Paper presented at the European Conference on Educational Research, University of Hamburg, 17-21 September 2003
(The Quality Assurance and School Effectiveness network)
Narkeviciene, Brone
The attitude of students with high achievements in mathematics towards education methods and conditions in Lithuanian secondary schools
Kaunas University of Technology, Studentu 50- 222, LT – 3031, Kaunas, Lithuania
Abstract
The aim of the research is to reveal the attitude of students with high mathematic achievements towards learning, teaching and teaching- learning conditions in Lithuanian secondary schools. The research was carried out in April, 2002. The questionnaire was given to all 92 students who participated in the Olympiad of mathematics of Lithuanian Republic. After having been adopted to meet the objectives of the study, the questionnaire of prof. D.H. Rost (1993) is used in this study. Main analysis methods used are: descriptive statistics (frequencies, characteristics of location, characteristics of variability and graphical data visualization). The Wilcoxon test for paired samples and Kruskal-Wallis test for independent samples were used for estimation of differences between groups of variables. For the testing of influence of various factors to means of analysed variables one way analysis of variance was used (ANOVA). Correlation analysis was used for the testing of reliability of investigation instrument. After the study has been carried out, it is revealed, what the attitude of the subjects is towards the current and desirable situation of education of students with high mathematic achievements in Lithuanian secondary schools. The data of the investigation lets distinguish the essential characteristics of education and its conditions at social educational (country), institutional (school), and interpersonal (class) level; to compare the current and desirable situation, comparing students' evaluations; to reveal how the evaluation of the situation of education of gifted students depends on the school type, the living place of the student and the gender of the student.
Key words: achievements; mathematics; education methods; conditions; secondary school.
Introduction
A decade ago, Lithuania and other post-sovietic countries that existed in a half-enclosed space suddenly had to encounter the collision of huge transformations: post-sovietic legacy (mentality), open democratic society and postmodernism (Grigas, 1998). Political and economic changes in Eastern Europe stimulated active reforms and many states were forced to take a new look at education process. Lithuania is not the exception – the education system is on the way of radical reforms, it is recognised as the essential force of the development of society, the force that aims to give basis for the dynamically shifting society with open and critical consciousness. The main objective of the reformed education is an independent and creative personality, expressing the maximum of his/her abilities already at school level (The Conception of Lithuania’s Education, 1992, p.5) Different scientists (Gagne, 1991;Gross, 1995; Heller, 1999;Lee – Corbin, Denicolo, 1998; Laužikas, 1974; Leites, 1996; Rost, 1993; 2000 etc.) name different forces of environment that can influence development of gifts. It is obvious, that there should be suitable conditions and education system for gifted students. Assembly debate on 7 October 1994 (31st Sitting Doc. 7140, report of the Committee on Culture and Education, Rapporteur: Mr Hadjidemetriou) confirmed the recommendations of education of gifted children. The need of such an education system can be particularly seen in the countries that encountered restrictions of the ideological past and could not avoid restortion of society. The attitude towards gifted children was rather ambivalent in the ex-Soviet Union (Babaeva, 1999) – on the one hand, a number of olimpiads, competitions (of different subjects, music, sports, etc.) were organized, on the other hand, there was the ideology of total equality. Thus, lack of applied studies with the results revealing the changes of education, especially in the post-soviet countries can be noticed. The study, carried out by the author of this article, is an attempt to supplement the knowledge in this field. The object of the study is the methods and conditions of education of 9-12th form students with high achievements in mathematics.
Method
The aim of the study – to determine how students with high achievements in mathematics evaluate the situation of education in secondary schools.
Goal of the study:
- To determine the motives of 9-12th form students with high achievements in mathematics to participate in mathematics competitions.
- To distinguish essential peculiarities of education and education conditions of students with high achievements in mathematics at state, school and class level, while investigating the existing and the desirable situation.
- To determine how gender, school type and place of residence of a student can influence the evaluation.
Methods:
- A questionnaire-based inquiry;
- Statistical analysis of data.
Rost (1993) questionnaire, adapted and supplemented by the author of the article, was used for the questionnaire-based inquiry.
