Curves of teaching and upbringing - Pedagogy. Theoretical pedagogy

5.3. Learning and parenting curves

Knowing the magnitude of the influence of each factor on the productivity of education and upbringing is certainly very important, but it is equally important to know the nature (form) of this influence, i.e. the law by which a change in one value is made with respect to the other. From the course of elementary mathematics it is known that if two variables are interrelated in a dynamic process, then this relationship can be described with the aid of some functional dependence, a visual reflection of which is the curve. The use of curves not only makes understanding of the dependence much easier, but also makes this relationship visible. The curve shows the dynamics of the mutual connection. Without knowing the latter, it is impossible to set and solve the problems of optimal control of the formation of the final product.

It is generally believed that the first in the psychology of learning, the relationship curve was built at the end of the 19th century. German psychologist G. Ebbinghaus (Figure 15), clearly showing how the process of forgetting the learned material in time is going on. Since then, the curves have been increasingly used to describe psychological and pedagogical dependencies (links), having received the general name of learning curve-upbringing.

Construct a curve - the ultimate and attractive goal of each study. The task is very difficult, taking into account the specifics of pedagogy. After all, in order to construct a curve, it is necessary to perform scrupulously experimental investigations, to find out all the features of the investigated connection. By now, with the help of curves, it has been possible to describe a relatively small number of pedagogical processes.

Historically, the overwhelming number of relationships recorded by means of curves refers to didactic processes. The processes of education as more complex and subtle curves are much more difficult to characterize, and in most cases it is impossible. The description with the help of formulas, say, the process of forming a world view is equivalent to the derivation of the formula of life. Not such a level of mathematics is needed to describe the most complex pedagogical processes.

Dynamics of forgetting

Fig. 15. Dynamics of forgetting

To study the forms of connection between factors and productivity of education, the so-called experimentally tested method was applied, the essence of which is that the primary hypothetical idea of ​​a possible form of communication is formulated first theoretically , then facts and experimental observations accumulate, and at the final stage the curves of relationships constructed on this material are verified by the experience (practice) of mass education and upbringing. Comparison of ideal and real, theory and practice provides the highest probability of conclusions and obtaining corrected (smoothed) curves.

It was already noted that in order to establish a hierarchy between the factors of eduction, it is necessary to have a common basis (basis), which is the productivity of learning. This is also the basis for plotting curves. It is difficult for this purpose to choose a more capacious education than all the same productivity, for the sake of which the process is carried out. Thus, the curves will show how different factors influence the productivity of the educational process. The crowning of theoretical pedagogy will be the creation of a catalog of curves, a description of the processes of education and upbringing in the language of functional dependencies. The work on the identification of new curves and the streamlining of the already known ones has been revived in connection with the effective solution of a number of problems in the computerization of the educational process, and one can hope that progress in this area will develop at a faster rate.

In Fig. 16 shows the curve of the dependence of the productivity of assimilation (II) on the amount of educational material (x).

In Fig. 17 depicts the curve of the dependence of the productivity of the educational process on quality (subjective difficulty and objective complexity) (II) of the educational material (x). As you can see, the difficulty and complexity of the teaching material on the productivity of teaching affect much more than its number, which is constantly confirmed by practice.

Knowing the quantity and quality of the educational material, it is possible to calculate easily and quickly by formulas how the productivity index of education will be. Theoretical pedagogy tends to refine empirically sensed interrelationships. There are new studies in which quantitative substantiation is given to the non-metric parameters of the educational process, and such studies are becoming ever more numerous.

Dependence of the productivity of training on the amount of teaching material

Fig. 16. Dependence of the productivity of training on the amount of teaching material

Dependence of the productivity of learning on the quality of the educational material

Fig. 17. Dependence of the productivity of learning on the quality of the teaching material

In Fig. 28-38 (in Chapter 6 "Patterns of the educational process"), the curves of the connections of some significant factors with the productivity of education are presented. On horizontal axes ( X) , in most cases, the values ​​that runs through factor. Vertical axes ( Y) postpone the productivity of education. Analyzing the curves, we see that they have different angles to the axis X: some of them are sloping, others steeply rise, quickly reaching a maximum. What does this show? First of all, the strength (degree) of the influence of factors is different. The closer the curve is pressed to the Y axis, the higher the correlation coefficient of this factor with the productivity of training, the more the latter depends on this factor. Some curves have a hypothetical character. All curves are smoothed against the experimental data and express a general trend.

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