Calculation of the difficulty index (ITER). Doughness and test tasks What is the difficulty of test

An indicator of the difficulty of test task as the most important dust factor.

Kraschinnikova Galina Gennadievna

cand. Ped. Sciences, Magadan branch of the RSUGU

One of the main characteristics of the test task is its difficulty. The level of difficulty tasks, as well as the level of preparedness of the tested - these are latent parameters that are not directly observation. In order to evaluate these parameters, you need to use closely related indicators. When testing students' knowledge as an indicator, test tasks themselves are. The task occurs: convert the values \u200b\u200bof the indicators into the values \u200b\u200bof the latent parameters. There are various approaches to solving this task. Classical and modern testing theories offer their methods for estimating latent parameters.

The traditional measure of the difficulty of tasks in the classical theory of tests for many years remains the ratio of the correct answers to this task to the total number of subjects in the group. The easier it is the task, the higher the percentage of those who coped with this task.

However, this definition carries a semantic inaccuracy: an increase in the number of statistical indicator indicates a decrease in the level of difficulty of task, and vice versa. Therefore, recently attempts are made to introduce new difficulty units. The classical measure of difficulties is replaced by the opposite and represents the share of incorrect answers in the group of subjects, which, in our opinion, more accurately reflects the meaning of the "Difficulty Difference" parameter.

Modern testing theory - Item Response Theory (IRT) - based on the Theory of Latent-Structural Analysis (LSA) created by P. Lazarsfeld (LSA). In IRT, in contrast to the classic theory, the latent parameter is interpreted not as a constant value, but as a continuous variable. IRT methods can be classified by the number of parameters used in them. The most famous single-parameter model of Rasha, two- and three-parametric models of A. Birnbauma are most well known.

Georg Rush posted on the same scale and the level of preparedness is tested and the level of task difficulty, introducing a total unit of measurement for them - logite. One logit of the task difficulty is equal to the natural logarithm of the relationship of the incorrect responses to this task to the share of the correct answers.

Despite the fact that IRT has recently received widespread, it, however, has many drawbacks. In particular, when testing academic achievements, significant discrepancies between the calculated values \u200b\u200band empirical data are noted. A high correlation is also proved (about 0.9) between the results obtained by the Rush model and the results obtained by the classical methods. This fact allows us without prejudice to the accuracy of calculations to use the methods of classical test theory to characterize the difficulty of test tasks.

Although the classical formula for calculating the difficulty of the task is quite convenient for execution and subsequent interpretation of the results obtained, in our opinion, it is not deprived of some subjectivism: the difficulty of the task is directly depends on the sample of the tested. In this regard, consider another look at the level of the level of difficulty of the test task, which, although it is not widespread, but presents for us some interest.

To approach the essence of the latent parameter "Difficulty", we turn to the classification of levels of learning of knowledge adopted in the pedagogical literature. It can be seen quite objective increase in the degree of difficulty of assimilation for each subsequent level of learning. Thus, we can conclude the existence of a direct relationship between the levels of assimilation and the levels of the difficulty of tasks corresponding to each level of assimilation. This allows us to identify such concepts as "the level of difficulty" and the "level of assimi" in relation to test tasks. Taking the basis of the classification of V.P. Bespalco, we highlight four levels of difficulty: "student", typical, heuristic, creative.

Currently, expert methods are widely used in pedagogy. Therefore, an expert assessment of the level of difficulty test tasks is worthy of as one of the options for evaluating the rate of difficulties. For example, in the work of A.P. Ivanova is a description of such an assessment, when, before the start of the test experiment, several experts are invited to evaluate the difficulty of tasks of all test options. To obtain an expert assessment, the author leads a list of eight factors with the relevant criteria for estimation from 1 to 5 points each.

In a well-compiled test, the difficulty of task should not influence neither the form nor the organization of testing. The performance indicator depends only on the content and level of preparedness of the tested. True, it is believed that the degree of difficulty tasks is influenced by the location of this task in the test structure. In this case, it is recommended to use several test options that are characterized by the setting of job location. V.S. Avanesov believes the basic principle of developing the content of pedagogical tests the increasing difficulty of test tasks. In his opinion, only after determining the degree of difficulty, the task has a chance to become a test. Prior to that, it remains just a task in test form.

The inclusion in the test of a large number of assignments of the average difficulty increases its reliability, but leads to a decrease in its substantive validity. A test consisting of easy tasks inspecting minimum knowledge cannot provide ideas about the real level of knowledge. Selection of test tasks to a high degree of difficulty can contribute to strengthening motivation in school, but can affect in the opposite direction. Thus, tests from difficult tasks also distort the test results. In addition, the test content should vary depending on the level of preparedness of group groups. The difficulty of the dough for weak students is noticeably different from the level of difficulty of the test offered to strong students.

According to A. Anastasi and S. Urbina Choosing the level of difficulty tasks depends on the purpose of the test, the test indicators are supposed to use. For subject-oriented tests, the difficulty of tasks should be at the level of 0.8-0.9. Determining in terms of the level of difficulty asking for its informativeness, the authors show that the most informative task with an average level of difficulty is 0.50.

Thus, we can conclude that tasks with an average level of difficulty have the greatest differentiating ability. And, if the purpose of testing is the differentiation of the tested, comparative assessment of their knowledge level, then the most simple and most difficult tasks should be excluded from the test. If the assignment of the test is determined whether the studied adequately as a certain set of competencies is necessary to transition to the next stage of learning, it may be both the easiest and most difficult tasks in it.

Bibliographic list

1. Avanesov V.S. Application of tasks in test form in new educational technologies // School technologies. - 2007. - № 3. - P. 146-163.

2. Anastasi A., urba S. Psychological testing. - St. Petersburg. : Peter, 2002. - 688 p.

3. Bespalko V.P. CONDITIONAL PEDAGOGICAL TECHNOLOGY - M.: Pedagogy, 1989. - 192 p.

4. Ivanov A.P. Systematization of knowledge in mathematics in profile classes using tests. - M.: Fizmatknigig, 2004. - 416 p.

5. Ingensp K. Pedagogical diagnostics. - M.: Pedagogy, 1991. - 240 s.

6. Kim V.S. Analysis of test results in the Rasch Measurement process // Pedagogical measurements. - 2005. - № 4. - P. 39-45.

7. Rasch G. Probabilistic Models for Some Intelligence and Attainment Tests. - Chicago & London, 1980. - 199 p.

Validity. To improve the quality of test materials, starting from the stage of their design and development, an examination is already used.

Test tasks satisfying "external" formal requirements (correctness of the wording, logical consistency, adequate form, etc.) are not always qualitative to consider such assignments of a priori or a posteriori as an effective means of assessing the level of training of trainees.

Test tasks (tests) measure the properties of certain samples of potential subjects. Examination of the quality of tasks and the entire test is an assessment of not only of its element (distractors, their number, etc.), but also the test, its structures, relationships with other tasks.

The quality of vocational education is both the level, the volume of knowledge, their systematic, sustainability, value, prospects, fundamentality, the ability to receive and build new knowledge, apply them to solve problems. Effective quality control Education is also impossible without relevant and operational information on the level of training. It is necessary to apply high-quality test materials that reliably evaluating training achievements.

The use of principles and means of qualimetry, system analysis focuses on integrity, emergenism, compatibility, adaptability and other system signs of tests. Test quality estimate the measure of compliance with the characteristics of test tasks and based on their tests of tests. Integrated test assessment (test) as a whole.