The questionnaire comprises questions – items about the purpose of mathematics competitions, the motives of participants, methods and ways of training, conditions of education at school and in the state. Every statement had to be evaluated on a five-stage scale, starting with –2 “totally disagree” and ending with +2 “totally agree”, in two aspects “I am taught so, such is the situation in my school” and “I wish I would be taught so, I wish the situation would be like this”.
The reliability of the instrument of the study was tested using correlational analysis. The Kronbach alpha of all summarized factors is larger than 0.6.
The following statistical methods were used for the analysis of the data:
- Descriptive statistics.
- Mann-Whitney-Wilcoxon criterion for independent samples and Wilcoxon criterion for dependant samples was used to test the hypotheses.
- One-factor dispersive analysis was used to test the hypotheses about the influence of different factors on investigated features.
- Correlational analysis was used to test the reliability of the instrument of the questionnaire.
- Spearman coefficient was used to calculate the rank correlation.
The subjects of the study – all 92 participants of republic competition of young mathematicians, students of 9-12th forms. The distribution of respondents according to their gender, place of residence, school type are demonstrated in Table 1.
Table 1
The data of the students of the study
Gender
/ N / Percentage / School type / N / Percentage / Place of residence / N / PercentageGymnasium / 58 / 63.0 / Town / 58 / 63.0
Boys / 62 / 67.4 / Secondary / 25 / 27.2 / Region centre / 22 / 23.9
Girls / 23 / 25 / Basic / 3 / 3.3 / Country / 6 / 6.5
Total / 85 / 92.4 / Total / 86 / 93.5 / Total / 86 / 93.5
Did not answer / 7 / 7.6 / Did not answer / 6 / 6.5 / Did not answer / 6 / 6.5
The purpose of mathematics competitions and the motives to participate in them
While determining the motives of participation in the competitions of young mathematicians, the respondents were asked to answer the question “Why does a student take part in this competition” by either choosing an appropriate evaluation of the items or writing “other”. The evaluation of students can be seen in Table 2.
Table 2
The evaluation of items about the purpose of mathematics competitions and the motivates to participate in them
No / Item / / SD1.1 / I want to compare my abilities in mathematics with the abilities of other students. / 1.10 / 0.74
1.2 / I think the participation in the olimpiad makes me become more interested in maths and study it more. / 0.88 / 0.88
1.3 / I think the olimpiad is the way to evaluate one’s achievements, to get the recognition from other people. / 0.78 / 0.92
1.4 / I get new knowledge and skills of mathematics at the olimpiad. / 1.13 / 0.73
1.5 / The teacher promised to give me “a ten“ (the highest mark) for the participation in the olimpiad. / -0.99 / 1.22
The strongest motive of participation in the competition is that students get new knowledge and skills of mathematics. The second important motive – the competitions provide students the opportunity to compare their abilities in mathematics with those of their peers, the encouragement by giving marks is not significant, it is not used by teachers. There is statistically significant difference between boys and girls in evaluating the item “I get new knowledge and skills of mathematics at the olimpiad” (p=0.037, d=-0.46). There are evaluation differences among students, living in the town, the region centre and the country (p=0.006, d=–1.20 and p=0,027, d=-1.01) in evaluating the item if the competitions provide opportunities to compare one’s knowledge of mathematics with those of the peers. The children from country schools agree the most with this item (the means are accordingly 1.0; 0.96 and 1.83). The school type did not influence the evaluation of the items.
While evaluating the mathematics competitions as the way of teaching mathematics, it is important to know, to what extent the teachers or other people take part in this process, and to what extent the student works independently. That is why four item were given about the preparation for the olimpiad (Table 3).
Table 3
Preparation of students for the olimpiad
No / Item / / SD2.1 / I was preparing only on my own. / -0.13 / 1.29
2.2 / My teacher of mathematics helped me prepare. / 0.62 / 1.24
2.3 / A teacher from our school who is responsible for preparation of students for the competitions helped me prepare. / -1.01 / 1.37
2.4 / I did not make any extra preparation for this competition. / -0.71 / 1.37
It can be stated that teachers of a certain specialization are appearing in schools, that would be quite natural, having in mind the necessity to differentiate the teaching of mathematics and possible great differences in abilities of students in the same class. However, the general evaluation mean (=–1.01) of the item “A teacher from our school who is responsible for preparation of students for the competitions helped me prepare” shows that such a form of work with students, interested in mathematics, is still not popular. No statistically significant differences were found between girls and boys. The place of residence and the school type did not have any influence, either.
