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Differences in Mathematical and Verbal Achievement between Girls and Boys: The Heuristic Potential of the Structural Typing Approach in Large-Scale Studies

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Title: Differences in Mathematical and Verbal Achievement between Girls and Boys: The Heuristic Potential of the Structural Typing Approach in Large-Scale Studies
Language: English
Authors: Gediminas Merkys (ORCID 0000-0002-9461-8105), Sigitas Vaitkevicius, Daiva Bubeliene (ORCID 0000-0003-3198-1633), Leonidas Sakalauskas
Source: European Journal of Education. 2025 60(1).
Availability: Wiley. Available from: John Wiley & Sons, Inc. 111 River Street, Hoboken, NJ 07030. Tel: 800-835-6770; e-mail: cs-journals@wiley.com; Web site: https://www.wiley.com/en-us
Peer Reviewed: Y
Page Count: 14
Publication Date: 2025
Document Type: Journal Articles
Reports - Research
Education Level: Elementary Secondary Education
Descriptors: Foreign Countries, Elementary Secondary Education, Mathematics Achievement, Verbal Development, Standardized Tests, National Competency Tests, Gender Differences, Data Collection, Sample Size, Evaluation Methods
Geographic Terms: Lithuania
DOI: 10.1111/ejed.12802
ISSN: 0141-8211
1465-3435
Abstract: The results of total testing from the years 2015-2022 on the mathematical and verbal achievement of Lithuanian pupils (N [approximately equal to] 250,000) are presented. These are the standardised tests from grades 4 to 12. The K-Means method has discovered six types of achievement. The highest achievement type is dominated by girls (61.1%) who perform well on both mathematical and verbal tasks. The lowest achievement type is dominated by boys (57.4%) who solve both mathematical and verbal tasks extremely poorly. Each of these types makes up 1/5 of the population, and the gap between the means of their groups is about 2.5 standard deviations. The remaining four types of achievement are in the 20th to 80th percentile and make up about 60% of the population. Differences in means within the same type between mathematic and verbal achievement average 0.85 standard deviations or span one quartile. Gender differences are clearly visible in this subgroup: boys solve mathematical tasks better and verbal tasks worse; girls solve verbal tasks better and mathematical tasks worse. Big data may form a mixed distribution. It is appropriate to first discover the basic types of achievement and only then look for gender-specific differences. Such a type-building approach is heuristically superior to the conventional approach of working only with the mixed dataset.
Abstractor: As Provided
Entry Date: 2025
Accession Number: EJ1461238
Database: ERIC
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  Value: <anid>AN0183654302;eje01mar.25;2025Mar17.06:27;v2.2.500</anid> <title id="AN0183654302-1">Differences in Mathematical and Verbal Achievement Between Girls and Boys: The Heuristic Potential of the Structural Typing Approach in Large‐Scale Studies </title> <p>The results of total testing from the years 2015–2022 on the mathematical and verbal achievement of Lithuanian pupils (N ≈ 250,000) are presented. These are the standardised tests from grades 4 to 12. The K‐Means method has discovered six types of achievement. The highest achievement type is dominated by girls (61.1%) who perform well on both mathematical and verbal tasks. The lowest achievement type is dominated by boys (57.4%) who solve both mathematical and verbal tasks extremely poorly. Each of these types makes up 1/5 of the population, and the gap between the means of their groups is about 2.5 standard deviations. The remaining four types of achievement are in the 20th to 80th percentile and make up about 60% of the population. Differences in means within the same type between mathematic and verbal achievement average 0.85 standard deviations or span one quartile. Gender differences are clearly visible in this subgroup: boys solve mathematical tasks better and verbal tasks worse; girls solve verbal tasks better and mathematical tasks worse. Big data may form a mixed distribution. It is appropriate to first discover the basic types of achievement and only then look for gender‐specific differences. Such a type‐building approach is heuristically superior to the conventional approach of working only with the mixed dataset.</p> <p>Keywords: gender differences; general education; K‐mean method; large‐scale study; mathematical and verbal achievement; standardised tests</p> <hd id="AN0183654302-2">Introduction</hd> <p>Most topics and their empirical findings, whether in the social sciences or other fields, often attract the attention of a limited, specialised audience within academia. However, gender studies stand out as a notable exception. Through their research and interpretations, they engage in public discourse, contributing to the broader discussion surrounding gender justice and antidiscrimination.