Test tasks, the entire test has structural elements characterized by internal and external properties, with its structure. These properties affect the definingly many factors:

the general population and sampling of the subjects;
quality indicators;
features of testing technology;
features of processing, analysis of test results (in particular, used mathematic-statistical apparatus and heuristic procedures);
qualifications of experts and the professionalization of the expert group;
system approach to testing and testing.

Complete accounting properties allows you to design "desired" tests - tests with deficient (according to testing hypothesis) by qualities, statistical properties, for example, "parallel" tests, subtests, etc. It is also necessary to take into account the measure of differentiation, the ability of tasks (tests) to differentiate the test, for example , the ability to differentiate relative to the maximum or minimum level of learning.

Such characteristics such as difficulty (complexity) of tasks and its distinguishable ability are paramount to analyze. The difficulty of task reflects the level of its feasibility in this statistical sample (standard). It is often estimated by the ratio of the number of correctly fulfilled the task to the number of test samples.

The closer this indicator to 1, the higher the difficulty of the task, the closer to 0, the lower its difficulty.

As an indicator, the difficulty of task is used diffuses U. Calculated by the formula:

where n is the number of correctly answering the task, n is the total number of subjects (samples).

When building a criterion-oriented test, to increase its difficulty add to higher difficulty tasks, to reduce - include more devices of low difficulty.

The difficulty of task (test) happens:

subjective, related to circumstances of the type of time limit, knowledge of technology, understanding of the conditions (formed the knowledge, skills and skills), mental readiness, etc.;
objective (statistical) associated with the share of the tests of the sample, solved the task (test).

The difficulty is a relative value depending on the age-related, professional and other differences of the subjects, therefore these features affect test results, on the reliability of the test. Measures to align the conditions (minimize such impacts on tested) are needed. To do this, use the directional picking, standardization of the testing procedure, i.e. An effective diagnostic technique is necessary, leading to the "golden middle", a balance sheet of difficult, average and simple tasks.

Too hard tasks worsen the statistical characteristics of the estimation (little decisive, failure on a difficult task may affect the solution of other tasks, etc.). Too simple tasks lead to a little-informative monotonous results, which make it difficult to analyze the quality of learning, cause a negative attitude of the test to test and testing.

Example. The criterion-oriented test should be complete, reflecting the entire volume of knowledge, planned to absorb. The normative-oriented test may contain only those sections that are required for differentiation by the level of training achievements of trainees, for example, 50-70% of the tasks of the average difficulty (Fig. 4.1, Fig. 4.2).

In criterion-oriented attestation tests, the main part of the tasks is easier, which limits the percentage of untesting students.

Example. If the projected percentage of incredited should be no more than 10%, and the criterion of "failure" - 70% (fulfilled only up to 30% of the tasks - not certified), in the test it should be included from 70% of light tasks, satisfied 90% of the tested (Fig. 4.2) .

Fig. 4.1.

Fig. 4.2.

Therefore, it is important to choose a test that is optimal for the complexity of tasks, groups of complexity, the structure of the test. If the question is correctly answered by most subjects, it is usually placed at the beginning of the test, and the rest of the questions - as they grow their difficulty. Such a job location allows you to estimate the threshold of difficulties for each subject, its place in the ranking.

Practical testing shows: the most reflects the individual level of knowledge, skills, the skills of the subjects using the tasks of the average difficulty with the inclusion of a small number of other tasks.

There is a special characteristic called differing ability Tasks. It shows the measure of the efficiency of distinguishing the tested in groups: mastered by educational material and did not master them.

The closer R to zero, the smaller the distinguishing of the task of the subjects, mastered or not mastered by educational material.

The closer R to the value -1, the same is also more distinguishes, but in inverse order: the tests that mastered the material, they answered wrong, and vice versa. This is a rare case, it testifies, for example, about gaps in the methodology, its spontaneity.

In the previous article, nine principles of developing the content of pedagogical tests were considered. In the focus of this article - the tenth principle: the increasing difficulty of tasks of the test.

If the pedagogical test is briefly determined as a system of tasks of evenly increasing difficulty, it will become clear that the difficulty of tasks is the most important, let's say, the test for the resulting indicator. A lot of school leaders believe that their teachers are able to "come up" in a short time any "tests". In fact, you can think of quite a lot of tasks in test form. And not at all tests, but only tasks. They cannot be included in this test until the famous measure of their difficulty, as well as other characteristics. Measure difficulty is checked empirically. From this requirement it becomes clear the obligation of the preliminary empirical check of each task, before the start of testing. In the process of verification, many tasks do not maintain the requirements for them, and therefore are not included in the test. The first requirement for test tasks: The task test should differ in terms of the level of difficulty, which follows from this previously determining the test and the principle under consideration.

The attentive reader probably already caught the difference in vocabulary of three as if "imperceptibly" the basic concepts of the theory of pedagogical measurements introduced here: the concept of pedagogical test, tasks in test form and test task. Requirements for the first of them have already been considered in the article "Defining Pedagogical Test" (ESS No. 30, August 1999).

Requirements for the second concept is better to introduce now, making it at least briefly listed them in order not to distract from the main topic of the article. The following requirements are presented to tasks in test form:

Brevity;

Manufacturability;

Correct form;

The correctness of the content

Logical form of statements;

The same response assessment rules;

Availability of a specific place to respond;

The same instruction for all subjects;

The correct position of the elements of the task;

Avanesov V.S. Basics of pedagogical theory of measurements // Pedagogical measurements, 1, 2004. P. 17.

A detailed interpretation of these requirements will follow in the following articles, and now I would like to draw the reader's attention to the fact that there is no requirement for a known task difficulty, while the test is presented to the test and test task. From reflections on this and previously published material, you can make two outputs. The first thing is that there is no place for assignments in the dough with an unknown difficulty measure. And the second is that not all proposed tasks in test form can become test tasks: these are different concepts. In the first concept, the requirements of content and form are the most significant. The test tasks primarily makes the requirement of a certain difficulty, something that is clearly not required for tasks in test form. You can repeat that the tasks have a chance to become test only after an empirical test of their difficulty, on typical groups of subjects.

An indicator of the difficulty of test and test tasks is meaningful and formal at the same time. Content, because in a good test, the difficulty may depend only on the difficulty of maintaining tasks and on the level of preparedness of the subjects themselves. While in a bad test, the results are noticeably influenced by the form of tasks (especially if it is not adequate to the content), poor testing organization, if there are covenants, information leaks. Special mention in this regard deserves the harmful practice of aimed training for students in a single state exam. Teachers who were engaged in such a matter, the Minister of Education of Russia of 1907, I. Tolstoy called the Natasyvators. But teachers are to blame for less. The erroneous system of "Egypt" is to blame, which pushes such an erroneous practice. What is the control, such and education.

The formal component of the indicator of the indicator of difficulties occurs when testing testing as the confrontation process of the subject with the assigned task. The outcome obtained at the same time is useful to consider as a result of such confrontation. With a simplified interpretation of each case of the presentation of the task often, two outgoings are necessarily considered: the victory of the subject with the right decision of the task, where he receives one score, or defeat, for which zero points is given. An assessment of the result of the confrontation depends on the ratio of knowledge of the knowledge tested to the level of the task, from the elected unit of measurement of knowledge and from a predetermined rule (Convention) - what to consider the "victory" of the subject, and whether a draw is admissible to speak the language of sports.

The principle of increasing difficulties is used in the presentation of the content of many textbooks and benefits, especially on those learning disciplines, which are built on a cumulative principle, which means: knowledge of subsequent elements of the course explicitly depends on the knowledge of previous educational elements. Such a construction is inherent in textbooks in mathematics, logic, foreign languages, statistics, technical and many other sciences. They have previously studied concepts are actively used in subsequent topics. Therefore, it is necessary to study such disciplines only from the very beginning, and without spaces.

