines:
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
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).
National 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
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
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.