</p> <p>Despite modernisation, social disparities remain. In Western countries, it is challenging to find instances where gender inequality is legalised or, worse, where legislative support for such inequality persists into the future. However, due to historical inertia, real inequality and its discriminatory manifestations unfortunately persist in modern societies. These are erroneous social stereotypes, inequality in actual income and professional and academic careers (Breda et al. [<reflink idref="bib8" id="ref1">8</reflink>]; Kaiser [<reflink idref="bib20" id="ref2">20</reflink>]). The emancipatory perspective discussed in this article applies to its subject matter as well. While there is gradual improvement year by year, the participation of women in mathematics, science and engineering courses, as well as in specific high‐paid and promising jobs, remains relatively low (Van Miegroet and Glass [<reflink idref="bib38" id="ref3">38</reflink>]; Ghasemi and Burley [<reflink idref="bib15" id="ref4">15</reflink>]). Why is there a lack of women university rectors, Nobel laureates, etc.?</p> <p>The theoretical discourse on gender equality has become increasingly challenging to encompass due to its vast scope. Originating in traditional fields such as humanities, cultural anthropology, law, psychology and sociology, it has now expanded to include all disciplines within the social sciences. Gender studies—in political science, education, management, economics, nursing, social work, communication studies, etc., have long become not only the norm but also a fashionable, promising research trend (Tierno‐García et al. [<reflink idref="bib37" id="ref5">37</reflink>]; Woodward and Woodward [<reflink idref="bib40" id="ref6">40</reflink>]).</p> <p>It employs both quantitative and qualitative methods, using more than just sources but also literary works, and confidently integrates into contemporary scientific discourse. Groups of discourse developers and scientific schools engage in ideological and political discussions with boldness and conscious intent (Verdugo‐Castro et al. [<reflink idref="bib39" id="ref7">39</reflink>]; Deitch [<reflink idref="bib13" id="ref8">13</reflink>]). Some scholars reference M. Weber's concept of value freedom and Popper's ([<reflink idref="bib30" id="ref9">30</reflink>]) methodological ideals of demarcation, aiming—whether in reality or perception—to create 'genuine' and 'objective' scientific knowledge concerning gender differences (Pigliucci and Boudry [<reflink idref="bib29" id="ref10">29</reflink>]; Ciaffa [<reflink idref="bib10" id="ref11">10</reflink>]). What is at stake here is an empirical‐analytic paradigm in gender studies that continues strong work in the social and behavioural sciences with deep traditions in the modern era. The research presented in this article is consistent with the aforementioned tradition and paradigm.</p> <p>Biomedical and psychophysiological studies of gender differences, including cognitive functioning, are a trend and are extremely authoritative in terms of modern science. The latter are usually completely divorced from culture due to the specificity of their subject matter and content, but their findings influence the discourse on gender equality and often cause uproar (Hentzen et al. [<reflink idref="bib17" id="ref12">17</reflink>]; Yuan et al. [<reflink idref="bib41" id="ref13">41</reflink>]). Somewhat lost between empirical psychology and culture, evolutionary psychology emerges in these discourses (Archer [<reflink idref="bib4" id="ref14">4</reflink>]). One important position has become increasingly established theoretically in recent decades and is repeatedly confirmed empirically in gender discourse. This is a question‐dilemma: Who is responsible for the psychological and cognitive differences between genders—the biological basis or the social environment and culture? The prevailing view is that the supposedly inferior mathematical and scientific knowledge and achievement of girls and women is not due to profound genetic, evolutionary, hormonal differences or gender‐specific features of brain function, but to the inert legacy of the social environment and cultural evolution. Even something like a backward, conservative teaching, stereotyped family milieu and classroom environment can be mentioned here (Milic and Simeunovic [<reflink idref="bib24" id="ref15">24</reflink>]; Copur‐Gencturk, Thacker, and Quinn [<reflink idref="bib12" id="ref16">12</reflink>]; Starr and Simpkins [<reflink idref="bib35" id="ref17">35</reflink>]; Eriksson [<reflink idref="bib14" id="ref18">14</reflink>]; Charles et al. [<reflink idref="bib9" id="ref19">9</reflink>]).