Test for mathematical potential. Psychological test "Analytical mathematical abilities. Form A" Check mathematical abilities

This is probably the only math test of its kind that does not involve any problem solving. 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 one 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 master the exact sciences more easily and quickly, and also achieve a higher level of understanding of mathematics.

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

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

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Perhaps most young people already know about testing for employment, especially those who are planning to “storm” corporate bastions. For middle-aged and older specialists, such a system is most likely a novelty, because they still saw the socialist “distribution” of future jobs, and even now the Western personnel evaluation system is used by many companies, but not yet everywhere. One of the most common tests is , the result of this test will give the employer an idea of ​​your analytical skills.

The selection used in companies and corporations, even if it has some shortcomings, is still the most objective assessment system, because all candidates solve the same questions. Subjectivism can arise at the interview stage, where personal impressions decide a lot, but testing is absolutely objective. In this case, it may turn out that you will be passing through, and not remotely.

Using Math Tests

When applying for a job, a mathematical test is used by all branches of Western companies, as well as by most domestic corporations. Employers are satisfied with the tests because they reduce the time spent on assessing each applicant, especially since the competition at Gazprom or Lukoil can include hundreds of applicants per position. Tests, especially their online versions, allow you to instantly process the results, compare them with any target group, and analyze them in any way you like.

For the candidates themselves, employment tests are a chance to apply for a high position. For example, Talent Q's dynamic scoring system reviews each candidate's answer and gives the next one based on accuracy and time spent. It is quite possible, by giving quickly correct answers, to reach a maximum level of complexity comparable to the results of managers and top managers.

Auditing, consulting companies, banks, representatives of the FMCG, IT, fuel and energy sectors use testing, and these are such well-known brands as: BAT, Google, L'Oreal, Raiffeisen Bank, Johnson&Johnson, Nestle, Danone, Lukoil, Mars, inBev, JTI, Apple, Cisco, JP Morgan, Rosneft, Unilever, Deutsche Bank, McKinsey&Company, Deloitte Touche Tohmatsu, KPMG, Ernst&Young. The list could take a long time, because these are only the most well-known companies, and there are hundreds and thousands of companies with lower financial indicators. It is possible to get a job in one of these corporations, but you need to pass a math test well when applying for a job, and go through several more selection stages.

Composition of a math test

Mathematical (numerical) tests are created by two leading companies: SHL and Talent Q. SHL was the first to create such tests, Talent Q was the first to introduce an online system for intelligent selection of tasks for each applicant.

The standard composition of a math test is approximately 15 tasks, which must be solved in 15-20 minutes. There is enough time; every educated person can solve an example of a mathematical test when applying for a job, but the presentation of the material is somewhat unusual. The data is presented in the format of graphs, charts, tables, below are the answer options, and there may be 4-5 of them, or maybe several dozen with small steps so that it is impossible to choose the correct option.

The problems themselves involve the use of simple arithmetic operations; to solve them you will need to calculate percentages, work with tables, histograms, charts, perform currency conversions, and calculate shares and dividends. Interview tests are often transformed for a specific company or industry, that is, for accountants it will be necessary to solve postings, for financiers - to calculate dividends, etc.

Sometimes, at complex levels, a large amount of information is given, and you need to find the data that is needed for calculations, while ignoring the rest. A large table, several graphs, or a histogram combined with a graph may be given. The options are different, but they make working with numbers much more difficult. and should not be very easy, especially when it comes to employment in a top company, because their employees will need to make complex decisions in the workplace, and for this they need to be able to count, make logical conclusions, and generally work with large amounts of information.

Many experienced job applicants pass the math test easily and score in the 80-90 percentile, but they trained for this or took so many attempts that the tests themselves turned into a training process. It must be admitted that it is easier to talk about success than failure, although on specialized forums visitors who are quite truthful often report failed tests.

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

The tasks included in the mathematical analogies test must meet the requirements for any ability tests: be standard, homogeneous in structure, 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 for the ecological validity of the test: its compliance with the scientific and practical task.

Since the most important requirement we placed on 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 is known, is a demonstrative or deductive science... But the proof is revealed with the help of plausible reasoning, with the help of a guess. The two types of reasoning – demonstrative and plausible – complement each other.” The problems proposed by Gaishtut are formulated on the basis of material from a mathematics course from 4th to 10th grade and consist of 5 series: 4th grade, 5th grade, 6-7th grades, 8th grade, 9th -10th grade. Solving problems of each type requires knowledge of the educational material, but, in addition, the ability to mentally detect relationships between spatial and symbolic elements of the problem conditions 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 using mathematical material.

Let's look at a sample problem:

1. Find Electricity XIII

Unknown mathematician?

These tasks include 4 elements, one of which is unknown. You need to find an unknown element. A solution can be found only when the auxiliary problem is solved: the relationships between the elements of the initial conditions of the problem are identified. Between the elements “electricity” and XIII there is a relation of identity: the number of letters in the word “electricity” is 13, between the elements “electricity” and “mathematician” there is a relation of difference: a different number of letters. Consequently, it is required that the unknown be in the same relation of identity with the element “mathematician” and in the same relation of quantitative difference with element XIII as the elements “mathematician” and “electricity”. The unknown element is the number IX. Consequently, the subject must perform operations of comparison of elements, identify the type of relationship - quantitative differences, and make a conclusion by analogy. As you can see, the relationships between the elements of the problem are arithmetic; the test subject is required to have knowledge of digital notations and the ability to read and count, as well as mastery 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, this problem can be successfully solved only by having a certain level of development of thinking ability, operating with symbolic (spatial-sign) structures. Consequently, the tasks satisfy the requirement we put forward: to simultaneously diagnose the level of development of productive mathematical thinking (discovering new relationships) and reproductive mathematical thinking (finding a solution through the application of knowledge). Since the test material must correspond to the high school curriculum, the test was divided into 5 subtests: 1) subtest for 4th grade, 2) subtest for 5th grade, 3) subtest for 6th grade, 4) subtest for 7th grade. 8th grade and 5) subtest for 9-10th grade.

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 educational class was 50. The following values ​​of means and variances were obtained, characterizing 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 of students in grades 9-10 of a regular school took place after the end of classes. A survey of students showed that they were tired and uninterested in completing assignments.

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

Let's consider the indicators of differentiating power and the difficulty of individual tasks using the example of a subtest for grades 7-8.

The difficulty coefficient 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 these task difficulties for all subtests, where the difficulty is equal to the ratio of the number of test takers who solved the test to the total number of test takers.

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

The proposed test of mathematical analogies “Gaishtut 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 tests and independent work, since it is standardized in these situations. Inclusion of the test in examination papers should be avoided. TMA should be applied after completing the relevant educational material, that is, at the end of the year (grades 4, 5, 6) or 2 years of study (grades 7-8, 9-10). The test tasks are highly homogeneous. If subjects solve more than 5 tasks, we can assume that they have a high level of development of the ability to think by analogies. If it is less, then a definite diagnosis should not be made. It is necessary to conduct a repeated examination after some time and use other similar tests as a supplement.

Literature

1. Gaishtut A. G. Mathematics in logic exercises. Kyiv: Radyanskaya 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. M.: Education, 1968. 432 p.

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

5. Matelsky P.V. Psychological and pedagogical foundations of mathematics didactics. 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.

Math Analogies Test