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11PSYCHOLOGICAL SCIENCES
DIAGNOSIS OF REASONING SKILLS IN YOUNGER ADOLESCENTS
Zak A.
Leading Researcher, Psychological Institute RAE, Moscow, Russia
Abstract
According to the provisions of the Federal State Educational Standard [7], cognitive meta-subject learning outcomes are associated, in particular, with mastering the ability to build logical reasoning. This article is devoted to the problem of diagnosing the marked skill in younger adolescents, in particular, in sixth graders. The requirements for the corresponding diagnostic task are presented. The content of its development is disclosed. It is shown that the proposed task differentiates sixth graders by the level of formation of logical actions in the implementation of reasoning in situations of solving plot-logical problems of different types in the conditions of a group survey.
Keywords: logical actions, reasoning construction, sixth graders, plot-logical problems.
1. Introduction
In assessing the ability to build logical reasoning, we relied on ideas about two types of cognitive activity, developed in dialectical logic [5] and implemented in psychological research (see, for example, [2], [3], [4]).
According to these ideas, a person's cognition of the surrounding world can be aimed at reflecting the internal connections of objects and phenomena (theoretical, meaningful, rational knowledge) and at the reflection of their external connections (empirical, formal, rational knowledge).
In the first case, human cognitive activity is quite effective, since its result is an understanding of the reasons for changing the objects of cognition. In the second case, cognitive activity is not effective enough, since its result is only a description and ordering of the observed features of changes in cognized objects.
When assessing the formation of the ability to build logical reasoning, it was assumed that in one case the inference can be based on the true relationships of the proposed judgments, in the other case - on their false relationships. When relying on true relationships, the action of building a reasoning will be meaningful, when relying on false relationships, it will be formal.
The purpose of our work was to develop and test a task for diagnosing the characteristics of the formation of logical actions - associated with the ability to build reasoning and carry out inferences - in secondary school students, in particular, in sixth graders.
At the same time, we proceeded from the fact that such a task should include verbal-logical tasks containing judgments of different types.
So, in logical science (see, for example, [1], [6]), among simple judgments, attributive (i.e, property judgments) and relational (i.e, relation judgments) are distinguished.
From the qualitative point of view, attributive judgments are characterized, firstly, as affirmative (if some property is attributed to the subject of the utterance), for example: "... the square is red ...". Secondly, attributive judgments are characterized as negative (if some property of the subject of the statement is absent), for example: "... the square is not red ..."
Among relational ones, judgments are distinguished that reflect symmetric and asymmetric relationships. In the first case, when the members of the relationship are rearranged, its character does not change (if A is equal to B, then B is equal to A), for example: "... if Dima was the same age as Kolya, then Kolya was the same age, how much is Dima ... ".
In the second case, when the previous and subsequent members of the relationship are rearranged, it changes to the opposite (if A is greater than B, therefore, B is less than A), for example: "... if Dima is older than Kolya, then Kolya is younger than Dima ...".
Thus, when characterizing logical actions, one should use tasks composed of relational judgments of both types.
2. Materials and methods 2.1 Problems with Relational Judgment When including problems with relational judgments into the diagnostic methodology, a number of the following provisions should be taken into account.
First, there should be several tasks of each type -with symmetric and asymmetric judgments.
Secondly, problems of each type - with symmetric and asymmetric judgments - should be of three degrees of complexity: simple (two judgments), less simple (three judgments) and complex (four judgments).
Third, in each pair of problems with relational symmetric judgments of the same degree of complexity (first, second, or third), the combination of judgments must be different. In particular, the following two combinations are possible.
For problems of the first degree of complexity (with two judgments in the conditions), such two variants of combinations of judgments in the conditions of the problems are realized.
Option 1: "Misha is as strong as Gena. Gena is as strong as Dima. Which of the schoolchildren is stronger - Misha or Dima? " Option 2: "Misha is as strong as Gena. Misha is as strong as Dima. Which of the schoolchildren is stronger - Misha or Dima? "
For problems of the second degree of complexity (with three judgments in the conditions), as in the previous case, two variants of combinations of judgments in the conditions of the problems are realized.
