THE UNIVERSITY OF LATVIA
INETA HELMANE
CORRELATION BETWEEN MATHEMATICAL SKILLS' ACQUISITION AND EMOTIONS OF PRIMARY SCHOOLCHILDREN
SCHOOL PEDAGOGY
DOCTORATE WORK SUMMARY
Rīga
2006
Dissertation's General Description
The great pace of life in the contemporary society demands emotionally powerful people, able to maintain a positive attitude towards life, overcome the fast increasing tension and stress, sustaining appropriate self-esteem, healthy self-confidence. Only a harmonious well-balanced individual perfectly participates in the social economic processes, developing one's own and also fellow-citizens' life quality.
One of the most meaningful components creating a harmonious individual is emotions. Namely emotions bring immense significance into the life of each personality. They mobilize each individual's psychic and physical strength for the further activity to reach the goal, or prevent and hinder the individual's activities, participation in the diverse life- activity processes.
Therefore, the emotions, felt by the pupil during the educational process, either initiate or hinder their psychic and physical abilities. In the educational process, positive emotions promote the attainment of skills and knowledge by the pupil, as well as stimulate the volition to perfect the acquired skills and use them in the miscellaneous life-activity situations. On the other hand, the pupil, enduring of the negative emotions in the learning process, generates reluctance to the studies, antipathy and avoiding from perfection and implementation of the skills acquired during the educational process into the further activities. The endured negative emotions in the educational process are preserved and they influence the future life development.
During the six years of the research, I obtained conclusive evidence, when at the first lecture on the mathematics' methodology, I asked the students - future teachers to reflect on the issue by recalling their primary school age and learning of mathematics in this period. As a result, the students discovered what had excited them, created positive emotions towards mathematics, as well as, what had intimidated, caused hatred, sadness - made them endure negative emotions. The research, carried out at Riga Teacher Training and Educational Management Academy from 1999 till 2000, revealed those factors, which had aroused negative emotions when the students were pupils of primary school age:
• 67% of the negative emotions were caused by the lack of skills, inability to solve some definite type of problem, e.g., text teasers, due to the inability to implement the respective mathematical skill;
• 54% of the cases were caused by the discrepancy to the individual psychological peculiarities - often the mathematical skill was formed on the basis of an abstraction, without any concrete activity based on objects sustaining this material;
• 52% of the cases do not include the correlations of the real life into the arithmetic training content, as well as the four rules of arithmetic, sums and problems devoid of the life realism, had to be done mechanically;
• in 36% of the cases, mathematical skills learning tempo, work forms and methods were the same type, monotonous, inadequate to the pupil's age period peculiarities, needs and interests;
• in 21% of the cases, the negative emotions were caused by the teacher's authoritative style of work, the lack of sensitivity;
• 6 % of the cases mentioned boring, dull text-book.
Due to these negative emotions experienced, the pupils were forming negative attitude towards learning of mathematics, which was preserved up to university studies, when after leaving secondary school the pupil had decided to become the primary school teacher. To these future pedagogues the negative emotions are still caused by the greatest part of the mathematical expressions requiring mathematical skills and knowledge. Therefore, a negative attitude towards themselves, low self-assessment is also revealed by the following phrases: "Mathematics is not for me; I can never do anything in maths; I don't push myself, anyway, I won't succeed". On the other hand, the students who had enjoyed positive emotions while learning mathematics, have preserved these positive emotions, the positive attitude to mathematics, as well as feel enthusiastic to develop the acquired mathematical skills, willingly implement them into diverse life activities.
Nevertheless, elderly people who commenced schooling and learned during the first independent Republic of Latvia do not associate mathematics with the negative emotions, on the contrary, they willingly recall how they enjoyed learning of mathematics at school and the skills acquired, they use the knowledge actively in the miscellaneous private life activities. Consequently, it is necessary to acknowledge the dominant paradigm of mathematics at that time in primary school, so perfecting the contemporary pedagogical process in primary school.
Subsequently, it is necessary to find the stimulus for fostering the positive emotions in pupils, acquisition of mathematics' skills, as well as amend those things in teaching syllabus of mathematics which create negative emotions in pupils learning at primary school, conditions of mathematical skills acquisition, include the achievement assessment in the education content, as well as self-assessment, mathematical skills acquisition forms, methods and ways.
