LS: Speaking of Science Column October 20, 2008

Logo lays the foundation for future math and science learning

Logo started out as a computer language but has ended up as an educational philosophy of considerable power. It also has proven a powerful way to expand children’s understanding of science and prepare them for abstract thought.

In the 1950s Seymour Papert, a mathematician, went to France and studied with Jean Piaget.
Piaget proposed the theory that children must construct their own understanding of the world through their experiences. This theory has become known as constructivism and is highly influential in educational circles.

Upon Papert’s return to the United States, he co-founded the first artificial intelligence laboratory in the United States, at MIT, along with logician Marvin Minsky.

While the artificial intelligence lab was about exploring the powers of the computer to “think,” Papert was interested in a side issue concerning education. He had an interest in developing a “math world” where children could become comfortable with mathematic principles and numbers through experiences, just as they learned language.

He thought that computers might be a way this could be accomplished. This was in the day of large mainframe computers, and most people did not think about giving children access to large expensive machines for which there was much competition for use.

The prevailing language used in artificial intelligence circles of the day was a language known as Lisp. Papert, and others, developed a variant of this language that was child-friendly and named it Logo. (This is Greek for “word” because it looked, and behaved, very much like English.)

Anything that could be done in any other languages could also be done in Logo. However, Logo was never a language for commercial use. It is the only computer language I know of expressly designed for learning and the exploration of ideas.

It was first used with large mainframe computers controlling a robot on the floor. Children could enter simple English, word-like commands through the terminal and the robot would respond. For example, telling the robot to “forward 10” would move the robot a certain direction, for a specific distance. This floor robot had a dust cover that was shaped like a bowl, making the robot appear to be a little like a turtle. Hence the first Logo robots were called “turtles” by the children.

When the floor turtle was later replaced by just a cursor on a screen, the terminology remained. All Logo systems are built around the idea of a moveable cursor that can respond to simple commands.

As Papert experimented with children using computers, he began to see that when children produce a tangible object, an external product, the motion of a robot, a melody or other physical manifestations, they learned not just mathematics, but language and history, and almost any subject better.

Papert named this phenomenon “constructionism.” In other words, people learn, experience constructivism, especially well when they construct something. This practical application of knowledge is very far from today’s emphasis on testing.

Children have difficulty thinking abstractly. There may be several reasons for this difficulty, but one is that they have not developed enough experiences with the sensory world. Until they have developed a rich experience with the spatial world of space, time and energy, they cannot hope to use those same ideas to discuss abstractions.

Providing more science and math instruction at an early age is not helpful because children usually do not have the necessary experiences to make sense of the abstractions necessary to study math and science. The way to develop greater facility with abstractions is to give the students greater experiences with the physical world.

Logo allows students a chance to experience the world, think about the world and manipulate the world in a spatial way that is very concrete and precise. With Logo, students can explore the sensory world and create art and practical projects of their own interests, in a way that has math embedded within the exploration and project development.

Probably the most popular version of Logo is the commercial version called Microworlds by LCSI. You can learn more about it at

There is also a web site called the Logo Foundation that manages almost all things logo at

Gary McCallister is a professor of biology at Mesa State College with research interests in infectious diseases, and also the biology of the mind.

Have a concrete or abstract question? E-mail .(JavaScript must be enabled to view this email address).


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