Option 1: "Misha is as strong as Gena. Gena is as strong as Dima. Dima is as strong as Yegor. Which of the schoolchildren is stronger - Misha or Yegor? " Option 2: "Misha is as strong as Gena. Misha is as strong as Dima. Dima is as strong as Yegor. Which of the schoolchildren is stronger - Gena or Yegor? "
For problems of the third degree of complexity (with four judgments in the conditions), like the two previous cases, two variants of combinations of judgments in the conditions of the problems are realized.
Option 1: "Misha is as strong as Gena. Gena is as strong as Dima. Dima is as strong as Yegor. Egor is as strong as Kolya. Which of the schoolchildren is stronger - Misha or Kolya? " Option 2: "Misha is as strong as Gena. Misha is as strong as Dima. Dima is as strong as Yegor. Dima is as strong as Kolya. Which of the schoolchildren is stronger - Gena or Kolya? "
Fourth, in each pair of problems with relational asymmetric judgments of the same degree of complexity, the combination of judgments should be different. For example, the following two combinations are possible.
For problems of the first degree of complexity (with two judgments in the conditions), such two variants of combinations of judgments in the conditions of the problems are realized. Option 1: "Misha is weaker than Gena. Gena is weaker than Dima. Which of the schoolchildren is weaker - Misha or Dima? " Option 2: "Misha is stronger than Gena. Misha is weaker than Dima. Which of the schoolchildren is stronger - Misha or Dima? "
For problems of the second degree of complexity (with three judgments in the conditions), as in the previous case, two variants of combinations of judgments in the conditions of the problems are realized.
Option 1: "Misha is weaker than Gena. Misha is weaker than Dima. Dima is weaker than Yegor. Which of the schoolchildren is weaker - Misha or Yegor? " Option 2: "Misha is stronger than Gena. Misha is weaker than Dima. Dima is weaker than Yegor. Which of the schoolchildren is stronger - Misha or Yegor? "
For problems of the third degree of complexity (with four judgments in the conditions), like the two previous cases, two variants of combinations of judgments in the conditions of the problems are realized.
Option 1: "Misha is weaker than Gena. Gena is weaker than Dima. Dima is weaker than Yegor. Egor is weaker than Kolya. Which of the schoolchildren is weaker - Misha or Kolya? " Option 2: "Misha is stronger than Gena. Misha is weaker than Dima. Dima is weaker than Yegor. Kolya is stronger than Yegor. Which of the schoolchildren is stronger - Gena or Kolya? "
Thus, the analysis of the structure of tasks shows that the successful solution of tasks with two, three, and, even more so, four relational judgments presupposes the implementation of controlled logical actions by schoolchildren. The meaning of such actions is to compare the proposed judgments with the judgments developed in the process of thinking as the problem is solved. Therefore, the successful solution of tasks by schoolchildren with three and, moreover, with four relational judgments indicates, respectively, an average
and high level of formation of cognitive competence associated with the development of the logical action of constructing reasoning.
2.2. Problems with attributive judgments When including tasks with attributive judgments into the diagnostic methodology, it should be borne in mind that one type of such problems contains only affirmative judgments under the conditions, and the other type contains only negative judgments.
The first type includes, for example, the following problem: "Masha, Galya and Katya drew geometric shapes: someone - red circles, someone - red squares, someone - blue squares. Masha drew red shapes. Galya drew circles. What did Katya draw? "
The second type includes, for example, the following problem: "Masha, Galya and Katya drew geometric shapes: someone - red circles, someone - red squares, someone - blue squares. Masha did not draw red shapes. Galya did not draw circles. What did Katya draw? "
To control the level of complexity of problems with positive and negative attributive judgments, one should take into account the number of subjects and predicates in the conditions.
The first level includes tasks in which the large premise contains three subjects of judgments, for example: "Masha, Galya and Katya drew geometric figures ...", and three predicates corresponding to them, for example: "... someone is red circles, someone then - blue circles, someone - blue squares ... ".