Most authors, especially foreign, do not make differences between the concepts of "difficulty" and "complexity". Many test developers are the same. However, there are works in which these concepts are determined differently. For example, A.N. Zakharov and A.M. Matyushkin noted that the degree of difficulty of learning tasks does not coincide with its complexity. The degree of complexity of the educational material is characterized by a real (objective) saturation of the learning task and the form of its presentation, and the degree of difficulty always implies the correlation of the learning material to be assimiced with the previously learned learning materials and intellectual possibilities of students (1).

L.N. Landa explained the difficulty of the learning task by the fact that students often do not know those operations that need to be produced to find a solution. If the system of operations to solve some class tasks to be called a solution method, then, in its opinion, the difficulty is associated with the ignorance of the method, with ignorance, as needed to think in the decision process, as in which sequence should be acting with the terms of the problem (2). The emerging difficulties are explained by the fact that the teacher often tries to give knowledge about the content of the studied and much less cares about how to think, arguing (ibid). Such interpretation intersects with an idea about the relationship of the complexity of the task with the number of operations that must be made to achieve success. These definitions of difficulties and difficulties are, for the most part, psychological; They are useful in psychological analysis of test tasks.

The traditional measure of the difficulty of each task for many years was the proportion of the correct answers in the subject group depicted by the symbol P j, where the index j indicates the number of the task of interest (1, 2, etc.). For example, if the correct responses of the test on the third test task are estimated by one point, and wrong with zero, then the value of the parameter P 3 can be found from the elementary ratio:

P 3 \u003d R 3 / N,

where R 3 means the number of correct answers to this task, and n is the total number of subjects in the group. The general formula for calculating the share of the correct answers to any task (j) has a view

p j \u003d r j / n

Indicator p j. Long used as a measure of difficulty in the so-called classical test theory (3). Later it was aware of the meaningful inaccuracy contained in it: after all, the increase in the value of P j does not indicate increasing difficulties, but, on the contrary, to increase ease, if such a word can be used. Therefore, in recent years, with an indicator, the difficulties of tasks began to associate opposite statistics - the share of incorrect answers (Q j). This proportion is calculated from the ratio of the number of incorrect answers (WRONG WRONG - wrong English) to the number of tests (N):

q j \u003d w j / n

It is naturally assumed that P j + q j \u003d 1. In the classical theory of tests, many years were considered only the empirical performance indicators. In the new versions of psychological and pedagogical theories of tests, more attention began to be given to the nature of the mental activity of students in the process of performing test tasks of various forms (4).

The test content cannot be only light, medium or difficult. Here is fully the well-known idea of \u200b\u200bthe dependence of the results of the method used. Easy tasks of the test create only the visibility of knowledge of students, because they are checked minimal knowledge. In this regard, it can be noted that the orientation of the federal education management body for checking the minimum level of knowledge does not give, and cannot, even by definition, give an idea of \u200b\u200bthe real level of knowledge, i.e. Give that information that has long been needed by society and management authorities. Distorting the results of testing and selection of knowingly difficult tasks, as a result of which majority of schoolchildren are understated points. Orientation for difficult tasks is often considered as a means of strengthening motivation to study. However, this tool acts ambiguously. Some difficult tasks can push to study, others - push off from it. Such orientation distorts the results and as a result, reduces the quality of the pedagogical dimension. If the test is built strictly from the tasks of increasing difficulty, this opens the way to create one of the most interesting scales of measurement - the scale of L. Gutman.

When determining the test, it was already noted that all tasks of the test, I would like to emphasize, regardless of the content of those, sections and from training disciplines, are arranged in the order of increasing difficulties. Until recently, the recommendation to include in the test more tasks of the average difficulty is justified from the point of view of determining the reliability of measurement according to the so-called formulas. Classical test theory. The methods that exist in this theory, the test reliability assessment provide reduction in reliability when inclusive in the test of light and difficult tasks. At the same time, the passion for the assignments of one average difficulty leads to serious deformation of the test content: the latter loses the ability to properly display the content of the discipline under study, in which there is always light and difficult material. Thus, in pursuit of abstract theoretically high reliability, the meaningful validity of test results is lost. The desire to raise the validity of the test results is often accompanied by a decrease in their accuracy. This phenomenon in theory is known as a paradox of the theorist American psychometric f.lord

If weak, according to the preparedness, a group of students is tested, it turns out that the difficult tasks of the test simply do not work, because no student can answer them correctly. Such tasks from further data processing are withdrawn. In adaptive control systems, they are not offered. The test content for weak students will noticeably differ from the test of the test for strengths. In the latter, on the contrary, easy tasks do not work, since all those who know the subjects for easy tasks are responsible correctly. Thus, the content of traditional test varies significantly depending on the level of preparedness of those groups of students, to measure the knowledge of which is a test.

The optimal display of the content of the educational material into the test tasks of the required level of difficulty involves the possibility of choosing a suitable form. The test content is expressed in one of the four main molds. This is: 1) tasks with a choice of one or more correct answers from among the proposed; 2) tasks of an open form, where the response test adds itself, in the place allotted for this; 3) Setting conformity, and 4) tasks to establish the correct sequence of actions.

Literature

1. Zakharov A.I., Matyushkin A.M. Problems of adaptive learning systems // Cybernetics and learning problems. - M.: Progress, 1970.- 389С.

2. Landa L.N. Algorithmization in training. M.., Enlightenment, 1966

3. Gulliksen H. Theory of Mental Tests. N - Y. Wiley.1950 - 486 p. and mn. Dr.

4. Tatsuoka, K.k. Item Construction And Psychometric Models Appriate for Constructed Response. Prinston, N-J, 1993. - 56 pp; Frederiksen, N., Mislevy R.J., BEJAR I. J. (EDS). Test Theory for a New Generations of Tests. Lawrence Erlbaum Ass. Publ. 1993, Hillsdale, N-J, 404PP.and etc .

If the pedagogical test is briefly brief as a system of tasks of increasing difficulty, it will become clear that the difficulty of tasks is the most important, let's say, the test for the resulting indicator. A lot of school leaders believe that their teachers are able to "come up" in a short time any "tests" can I myself read the order at school, where teachers were prescribed for three days to imagine "tests". In fact, you can come up with how many sets of tasks in test form (and this is not tests). They cannot be included in the present test until the well-known measure of the difficulty verifiable. From this requirement it becomes clear the obligation of the preliminary empirical check of each task, before the start of testing. In the process of checking, many tasks (usually more than half) do not withstand the requirements for them and therefore are not included in the test. The first requirement for test tasks: The task test should differ in terms of the level of difficulty, which follows from this previously determining the test and the principle under consideration.

The attentive reader probably already caught the difference in the vocabulary of three as if "imperceptibly" the basic concepts of test theory introduced here: pedagogical test, tasks in test form and test task. Requirements for the first of them have already been considered in the article "Defining Pedagogical Test" (ESS No. 30, August 1999).

the correctness of the content
logical form of statements;
correct form;
brevity;
availability of a specific place to respond;
the correct position of the elements of the task;
the same response assessment rules;
the same instruction for all subjects;
adequacy instructions form and content content.

