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DIFFERENCES BETWEEN FOURTH-GRADERS SOLVING SEARCH PROBLEMS
A.Z. Zak, Leading Researcher
Psychological Institute of Russian Academy of Education (Russia, Moscow)
DOI:10.24412/2500-1000-2022-12-2-94-101
Abstract. The article presents a study aimed at determining the possibilities of primary school graduates in successful education in secondary school (in particular, in the fifth grade). On the basis of solving problems in three forms of action, three groups offourth-graders with different degrees of readiness for further learning were identified. As it turned out in conversations with teachers of the fifth grade, those who were able to correctly solve problems in a verbal-sign form turned out to be the most ready, those who correctly solved problems only in a subject-effective form, the average degree of readiness was among those who could correctly solve problems not only in an objective-effective form, but also in a visual-figurative one.
Keywords: fourth-graders, search tasks, verbal-sign, visual-figurative, object-effective forms of action.
1. Introduction. At the beginning of classes in the fifth grade, children often experience disadaptation to learning conditions, which is expressed in a decrease in academic performance, a deterioration in intelligence, memory and attention, a weakening of school motivation, increased fatigue, and fear of lessons and tests. During this adaptation period, most children become more anxious, their performance decreases, they are forgetful and disorganized.
In order to timely and effectively help children adapt to the requirements of the main school at the beginning of education in the fifth grade, it is expedient, in our opinion, already at the end of elementary school to identify those children who may have difficulties in the future, in particular, due to insufficient intellectual readiness to master the curriculum of middle classes. This will allow organizing special developmental classes for such children (see, for example, [4, 5]).
When considering the issue of readiness for studying in a basic school, it should be borne in mind that the curriculum of the middle classes, as you know, includes, on the one hand, theoretical material (statement and explanation of patterns and rules) that children encounter when studying natural sciences and the humanities. disciplines, and, on the other hand, practical material related to solving var-
ious problems (mathematical, grammatical, etc.).
The noted heterogeneity of the content of curricula allows us to speak of at least three levels of intellectual readiness of younger students - medium, high and low. The average level can be characterized as sufficient for the successful mastering of the practical material of the curricula of the middle classes of the school, but insufficient for a full understanding of the theoretical material, which, of course, is not associated only with the ability to learn general provisions, but, most importantly, involves mastering the ability to deduce from them private assertions.
A high level of intellectual readiness allows students to actively operate both practical and, most importantly, theoretical material. Children with a low level of this readiness experience difficulties in mastering practical material (methods for solving problems) and poorly understand explanations and evidence.
1.1. Ways of theoretical thinking
The issues of diagnosing the intellectual readiness of children for learning in secondary school were developed by us in line with the conceptual approach to the development of schoolchildren's thinking, laid down by S.L. Rubinshtein [8], developed by V.V. Davydov [2] and specified by us [3, 6].
Thus, in our studies [3, 6] it was found, in particular, that in elementary school there is
not only a transition from empirical thinking to theoretical thinking, but also the development of theoretical thinking itself as a consistent mastering of its methods by children -ideas about theoretical thinking as a complex cognitive action, the purpose of which is to form the concept of a reflected object, were developed by us on the basis of the theory of activity of A.N. Leontiev [7].
Based on the provisions of dialectical logic that characterize the features of reflecting the content of a cognizable object in a concept was assumed that this complex action includes three particular actions aimed, respectively, at the formation of categories of the universal, especially and single (whole) [1].
On the basis of philosophical ideas about theoretical thinking as a reasonable way of cognition, we believed that the basis of these particular actions is a single operational core, which is realized through the implementation of acts of analysis and reflection.
Each particular action acted as a special way of carrying out theoretical thinking, associated with the conditions in which the formation of a concept occurs at the stages of comprehending the universal, particular and individual as a whole. The methods of successive allocation of this conceptual content were conditionally named, respectively, as "analytical", "reflexive" and "synthesizing".
