The structure of any particular ability consists of universal and general qualities necessary for various types of activity, as well as special qualities, without which success cannot be ensured in any one type of activity.

Conditions for successful mathematical activity

V.A. Krutetsky established that for the successful completion of mathematical activity it is necessary:

• To have a penchant for doing mathematics, actively and positively relates to it to the point of passionate enthusiasm.
• To have such character traits as diligence, organization, independence, purposefulness, perseverance and stable intellectual feelings.
• To have mental states favorable for its implementation during the activity.
• Have a certain stock of knowledge, skills and abilities in this area.
• To have certain individual psychological characteristics in the sensory and mental spheres that meet the requirements of this activity.

The first four points can be seen as general properties necessary for any activity, but the fifth point is specific, showing success specifically in mathematical activity.

General abilities make it possible to ensure comparative ease and productivity in obtaining knowledge and in various activities, they can be designated as giftedness. But specific differences in giftedness are manifested in the direction of the interests of students, why some are interested in mathematics, others in music, others in literature, etc.

About the psychological test

The psychological test is designed to determine the coefficient of mathematical intelligence in children of adolescence, youth and adults (from 14 to 50 years old). Contains 29 tasks that require mathematical calculations, understanding of simple mathematical rules, logical thinking. In each task, subjects must choose the correct answer from four options.

The duration of the test is 15 minutes.

Each correct answer is worth one point. The coefficient of mathematical intelligence is determined using a special evaluation table. The scale assessment has six gradations:

• very good- coefficient of mathematical intelligence> 130 points,
• Good- coefficient of mathematical intelligence = 120 points,
• above- coefficient of mathematical intelligence = 110 points,
• below the average- coefficient of mathematical intelligence = 90 points,
• short- coefficient of mathematical intelligence = 80 points,
• very low- coefficient of mathematical intelligence< 70 баллов.

Demo version of the complex

Numerical tests are tasks based on the need for calculations - from basic mathematical and arithmetic to complex tasks in dozens of actions. The variety of numerical tests is explained by the need to evaluate applicants for different areas business, positions and roles within different companies. Numerical tests are always used by employers, as they provide the most objective assessment of a candidate's ability to analyze digital information and the ability to draw conclusions from it.

What is a math (numeric) test?

These tests may vary. For representatives of mathematical professions (engineers, economists, accountants, IT), this will be a more serious test. But when hiring representatives of other professions, such tasks can also be used. They allow you to identify the level of attentiveness, concentration, the ability to quickly make calculations, work with graphs or tables.

The famous Eysenck test (IQ) is often used to determine numerical abilities, since a large proportion of the questions presented in it are numerical tasks.

How to prepare for numerical tests?

When preparing, we recommend that you focus on numerical tests from the following developers: SHL, Talent Q, IBM Kenexa, Saville, HT Line. More than 95% of the largest employers in Russia and the world use these math tests.

Read more about number tests in our big article

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Diagnostics of mathematical intelligence Test of mathematical analogies ( V. N. Druzhinin )

Tasks included in the test of mathematical analogies must meet the requirements for any ability tests: be standard, homogeneous in structure, be equivalent or ordered by difficulty. In addition, they must satisfy the requirements of theoretical validity: to diagnose mathematical ability as such. To this is added the requirement of environmental validity of the test: its compliance with the scientific and practical task.

Since the most important requirement that we set for the tasks was their applicability in school practice, as test material we used tasks developed by A. G. Gaishtut, aimed at developing in students such mental operations as analysis, synthesis, analogy, and generalization.

From the author's point of view, “mathematics, as you know, is a demonstrative or deductive science ... But the proof is opened with the help of plausible reasoning, with the help of conjecture. The two types of reasoning - demonstrative and plausible - complement each other. The tasks proposed by Gaishtut are formulated on the basis of material from the mathematics course from 4th to 10th grade and consist of 5 series: 4th grade, 5th grade, 6-7th grades, 8th grade, 9 -10th grade. Solving problems of each type requires knowledge educational material, but, in addition, the ability to mentally discover the relationship between the spatial and sign elements of the conditions of the problem and the ability to perform mathematical operations with mathematical structures. Thus, the tasks proposed by Gaishtut can be used to diagnose the level of development of thinking, the mental ability to operate with abstract structures on mathematical material.

Consider a sample task:

1. Find Electricity XIII

Unknown mathematician?