A detailed interpretation of these requirements will follow in the following articles, and now I would like to draw the reader's attention to the fact that there is no requirement for a known task difficulty, while the test is presented to the test and test task. From reflections on this and previously published material, you can make two outputs. The first thing is that there is no place for assignments in the dough with an unknown difficulty measure. And the second is that not all proposed tasks in test form can become test tasks: these are different concepts. In the first concept, the requirements of content and form are the most significant. The test tasks primarily makes the requirement of a certain difficulty, something that is clearly not required for tasks in test form. The tasks have a chance to become test only after an experienced, say stricter, empirical verification of their difficulty, on typical groups of subjects.

An indicator of the difficulty of test and test tasks is meaningful and formal at the same time. Meaningful indicator, because in a good test, the difficulty may depend only on the content and on the level of the preparedness of the subjects themselves, while in a bad test of the results, it is noticeable to influence the form of tasks (especially if it is not adequate), poor testing organization, if available Capabilities, information leakage. Special mention in this regard deserves a controversial practice of aimed preparation for centralized testing.

The formal component of the performance of the indicator of difficulties occurs when testing as a process of confrontation of each subject with each task offered to it. The outcome obtained at the same time is useful to consider as a result of such confrontation. With a simplified interpretation of each case of the confrontation of the subject with the next task, only two outcomes are usually considered: the victory of the subject with the right decision, where he receives one score, or defeat, for which zero points is given. The assessment of the result of the confrontation depends on the ratio of knowledge of the knowledge of the task tested to the level, from the chosen unit of measurement of knowledge and from a previously adopted rule (convention) - what to consider the "victory" of the subject and is permissible to draw a draw on the language of sports.

L.N. Landa explains the difficulty of the learning task by the fact that students often do not know those operations that need to be produced to find a solution. If the system of operations to solve some class tasks to be called a solution method, then, in its opinion, the difficulty is associated with the ignorance of the method, with ignorance, as needed to think in the decision process, as in which sequence should be acting with the terms of the problem (2). The emerging difficulties are explained by the fact that the teacher often tries to give knowledge about the content of the studied and much less cares about how to think, arguing (ibid). Such interpretation intersects with an idea about the relationship of the complexity of the task with the number of operations that must be made to achieve success. These definitions of difficulties and difficulties are, for the most part, psychological; They are useful in psychological analysis of test tasks.

The traditional measure of the difficulty of each task for many years was the proportion of the correct answers in the subject group depicted by the PJ symbol where the index j indicates the number of the task of interest (1, 2, etc.). For example, if the correct responses of the test for the third test task are estimated by one point, and wrong - zero, then the value of the P3 indicator can be found from the elementary relationship

where R3 means the number of correct answers to this task, and n is the total number of subjects in the group. The general formula for calculating the share of the correct answers to any task (j) has a view

PJ indicator. Long used as a measure of difficulty in the so-called classical test theory (3). Later, the meaningful inaccuracy contained in it was aware: after all, the increase in the value of PJ indicates not to increase difficulties, but, on the contrary, to increasing the ease, if such a word can be used. Therefore, in recent years, with an indicator, the difficulty of tasks began to associate opposite statistics - the share of incorrect answers (QJ). This proportion is calculated from the ratio of the number of incorrect answers (WRONG WRONG - wrong English) to the number of tests (N):

It is naturally assumed that PJ + QJ \u003d 1. In the classical theory of tests, for many years, only empirical differences of difficulties were considered. In the new versions of psychological and pedagogical theories of tests, more attention began to be given to the nature of the mental activity of students in the process of performing test tasks of various forms (4).

When determining the test, it was already noted that all tasks of the test, I would like to emphasize, regardless of the content of those, sections and from training disciplines, are arranged in the order of increasing difficulties. Until recently, the recommendation to include in the test more tasks of the average difficulty is justified from the point of view of determining the reliability of measurement according to the so-called formulas. Classical test theory. The methods that exist in this theory, the test reliability assessment provide reduction in reliability when inclusive in the test of light and difficult tasks. At the same time, the passion for the assignments of one average difficulty leads to serious deformation of the test content: the latter loses the ability to properly display the content of the discipline under study, in which there is always light and difficult material. Thus, in pursuit of theoretically high reliability, the meaningful validity of test results is lost. The desire to raise the validity of the test results is often accompanied by a decrease in their accuracy.

Home\u003e Tests

Article 7. Distance difficulty and test tasks

In the previous article, nine principles for the development of the content of pedagogical tests were considered. Today we continue to consider the tenth principle - the increasing difficulty of test tasks. If the pedagogical test is briefly brief as a system of tasks of increasing difficulty, it will become clear that the difficulty of tasks is the most important, let's say, the test for the resulting indicator. A lot of school leaders believe that their teachers are able to "come up" in a short time any "tests" can; I myself read the order at school, where teachers were prescribed for three days to imagine "tests". In fact, you can come up with how many sets of tasks in test form (and this is not tests). They cannot be included in the present test until the well-known measure of the difficulty verifiable. From this requirement it becomes clear the obligation of the preliminary empirical check of each task, before the start of testing. In the process of checking, many tasks (usually more than half) do not withstand the requirements for them and therefore are not included in the test. The first requirement for test tasks: The task test should differ in terms of the level of difficulty, which follows from this previously determining the test and the principle under consideration. The attentive reader probably already caught the difference in the vocabulary of three, as it were, "imperceptibly" the basic concepts of test theory of tests introduced here: pedagogical test, tasks in test form and test task. Requirements for the first of them have already been reviewed in the article "Defining Pedagogical Test" (ESS No. 30, August 1999). Requirements for the second concept is better to introduce now, making it at least briefly listed them in order not to distract from the main topic of the article. The following requirements are presented to tasks in test form:

correctness of the content; logical form of statements; correct form; brevity; Availability of a specific place to respond; The correct position of the elements of the task; the same response assessment rules; the same instruction for all subjects; Adequacy instructions form and content content. A detailed interpretation of these requirements will follow in the following articles, and now I would like to draw the reader's attention to the fact that there is no requirement for a known task difficulty, while the test is presented to the test and test task. From reflections on this and previously published material, you can make two outputs. The first thing is that there is no place for assignments in the dough with an unknown difficulty measure. And the second is that not all proposed tasks in test form can become test tasks: these are different concepts. In the first concept, the requirements of content and form are the most significant. The test tasks primarily makes the requirement of a certain difficulty, something that is clearly not required for tasks in test form. The tasks have a chance to become test only after an experienced, say stricter, empirical verification of their difficulty, on typical groups of subjects. An indicator of the difficulty of test and test tasks is meaningful and formal at the same time. Meaningful indicator, because in a good test, the difficulty may depend only on the content and on the level of the preparedness of the subjects themselves, while in a bad test of the results, it is noticeable to influence the form of tasks (especially if it is not adequate), poor testing organization, if available Capabilities, information leakage. Special mention in this regard deserves a controversial practice of aimed preparation for centralized testing. The formal component of the performance of the indicator of difficulties occurs when testing as a process of confrontation of each subject with each task offered to it. The outcome obtained at the same time is useful to consider as a result of such confrontation. With a simplified interpretation of each case of the confrontation of the subject with the next task, only two outcomes are usually considered: the victory of the subject with the right decision, where he receives one score, or defeat, for which zero points is given. Assessment of the result of confrontation depends on the ratio of knowledge of the knowledge tested to the level of the task, from the elected unit of measurement of knowledge and from a pre-adopted rule (Convention) - what to consider the "victory" of the subject and is permissible to draw a draw, if we speak the language of sports. The principle of increasing difficulties is used in the presentation of the content of many textbooks and benefits, especially on those learning disciplines, which are built on a cumulative principle, which means: knowledge of subsequent elements of the course explicitly depends on the knowledge of previous educational elements. Such a construction is inherent in textbooks in mathematics, logic, foreign languages, statistics, technical and many other sciences. They have previously studied concepts are actively used in subsequent topics. Therefore, it is necessary to study such disciplines only from the very beginning, and without spaces. Most authors, especially foreign, do not make differences between the concepts of "difficulty" and "complexity". Many test developers are the same. However, there are works in which these concepts are determined differently. For example, A.N. Zakharov and A.M. Matyushkin noted that the degree of difficulty of learning tasks does not coincide with its complexity. The degree of complexity of the educational material is characterized by a real (objective) saturation of the learning assignment and the form of its presentation, and the degree of difficulties always implies the correlation of the learning material to be assimiced with the previously learned learning materials and intellectual possibilities of students. L.N. Landa explains the difficulty of the learning task by the fact that students often do not know those operations that need to be produced to find a solution. If the system of operations to solve some class tasks to be called a solution method, then, in its opinion, the difficulty is associated with the ignorance of the method, with ignorance, as needed to think during the solution, as in which sequence should be acting with the terms of the task. The emerging difficulties are explained by the fact that the teacher often tries to give knowledge about the content of the studied and much less cares about how to think, reason. Such interpretation intersects with an idea about the relationship of the complexity of the task with the number of operations that must be made to achieve success. These definitions of difficulties and difficulties are, for the most part, psychological; They are useful in psychological analysis of test tasks. The traditional measure of the difficulty of each task for many years was the proportion of the correct answers in the subject group depicted by the PJ symbol where the index j indicates the number of the task of interest (1, 2, etc.). For example, if the correct responses of the test for the third task of the test are assessed with one point, and the wrong - zero, the value of the P3 indicator can be found from the elementary ratio:

