The article presents the results of a cross-cultural analysis of the correlation of various success indicators in learning mathematics
Keywords: Success in learning mathematicsState examAnnual gradesMath test scoreNational educational systemHigh school age
The problem of measuring success in learning is relevant both for educational practice and for research in education sciences. It has been shown that success in school education is associated with a whole spectrum of events in later life - further education, career achievements, and mental and physical well-being (Goodman et al., 2011; Power et al., 2013, etc.). During the school-age period, success in learning is the most important criterion for children's social status, an indicator of their psychological comfort and the basis of relationships with peers and educators (Tikhomirova, Malykh, 2017; Nisbett et al., 2012).
In studies aimed at finding the factors of individual differences in academic success, this psychological trait is analyzed on the basis of teachers' assessments (Tikhomirova et al., 2015a; Tikhomirova et al., 2015b), test scores (Tikhomirova, 2017; Rodic et al., 2015) and the results of state examinations (Verbitskaya et al., 2017a; Verbitskaya et al., 2017b). At the same time, the analysis of academic success based on each of these indicators has a number of advantages and disadvantages. Grades given by teachers vary only from 2 to 5, and annual grades, as a rule, vary from 3 to 5. This circumstance makes it difficult to conduct statistical procedures in the studies. At the same time, school assessment is an indicator of the success in learning, which can be used throughout the period of schooling. Tests are easy to use, but their content does not usually correlate with the state educational standards. The results of the exams
The observed differences in the results of studies of cognitive predictors of academic success are associated, among other things, with the specifics of expert, test and exam success indicators. For example, the study of the success in learning the Russian language showed differences in the relationship between cognitive characteristics and the results of the two exams (Verbitskaya et al., 2015). In the study of cognitive predictors of success in learning mathematics, differences were revealed for two mathematical tests – with and without the time limit (for example, Tikhomirova et al., 2014).
At the same time, the results of studies of mathematical success indicate the existence of stable cross-cultural differences (see more Tikhomirova, Malykh, 2017). Thus, according to the results of a large-scale cross-cultural rating of the Program for International Student Assessment (PISA, URL: http://www.oecd.org/pisa/aboutpisa), within mathematical achievement among 15-year-olds the first ten positions are usually occupied by the countries of the Asian-Pacific region and Finland, Great Britain holds middle positions, Russia shows results slightly below average, and schoolchildren from Kyrgyzstan take the last place (OECD, 2010). These cross-cultural differences in the mathematical success are usually associated with the effect of macro-environment factors reflecting the specifics of national education systems, for example, the orientation of the education system on mathematical achievement, the duration of schooling and others (Malykh et al., 2012; Rodic et al., 2015; Brinch & Galloway, 2012; Nisbett et al., 2012). It is concluded that there is a significant influence not only on the indicators of success in learning, but also on the structure of their interrelations (Tikhomirova, Malykh, 2017).
Thus, the study of the correlation of different indicators of success in learning mathematics is important in the context of the different conditions of the educational environment.
The main issue addressed in this study is related to the understanding of cross-cultural similarities and / or differences in the structure of the interrelationships between different types of tasks that measure success in learning mathematics; and to what extent teachers' assessments will match the scores of computerized with and without the time limit, as well as the results of the state exam in mathematics.
Purpose of the Study
The aim of the current work is to study the relation of various success indicators in learning mathematics – teacher assessments, indicators of computerized tests and the results of the state exam – in different national educational systems. The study will be conducted with the participation of Russian and Kyrgyz schoolchildren of Grade 11, at the time when it is possible to analyze all three types of indicators of success in learning.
The study included 304 students studying in Grade 11 from two general education institutions in Russia and Kyrgyzstan with similar educational conditions in terms of the quality of education, qualifications and structure of the teaching staff, departmental affiliation and educational programs implemented at school. The Russian sample is represented by 120 students (mean age = 17.4, SD = 0.4, 41.9% male); the Kyrgyz sample included 184 students (mean age = 17.1, SD = 0.5, 36.4% male).
Assessment of success in learning mathematics
In the current study the success in learning mathematics was analyzed on the basis of three types of indicators.
