A Cybernetic Approach to Study the Learnability of the Logo Turtle World

Abstract

Research has demonstrated that children experience great difficulty in gaining mastery of the syntax and the semantic structure of the LOGO programming environment. The study presented in this article tests the hypothesis that simplification of the semantic structure will facilitate semantic understanding and acquisition of syntax knowledge within the LOGO Turtle World. Two microworlds were designed to carry out the same class of tasks using an identical set of basic commands, but comprising a different semantic structure. They were designed applying the theory of automata and abstract languages. The article demonstrates that different formal grammars can be formulated from one set of terminal symbols (i.e., basic commands of the LOGO Turtle World). Furthermore, it demonstrates how different finite-state machines correspond with these different grammars. In this study, two finite-state machines are defined: a one-state machine (ORTHO-1) and a four-state machine (ORTHO-4). Both machines can produce analogous rectangular figures in response to sequences of input symbols chosen from an identical input alphabet. Each of these abstract machines was physically realized as a computer-based microworld similar to the LOGO Turtle World. In an experiment with second and third grade children, it was found that the semantically simpler microworld (i.e., ORTHO-1) produced better semantic understanding as well as better mastery of the syntax of the input commands. The result occurred despite the fact that these microworlds used identical input commands.