Where RSUB\u003e 3 means the number of correct answers to this task, and n is the total number of subjects in the group. The general formula for calculating the share of the correct answers to any task (j) has a form:

Indicator p j. Long used as a measure of difficulty in the so-called classic test theory. Later, the meaningful inaccuracy contained in it was aware: after all, the increase in the value of PJ indicates not to increase difficulties, but, on the contrary, to increasing the ease, if such a word can be used. Therefore, in recent years, with an indicator, the difficulties of tasks began to associate opposite statistics - the share of incorrect answers (Q j). This share is calculated from the ratio of the number of incorrect replies (W J - from the English of the word WRONG is wrong) to the number of tests (N):

It is naturally assumed that P j + q j \u003d 1. In the classical theory of tests, many years were considered only the empirical performance indicators. In new options for psychological and pedagogical theories of tests, more attention began to be given to the nature of the mental activity of students in the process of performing test tasks of various forms. The test content cannot be only light, medium or difficult. Here is fully the well-known idea of \u200b\u200bthe dependence of the results of the method used. Easy tasks of the test create only the visibility of knowledge of students, because they are checked minimal knowledge. In this regard, it can be noted that the orientation of the federal education management body for checking the minimum level of knowledge does not give, and cannot, even by definition, give an idea of \u200b\u200bthe real level of knowledge, i.e. Give that information that has long been needed by society and management authorities. Distorting the results of testing and selection of knowingly difficult tasks, as a result of which majority of schoolchildren are understated points. Orientation for difficult tasks is often considered as a means of strengthening motivation to study. However, this tool acts ambiguously. Some difficult tasks can push to study, others - push off from it. Such orientation distorts the results and as a result, reduces the quality of the pedagogical dimension. If the test is built strictly from the tasks of increasing difficulty, this opens the way to create one of the most interesting scales of measurement - the scale of L. Gutman. When determining the test, it was already noted that all tasks of the test, I would like to emphasize, regardless of the content of those, sections and from training disciplines, are arranged in the order of increasing difficulties. Until recently, the recommendation to include in the test more tasks of the average difficulty is justified from the point of view of determining the reliability of measurement according to the so-called formulas. Classical test theory. The methods that exist in this theory, the test reliability assessment provide reduction in reliability when inclusive in the test of light and difficult tasks. At the same time, the passion for the assignments of one average difficulty leads to serious deformation of the test content: the latter loses the ability to properly display the content of the discipline under study, in which there is always light and difficult material. Thus, in pursuit of theoretically high reliability, the meaningful validity of test results is lost. The desire to raise the validity of the test results is often accompanied by a decrease in their accuracy. If weak, according to the preparedness, a group of students is tested, it turns out that the difficult tasks of the test simply do not work, because no student can answer them correctly. Such tasks from further data processing are withdrawn. In adaptive control systems, they are not offered. The test content for weak students will noticeably differ from the test of the test for strengths. In the latter, on the contrary, easy tasks do not work, since all those who know the subjects for easy tasks are responsible correctly. Thus, the content of traditional test varies significantly depending on the level of preparedness of those groups of students, to measure the knowledge of which is a test. The optimal display of the content of the educational material into the test tasks of the required level of difficulty involves the possibility of choosing a suitable form. The test content is expressed in one of the four main molds. It:

tasks with the choice of one or more correct answers from among the proposed; The tasks of the open form, where the responser's response adds itself, in the place allotted for this; assignment assignments; Tasks for establishing the correct sequence of actions.

Article 8. Logical requirements for testing test

Test tasks differ from inside not only in content, but also in the style of building a sentence. From the test task, the ambiguity is completely eliminated when, for example, the fabulous supplement is easily confused with a direct addition in the vinegenous case (like "mother loves daughter"). In addition, sometimes the test task is mistakenly identified with the mystery. Although in both cases there is a task to find the correct answer, the noted similarity is not enough to identify the riddles and test task. There are signs that are clearly separated by them. For the riddle, the most important, specifically distinctive feature is metaphoricity, puzzle formation. It is known that the metaphorical expression becomes when it is not in direct, but in a figurative value. The test task, on the contrary, is always autologically: in it, words are used only in their direct, immediate meaning. Autoological style is the one about which V.Mikovsky wrote: "We are looking for a speech with accurate and naked." The test task is formulated from precise terms and never contains metaphors, but unnecessary words and unnecessary sign. An example of a metaphorically formulated task in an open test form: "The father of Russian physiology is considered to be ___________. In previous articles, pedagogical requirements for the test content were considered. Now it's time to consider the logical principles for determining the content of the pedagogical test. Logically, such laws of proper thinking as the laws of identity, non-contradiction, excluded third and sufficient foundation are known. This allows you to allocate such basic properties of proper thinking as certainty, consistency, validity. With regard to test theory and practice, these general properties of proper thinking acquire the functions of specific regulators of test activities, as a result of which the importance of principles acquire. Consider them in more detail. 1. Definition of test content The definition of the test of the test is formed by the subject of pedagogical measurement. In the case of a homogeneous test, the question arises about the confidence that all tasks of the test check the knowledge precisely on a certain academic discipline, and not for some other. It often happens that the correct answers to some tasks require knowledge of not only the discipline of interest, but also a number of others, commonly related and preceding academic disciplines. The proximity and connectedness of which make it difficult to accurately determine the subject affiliation of the measured knowledge. For example, there are many mathematical knowledge in physical calculations and therefore the mathematics is usually included in the physical knowledge system, which is used in solving physical problems. Failure in mathematical calculations breeds failure in responses to the tasks of the physical test. The negative score is placed, respectively, for ignorance of physics, although the subject allowed mumatic sense errors. If there are many such tasks in such a test, which require not so much physical knowledge for the correct solution, how many skills perform complicated calculations, this may be an example of inaccurately determined testing in physics. The less the intersection of knowledge of one academic discipline with knowledge of the other, the definitely expressed in the test the content of the academic discipline. Definition of content is required in all other tests. In heterogeneous test, this is achieved by means of explicit allocation of tasks of one academic discipline in a separate scale. At the same time, tasks are often found, well-working not only on one, but also two, three and even more scales. In any test task, it is determined in advance, which is definitely considered an answer to the task, with which degree of completeness should be the correct answer. It is not allowed to determine the concept through the transfer of elements that are not included in it. Consider an example of the open-end task, where the subject is offered, on the point of docking, to supplement the approval by its answer: the point is what does not have ______________. In consciousness, the question arises: "Doesn't what? The answer, by Euclide, the "point does not have parts", but it is just a case of unsuccessful determination of the content, both tasks and the very concept of the point. As you know, the point does not have, for example, colors, taste, odor and much more, and not Only parts. A significant role in the formation of the test as the system plays the requirement of the logical correctness of tasks included in the test. As noted in the literature, the logical correctness in the formulation of test tasks is achieved under the following conditions:

2. Constability of tasks The consistency of the content of tasks requires that judgments simultaneously arise relative to the same thought, at the same time asserting and denying it. Unacceptably the existence of two exclusive answers to the same test of the test. If the test instructions are given: "Circle the circle number of the correct answer", and then in one of the answers it is argued that there is no correct answer, then this is generated an example of the inconsistency of the test developer thinking. In some tests there are answers that are generally not related to the content of the task. The same answers are fairly easily recognized by the subjects as erroneous, and therefore the test turns out to be ineffective. To increase the efficiency, the test is pre-tested on a typical sample of subjects. And if such answers are found to the tasks that the subjects do not choose at all, such answers from the test are deleted. Because they do not perform the function of the so-called distractors designed to distract the attention of those who do not know the subjects subject to the correct answer. In addition, such distractors are harmful to the test, for reduce measurement accuracy (but about it in the articles where the reliability of tests will be considered). 3. Significance The validity of the content of test tasks means that they have the basis of truth. Rationalth is related to arguments that can be presented in favor of a particular wording of test tasks. In the absence of evidence arguments in favor of the correctness of the formulated task, it is not included in the test, nor under any pretext. The same happens if at least one counterprovement occurs during the expert discussion, or a condition is allowed in which this statement may be ambiguous or false. The idea of \u200b\u200bvalidity of the test of the test is closely intertwined with the principle of meaningful correctness of test tasks, which has already been said in the previous article. Recall that the test includes only the content of the academic discipline, which is objectively true and that is amenable to some rational argument. Accordingly, controversial points of view, quite acceptable in science, are not recommended to include in the content of test tasks. The unusual content of test tasks differs from the incorrect of their wording. Neisetness, as noted above, is determined by the corresponding response, while incorrectly formulated task can produce the answers as correct and incorrect, or even cause bewilderment. This can also include inacciable or ambiguously formulated tasks that generate several correct or conditionally correct answers. Hence the need to introduce additional conditions for truth, which lengthens the assignment itself and complicates its semantics. The incorrect of the wording usually finds out in the process of discussing the content of tasks with experienced expert teachers. The success of such a discussion is possible when creating an appropriate cultural environment, where only structural and tactful judgments are allowed. Alas, the experience convinces that this is not often found. Meanwhile, only a joint and friendly discussion of materials by developers and experts can generate the atmosphere of finding the best test options. This search is almost infinite, and there is no truth here in the last instance.

In addition to the three listed properties of the logically correct thinking, we note another requirement for test tasks, which is as formal as if substantive. This is the requirement of brief test tasks. The brevity is ensured by the careful selection of words, symbols, graphs that allow minimum tools to achieve a maximum of clarity of the semantic content of the task. Reints are excluded, low-touch, rarely used, as well as unknown symbols for students, foreign words, impercepting the perception of meaning. The approximate amount of words in the task is five or nine, but, in general, the smaller the better. For example:
Power is
1) Vector
2) Scalar

Well, when the tasks contain no more than one apparent offer. As noted by the famous linguist A.M.Peshkovsky, accuracy and ease of understanding are growing as the verbal composition of the phrase and an increase in its wordless subsoil decreases. The smaller words, the less misunderstandings. A good way to achieve shortness of task is to ask something one. Frequently encountered cases of weighting tasks to find something to find, decide and then also explain adversely affect the quality of the task and test in general, although from a pedagogical point of view it is easy to understand the reason for the formulation of this kind of tasks. If the student decides something in such tasks without a teacher, then something explains something to him, then conjugates an objective method with subjective, plus to this - difficulties with estimates in solving the question of which to set a score. In contrast, one of the important test requirements - to have pre-developed points for the payment of points without the participation of the teacher.

Article 9. Knowledge as a subject of test control

What does it mean to know? Here, my friend, what is the question.
Goethe. Faust.