Using the analytical method, a person, when solving problems of a certain class, singles out in their content a general relation, a general principle underlying their construction and solution, using a reflexive method -special forms of the existence of this general relation, - specific principles, underlying the construction and solution of subclasses of problems of a certain class, with the help of a synthesizing method - the unity of a universal relation and special forms of its implementation, general and specific principles.
The criterion for the implementation of the analytical method is the successful solution of a number of problems of an objectively one class, the reflexive method is not only the solution of problems of one class, but also the selection of problems of its two subclasses among them, the synthesizing method is the ability of a person who has solved problems in a reflexive way to propose a new problem,
objectively related to another subclass of problems of the class being solved.
In our research [3, 6] a connection between the method of theoretical thinking and the form of action in solving problems was revealed: the more specific the form of action (subject-effective compared to visual-figurative, and, especially with verbal-sign), the more complex (developed) way of theoretical thinking is used. So, when moving from a visual-figurative form of action to an objective one, or from a verbal-sign to a visual-figurative, the analytical method of solving problems changes to a reflexive one, and a reflexive one to a synthesizing one.
It was also found that education in elementary school is the period of formation of the analytical way of theoretical thinking in children, and education in secondary school is the period of formation of the reflexive way. This means that the formation of the noted methods in these periods occurs through the consistent development of successful problem solving, first in subject-effective, then in visual-figurative and then in verbal-sign forms.
Based on the noted results of the study of theoretical thinking, it is advisable to choose the degree of formation of the analytical method of theoretical thinking as the subject of diagnosing the intellectual readiness of primary school graduates to study in the middle classes: when solving problems only in an objective-effective form (first degree), in an objective-effective and visual- figurative (second degree) and in subject-effective, visual-figurative and verbal-sign forms (third degree).
2. Materials and methods.
In order to create conditions for a full characterization of the formation of the analytical method and distinguish between children with high, medium and low levels of intellectual readiness for learning in secondary school, it is advisable to use tasks of various kinds: solved in a visual-figurative form, subject-effective and verbal-sign.
2.1. Methodology "Game in exchange "
In the group form of the survey (52 fourth-graders participated), the "Game in exchange" technique was used, including spatial-combinatorial tasks solved in a visual-figurative form. In these tasks, one location of objects is transformed into another based on
the "reciprocal exchange of places" rule. According to this rule, a simultaneous exchange of places of any two objects is taken as one action. For example: 8 M + , - initial, initial location of objects (number, letter, sign) is converted in one action to + M 8, - final, required location. At the same time, 8 and + (i.e., a number and a sign) are simultaneously interchanged.
At the beginning of the lesson, sheets are distributed where the students indicate the names and write down the solution to the problems.
Next, the organizer of the lesson depicts the condition of the problem on the board:
S R P-R S P
The student says: "Letters located on the left must be swapped in one action so that they are located as on the right. One action is the exchange of places of any two letters. Here the solution will be the interchange of the letters "S" and "R".
The following is the solution:
S R P-R S P
1) R S P
After that, the condition of the second task is displayed, where the required location must be obtained from the initial one in two steps:
V N L K-N V K L
The solution to this problem is collectively analyzed (first, for example, the letters V and N are changed, and then L and K) and it is written on the board:
V N L K-N V K L
1) N V L K, 2) N V K L
At the same time, the students' attention is specifically drawn to the fact that only two letters change places in one action, and the remaining letters (two, three, four or more) are rewritten without changes.
It is further explained that in the first step (and, accordingly, in the second one), the other two letters can also be interchanged, first L and K, and then V and N:
1) V N K L, 2) N V K L
After that, forms are distributed with two training and six main tasks.
Form
Training tasks
1. NCP - KNP (one action).
2. R K M TV - K R V T M (two actions).
Main goals
1. M B T N K R - N K R M B T (3 actions).
2. R V W K L D - K L D R V W (3 actions).
3. W A U O E Y I - E Y I O W A U (3 actions).
4. R D K S V F M C - V F M C R D K S (4 actions).
5. P S N G L V R K - L V R K P S N G (4 actions).
6. R K N S W T B M D - T M B D W R K
N S (4 actions).
* * *
The content of the form is explained to the children, - two training tasks, three main ones in 3 actions and three main ones in 4 actions, - and it is proposed to solve training tasks.