</p> <p>The authors welcome the diversity of scientific paradigms and are far from suggesting that there are supposedly 'superior' and 'lesser' paradigms in gender studies. Here it is worth recalling the historical era of the emergence of the social and behavioural and behavioural sciences, when it was fashionable to look for cognitive differences between races and genders, obviously to the detriment of African Americans and women. Studies that found such ideologically expected 'differences' (real differences or putative differences discovered because of flawed methodology) were widely published. Studies in which expected differences were not found, in which hypotheses were not confirmed, were considered uninteresting, unasked for, and therefore more often kept quiet (Grebe [<reflink idref="bib16" id="ref20">16</reflink>]). Paradox: 'positivist' science, zealously devoted to the ideals of 'value‐free science' and 'demarcation', has often instilled false stereotypes and misleading knowledge even from the heights of scientific authority. A certain epistemological alternative is also found in other paradigms. It is necessary to develop a suitable methodology for feminist studies, because historically, university education has been dominated by men for a long time. Therefore, all theories and proposed research methods established by men are inherently flawed and in need of revision (Naples [<reflink idref="bib26" id="ref21">26</reflink>]; Deitch [<reflink idref="bib13" id="ref22">13</reflink>]; Reinharz and Davidman [<reflink idref="bib31" id="ref23">31</reflink>]). The temptation to conflate research findings into a single 'correct' doctrine may still exist today as a certain epistemological risk.</p> <p>A separate branch of gender equality research and the corresponding discourse is the study of cognitive differences between the sexes. The material of this article also fits into this trend. The famous work of Maccoby and Jacklin ([<reflink idref="bib21" id="ref24">21</reflink>]) could be seen as a historical sign when the modern phase of research on gender differences began precisely within the framework of the empirical‐analytical paradigm. The analysis of cognitive differences also occupies a significant place in the aforementioned work.</p> <p>In the cognitive discourse on gender differences, a distinction can be made between purely psychological studies, which are usually conducted with IQ tests, and educational research, where test task material is generated only from the school curriculum. A separate subtopic of cognitive discourse is gender differences in mathematics and natural sciences. No less attention is paid to the comparison of reading skills from a gender perspective. In this context, the work and main results of international studies initiated by IEA and OECD, such as TIMSS, PISA and PIRLS, are of particular importance. The undeniable methodological advantage of the aforementioned educational studies is their big data format and large‐scale study format.</p> <p>Some findings of psychological science and the studies mentioned above, especially those that can be systematically replicated, need to be named more specifically.</p> <p></p> <ulist> <item> ‐ The general IQ and learning achievement of girls and boys does not differ overall, but girls have better verbal achievement and boys—mathematical and spatial reasoning achievement. In addition, the variance in cognitive estimates is generally greater in the boys' subgroup than in the girls' subgroup. Therefore, the probability of detecting a highly gifted boy and a very moderately gifted boy is relatively higher (Schwippert et al. [<reflink idref="bib34" id="ref25">34</reflink>]; Bergold et al. [<reflink idref="bib6" id="ref26">6</reflink>]; Baye and Monseur [<reflink idref="bib5" id="ref27">5</reflink>]).</item> <p></p> <item> ‐ In reading studies (PIRLS, PISA), girls' abilities are generally higher than those of their peers and schoolmates‐boys (Oberleiter et al. [<reflink idref="bib27" id="ref28">27</reflink>]; Steinmann, Strietholt, and Rosén [<reflink idref="bib36" id="ref29">36</reflink>]).</item> <p></p> <item> ‐ In TIMSS and PISA studies, boys' achievement in mathematics and science is generally higher than girls (Perez Mejias et al. [<reflink idref="bib28" id="ref30">28</reflink>]; Contini, Di Tommaso, and Mendolia [<reflink idref="bib11" id="ref31">11</reflink>]). However, this conclusion is not absolute, as there are precedents and countries where the mentioned statistical regularity is not confirmed (Mejía‐Rodríguez, Luyten, and Meelissen [<reflink idref="bib23" id="ref32">23</reflink>]; Meinck and Brese [<reflink idref="bib22" id="ref33">22</reflink>]; Contini, Di Tommaso, and Mendolia [<reflink idref="bib11" id="ref34">11</reflink>]).</item> <p></p> <item> ‐ In the area of educational tests, where the test material is generated from the school curriculum and not from psychometric cognitive instruments, the achievement of boys is relatively weaker than that of girls. Girls generally tend to have more favourable school trajectories. Recently, a general trend has emerged that boys and young men are the inferior and losing gender in education (Schwippert et al. [<reflink idref="bib34" id="ref35">34</reflink>]; Hurrelmann and Schultz [<reflink idref="bib18" id="ref36">18</reflink>]).</item> </ulist> <p>It should be noted that the methodological‐epistemological discourse in gender studies is much more modest than the theoretical‐ontological discourse. How does one conduct gender difference research methodologically correctly and properly? If one disregards the current fashionable discourse on the promotion of qualitative research, triangulation and multimethod research, one must conclude that there is a kind of silence, especially in the empirical‐analytical paradigm.