Knowledge We now know about knowledge about not many more things that they knew about them in the time of Goethe. Pedagogical science did not do with this phenomenon, or it was done very little, oddly enough. Confirmation of this is the absence of pedagogy in textbooks to determine the concept of "knowledge" and related materials. Meanwhile, the formation of a knowledge system in students is the most important goal of the educational process, the cardinal problem of pedagogy. In turn, the lack of knowledge of the knowledge system on educational discipline makes it impossible to create a full-fledged test for measuring knowledge. It was such a case once a place when checking the test version on the history of the fatherland for centralized testing. The history of the question of knowledge goes into the depths of the centuries. The first documentary evidence of the systematic research of knowledge is associated with the names of Pythagora and Socrates. Pythagoras inherited from Egyptian priests, where he studied, the so-called esoteric tradition of attitudes towards knowledge. In accordance with this tradition, knowledge should be transmitted by the teacher from the mouth to the mouth, and not everyone, but only worthy (dedicated) to students. Socrates, on the contrary, the teacher never considered himself, was a supporter of open, publicly available knowledge. In their dialogues, Socrates has repeatedly set the question of the essence of knowledge, the relationship of knowledge with ignorance, ignorance, with the mind, morality, opinion, with ideas and skills. In contrast, openly praised themselves to the sophists, Socrates did not hurry to show his understanding. He was not a debate, though, it would seem, often immersed in the discussion of a particular issue. It is possible to find out its skills to find out the essence of the subject through a series of consecutive issues, in the process of a relaxed conversation, Socrates called, joking, "obequious" art. The results of his search history has kept for us in the works of "Dialogues" of Plato and "Memories" of Xenophon. For example, in the "Menon" dialogue of Plato, the concepts of "knowledge" and "opinion" are distinguished. This is done on the example of the knowledge of the road to the city and opinions on the knowledge of the road. The opinion is characterized by the person correctly suggests where this road, but never went on it, and does not know it (1; T.1, p. 406.). Knowing the road is different from the opinion of it because the person has already walked on it, and has, so to speak, empirical experience. It also notes that according to practical significance, the opinion may not give way to know. The one who has a faithful opinion about where the road passes can lead to this city of people no less successful than the one who knows this road. Socrates put the current question about the types of knowledge, in response to which his interlocutor allocates two types of knowledge. To the first one, he refers geometry, astronomy, an account and music, and the second - craft of a shoemaker and other crafts; "After all, they are nothing but knowledge of how to manufacture shoes, wooden utensils or other items" (2, p. 225-226). Now we can say that the first of these species is more like the theoretical, and the second is on practical knowledge. It would be possible to expect that the essence of knowledge is expressed in the scientific definitions of this concept. But there is a disappointment. For example, in the philosophical encyclopedic dictionary, knowledge is determined by general words: as a proven by social and historical practice and certified by the logic, the result of the process of cognition of reality, adequately reflected in the consciousness of a person in the form of ideas, concepts, judgments, theories. Another definition of knowledge is too general and short: knowledge is information about the world and about the human itself (3; 190). Knowledge and mind It is believed that knowledge is associated with the mind. But since the time of Herclite, Efessky, it was known that "Multivissal Mind does not teach." Some knowledge can be purchased at low, and some are only with a high mind. If you go from the use of the word "mind" to his scientific equivalent "Intellect", then it can be noted that the rate of learning material is depends on the intellect, as well as the results of knowledge testing. Usually the higher the intellect, the more knowledge. Above and test points, but not always. It all depends on the content of the tasks. In each school class, intellectually developed children can meet, who, however, know little due to reluctance to learn well. Intellect of children, according to some sources, about 36 percent is associated with the level of intellectual development of mothers, and only by 26 percent - with the level of the same development of fathers. In modern foreign theories, such a factor of intelligence is known as the "critical mind". As if anticipating these theories, the famous Russian doctor V.M. Behterev said back in 1905 that the school should take care of not so much about the template memorization of ready-made forms borrowed most of the classics, how much about the development of an amateur person with a critical intelligence and amateur relation to the surrounding reality. At the adoptive exams in universities, they often had to hear about the desire of some examiners to check not only knowledge, but also the "skills to think". In other words, the question of checking not only knowledge, but also the intelligence of applicants. It is useful to recall that the content of tests for measuring knowledge is significantly different from the content of the intellectual test. This idea opens the road to a subjectivity when checking knowledge and too often turns into a baton against those applicants that do not take, on the eve of exams, paid advice from those most teachers-examiners, and part-time tutors. Ignorance The difficulties of determining knowledge suggests the search for the answer to the opposite question - what is ignorance? The thought of ignorance comes to mind, as the absence of the necessary information. If a person knows that he does not know, doesn't know knowledge about such an ignorance? This is quite aware knowledge of a lack of knowledge on a particular problem. In science, such a cognitive situation is called problematic. Two distinguished molds of ignorance are distinguished: 1) ignorance in the sense of not awareness and 2) ignorance in the sense of insignificant properties of acquired knowledge. The first form is a temporary state that encourages information from finding information, and this is its motivating side. The second form of ignorance is characteristic of poor-quality education, which, speaking by the words of Spencer, contributes to the spread of pleasant delusions than bitter truths. In this regard, it is appropriate to mention the attempts of learning differentiation, such as mathematics, for two options "A" and "B". (four). This is a departure from the practice of a single basic education for the country, which was previously offered to the state school to the young generation. If earlier students' knowledge differed depending on their personal efforts and the quality of teachers and schools, now the knowledge will also differ from the variant of the knowledge of the knowledge. In the introduction of these options, the spread of pleasant delusions from a large part of students on their knowledge will be delivered to the stream. Education will remain a full average by the title, but according to the content of acquired knowledge it will become incompatible. Thus, the differentiation of training options actually opens up the possibility of reducing the requirements for the level of education, this time by the federal authority by the management of education. But is it necessary to reduce children and their parents, society, state? - Not a departmental question. In the educational process, the knowledge gained almost always, to some extent, is distorted by students by virtue of the habit of simplifying the perceived material and the lack of ownership of the conceptual apparatus. You can even talk about psychological patterns and, in this regard, about a marked difference of knowledge proposed by students from the knowledge absorbed by them really. Especially noticeable these differences can be at low intelligence and low students' motivation. Another reason for the distortion of the proposed knowledge among senior schoolchildren is extensive outlining, distracting them from understanding the essence of the issued issues. The latter circumstance encourages, for example, the author of these lines in working with teachers to give a structured ability of lectures in their course and visualize the supply of all major materials, which gives a positive learning effect (5). You can talk about this form of ignorance that is not realized, and therefore it refers to implicit knowledge. It's like the form of "ignorance about knowledge." Philosopher M. Balani believes that implicit knowledge is not fixed in a logical way and manifests itself (transmitted) only in the process of human communication. The form of implicit knowledge can also be attributed to intuition, which is defined as a way to comprehend the truth by discretion without justifying. A much worse case when a person thinks he knows, but does not know that he does not know. This case is quite frequent. He precedes delusions, and under certain circumstances - and to ignorance. Ignorance It is unlikely randomly Socrates opposed knowledge is not ignorance, but ignorance, claiming that there is one thing only - knowledge, and there is one evil - ignorance. There is a question - why? Maybe because ignorance does not interfere with the acquisition of knowledge, and sometimes contributes to this, while ignorance is a valid evil in the form of admission to knowledge. One cause of ignorance allocated T. Gobbs "There is one defect of the mind," he wrote, which consists of immunity to the teaching. This disadvantage, apparently, follows from the false opinion of the appropriate person, as if it already knows the truth about the object that it is about ... The direct cause of immunity to know is, therefore, the prejudice, and the direct cause of the prejudice is a false opinion ... About his own knowledge "(6) Pupils with this kind of prejudice there are, apparently, in each school. Ignorance occurs when the unification of uneducation, non-ultimate and non-competitance. It's not just a separate person. Ignorance arises as a result of a social model of society. It is not temporary or random; There is intentional and conscious ignorance, entrusted with the help of a well-established mechanism intended to contribute to the celebration of ignorance (7). As recalled V.M. Bekhterev, "... The most important thing that saved us from ignorance," he wrote, - this is some residue free of high-speed time, which we are based on urgency, especially in the senior class of gymnasium, dedicated to reading outsiders. " Nearby more others suffer from knowledgeable and talented people. In history, the author of the pedagogical composition "City of the Sun" T. Campanella (1568-1639). He spent 27 years in imprisonment (where he wrote this book) on charges that "he knows what he was not taught." Nowadays, the time to plant knowledgeable people for such dates in prison seems to have ceased, but they have learned by bureaucratic tricks to move them aside.

