1. LOGO as a Programming Language for Education

2. Background LOGO  The LOGO language was developed in 1967 by the Logo Group at MIT under the direction of Seymour Pappert (Mindstorms: Children, Computers, and Powerful Ideas).  It was the first language specifically designed to enable children to learn by discovery and exploration. (Billstein et al. 1980)

3. Background  Originally designed to conform to the child developmental theories of Jean Piaget:  Sensorimotor stage (Infancy)  Pre-operational stage (Toddler and Early Childhood)  Concrete operational stage (Elementary and early adolescence)  Formal operational stage (Adolescence and adulthood)

4. BackgroundBruner Knowledge representation EnactiveIconicSymbolic linguistic in nature representing external objects with images, either internal or external the significance of a stimulus is in the motor reaction it produces

5. Logo Programming  One of the two major capabilities which were designed into Logo is the so-called turtle graphics.  A "turtle" composed of a triangle or a turtle symbol may be controlled by commands from the keyboard or from within a Logo program.

6. Logo Programming  For example, the command FD 50 RT 90 will cause the turtle to move forward 50 units and turn right 90 degrees.  Complex programs for the turtle to follow are built up from a small number of primitives.

7. MSLogo command entry

8. Logo: A Language for Integrated, Experimental Learning  Why Logo is seen as a powerful tool for education?  The concept of a geometric figure, can be translated into enactive mode.  The child may be instructed to walk forward 10 paces, turn right, walk forward 10 more paces, and so forth, until a square has been described on the floor.

9. Logo: A Language for Integrated, Experimental Learning  Why Logo is seen as a powerful tool for education?  A connection can be made between these movements and the symbols FD 10 RT 90 FD 10 in this way, giving a concrete interpretation of a symbolic language. Finally, what the child sees as these commands are executed, is a visual image of a turtle drawing a square on the monitor--the iconic mode.

10. Logo: A Language for Integrated, Experimental Learning  Why Logo is seen as a powerful tool for education?  A more contemporary approach to holistic education emphasizes "whole-brain learning".  The right brain tends to specialize in schematic thinking and detailed visual imagery, the left brain, in categorical and linguistic thinking.  Symbols such as FD 50 RT 90 are processed by the left brain.

11. Logo: A Language for Integrated, Experimental Learning  Why Logo is seen as a powerful tool for education?  Images such as a square drawn on the monitor screen are processed by the right brain.  Logo turtle graphics makes it possible to have these two modes working in concert, or if a learner has a preferred modality, Logo allows that modality to dominate.

12. Logo: A Language for Learning Problem Solving Skills  At a deeper level of the Logo language (beyond its procedurality), we can discern still other ways in which it significantly reflects the characteristics of human problem solving. recursive generalhierarchical  Human problem solving is recursive, general, and hierarchical.  The Logo language reflects all of these characteristics, some better than others.

13. Logo: A Language for Learning Problem Solving Skills  Recursion  Recursion may be defined as repetition. For example the procedure  TO SQUARE  FD 50 RT 90 FD 50 RT 90 FD 50 RT 90 FD 50 RT 90  END  will solve the problem of finding a way to draw a square in Logo.

14. Logo: A Language for Learning Problem Solving Skills  On the other hand, the procedure  TO SQUARE  REPEAT 4[RT 90 FD 50]  END  solves the same problem without writing out the directions for drawing each side of the square. Instead, it simply says "draw a side, four times." Incidentally, this is called finite recursion, because we are counting to a finite number.

15. Logo: A Language for Learning Problem Solving Skills  The procedure  TO SQUARE  RT 90 FD 50  SQUARE  END (P.S.: CTRL-S to stop!)  solves the same problem with an infinite recursion. (P.S.: CTRL-S to stop!)

16. Logo: A Language for Learning Problem Solving Skills  Generality  Generality: we would prefer to solve a problem for a whole set of cases rather than have to solve the problem separately for each case in the set.  Translated into our square problem, we might ask, why write a procedure for drawing a square of fixed size, when one can be written for drawing a square of any size?

17. Logo: A Language for Learning Problem Solving Skills  The procedure  TO SQUARE :N  REPEAT 4[FD :N RT 90]  END  solves the problem of drawing a square of size N.

18. Logo: A Language for Learning Problem Solving Skills  Perhaps and even more amazing demonstration of the power of recursion and generality combined is based on the fact that the exterior angles of a regular polygon are given by the formula 360/s, where s is the number of sides of the polygon.

19. Logo: A Language for Learning Problem Solving Skills  The following procedure draws a regular polygon of side, n, and number of sides, s.  TO POLY :S :N  REPEAT :S[FD :N RT 360/:S]  END

20. Logo: A Language for Learning Problem Solving Skills  Hierarchicality  Hierarchicality is perhaps the most significant characteristic of human problem solving.  This is the quality of analyzing a complex task down into subtasks, and those subtasks into still other subtasks.  Logo is outstanding in its ability to reflect this important quality in its procedure.

21. Logo: A Language for Learning Problem Solving Skills  The key here is the fact that if one writes the name of procedure A as a step in procedure B, procedure A is automatically executed in proper sequence.  The following procedure for drawing a house demonstrates hierarchicality, in that it is broken down into a square and a triangle, which are accomplished with the procedure POLY.

22. Logo: A Language for Learning Problem Solving Skills  TO HOUSE :N  POLY 4 :N  FD :N  RT 30  POLY 3 :N  END

23. Reflection  TO What are the strengths and limitations of choosing LOGO as a programming language for the computer literacy curriculum?  Can LOGO be replaced by another programming languages? WHY?  Can we just teach pseudo-code instead of any real programming languages?

24. Meaningful Learning Logo/Pascal/…etc Pseudo-code Iconic programming Language interesting/ challenging realistic high- order thinkingX X