Further, passing through the class, the organizer checks the solution of these problems, considering that the most common mistake is to move (mentally) only one letter, not two, in one action. So, when solving the second training problem "R K M T V - K R V T M", some students can write in the first action: "1) R K V M T". This means that in this case they moved only one letter, "V", instead of swapping two letters, "V" and "M": 1) R K V T M.
After correcting errors, it is proposed to solve the main tasks: students are reminded that the conditions of the tasks given on the form are not copied (although if it is difficult for someone, such cheating can be allowed), and on the sheet with the last name you need to write only the task number and next to the result the first exchange (literally in places), the second and third.
Since the main tasks, like the training one, have several options for the correct solution, the children are told that they need to write down only one answer. Then it is shown on the board how to format the answer to the main tasks, for example:
No. 1. 1)........2)........3).........
No. 4. 1)........ 2) ........ 3) .........
4)...........
When checking the solutions proposed by the children for each main problem, it should be borne in mind that the exchange of letters in places can be done in a different order. It is clear that in the main tasks there are more solutions: tasks 1 - 3, where you need to find
three exchanges, have six solutions, and tasks 4 - 6 (where four exchanges are unknown) -eight options.
Therefore, the answers to the main tasks are easiest to check, based on a single principle of their construction and solution - the letters from the left and right parts in their initial location should change places.
According to the results of solving problems, the subjects were divided into two groups. One of them - group A (30 students, - 57.7%) were those children who correctly solved all the problems - this indicates the implementation of the analytical method of theoretical thinking.
Group B (correspondingly, 22 students -42.3%) consisted of those children who solved several initial tasks correctly, and all subsequent ones incorrectly. This (as could be observed in individual experiments) is due to the fact that the initial problems were solved successfully not on the basis of an analytical method of orientation in their content, associated with the selection of essential relations, but only due to a relatively small number of exchanges, since it was possible to find each
exchange separately (out of connection with others) on the basis of an empirical method of orientation in their content. The use of just such a method led the children to make mistakes when solving problems with four exchanges.
The children of group B (22 students, -42.3% of the entire sample), - in order to distinguish them by the level of intellectual readiness for learning in high school, - were asked to solve problems in a subject-effective form.
2.2. Methodology "Game of permutations"
To solve the problems of the "Game of Permutations" methodology, an individual form of examination of children was used, which was carried out as follows.
At first, the child masters the formal rule for solving the problems of this technique -"to rearrange any object in a free cell" - on the basis of two training problems. For this, a sheet of paper was placed on the table. On its left side, a regular rectangle of three equal square cells was drawn, and on the right side, a rounded rectangle. Cards with letters were placed in two cells of each rectangle (Fig. 1):
Fig. 1. Initial and required arrangement of cards
The child was told that the arrangement of cards in a regular rectangle is the initial one, and their arrangement in a rounded rectangle is the final, required one. It had to be obtained after rearranging the cards in the initial location. At the same time, it was indicated that for one action, one move, the movement of any card to a free cell is accepted.
It was further reported: "In this problem, you need to make such two permutations so
that the cards in the regular rectangle are in the same cells as in the rounded rectangle. Tell me, what will be the first permutation?... A card with the letter C?.. That's right, rearrange. ... And what will be the second permutation? ... That's right, a card with the letter G, - rearrange".
Next, it was proposed to solve the second training problem:
M
M
Fig. 2. The second problem with two permutations
"In this problem, you also need to find two permutations so that the letters in a regular rectangle are arranged in the same way as in a rounded rectangle. What will be the first per-
mutation? ... The letter T? ... That's right, rearrange. ... What will be the second permutation? ... That's right, the letter M - rearrange".
After that, the child is asked to solve five Cards were given on a separate sheet (see fig. basic problems, three permutations in each. 3).
с N T
В M D L
С w G F H
К P С X M в
Fig. 3. Main tasks
All the main tasks are built according to a single principle - the first and last letters are swapped in three permutations: first, the extreme letter on the left is moved to the free cell, then the extreme letter on the right is moved to the vacant place, and then the letter that was rearranged first gets into the vacated place.
