Profile mathematical training: particular qualities of intellect structure of high school students

Размещено на http://www.allbest.ru/

UDC 37.376:159.92:004.9

Institute of Information Technologies and Learning Tools of the NAPS of Ukraine

PROFILE MATHEMATICAL TRAINING: PARTICULAR QUALITIES OF INTELLECT STRUCTURE OF HIGH SCHOOL STUDENTS

The problem setting.

The time changes everything very quickly and the rate of these changes increases. This trend generates new demands on the workforce and its preparation. Knowledge-based approach has been replaced by competency-based one. Key competences were defined and recognized at the international level, one of them is mathematics [1]. As a result, "Rapid economic, technological and social changes are creating a world that is ever more interconnected and interdependent. Globalization of economies, the digital revolution, mass migration, and the prospect of climate instability are triggering new concerns and demanding a new kind of graduate" [2]. And this process will accelerate in near future evoking the necessity of lifelong learning [3] to build successful career which needs the high personal intelligence [4].

Analysis of actual studies.

As the main background to solve the problem mentioned above, one can point to on-line learning with additional opportunities for mental development of schoolchildren [5] with regards to new opportunities for education and development in social networks [6]. The main features of the intelligence development are analyzed and described quite thoroughly and deeply [7; 8], including from various positions of its use and meaning [9]. But not the intellect in general plays important role in education and successful work of a human, but its structure and dynamic nature should be taken into account as well [10; 11] with special attention to social dimension [12] and effect of education workload on schoolchildren mental and physical health and effectiveness [13]. Specific features of mathematically gifted children are important [14] to understand ways of intellect formation, but analysis of effect of math profile education in special schools/classes on the intellect structure can give useful information for teachers.

The article's goal is to compare development of intelligence structure of schoolchildren of math profile school/classes and general ones.

Presentation of the main material.

Experiments included psychological tests performance by subjects at the computer according to technique developed and validated for the professional selection. There were used tests as follows:

• Modified R. Amthauer test of intelligence structure, assessment skills in the areas of mental activity.

• Color-associated Lusher test (paired choice), assessment of stress levels, readiness to perform tests, the balance of psychological qualities.

• Myers-Briggs Type Indicator (MBTI).

There were observed 3596 schoolchildren of 7...11 academic years (K7 ... K11). According to method used, indices for every student ('primary' data) were measured and "secondary" marks were calculated.

The core test technique was R. Amthauer Intellectual Structure Test. The aim of testing consists in assessment of the level of development and structural peculiarities of intellect as well as attention and memory. 160 questions were grouped into 8 subtests:

1. LS - the logical selection.

2. GE - search for common features.

3. AN - search for similarity, analogy.

4. RA - mathematical calculation.

5. ZR - revealing of regularities.

6. FS - the choice of figures on the plane forming an integral figure from its fragments.

7. WU - tasks with cubes (tests spatial and constructive thinking).

8. ME - task for the ability to focus and memorize the learned words.

Calculation of testing results was made in such a way:

1. The number of correct answers in all subtests was counted. Each correct solution gave one point.

2. The index of verbal intellect development level shall be calculated (VI - i.e. the one based on verbal notions), by summarizing of points achieved in subtests 1-3 and 8.

3. The level of nonverbal intellect development shall be calculated (NI) by means of summarizing of points achieved in subtests 4-7.

4. The integral index (II) of intellect development level shall be calculated by means of summarizing points achieved for each of 8 subtests and recalculated into recognized IQ scale.

Lusher test has been used to obtain such indices: the K.Shiposhi coefficient of vegetation (associated with the level of ergotropic tone, stress, readiness for energy expenditure), stress level and capability. Those indices served as markers for the reliability of test results.

In earlier research there were revealed individual-psychological peculiarities of transforming process of the intellectual qualities structure of gifted adolescents depending on age (micro-intervals: from K7 to K11), profile/"directions of differentiation" of learning (physical and mathematical, chemical and biological, humanitarian, economic, etc.) and gender aspects were revealed [16]. Results were obtained by screening method of observation of Natural sciences lyceum # 145 students.

The highest level of general intelligence was recorded in the students of the physical and mathematical profile, whose level of general intellectual development was 70.44%. They were characterized by a harmonic structure of intelligence, with a slight predominance of nonverbal intelligence (verbal intelligence VI = 69.85%, non-verbal intellect NI = 71.78%). In the structure of non-verbal intelligence more noticeable individual differences were found than in the structure of verbal intelligence. The higher indicators were obtained for memory parameters (85.3%), as well as the level of general awareness (72.2%), the ability to search analogies (75.1%), the ability to operate mathematical regularity (74.3 %), spatial imagination, and combinatorial abilities (73.2%).

Lyceum 145 had a long history of effective work with gifted children if the field of math and physics, as well as traditionally a high rating to choose children with high abilities. So the question "abilities or teaching ?" remained open. To answer it, we carried out investigation of the intellect development in another math profile school (Lyceum 157, Kyiv). As it was demonstrated, the level of intellect development differed as well in adolescents of math and general schools [15].

To investigate common and specific features of the adolescence intelligence they were compared micro-interval dynamics of the general intellect (Fig.1), as well as its verbal and nonverbal components (Fig. 2) according to all data observation (without geographical, gender and profile specific) and data obtained in schools of math profile. The above results confirm the well-known data on the steady growth of the level of development of intelligence with the advance of the verbal component in the senior adolescence. At the same time, the differential analysis of individual components of intelligence indicates the heterochronity of this process, with various accelerations in grades 10-11.

The screening method of survey gives general view on the static situation, but does not allow analyzing real changes in the intellect of students. To study such a dynamics, the analysis was provided in relation to monitor changes in intellect level of adolescences of the Lyceum 157 over two consequent school years. Namely, they were monitored results of intellect test performance of students K8 ... K11 in school years 2011-2012 and 2012-2013. Students of K8 in school year 2011-2012 moved to K9, K9 to K10 and K10 to K11 respectively.

It follows from the graphs that the highest acceleration of the intellect development has been demonstrated by students of K9 in comparison with K8. This result does not correspondent previous research regards general tendency (the highest increase was revealed from K8 to K9). It can be assumed that selection children with high mathematical abilities and appropriate training in 8-th class ensure not only good math skills, but development of higher intelligence at earlier age than the average population.

To compare intellect structure of students of different age, they were compared components of the intellect for K8 ... K11. It was expected that all components in K8 are not higher than the older ones. But the attention was drawn to the fact that GE (search for common features) and FS (special thinking with objects on the plane) did not differ practically in all micro-interval groups (Fig.2). And components of GE, AN, RA and ZR increased after in K9 some level and did not differ in K9, K10 and K11.

One can draw a conclusion from this, that such structural components of the intellect as search for common features, search for similarity and analogy, mathematical calculation as well as revealing of regularities are results of development by math training. This is confirmed by the comparison analysis with the same diagram on general schools (Fig. 3), where significant variation was revealed in all components of the intellect, as well as their lower level of development.