Landa’s theory is concerned with identifying mental processes — conscious and especially unconscious — that underlie expert learning, thinking and performance in any area. His methods represent a system of techniques for getting inside the mind of expert learners and performers which enable one to uncover the processes involved. Once uncovered, they are broken down into their relative elementary components — mental operations and knowledge units which can be viewed as a kind of psychological “atoms” and “molecules”. Performing a task or solving a problem always requires a certain system of elementary knowledge units and operations.
There are classes of problems for which it is necessary to execute operations in a well structured, predefined sequence (algorithmic problems). For such problem classes, it is possible to formulate a set of precise unambiguous instructions (algorithms) as to what one should do mentally and/or physically in order to successfully solve any problem belonging to that class. There are also classes of problems (creative or heuristic problems) for which precise and unambiguous sets of instructions cannot be formulated. For such classes of problems, it is possible to formulate instructions that contain a certain degree of uncertainty (heuristics). Landa also describes semi-algorithmic and semi-heuristic problems, processes and instructions.
The theory suggests that all cognitive activities can be analyzed into operations of an algorithmic, semi-algorithmic, heuristic, or semi-heuristic nature. Once discovered, these operations and their systems can serve as the basis for instructional strategies and methods. The theory specifies that students ought to be taught not only knowledge but the algorithms and heuristics of experts as well. They also have to be taught how to discover algorithms and heuristics on their own. Special emphasis is placed on teaching students cognitive operations, algorithms and heuristics which make up general methods of thinking (i.e., intelligence).
With respect to sequencing of instruction, Landa proposes a number of strategies, the most important of which is the “snowball” method. This method applies to teaching a system of cognitive operations by teaching the first operation, then the second which is practiced with the first, and so on.
Application
While this is a general theory of learning, it is illustrated primarily in the context of mathematics and foreign language instruction. In recent years, Landa has applied his theory to training settings under the name “Landamatics” (Educational Technology, 1993)
Example
Landa (1976) provides the following example of an algorithm for teaching a foreign speaker how to choose among the English verbs “to offer”, “to suggest” and “to propose”:
Check to see whether something that one presents to another person is a tangible object or viewed as tangible. If yes, use “offer”. If no, it is an idea about some action to be performed. Check to see if this idea is presented formally. If yes, use “propose”, otherwise use “suggest”.
Applying the snowball method would involve teaching the student the action of checking the first condition and then the action of checking the second condition followed by practice that requires both conditions to be checked. Landa explains that after sufficient practice the application of the algorithm would become automatic and unconscious.
Principles
- It is more important to teach algo-heuristic processes to students than prescriptions (knowledge of processes); on the other hand, teachers need to know both.
- Processes can be taught through prescriptions and demonstrations of operations.
- Teaching students how to discover processes is more valuable than providing them already formulated.
- Break processes down into elementary operations of size and length suitable for each student (individualization of instruction).
References
- Educational Technology (1993). Landamatics ten years later. Educational Technology, 33(6), 7-18.
- Landa, L. (1974). Algorithmization in Learning and Instruction. Englewood Cliffs, NJ: Educational Technology Publications.
- Landa, L. (1976). Instructional Regulation and Control: Cybernetics, Algorithmization, and Heuristics in Education. Englewood Cliffs, NJ: Educational Technology Publications.
Related Websites
For more about Landa and his work, see:
http://www.wiu.edu/users/mflll/landa.htm
http://tecfa.unige.ch/staf/staf9698/mullerc/3/landa.html