The existing situation
Class level
Investigating the methods used in the class in education of young mathematicians, students had to evaluate 7 item. Their evaluation mean is shown in Table 4. The data in the table is given according to the evaluation mean, i.e. at the top of the table there is an item which was mostly approved on the five-stage scale, starting with –2 “totally disagree” and ending with +2 “totally agree”.
Table 4
The existing situation: inner differentiation, class level
Item No / Item(“I am taught so”; agree :+, disagree:-) / / SDK3_3 / Students gifted at mathematics are given particular, more complex tasks during the lessons. / 0.36 / 1.35
K3_5 / Students gifted at mathematics are taught additionally after classes. / 0.26 / 1.47
K3_2 / Students, gifted at mathematics, help students possessing poorer knowledge. / -0.05 / 1.30
K3_4 / Students gifted at mathematics are offered particular tasks for homework. / -0.12 / 1.47
K3_6 / Part of week work can be done not at school, but at home, in the library, i.e. studying additional literature, doing project work. / -0.68 / 1.24
K3_7 / Students gifted at mathematics study under a particular curriculum, adapted to their needs. / -0.73 / 1.21
K3_1 / Students gifted at mathematics are allowed not to attend certain lessons because the material is already known to them. / -1.13 / 1.18
Only three of all possible methods of inner differentiation have positive means and all of them are not large. 28 per cent of respondents do not get (or get very rarely) particular tasks of mathematics during the lessons and 28 per cent never get particular tasks for homework. The item that students gifted at mathematics study under a particular curriculum, adapted to their needs has a negative mean. Only 6 students (7 per cent) totally agreed with this item, and 52 (57 per cent) absolutely denied it. Evaluation differences: girls are more often asked to help those who possess poorer knowledge (p=0.022; d=-0.56); children from town schools are more often taught after lessons than children from region centre or country schools (item K3_5) (p=0.028; d=0.62; p=0.015; d=1.15).
School level
How the opportunities of outer differentiation are used in work with young mathematicians is shown in Table 5.
Table 5
The existing situation: outer differentiation, school level
Item(“It is so”, Agree:+, disagree:-) / / SDK4_5 / Olimpiads and competitions are held at our school. / 0.80 / 1.24
K4_8 / Gifted children are taught in special classes at ordinary school. / -0.65 / 1.25
K4_3 / The course is “compressed”, i.e. the material that should be taught in 4 years, is taught in 3 years time. / -0.85 / 1.12
K4_2 / Gifted students are allowed to “skip” forms. / -0.98 / 1.23
K4_1 / Gifted students are allowed to take one or several subjects at the senior forms. / -1.33 / 0.98
The use of only one opportunity of outer differentiation is undoubtful - the competitions are held at schools – 72 per cent of respondents claim that. The opportunities of acceleration (items K4_3; K4_2 and K4_1) are not used. No statistically significant differences were found in gender, place of residence or school type.
How students evaluate conditions of learning and teaching at schools can be seen in Table 6.
Table 6
The existing situation: conditions of learning and teaching, school level
Item (“It is so”, agree:+, disagree:-) / / SDK4_10 / Exceptionally gifted students are loved and respected by teachers at school. / 0.98 / 0.80
K4_7 / Teachers are well-prepared for work with gifted students. / 0.53 / 1.18
K4_4 / Even after lessons gifted students can use certain means for satisfaction of their particular needs at special places at school, e.g. library, computer class. / 0.42 / 1.18
K4_9 / Exceptionally gifted students are loved and respected by their peers at school. / 0.37 / 1.05
K4_6 / Teachers are encouraged to work with gifted children. / 0.16 / 1.09
The evaluation of item K4_6 is the most poliarized - 11 per cent of the respondents totally agree with it and 11 per cent absolutely disagree with it, 45 per cent chose a neutral answer.
Boys and girls evaluate the item differently K4_10 – the evaluation means are 1.39 and 0.79 (p=0.002; d=–0.79). The students of gymnasiums and non-gymnasiums differently evaluate (p=0.046; d=0.41) item K4_4 (the evaluation means are 0.64 and 0.20).