These problems include 4 elements, one of which is unknown. It is required to find an unknown element. The solution can be found only when the auxiliary problem is solved: the ratios of the elements of the initial conditions of the problem are identified. Between the elements "electricity" and XIII the relation of identity: the number of letters in the word "electricity" is 13, between the elements "electricity" and "mathematician" - the relation of difference: a different number of letters. Therefore, it is required that the unknown be in relation to identity with the element "mathematician" and in the same relation of quantitative difference with the element XIII, as the elements "mathematician" and "electricity". The unknown element is the number IX. Therefore, the subject must perform the operations of comparing elements, highlight the type of relationship - quantitative differences and draw a conclusion by analogy. As you can see, the relationship between the elements of the problem is arithmetic, the subject is required to know the digital notation and the ability to read and count, as well as the knowledge of arithmetic operations. Therefore, this task corresponds to the level of preparation of a 4th grade student. Thus, despite the fact that the problem contains specific material and its solution requires standard knowledge and skills, it is possible to successfully solve this problem only with a certain level of development of mental ability, operating with symbolic (spatial-sign) structures. Consequently, the tasks satisfy the requirement put forward by us: to diagnose simultaneously the level of development of productive mathematical thinking (discovery of new relationships) and reproductive mathematical thinking (finding a solution using knowledge). Since the test material must comply curriculum high school, the test was divided into 5 subtests: 1) subtest for grade 4, 2) subtest for grade 5, 3) subtest for grade 6, 4) subtest for grades 7-8 and 5) subtest for 9th-10th grades.

Now we present the results of standardization of the test of mathematical analogies (TMA).

The total number of subjects was 350. The number of subjects in each class was 50. The following mean and variance values ​​were obtained, which characterize the difficulty and differentiating power of the test.

It turned out that the subtests for the 5th and 9th grades caused difficulties for students. However, it should be noted that testing students in grades 9-10 regular school took place after class. A survey of students showed that they were tired and had no interest in completing tasks.

When testing in other classes, the values ​​of x" were obtained, close to 5 points (5 correctly solved problems), which indicates the equivalence of tasks. The variances of the average score do not differ significantly. Therefore, all subtests have approximately equal differentiating power.

Consider indicators of differentiating power and difficulty individual tasks on the example of a subtest for grades 7-8.

The coefficient of difficulty of individual tasks is within 0.25< р <0,71.

Thus, it can be argued that the test tasks belong to the group of tasks of medium difficulty.

Let us present the difficulty data of the tasks for all subtests, where the difficulty is equal to the ratio of the number of subjects who solved the test to the total number of subjects.

Corresponding results of assessing the differentiating power of problems in units of standard deviation (?).

The proposed test of mathematical analogies "Heistut's Problems" (TMA) can be used to diagnose the level of development of general intelligence and mathematical abilities. The test has sufficient internal and external validity. The success of the test is related to the level of development of the ability to mentally solve problems, conceptual and spatial thinking. The test should be tested during control and independent work, as it is standardized in these situations. The inclusion of the test in examination papers should be avoided. TMA should be applied after passing the appropriate educational material, that is, at the end of the year (4th, 5th, 6th grades) or 2 years of study (7-8th, 9-10th grades). The tasks of the test are highly homogeneous. If the subjects solve more than 5 tasks, we can assume that they have a high level of development of the ability to think in analogies. If less, then a definite diagnosis should not be made. It is necessary to conduct a re-examination after some time and use other similar tests as an addition.

Literature

1. Gaishtut A. G. Mathematics in logical exercises. Kyiv: Radyansk school, 1985. 192 p.

2. Gurevich K. M. Intelligence tests in psychology. // Questions of psychology. 1982. No. 2.S. 28-32.

3. Krutetsky V. A. Psychology of mathematical abilities. Moscow: Education, 1968. 432 p.

4. Kulagin B.V. Fundamentals of professional psychodiagnostics. L., 1984.

5. Matelsky P.V. Psychological and pedagogical foundations of didactics of mathematics. Minsk: Higher School, 1977, pp. 149-160.

6. Piaget J., Inelder B. Genesis of elementary logical structures: classification and seriation. M.: Foreign Literature, 1963. 446 p.

7. Psychodiagnostics. Theory and practice / Ed. N. F. Talyzina. M.: Progress, 1986. 207 p.

8. Guilford J. T. The nature of human intelligence. N.Y.: McGraw-Hills, 1967. 538 p.

9. witzlack G. Grundlagen der Psychodiagnostik. Berlin, 1977.

Test of mathematical analogies

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This is probably the only test of its kind to determine the mathematical ability, in which you do not need to solve any problems. The point is completely different.

The fact is that every person by nature, to one degree or another, has a sense of quantity. This is when, looking at several groups of objects, you can determine by eye which of them is larger.

So, psychologists have found that the more developed the natural sense of quantity, the greater the mathematical potential a person has. People with high mathematical potential learn the exact sciences more easily and quickly, and also reach a higher level in understanding mathematics.

During the test, for a short time, you will be shown two groups of circles of different colors. When they disappear, you will need to decide which color circles had more.

Click on the button below to start the test. To exit the test mode, press the ESC button on the keyboard, but note that the test will be interrupted and it will need to be started again.

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