The greatest part of the above mentioned amendments for contemporary mathematics teaching/learning can be found in Latvia in the 20 - 30s, when the acquisition of mathematics was associated with life activity, accentuating its practical importance and gradualism and continuity of the mastering of mathematics' skills. Contemporary actualities in the education process, especially in the acquisition of mathematics are considered as innovations, e.g., correlation of the education
content with the socialisation processes, integrated studies, etc. Yet, it is relevant to comprehend and understand also that period of time, when they did not have to serve and learn suffering from oppression of some political power, thus, anew discovering mighty roots of the present changes in mastering of mathematics.
Consequently, it is important to involve the means stimulating positive emotions in pupils -practical mathematics' activities into mastering of mathematics, the ones exciting, enjoyed by the pupils: Mathematics' content should be feasible, comprehensible, stimulating, well divided, of favourable intensity, possessing appropriate degree of difficulty for the pupils; rational methods of teaching/learning should be used, visual study means, as well as the activities of the pupils are practical, self-dependent; miscellaneous forms of work, methods, especially play method, which facilitates pupils' active involvement, mobilize the energy to reach the foreseen goal; communication with peers and the teacher; success and achievement self-assessment, assessment by the teacher and peers. How the attained mathematical skills provide the pupils with the opportunities to implement them in their future life- performance, promoting and mounting the pupil's life onto a new quality, how to organize an interesting training process in mathematics -these are urgent problems of contemporary pedagogy.
In order to solve the contradiction between the real process of attaining of mathematical skills and the desired mathematical skills' attaining, stimulated by the positive emotions, I have chosen the doctorate dissertation theme: "Correlation between mathematical skills' acquisition and emotions of primary schoolchildren".
Research object:
• mathematics acquisition process in primary school
Research subject:
• Correlation between learning and emotions in primary schoolchildren's mathematical skills
acquisition
Aim:
To research the pedagogical psychological conditions and peculiarities of primary schoolchildren in the correlation between learning and emotions in the process of acquisition of mathematical skills and elaborate appropriate curriculum and text-books for the implementation.
Hypothesis:
Primary school pupil’s correlation between mathematical skills acquisition and emotions is accomplished, if
• the aim of mathematics teaching/learning is targeted at the formation of the pupil's intellectual and emotional balance,
• the pupil's emotions in mathematics are created by the concrete object orientated activities, purposeful system of exercising and skills implementation in the life-activity situations,
• pupils attain deliberately 1st, 2nd or 3rd stage of mathematical skills in successively organized teaching/learning process in mathematics.
Research objectives:
1. To accomplish the analysis of pedagogical and psychological literature on the essence of mathematical skills acquisition and emotions' correlation.
2. To establish the correlations between the primary school pupil's mathematical skills and emotions in a real pedagogical process.
3. To elaborate mathematics' curriculum and text-books stimulating the primary pupils' mathematical skills acquisition and emotions' correlation implementation.
4. To test by an experiment and assess the efficiency of the teaching/learning means.
Research methods:
• Theoretical methods: analysis of pedagogical and psychological literature; analysis of the document contents
• Empirical methods: opinion poll: questionnaires - written, verbal-interview, discussion; observation; document analysis; children activity products' analysis; shaping of pedagogical situations, analysis, tests: A.A.Krilov, S.A.Manchyev "Establishing of emotions after certain expressions ", T.Dembo's methodology for self-assessment of basis emotions modified by E.V.Trubanova; natural developing pedagogical experiment.
• Mathematical statistics methods: histogram, Kolmogorov- Smirnov test, analysis of correlation, multi-factor analysis, analysis of dispersion; the natural developing pedagogical experiment data processed by the statistical data processing set - SPSS 10.1.
Research theoretical basis:
• Verities on the aim of the intellectually and emotionally balanced personality development
and readiness to life activity T.Erns, O.Priedītis (1927), A.Anning (1991), A.Špona (2004),
appropriate concentric education content distribution in primary school by M.T.Ķurzens
(1903), K.Dukurs (1965), S.Capel (1997) and life activity principles by Ed.Pētersons (1931), L.Ausējs (1935), E.J.King (1977), Z.F.Chehlova (1995).
• Verities on the stimuli facilitating the acquisition of mathematical skills: activities based on definite objects: E.Otto (1909), P.Birkerts (1923), N.F.Talizina (1984), D.E.Papalia (1996), A.Arcavi (2003), exercising: Dz.Jūzs (1926), N.V.Konobejevskij (1958), I.Maslo (1995), S.N.Elliotts (1996), R.Digiulio (2000) and implementation of the skills in practice: A.Hergerts (1923), T.Erns, O.Priedītis (1927), D.Prets (2000), E.R.Pedro (1981), N.V.Mekelsky(1982).