If all five main tasks are solved correctly, then this indicates the use of an analytical method of understanding their content, -group B1 (7 students, - 31.8% of group B, 13.5% of the entire sample). If mistakes are made in the tasks (in particular, the leftmost letter is not always rearranged first), then this indicates the absence of the use of the analytical method in solving problems, - group B2 (15 students, - 68.2% of group B, 28, 8% of the entire sample).
2.3. Methodology "Comparison"
The children of group A (after solving the problems of the "Game for exchange" methodology) - in order to distinguish them by the level of intellectual readiness for learning in high school - were asked to solve problems in a verbal-sign form. For this, the "Comparison" methodology was used, composed of tasks that are inferences built on plot material.
At the beginning of the group diagnostic session, the children are given sheets where they indicate their names and write down the answers to the tasks.
Then forms are distributed and the following requirements are explained.
"To solve the problem correctly, you need to read it silently ("to yourself') several times so as not to disturb your neighbors, then think (also silently) and, when the answer is clear, write it on the sheet of paper on which the surname is written.
In the answer you need to write one or two words, depending on what is asked in the problem.
Tasks need to be solved only "in the mind": you can't write something and make some notes".
The first two tasks of the form, the simplest ones, play the role of familiarizing the child with conclusions, preparing for solving the following, more complex tasks.
It is desirable for group classes to have several (two, four, six or eight) variants of the form with tasks in order to provide children with more favorable conditions for independent decision. This is easy to do by changing only the names of the characters presented in the task conditions.
Form
1. Vova solves problems more correctly than Kolya. Kolya solves problems more correctly than Misha. Who solves problems the best?
2. Sasha sees better than Katya. Katya sees better than Gali. Who sees worse?
3. Polkan barks more often than Bugs. Polkan barks less often than Barbosa. Who barks the most?
4. Murka meows quieter than Barsik, but louder than Pushka. Who meows the loudest?
5. If, when comparing girls, instead of the word "more", use the new word "iaee" and write in the condition of the problem: "Katya iaee than Lyuba. Luba iaee than Nina", then how to answer the question: "Which of the girls is "iaee" of all?"
6. If, when comparing boys, instead of the word "less", use the new word "tprk" and write in the condition: "Igor tprk than Vova. Vova Tprk than Oleg", then how to answer the question: "Which of the boys is Tprk of all?"
7. If a dog were lighter than a beetle and heavier than an elephant, who would be the lightest?
8. If a tiger was shorter than a rabbit and taller than a giraffe, who would be tallest?
9. Spruce is 79 years older than oak and 3 years younger than pine. What is the oldest tree?
10. Wardrobe is 2 kg lighter than a table and 94 kg heavier than a sofa. What is the heaviest?
11. Misha lived a little closer to school than Kolya, and much farther from her than Vitya. Who lived farthest from school?
12. There are many more letters in a book than in a magazine, and a little less letters than in a newspaper. Where are the most letters?
* * *
All problems are built on the basis of the transitivity of the ratio of quantities. At the same time, in tasks 1 and 2 the simplest formulations are given, in tasks 3 and 4 - more complex ones, in tasks 5 and 6 - formulations using artificial words, in tasks 7 and 8 - formulations using descriptions that contradict the experience of children, 9 and 10 - formulations provoking the wrong solution of problems, 11 and 12 - formulations containing extra words "a little" and "much".
If the children solve all the problems correctly, this means that the analytical method of theoretical thinking was used - group A1 (18 students, - 60.0% of group A, 34.6% of
the entire sample). If some tasks were solved correctly and others incorrectly, then this method was not used - group A2 (12 students, - 40.0% of group A, 23.1% of the entire sample).
3. Results
So, the diagnostics of the formation of the analytical method of theoretical thinking was carried out in 52 primary school graduates using three methods.
In group experiments on the material of the "Game for exchange" methodology, children solved spatial-combinatorial problems in a visual-figurative form. All tasks were correctly solved by 30 people (57.7% of the sample of 52 people).