Expert teacher assessment
As an expert assessment of the mathematical success of students in Grade 11, annual grades for algebra and geometry given by the teacher of mathematics were analyzed. The average grade was calculated.
«Understanding numbers», success in solving mathematical tasks without time limit
The test includes 18 mathematical tasks the successful solution of which requires an understanding of mathematical operations and their relations formulated in the form of mathematical tasks and logical problems. The mathematical tasks are organized into 3 levels of different complexity, each consisting of 6 tasks. The test represents an hierarchical system: the starting point is the same task for all participants, but the order in which further tasks are presented is determined by student's performance in solving mathematical tasks. The program registers the number of correct answers. Examples of tasks and their detailed description are presented in the works of Tikhomirova, Kovas, 2013; Tikhomirova et al., 2014; Tosto et al., 2013.
«Problem Verification», success in solving mathematical tasks within limited time
The test consists of 48 already solved mathematical tasks with numbers and ratios at the top of the screen and "keys"
Cross-cultural differences in test indicators of mathematical success
In the course of a one-way analysis of variance (ANOVA) on the test indicators of mathematical success, where the categorical factor was the belonging to Russia or Kyrgyzstan, cross-cultural similarities and differences in the indicators of mathematical success were studied. Table
According to Table
Cross-cultural analysis of interrelationships of success indicators in learning mathematics
According to Table
For computerized test tasks, the teacher's assessment is almost equally related on the samples of Russian and Kyrgyz schoolchildren (for mathematical fluency, respectively, r = 0.40 and r = 0.30,
In general, cross-cultural analysis revealed both similarities and differences in the relationship between different indicators of success in learning mathematics at high school age.
Thus, we found moderate, and in some cases, weak interrelations between teacher's, test and exam results on mathematics on both samples. These statistically significant moderate interrelationships between success indicators support the hypothesis of the possible use of various cognitive, motivational and emotional resources in solving problems of different types – with and without the time limit, in written or oral form (Tikhomirova et al., 2015a; Tikhomirova, 2017). This result obtained on the two cross-cultural samples indicates the need for increased attention to the analyzed indicators of mathematical success, the development of standardized tasks that could be used throughout the schooling and ethical principles in education practice.
Cross-cultural differences are more closely related to the specific relationship between the results of the state examinations and other analyzed indicators of mathematical success. In particular, it was shown that on the Kyrgyz sample the results of the state examination (ART) are more associated with the results of a computerized test task aimed at understanding mathematical operations and their relations, formulated in the form of mathematical and logical tasks. At the same time, on the Russian sample, the successful performance at the state exam (USE) was more correlated with the annual grade given by a teacher. These differences can be explained by the content and objectives of examinations in Russia and Kyrgyzstan. Thus, the purpose of the USE is to certify students who are learning to master basic general education programs of secondary general education using sets of tasks of a standardized form for school disciplines. At the same time, ART is not aimed at revealing the actual knowledge, but on researching the analytic abilities of a student, their ability for further education. In addition, higher correlations can be a consequence of the subject orientation of the USE and ART. In particular, the USE is conducted both in mathematics and the Russian language separately, and ART only includes sections on mathematics and the Russian language.
It should be noted that the ratio of teachers', test and examination evaluations of success in learning mathematics was analyzed on the data collected at one point in time. At the same time, in order to assess the temporal stability of the relationship between success indicators in the learning mathematics it is required to conduct longitudinal studies.
This study was supported by the grant from the Russian Science Foundation №17-78-30028
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13 December 2017
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Cognitive theory, educational equipment, educational technology, computer-aided learning (CAL), psycholinguistics
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Tikhomirova, T., Gaydamashko, I., Malykh, A., Lysenkova, I., Khusnutdinova, E., & Malykh, S. (2017). Assessment Of Success In Learning Mathematics: Cross-Cultural Analysis. In S. B. Malykh, & E. V. Nikulchev (Eds.), Psychology and Education - ICPE 2017, vol 33. European Proceedings of Social and Behavioural Sciences (pp. 345-352). Future Academy. https://doi.org/10.15405/epsbs.2017.12.37