The second level includes tasks in which the large premise contains four subjects of judgments, for example: "Masha, Galya, Katya and Nina drew geometric figures ...", and four predicates corresponding to them, for example: "... someone is red circles, someone - blue circles, someone - blue squares, someone - yellow triangles ... ".
Each of the marked levels includes tasks of three degrees of complexity, depending on the number of simple and complex judgments in the conditions of tasks in a smaller premise.
Problems of the first degree of complexity with three subjects and predicates and with affirmative judgments include problems in which the smaller premise contains two definite (unambiguous) affirmative judgments.
For example, such a task: "Masha, Galya and Katya drew geometric shapes: someone - red circles, someone - red squares, someone - blue squares. Masha drew red circles. Galya drew blue squares. What did Katya draw? "
Problems of the first degree of complexity with three subjects and predicates and with negative judgments also include problems in which the smaller premise contains two definite (unambiguously understood) negative judgments.
For example, such a task: "Masha, Galya and Katya drew geometric shapes: someone - red circles, someone - red squares, someone - blue squares. Masha did not draw squares. Galya did not draw red shapes. What did Katya draw? "
In this problem, the judgments "Masha did not draw squares" and "Galya did not draw red shapes" are understood unambiguously, since in the first case, the
conclusion "Masha drew to circles", and in the second case, "Galya drew blue squares".
Problems of the second degree of complexity with three subjects and predicates and with affirmative judgments include problems in which the lesser premise contains one indefinite proposition and one definite proposition.
For example, such a task: "Masha, Galya and Katya drew geometric shapes: someone - red circles, someone - red squares, someone - blue squares. Masha drew red shapes. Galya drew circles. What did Katya draw? "
In this problem, the judgment "Masha drew red figures" is indefinite (ambiguous), since it is not clear which red figures Masha drew - circles or squares. The judgment "Galya drew circles" is quite definite and unambiguous, since it is clear that she drew red circles, since there are no other circles in the problem statement.
Problems of the second degree of complexity with three subjects and predicates and with negative judgments include problems in which the lesser premise contains one indefinite proposition and one definite proposition.
For example, such a task: "Masha, Galya and Katya drew geometric shapes: someone - red circles, someone - red squares, someone - blue squares. Masha did not draw circles. Galya did not draw red figures. What did Katya draw? "
Problems of the third degree of complexity with three subjects and predicates and affirmative judgments include problems in which the lesser premise contains two complex judgments and one simple one.
For example, such a task: "Masha, Galya and Katya drew geometric shapes: someone - red circles, someone - red squares, someone - blue squares. Masha did not draw blue figures. Galya did not draw circles. Katya did not draw red shapes. What did Masha draw?
Problems of the first degree of complexity with four subjects and predicates and with affirmative judgments include those problems in which the lesser premise contains three simple judgments.
For example, such a task: "Masha, Galya, Katya and Nina drew geometric shapes: someone - red circles, someone - red squares, someone - blue squares, someone yellow triangles. Masha drew circles. Galya drew blue figures. Katya drew triangles. What did Nina draw? "
Problems of the first degree of complexity with four subjects and predicates and with negative judgments include those problems in which the smaller premise contains three simple judgments.
For example, such a task: "Masha, Galya, Katya and Nina drew geometric shapes: someone - red circles, someone - red squares, someone - blue squares, someone yellow triangles. Masha did not draw squares and triangles. Galya did not draw red and yellow figures. Katya did not draw red and blue figures. What did Nina draw?
Problems of the second degree of complexity with four subjects and predicates and with affirmative judgments include those problems in which the smaller
premise contains one complex judgment and two simple ones.
For example, such a task: "Masha, Galya, Katya and Nina drew geometric figures: someone - red circles, someone - red squares, someone - blue squares, someone yellow triangles. Masha drew red shapes. Galya drew circles. Katya drew yellow figures. What did Nina draw? "
Problems of the second degree of complexity with four subjects and predicates and with negative judgments include those problems in which the smaller premise contains one complex judgment and two simple ones.