In individual experiments on the material of the "Game of permutations" methodology, 22 students solved spatial-combinatorial problems in an objective-effective form. All tasks were correctly solved by 7 people (31.8% of 22, 13.5% of 52).
30 pupils (out of 52) participated in group experiments on the material of the "Comparison" method, who solved plot-logical problems in a verbal-sign form. Prior to that, also in the conditions of group experiments, they correctly solved all the spatial-combinatorial problems of the "Game for Exchange" technique in a visual-figurative form.
All tasks of the "Comparison" method were correctly solved by 18 people (60.0% of 30, 34.6% of 52).
Thus, the results obtained allow us to distinguish four groups according to the success of solving problems in verbal-sign, visual-figurative and subject-effective forms.
The first group - students who correctly solved problems in the verbal-sign form (34.6% of 52 people); the second group - students who correctly solved problems in a visual-figurative form (57.7% of 52 people); the third group - students who correctly solved the tasks in the subject-active form (13.5% of 52 people), the fourth group - students who incorrectly solved the tasks in the subject-active form (28.8% of 52 people), see table.
Table. The number of students in the first, second, third and fourth groups who solved correctly and incorrectly tasks in subject-effective, visual-figurative and verbal-sign forms (in %)
Groups
Forms of action
Subject-effective
Visual-figurative
Verbal-sign
Correct Incorrect
Problem solving
Correct
Incorrect
Correct
Incorrect
First
34,6 65,4
Second
57,7
42,3
Third
13,5
Fourth
28,8
The data presented in the table indicate that most of the children (the second group -57.7%) can correctly solve problems in a visual-figurative form, and the fewest children (the third group - 13.5%) can correctly solve problems only in an objective-effective form, and the average number of children (the first group, 34.6%) can correctly solve problems not only in a visual-figurative form, and even more so, in an objective-effective form, but also in verbal-sign form.
4. Conclusion.
Observations of the peculiarities of teaching in the fifth grade of the four groups of students presented in the table and conversations with their teachers showed the following.
problems in natural science courses, but experienced difficulties in understanding explanations and evidence.
The children of the third group, who could only correctly solve the tasks of the Permutation Game technique in an objective-active form, and, moreover, the children of the fourth group, who could not correctly solve the tasks of the "Permutation game" technique in an object-effective form, experienced difficulties in the course of learning and required constant help and support.
Correlation of the results of children performing diagnostic tasks at the end of elementary school and the data characterizing the peculiarities of their learning in the fifth grade makes it possible, in our opinion, to characterize the level of intellectual readiness of children in the first group as high, in the second group as medium, in the third and fourth groups as low.
On the whole, the results of the performed study create opportunities for developing an effective forecast of the success of teaching primary school graduates in secondary school.
The children of the first group, who correctly solved the tasks of the "Comparison" technique in a verbal-sign form, successfully mastered not only the methods for solving typical problems, but also the content of explanations and proofs.
The children of the second group, who correctly solved the tasks of the "Game for exchange" method in a visual-figurative form, successfully mastered the solution of typical
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РАЗЛИЧИЯ ЧЕТВЕРОКЛАССНИКОВ В РЕШЕНИИ ПОИСКОВЫХ ПРОБЛЕМ
А.З. Зак, вед. науч. сотр. Психологический институт РАО (Россия. г. Москва)
Аннотация. В статье представлено исследование, направленное на определение возможностей выпускников начальной школы в успешном обучении в средней школе (в частности, в пятом классе). На материале решения задач в трех формах действия было выделено три группы четвероклассников с разной степенью готовности к дальнейшему обучению. Как выяснилось в беседах с учителями пятых классов, наиболее готовыми оказались те дети, кто смог верно решить задачи в словесно-знаковой форме, наименее готовыми - те, кто верно решил задачи только в предметно-действенной форме, средняя степень готовности была у тех, кто смог верно решить задачи не только в предметно-действенной форме, но и в наглядно-образной.
Ключевые слова: четвероклассники, поисковые задачи, словесно-знаковая, наглядно-образная, предметно-действенная формы действия.
