Why Use Logo?An Overview of Logo in Education
- What is Logo?
- A quick lesson in Logo
- Why is Logo good for learning?
- Who is using Logo and for what?
- How does Logo fit into the curriculum?
- What do students and teachers say about Logo?
- What does Logo research tell us?
- What is the role of the teacher?
- How can parents get involved?
- How does Logo compare with other educational software?
- How does Logo compare with other languages?
- How can I learn more about Logo?
- understand 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
- establish 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
- experimenting with Logo commands to understand them and be confident in their use
- planning their task and organize it into its various components
- writing a set of instructions to perform each small task
- constructing a program to perform all the tasks in the right order
- evaluating their program to assess whether the task is performed correctly
- debugging their program by locating and correcting errors or restructuring their approach
|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.|
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.
By combining these commands, it is easy to draw a square.
forward 50 (You can also abbreviate forward as fd.)
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 instruction line:
repeat 4 [forward 50 right 90]
Because Logo 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.
You could draw a flag:
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).
repeat 3 [forward 50 left 120]
You can also use a name to represent the size of the square.
to sq :size
repeat 4 [forward :size right 90]
Now you 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 to run the program.
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 with Logo!
Logo is a classic. Although it was one of the first pieces of educational software available, it is not outdated.Professor Seymour Papert, designer of the Logo language, tells us what is important about Logo in his book, Mindstorms: Children, Computers and Powerful Ideas (p. 6).
"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."
Since Logo's 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.
- 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.
- Secondary students in California use Logo to create scatter plots in their statistics class.
- Secondary students in Colorado learn to program using Logo.
- Paralyzed 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.
- Students all around the world use Logo to learn.
|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|
|"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."|
|"Does the 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?"|
Classroom teachers offer these comments about Logo:
"It 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."
- plan more efficiently
- represent planning tasks differently
- have an increased understanding of geometry
- persevere in solving problems
- are better at resolving conflict
- are more self-directed
- exhibit desirable social interactions
- teachers' lack of familiarity with an appropriate teaching style
- unaddressed 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 study
- the individual teacher
- 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 direction
Doug Clements summarizes Logo research results (Logo Exchange, January 1988):
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.
One conclusion is clear:
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.Logo author 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 for publication.
- 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
- volunteer in the classroom to give teachers extra time to plan for and use Logo
- help prepare displays of student Logo projects
- 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
- control the student
- 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
- 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
- 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
- it encourages the development of short programs (procedures)
- procedures are then used as building blocks by other procedures
- there are no line numbers that encourage jumping around the code
- 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
- programs 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
- Logo is derived from LISP, the language of artificial intelligence
- Logo is a recursive language
- Logo offers dynamic variable scoping
- Logo offers a full range of disk and file handling commands
- Attend in-service training provided by your school district.
- Investigate courses or summer seminars at colleges in your area.
- Inquire about Logo training from your Logo manufacturer.
- Look for privately run workshops for educators.
- Subscribe 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.