For example, such a task: "Masha, Galya, Katya and Nina drew geometric shapes: someone - red circles, someone - red squares, someone - blue squares, someone yellow triangles. Masha did not draw blue and yellow figures. Galya did not draw squares and triangles. Katya did not draw red and blue figures. What did Nina draw? "
Problems of the third degree of complexity with four subjects and predicates and affirmative judgments include those problems in which the smaller premise contains two complex judgments and two simple ones.
For example, such a task: "Masha, Galya, Katya and Nina drew geometric shapes: someone - red circles, someone - red squares, someone - blue squares, someone yellow triangles. Masha drew red shapes. Galya drew squares. Nina drew blue figures. Katya drew yellow figures. What did Masha draw? "
Problems of the third degree of complexity with four subjects and predicates and negative judgments include problems in which the lesser premise contains two complex judgments and two simple ones.
For example, such a task: "Masha, Galya, Katya and Nina drew geometric shapes: someone - red circles, someone - red squares, someone - blue squares, someone yellow triangles. Masha did not draw blue and yellow figures. Galya did not draw circles and triangles. Nina did not draw red and yellow figures. Katya did not draw blue and red figures. What did Masha draw? "
In problems with affirmative and negative attributive judgments of the first, second and third degree of complexity with three subjects and three predicates in the big premise and problems of the first, second and third degree of complexity with four subjects and four predicates in the big premise, two variants of the question formulation are possible.
The first version of the question formulation is characterized by the fact that the predicate of the judgment is the desired one, and the known is the subject of the judgment, for example: "What did Masha draw?"
The second version of the question formulation is characterized by the fact that the subject of the judgment is the desired one, and the predicate of the judgment is the known one, for example: "Who drew the red circles?"
Moreover, each version of the question formulation may contain not only an assertion, as in the above examples, but also a negation, for example, respectively: "What did Masha not draw?" and "Who Didn't Draw Red Circles?"
2.3. Diagnostic technique
Based on the analysis of the content of different variants of verbal-logical tasks with relational and attributive judgments, the "Conclusions" methodology was developed, designed to assess the characteristics of the formation of logical actions associated with the construction of consistent reasoning and the implementation of deductive inferences.
Since search experiments with fifth-graders showed that solving problems with symmetric relational judgments (even with the most difficult ones) did not cause difficulties for any of the children, the final version of the methodology does not contain such problems.
The "Conclusions" methodology includes 12 tasks of different types and complexity, placed on the form, which each student received in group experiments. Problems 1 - 4 of the first degree of complexity, tasks 1 - 8 of the first and second complexity, tasks 1 - 12 of the first, second and third degree of complexity.
FORM
1. Masha ran faster than Galya. Galya ran faster than Dasha. Which of the girls ran faster - Misha or Da-sha?
Answers: 1. Masha did not run as fast as Dasha. 2. Dasha did not run as fast as Masha. 3. Masha ran as fast as Dasha. 4. It is impossible to say which of the girls ran faster.
2. Nina, Olya and Nastya lived on different floors in different houses: someone on the second floor of a high building, someone on the second floor of a low building, someone on the first floor of a low building. Nina lived in a tall building. Olya lived on the first floor. Where did Nastya live?
Answers: 1. Nastya lived on the second floor of a tall building. 2. Nastya lived on the second floor of a low-rise building. 3. It is not known where Nastya lived. 4. Nastya lived on the first floor of a low-rise building. 5. Nastya lived on the first floor of a tall building.
3. Alik sang louder than Borya. Alik sang quieter than Igor. Which of the boys sang louder - Alik or Igor?
Answers: 1. Alik sang not as loudly as Igor. 2. Igor sang not as loudly as Alik. 3. Alik sang as loudly as Igor. 4. It is impossible to say which of the schoolchildren sang louder - Alik or Igor.