Article 10. Knowledge as a subject of test control

Concept of knowledge In the previous article, there was an analysis of three concepts: knowledge, ignorance, and ignorance. Of these concepts, pedagogical testing relieve only knowledge; At the same time, ignorance is considered quite simplified as an alternative to knowing. Although it has already been shown that since the Socrates, knowledge is not ignorance, but ignorance. The level of ignorance and ignorance can hardly be measured due to the non-specificity and infinity of the world, which is formed by a particle with denials "not" with various words. While the concepts of "know" and "lead" can be correlated with a specific set of elements forming many features of this property of the subjects. Thus, the main complexity of measuring knowledge lies in the general conceptualization of this phenomenon. This is exactly what the pedagogical science clearly lacks. In the absence of a general concept of knowledge, test developers begin to build their own understanding of the essence of knowledge, in relation to the academic discipline, with the teaching they deal. Thus, they become - or begin to read themselves - experts. There are signs on the basis of which surrounding believe; What experts know what it means to know: this is the level and quality of the common and vocational education obtained by them, the experience of teaching, performance performance, scientific and methodological works, recognition from managers. Unfortunately, in Soviet and especially in the post-Soviet time, a considerable number of incompetent persons have learned to acquire the reputation of experts, without being such, essentially. This was done by building a system of mutually beneficial relations with higher figures, protecting lime dissertations, writing collective "scientific papers", as well as unceremonious borrowing from the works of knowledgeable people. This is a kind of Hunweist, famous for the latest history of China, after which the country was thrown back in many directions, for decades. There is a lot, if not all, I had to redo it again. Similar period has come in Russia now. For the purposes of pedagogical dimension, it is conceptually distinguished by four main areas of knowledge: knowledge of the world, knowledge of people, knowledge of oneself, and knowledge of ways of activity. Further, these four spheres are useful to divide on the natural scientific and humanitarian sphere of knowledge, and then share by industry practitioners, according to the sciences. For example, scientific knowledge is divided into philological, mathematical, historical, physical, chemical, etc. But not all knowledge is scientific. In addition to them, there are layers of dock and indecent knowledge, objective and subjective. Advanced knowledge differ from scientific ways to obtain, storage and transmission. Scientific methods provide relatively greater objectivity, confirmability and reproducibility of knowledge. The incidence of such activities such as magic, astrology, numerology, chiromantia, and the doctrine of living space, levitation and clairvoyance, and many others are possible. The controversial is the status of religious knowledge, although their existence in religious texts and the impact on the consciousness of many people cannot be questioned. The main criterion for the differences in donuclear knowledge from scientific is the measure of their rational substantiation: the higher such validity, the more knowledge claims to be scientifically. Rational cognition is a complex inherent in a person to reflect reality by thinking. It is characteristic of it: support for the results of sensual reflection, indirectness of feelings; abstractness and generalization of emerging images; Reproduction of objects at the level of entities, internal natural links and relationships. The basic forms of rational knowledge include concepts, judgments, conclusions, laws, hypothesis, theories. Educational knowledge is noticeably stated from the process of scientific knowledge, are ordered, coented, expressed by the language accessible for students and, finally, are presented in the textbook in a variety of tasks accompanying the textbook and the educational process. In a sense, educational knowledge is objective and subjective at the same time. Being objective generally outlined in scientific texts and in educational materials, they turn into subjective knowledge in the process of their assimilation. At the same time, there is almost a subjective distortion of the proposed knowledge. Knowledge can also be objectively true and objectively false. False knowledge arises as a result of distortion, and, moreover, due to intentional propaganda from interested groups, parties, associations, etc. Objectively false knowledge of the formation organs do not distribute in principle, with the exception of some of the changing ideologues and political myths, combined with objective or partially objective knowledge in the field of history, philosophy, religion, political science, and the like attributable to humanitarian sciences. Objectively false knowledge exists in the form of ignorance, psevdannation and just lies. A lot of false knowledge was in history courses. Therefore, it is not by chance that history textbooks had (and apparently still) change more often than others. Some knowledge may be meaningful or unconference. In the latter case, you can talk about not understanding the essence. On the contrary, understanding, according to Z.I. Kalmykova is a mental penetration into the essence of the reality, abstraction and generalization of its patterns. It also highlights several levels of understanding. The first level is elementary - as an act of reading the text, in the process of which the transition from graphic signs to words and suggestions is occurring. The second level of understanding is lexical - the links between the words and the corresponding subjects and the phenomena of reality are established, without taking into account the content of the text as a whole. At the third level - syntactic - the meaning of words depending on their formal logical bonds in the proposal (1, p. 84-105). Knowledge, Culture, Morality and Education The concept of knowledge cannot be considered outside of cultural issues. "Culture, true culture," the French scientist and writer Jean Rostan wrote, - much less than it is customary to think is related to the accumulation of actual data. It is rather a famous ability to understand, refract, think. Be cultivated is not to start your brain with numbers, dates, names. This is the level of judgment, logical demand, desire for evidence, understanding the complexity of things and difficulties of the problems. This is the ability to doubt, to the sense of measure, to the modesty of judgment, and tolerance for ignorance. This is the confidence that "you can never be right to finish." The connection of knowledge and culture is regulated by the so-called sense of measure. It is not by chance in ancient China a perfect person rightly considered the one who knew how to dwell on the fact that he is unknown. An example of a violation of the noted The senses can be found in the latest history of the Soviet pedagogy. In it, each element of training knowledge, in the framework of the so-called raising learning, was to form a devotion to famous ideas, persons and unshakable conviction in the correctness of all offered (often forced) knowledge, which was often done to The same, in vulgarized form. It is unlikely that anyone will argue with the fact that the study of sciences does not always have a positive educational impact on students. Education without education is dangerous, both for personality, and for society. In previous articles, the conviction of the ancient Egyptian priests and members has already been The Order of Pythagoreans is that for the benefit of the company in the secrets of sciences Decode only worthy, decent people. The same thought is confirmed in the so-called hermetic philosophy, which emphasizes that the falsely understood "progress" of mankind creates the titans of the mind and the figmeys of the Spirit, people with a dull conscience and sensuality (2). The most clearly this situation was expressed by the Russian philosopher I. A. Ilyin. "Education without education does not form, but it dismisses and spoils a person, because it gives its disposal vital opportunities, the technical skills with which he, is a bad, begins to abuse." Classification of types of knowledge There are many attempts to classify the types of knowledge, but not yet any one that would fully satisfy practical needs. For example, in the knowledge of I.Ya. Lerner included terms and concepts, facts, laws and theories, methodological knowledge (knowledge of methods), appraisal knowledge, abstract and specific knowledge, empirical and theoretical knowledge (3). Attempting to build a classification of knowledge, using several bases of division, made E.T. Dryeckova (4). Hierarchy of species of knowledge of schoolchildren can be found in the work of V.P. Maxakovsky. The highest place in his hierarchy is occupied by knowledge of scientific laws, patterns. Then follow the knowledge of scientific theories, paradigms, concepts, hypotheses, general and single concepts, terms, facts. Close this series of representations (5, p. 6). In the already classical work of B. Blum and his colleagues (6), three spheres of educational activities and hierarchy of levels of preparedness are distinguished. IN cognitive The sphere is formulated such levels: 1. Knowledge to reproduce the facts, list the names of studied phenomena and objects. Here everything is based on the reproduction of remembered information; 2. Understanding those knowledge that are reproduced. A good way to test understanding - to ask students to reproduce the material in your own words, bring examples; 3. Application of knowledge, especially in a new situation; 4. Ability to analyze and synthesize the signs; 5. Ability to evaluate, make a general conclusion. This is the highest level of preparedness. In sphere psychological Allocated:

perception of individual indications, signs, responding to them;

manifestation of interest in the necessary information;

organization, structuring received information, systematization;

the skill hierarchizes the received information on levels.

IN Psychomoter sphere:

the idea of \u200b\u200bhow to act;
readiness to perform actions under the guidance of the teacher;
self performing actions.

These well-known classifications, the author of this article adds its own list of knowledge species, formulated solely to solve the tasks of the pedagogical dimension. But about it - in the next article.

When preparing the collection, materials were used

doctor of Pedagogical Sciences, Professor Vadim Avanesov

Prepared by A.N. Osmarin,

methodist of the educational and methodological center

department of Education of the Janka Riegospandine,

Chapter First Tests: History and Theory

1. The depths of the centuries ..........................................................1

2. Concrete 19th century ............................................................... 4

3. Incident on the 20th century ............................................................ .6

4. Tencies of the 20th century ...................................................... ... 8

5. Soviet period ........................................................... 11

6.The these years .................................................................... ... 14

7. System of complete learning of knowledge ..................................17

Chapter Second Tests: Theory and Methods of their Development

1. Invoice theory. Attitude to tests ............................ ... 20

2. Determination of the pedagogical test .............................. ..23

3. Starty tests .....................................................26

4. Receiving tests ................................................. ..29

6. Principles of the development of the test of the test ........................ ..37

7. Power test and test tasks ............................... .40

Document

Often, students ask a question: why do we need to study the story of sociology, know what happened forever in the past and is hardly useful in current activities? Whether it is not better to immediately start with the study of the methodology and the principles of the development of social technologies,