This part is based on the monograph of T.Talysyna (Talysyna, 1975). According to this
theory the major goal of instruction is developing mental actions with objects of the studied field.
Instruction is viewed as controlling students' activities and hence controlling the process of
development. Thus, instruction efficiency is determined to a great extent by a well developed
system of control.
All actions can be referred to two categories: to general logic actions and specific actions.
General logic actions are inherent in every subject field and are different only in objects at which
they are directed. Examples of such type of actions are qualification, break up into classed,
comparison. For example, qualification as a type of action, exists in mathematics (qualification of
the conics and differential equations) as well as in biology (qualification of animal objects).
Specific actions are basically inherent to a given subject field. For example, in mathematics they
are arithmetic operations, differentiation, etc.
As a rule, the performed actions themselves consist of other, more primitive actions and in
their turn can be part of other actions. Actions that are part of a given whole, are called
operations. That is operations are also actions, hence the term emphasizes only the hierarchial
subordination among actions.
The theory of stage-by-stage development of mental actions specifies four independent
characteristics of any actions used to judge the level of development of an action.
a. Form of action. An action can be in a materialized (material), speech or mental form. A
materialized form of action is connected with manual activities (manipulation, hand-on activities,
etc.), objects of action (or their models) are presented in a material form, results of action should
be real transformations of these objects or of their models. For example, if animal objects are
written on cards and one is doing a general logic action of qualification, then by handling these
cards a subject puts cards with mammals on them on the left and cards with fishes on the right. If
conic sections are presented on computer screen (it can be equations or graphs), then a
qualification action in a materialized form may consist of pasting degenerated conics and
importing them with the help of a mouse to the top part of the screen and non-degenerated conics
to the bottom part of the screen.
There is no need to discuss the speech form of action. It should be noted that according to the
theory of stage-by-stage development of actions, writing belongs to the same speech form. If we
continue our example of qualification then the speech form will mean articulation of the
performed actions. There is no need for these objects to be present in material form. For
example, in the process of instruction a student may be asked: "We have a wolf, a dolphin, a
whale and a shark. Which of them are mammals and which are fishes?" An action can be an
answer in a form of oral speech or a note in a copybook.
Mental form of action is the highest form of action development. An action in this form is
imperceptible for one's associates and its results are also recorded in an imperceptible for others
form.
The mental form of action means that its objects are representations, notions, concepts and all
operations are performed to oneself. The ability to perform a whole action in the mental form
indicates that it has gone through all the stages of development and interiorization.
b. Three independent characteristics of action. Each of the described forms of actions has another
three independent characteristics:
- degree of generalization;
- degree of completeness;
- degree of assimilation
Generalization of an action means ability to apply it to objects of a different nature.
The degree of completeness indicates if all the operations that were to be performed in the
process of performing an action have been actually completed.
The degree of assimilation, as a rule is connected with such indicators as the speed of
performing an action, technical errors and mistakes, the level of automatism, etc.
The analysis of component operations of any action shows that they perform different
functions. For example, in a qualification action of animal objects the qualification action itself is
performed when a card with a word "wolf" is put on the right, and a card with a word "shark" is
put on the left. This action is proceeded by another preliminary action, which in this case consists
of handling, fingering the cards, referring different characteristics (which can also be given in a
material form) to different cards, etc.
A significant part of performing an action is taken up by some preliminary work, a preparation
for an action in a certain sense. This preparatory part is called an orientation part of an action.
The performance itself is called an executive part . Analysis of an action and experiments carried
out in this respect shows that there also exists a control part which takes place after the executive
part when a subject compares the results achieved in the executive part of an action with the goals
of an action and a draft plan of an execution planned in the orientation part.
Numerous experiments demonstrated that in the process of instruction with the final goal of
acquiring theoretical knowledge it is the orientation operations that play the decisive role.
In every point of performing an action, declarative and heuristic knowledge that a subject has,
along with procedures of their application for performing the required action, and procedures of
replenishing declarative knowledge when the action is completed, is called the orientation basis of
an action.
The theory of stage-by-stage development of mental actions singles out five stages in the
process of instruction. We will provide a brief outline of these stages in the fifth paragraph.
An important role in designing methodology of instruction based on the theory of
stage-by-stage development of mental actions is played by appropriate forms of assessment and
feedback. At the initial stage of instruction the feedback should be continuous, i.e. at each
operation. When the action is already well developed it could be periodical.
As it was pointed out in the Introduction, an important element of designing methods and
strategy of computer oriented instruction is its analysis from the point of view of the studied
course content, instruction goals and psychological peculiarities of the group of students.
Go on to the next section of this paper.
Mikhail Bouniaev
Southern Utah University
Math/CS Department
351 W. Center
Cedar City, Utah, USA, 84720
E-mail: BOUNIAEV@SUU.EDU
Moscow Pedagogical State University
Department of Mathematical Analysis
Moscow, Russia
The Math Forum is a research and educational enterprise of the Drexel School of Education.