4. Misha, Gena, Kostya and Andrey solved arithmetic examples: someone added three-digit numbers, someone added two-digit numbers, someone multiplied two-digit numbers, someone divided single-digit numbers. Misha did not solve examples with two-digit and one-digit numbers. Gena did not solve examples for addition and division. Kostya did not solve examples for addition and multiplication. What examples did Andrey solve?
Answers: 1. Andrey solved examples of multiplication of two-digit numbers. 2. Andrey solved examples for the addition of two-digit numbers. 3. It is not known what examples Andrey solved. 4. Andrey solved examples of division of single-digit numbers. 5. Andrey solved examples of adding three-digit numbers. 6. Andrey solved examples of adding single-digit numbers. 7. Andrey solved examples of multiplication of three-digit numbers.
5. Alla teaches poetry easier than Valya. Alla teaches poetry easier than Galya. Galya teaches poetry easier than Zhanna. Which of the girls is easier to learn poetry - Alla or Zhanna?
Answers: 1. Alla does not learn poetry as easily as Zhanna. 2. Zhanna does not learn poetry as easily as Alla. 3. Alla teaches poetry as easily as Jeanne. 4. It is impossible to say which of the girls teaches poetry more easily - Alla or Zhanna.
6. Natasha, Rita and Sveta baked pies: someone with an egg and rice, someone with an egg and cabbage, someone with meat and cabbage. Natasha baked pies with an egg. Rita baked rice pies. What pies did Sveta bake?
Answers: 1. Sveta baked pies with egg and rice. 2. Sveta baked pies with egg and cabbage. 3. It is not known what pies were baked by Sveta. 4. Sveta baked pies with meat and cabbage. 5. Sveta baked pies with meat and carrots.
7. Alyosha lived farther from school than Vova. Alyosha lived closer to school than Grisha. Grisha lived closer to school than Vanya. Which of the boys lived farther from the school - Alyosha or Vanya?
Answers: 1. Alyosha lived not so far from the school as Vanya. 2. Vanya lived not so far from the school as Alyosha. 3. Alyosha lived as far from school as Vanya. 4. It is impossible to say which of the boys lived farther from the school - Alyosha or Vanya.
8. Slava, Grisha, Kolya and Fedya went on trips: some - by car to the north, some - by car to the east, some - on a motorcycle to the east, some - on a bike to the south. Slava did not ride a motorcycle or a bicycle. Grisha did not go east or south. Kolya did not ride a car or motorcycle. On what and where did Fedya go?
Answers: 1. Fedya was driving to the north. 2. Fedya was driving eastward. 3. It is not known what Fedya was driving and where. 4. Fedya was cycling south. 5. Fedya was cycling north.
9. Zina jumped higher than Katya. Katya jumped higher than Ira. Ira jumped higher than Lena. Lena jumped higher than Masha. Which of the girls jumped higher - Zina or Masha?
Answers: 1. Zina jumped not as high as Masha. 2. Masha jumped not as high as Zina. 3. Zina jumped as high as Masha. 4. It is impossible to say which of the girls jumped higher - Zina or Masha.
10. Alla, Nadya and Lyuba weeded the beds with vegetables: someone - long beds with tomatoes, someone - long beds with cucumbers, someone - short beds with cucumbers. Alla weeded long beds. Nadia weeded the cucumber beds. Lyuba weeded short beds. What beds did Alla weed?
Answers: 1. Alla weeded long beds with tomatoes. 2. Alla weeded long beds with cucumbers. 3. It is not known which beds Alla weeded. 4. Alla weeded short beds with cucumbers. 5. Alla weeded short beds with tomatoes.
11. Misha is more fun than Oleg. Misha is sadder than Petya. Petya is sadder than Pasha. Roma is more fun than Pasha. Which of the schoolchildren is more fun - Oleg or Roma?
Answers: 1. Oleg is not as funny as Kolya. 2. Kolya is not as cheerful as Oleg. 3. Oleg is as cheerful
as Kolya. 4. It is impossible to say which of the boys is more fun - Oleg or Roma.
