Recognition of objects as patterns

At the second stage, operations become actuated internally (from the inside) by the self-instructions. This is the stage of the method’s internalization. At the third stage, a need in any instructions (external or internal) disappears and the operations start to get actuated by the goals and problem conditions themselves. This stage is the stage of operations’ internalization.

In the course of moving from stage to stage, internal psychological mechanisms of mental processes undergo, according to Landamatics, one critical change: executed successively (in a step-by-step manner) at stages 1 and 2, mental operations start to be performed simultaneously (or partially simultaneously) at stage 3. Simultanization of mental operations makes possible the following: Parallel processing of information instead of initial sequential (successive? ) processing


Carrying out mental operations (processes) very fast, instantaneously or almost instantaneously These characteristics of mental processes are signs of their mastery and automatization. In conventional instruction, these characteristics are formed (if formed) in a spontaneous, haphazard and often ineffective way. The Landamatics makes their formation a well planned and instructionally well managed process, thus guaranteeing the high quality of mental abilities developed as a result of simultanization.

With strategy 2 (teaching concepts, terms, definitions, and methods in ready-made form), instead of having the students discover the concept of a right triangle, figure out its term and frame its definition (as was the case with strategy 1), the teacher simply teaches all this knowledge to the students in ready-made form (with appropriate illustrations and exercises). It is obvious that strategy 1 is educationally more valuable, advantageous and beneficial than strategy 2. But strategy 1 takes more time.

It seems that the only condition for choosing one or another strategy is the amount of available time. Not infrequently, however, there is not enough time for using full-fledged discover strategy 1 but more time available than needed for using strategy 2. For this situation Landamatics suggests to use both strategies in a certain proportion. We call this a mixed, or combination, strategy (strategy 3). With this strategy, certain things within a topic are taught using the discovery strategy, and certain other things are taught by providing knowledge in ready-made form.

Which topics should be taught by one or by the other strategy is determined by the teacher’s objectives at the given moment and by the relative benefits that each of the method would provide with regard to each particular topic to be taught. Main points 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). Implications of Algo-Heuristic theory for Education 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 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 that 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 that is practiced with the first, and so on.

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