State level
How students evaluate the existing educational situation at state level can be seen at Table 7.
Table 7
The existing situation: outer differentiation, state level
Statement (“It is so”, agree:+, disagree:-) / / SDK5_2 / Exceptionally gifted students study at special extramural school of mathematics. / 0.12 / 1.29
K5_1 / Exceptionally gifted students study at courses, camps of yong mathematicians, etc. / -0.21 / 1.24
K5_3 / Exceptionally gifted students study at special secondary schools, designed for gifted students. / -0.25 / 1.29
K5_4 / The specialist of mathematics helps the exceptionally gifted students via the Internet. / -0.72 / 1.12
There is the only one item, describing the way of outer differentiation that has a positive evaluation mean. The negative mean of other item were determined by the fact, that only 11 per cent of the participants of republic olimpiad get the consultations of the specialist via the Internet, 29 per cent had the opportunity to take part at courses or camps for young mathematicians. There are gender differences in evaluation of three items: K5_1 (p=0.003; d=0.77); K5_2 (p=0.018; d=0.61) and K5_4 (p=0.013; d=1.65). All the evaluation means are unfavourable for girls, accordingly 0.00 and –0.91; 0.24 and –0.52; 0.55 and –1.22. The place of residence or school type did not any influence the evaluation.
The comparison of the existing and the desirable situation
The fact that the items in the questionnaire were evaluated in two aspects, the existing and the desirable, allowed to compare the existing situation of education of students with high achievements in mathematics with the situation that would be desired. We will compare these evaluations (Figures 1-4). The contraction “E-D” will be used in the text.
Figure 1. The comparison of the existing and the desirable situation: inner differentiation, class level.
Evaluation means of all the items differ, except for the item K3_2, help for students possessing poorer knowledge – the strenght of effect d for subsequent statements can be seen in Table 8.
Table 8
The differences of evaluation of items about inner differentiation for the existing – desirable situation
(for all items)
Item No / K3_1 / K3_2 / K3_3 / K3_4 / K3_5 / K3_6 / K3_7d / -1.21 / -0.13 / -0.73 / -0.6 / -0.62 / -0.81 / -1.34
The most significant difference “E-D” is for individualized curriculum (item K3_7)
There are no differences in requests for the methods of inner differentiation depending on the gender. The students of town schools are more willing to be taught after lessons, than students from the country (p=0.044;d=0.69) schools (item K3_5). Students from country schools are more willing to do part of their week work not at school, but at home, in the library, to do projects, than students of schools in towns (p=0.019; d=-0.98) and region centres (p=0.015; d=-1.08) (Item K3_6). The methods mentioned in items K3_2 (p=0.047; d=–042); K3_6 (p=0.026; d=–0.55) and K3_7 (p=0.021; d=– 0.55) are more desired by non-gymnasium students.
Figure 2. The comparison of the existing-desirable situation: outer differentiation, school and country level.
Evaluation means of all items “E-D” differ (Table 9).
Table 9
Evaluation differences of item, describing outer differentiation for the existing – desirable situation
(for all items)
Item No / K4_1 / K4_2 / K4_3 / K4_5 / K4_8 / K5_1 / K5_2 / K5_3 / K5_4d / -1.46 / -0.98 / -0.99 / -0.61 / -0.83 / -1.47 / -0.45 / -0.65 / -1.53
The most desired way, which is also popular in existing situation, are olimpiads and cpmpetitions. The second popular way – special courses and camps of young mathematicians. The following differences were noticed: students from non-gymnasiums are more willing to take one or several subjects at senior form than students from gymnasiums (item K4_1, non-gymnasium students gymnasium students ; p= 0,048; d=-0.42) They are also willing to have more olimpiads, competitions at school (item K4_5, non-gymnasium students gymnasium students ; p=0.019; d=-0.53). Non-gymnasium students are more in need of help by a specialist via the Internet (item K5_4, the means are accordingly; p=0.025; d=-0.62). Boys are more willing to study at extramural school of mathematicians (boys: girls ; p=0.028; d=0.57).
When evaluating the means of every item, the difference “E-D” seems to be rather significant. There is a question worth mentioning: which differentiation – inner or outer is dominating at present situation and what situation is more desirable in this sense.