• Theory on basis emotions, which are displayed already during the first years of the child's life and is preserved throughout the life, inherent specific internally determined nerve substratum, that are reflected by mimicry or nerve muscle expression complexes, different subjective emotional experiences: K.Izard (2000), E.P.Ilyin (2001).
• Cognitions on the positive emotions as stimuli to learning activity: P.F.Leshaft (1912), P.Birkerts (1923), A.Ļublyinska (1941), A.Kovalov (1967), A.Markova (1986), I.Maslo (1995), M.Stockers (1996), J.DeLoux (1998), I.Žogla (2001), E.Maslo (2003).
• Cognitions on the primary pupil's emotion development by the mathematical skills acquisition process and the realization of correlation by teaching/learning: Ed.Pētersons (1931), O.Svenne (1930), E.C.Wragg (1993), J.Dean (1996), G.S.Abramova (2003), V.N.Druzhyinina (2002), J.Engestrom (2003).
Research basis
Natural developing pedagogical experiment was carried out in the private school "Patnis". 13 pupils from one grade and 1 teacher participate in the experiment; the control group consists of 21 pupils and 1 teacher from the primary school branch of Rīga Secondary School No. The research on the establishment of the correlation between the mathematical skills acquisition and primary school pupils' emotions was carried out in 10 schools, including primary school grades in 4 secondary schools, 3 basic compulsory schools, 3 gymnasiums (grammar schools), and the schools are located in diverse Latvia's areas - in cities, towns and rural ones; 216 pupils and 10 primary school teachers participated in the assessment process of the teaching/learning aid. Thus, total of 250 primary school pupils and 12 primary school teachers participated in the research.
Research innovation, theoretical significance of the work
• actualized mathematics teaching/learning content development conditions: concentric layout
of mathematics teaching/learning content, the life-activity principle, thematic approach as
an integrated teaching/learning component and pupils' individual psychological development;
• the mathematical skills definition as purposeful and successful implementation of mathematical expressions by rational means is perfected; the mathematical skills acquisition stages, their acquisition conditions are elaborated: the 1st stage mathematical skills are learned with the help of definite activities with the objects, the 2nd stage mathematical skills are mastered as the result of purposeful system of exercises, the 3rd stage mathematical skills are attained when used as skills in the life-activity situations; each mathematical skill according to the stages is assessed by the following criteria: result's quality, automation stage efficiency, necessity of the assistance, usage based on the example, in analogous or new situations;
• primary school pupil's mathematical skills acquisition and emotions' correlation is established as pupil's positive emotion and definite object oriented activity mutual interrelation, creating a basis for qualitative mathematical skills acquisition corresponding to the appropriate stage; pupils' emotions are aroused by activities with concrete objects, based on miscellaneous visual aids, practical activities, rational work methods; while mastering the 2nd stage mathematical skills, the pupils' emotions are excited by the purposeful system of exercising, where the aim of the exercise, the performance of the exercises, diversity of the exercises is understood; while mastering the 3rd stage mathematical skills the pupils' emotions are excited by the skills implementation in miscellaneous life-activity situations using diverse work forms, diverse problem solving means, integration opportunities.
Research practical significance
• is reasonable for the primary school pupils' mathematical skills acquisition and emotions correlation implementation by pedagogical means in mastering of mathematics;
• mathematics teaching/learning experimental curriculum and mathematics text-books for Grades 1, 2, 3 with workbook sheets, teacher's books for teaching mathematics to Grades 1,2, 3 are elaborated, tested and their efficiency in the realization of the correlation is established.
Research periods
• ас. у. 1999/2000 - theoretical study of the primary school pupil mathematical skills
acquisition and emotions' correlation; completion of the mathematics teaching/learning
experimental curriculum and mathematics teaching/learning aid set for Grade 1;
• ас. у. 2000/2001 - implementation of the mathematics teaching/learning experimental curriculum, adaptation of the mathematics teaching/learning aid set for Grade 1;
• ас. у. 2001/2002 - implementation of the mathematics teaching/learning experimental curriculum, adaptation of the mathematics teaching/learning aid set for Grade 2; research data obtaining for the 2nd grade pupil mathematical skills' stages and description of the emotions based on the previously elaborated criteria and indexes; completion of the mathematics teaching/learning aid set for Grade 3;
• ac. y. 2002/2003 - implementation of the mathematics teaching/learning experimental curriculum, adaptation of the mathematics teaching/learning aid set for Grade 3; research data analysis and interpretation according to the research criteria and indexes of the mathematical skills acquisition and emotions' correlation of the primary school pupils;