12. Misha, Gena, Kolya and Nikita learned to play musical instruments: someone - two years on the violin, someone - two years on the flute, someone - three years on the flute, someone - four years on the trumpet ... Misha did not study for three or four years. Gena did not learn to play the violin and trumpet. Nikita did not study for two or four years. Kolya did not study for three or three years. What musical instrument and how many years did Misha study?
Answers: 1. Misha studied violin for two years. 2. Misha studied flute for two years. 3. It is not known
what musical instrument and how many years Misha studied. 4. Misha studied flute for three years. 5. Misha studied trumpet for four years.
3. Results
At the beginning of the school year (the first week of September), 54 sixth graders participated in group experiments based on the "Conclusions" methodology, and 52 sixth graders at the end of the school year (the twentieth of April). It should be noted that only 49 sixth graders took part in September and May, - their results are reflected in the table.
The results of solving problems by sixth graders (1 - 4, 1 - 8 and 1
ber and April (in%)
Table
12) methodology "Conclusions" in Septem-
Problems September April
1 - 4 85,7 61,2
1 - 8 63,3 77,1
1 - 12 44,9 55,1
The results of both series of experiments indicate that the developed methodology quite clearly differentiates schoolchildren according to the level of formation of logical actions associated with the construction of reasoning.
So, in September, problems of only the first degree of complexity of various types (i.e., problems 1 - 4) were solved by 85.7% of schoolchildren (with unsuccessful solution of problems 5 - 12), problems only of the first and second degrees of complexity (i.e., problems 1 - 8) - 63.3% of schoolchildren (with unsuccessful solution of problems 9 - 12), problems of three degrees of difficulty (i.e., all the problems proposed on the form) - 44.9% of schoolchildren.
In April, the results changed: problems of only the first degree of difficulty were solved by 61.2%, problems of only the first and second degree of difficulty -77.6% of schoolchildren, problems of three degrees of complexity - 55.1% of schoolchildren.
4. Conclusion
The conducted research, - it was associated with the development and testing of diagnostic methods, -showed that during the period of study in the sixth grade, the number of schoolchildren who solve only the simplest problems decreases - by 24.5% (from 61.2% to 36.7% ), and the number of schoolchildren who are able to solve problems of the first and second degrees of difficulty increases - by 14.3% (from 77.6% to 91.9%), and who have coped with problems of the third degree of difficulty - by 10.2% (from 55 , 1% to 65.3%).
Such data allows us to conclude that teaching in middle school programs that meets the requirements of the new FSES creates favorable conditions for the further formation of logical actions in schoolchildren that underlie the ability to draw conclusions that consistently follow from the proposed judgments.
In general, the results obtained allow us to note that for the diagnosis of such an important cognitive competence as the ability to build logical reasoning, it was possible to develop and test the "Conclusions" method, which, as the work showed, is suitable for performing group examinations of middle school students, in particular sixth graders.
In the future, it is planned to use the methodology under consideration to conduct meaningful monitoring of the formation of this competence in the course of teaching children in secondary school. The data of such monitoring are necessary to achieve important psychological and pedagogical goals: determining the features of the formation of logical actions for constructing reasoning in each grade of secondary school, identifying the influence of teaching methods, the content of curricula, as well as certain learning conditions on the formation of the ability to reason.
References
1. Getmanova A.D. Logic: a tutorial. Moscow: Higher school, 1986. 288 p. [in Russian].
2. Davydov V. V. The theory of the developing training. Moscow: Intor, 1996. 497 p. [in Russian].
3. Zak A.Z. The thinking of younger school students. St. Petersburg: Sodeystviye, 2004. 828 p. [in Russian].
4. Zak A. Z. Development and diagnostics of thinking of teenagers and high school students. Moscow: Obninsk: IG-SOCIN, 2010. 350 p. [in Russian].
5. Ilyenkov E.V. Dialectical logic: essays on history and theory. Moscow: Science, 1984. 427 p. [in Russian].
6. Kondakov N.I. Logical dictionary. Moscow: Science,1975. 720 p. [in Russian].
7. Federal state educational standard of basic general education. Moscow: Prosveshchenie, 2019. 61 p. [in Russian].