</p> <p>Paradigm has its own direction of development. The latter can be described as improving the application of prefabricated mathematical models. It mainly means IRT item response theory, SEM structural equation modelling, etc. However, from the point of view of special research methodology on gender differences, we cannot see any clear progress.</p> <p>How to deal with the fact scientifically and logically when very contradictory empirical results regarding gender differences come out? Suppose sometimes the cognitive gender differences are clearly detected, but sometimes they are not. In one study a clear profile of differences is found, but it cannot be documented in a similar study.</p> <p>As will be shown, the empirical findings of this study are also partially contradictory. The controversy is not due to the inferiority of the research discipline, but to the objective specificity of the social and behavioural sciences. The latter is purely inductive in nature. The formulation of universal statements with a generality quantifier is impossible here; at best, only probabilistic statements are formulated. Their validity is always limited in time and space and bound to a certain period of time, a certain sample, the geographical location and sociocultural environment of the individual study conducted (Popper [<reflink idref="bib30" id="ref37">30</reflink>]). Even a single cognitive study whose data contradict the general trend immediately falsifies the entire paradigm, or at least the research direction, from the perspective of formal inductivism. The methodological discourse does not emphasise enough that international large‐scale studies, entire population testing, and especially meta‐analyses should play a distinctive role in cognitive studies of gender differences. Single sampling studies, especially those with discrepant results, should be compared with studies of the above format, which have a much stronger inductive basis and are less likely to introduce bias or statistical artefacts. Another question that remains open is how to be methodologically precise in a single cognitive comparative study. Can any specific methodological guidelines emerge in addition to the universal ones that apply to every empirical study, such as objectivity, validity and reliability (Scherer [<reflink idref="bib33" id="ref38">33</reflink>])? This paper attempts to substantiate and demonstrate one of these recommendations. This recommendation was not derived deductively, but it was discovered and formulated in the practice of empirical research.</p> <p>What are the research questions presented in the paper? Are there gender differences in school‐age achievement for boys and girls? The subjects covered are mathematics and language subjects (reading, writing, mother tongue, foreign language, literature). If there are differences, what is their profile? How strong are these differences? A final question is, what statistical strategies and methods should be used in gender gap studies that are based on big data and entire population testing rather than samples? How to achieve better heuristic results for such studies?</p> <hd id="AN0183654302-3">Methods</hd> <p>The entire population testing data spanning from 2015 to 2021 was given to the research team by the National Agency for Education (Agency). This agency is responsible for the nationwide compulsory testing of all pupils from grades 4 to 12. Learning achievement is always assessed with standardised tests. Information on the classes tested in the study (age cohorts of pupils), the number of test takers and the distribution by gender are shown in Table 1.</p> <p>1 TABLE Number of pupils tested in age cohorts/grades and their distribution (%) by gender.</p> <p> <ephtml> <table><thead valign="bottom"><tr><th align="left">4th grades</th><th align="center">6th grades</th><th align="center">8th grades</th><th align="center">10th grades</th><th align="center">12th grades</th></tr></thead><tbody valign="top"><tr><td align="left">N<sub>pupils</sub> = 89,531</td><td align="center">N<sub>pupils</sub> = 22,774</td><td align="center">N<sub>pupils</sub> = 35,722</td><td align="center">N<sub>pupils</sub> = 71,901</td><td align="center">N<sub>pupils</sub> = 28,736</td></tr><tr><td align="left">Girls</td><td align="center">Boys</td><td align="center">Girls</td><td align="center">Boys</td><td align="center">Girls</td><td align="center">Boys</td><td align="center">Girls</td><td align="center">Boys</td><td align="center">Girls</td><td align="center">Boys</td></tr><tr><td align="left">49.4</td><td align="center">50.6</td><td align="center">50.1</td><td align="center">49.9</td><td align="center">50.5</td><td align="center">49.5</td><td align="center">50.0</td><td align="center">50.0</td><td align="center">54.7</td><td align="center">45.3</td></tr></tbody></table> </ephtml> </p> <p>1 <emph>Note:</emph> Total data: pupils = 248,664; girls = 125,371 (50.4%); boys = 123,293 (49.6%).</p> <p>The data are consistently collected, maintaining an identical format, thereby naturally forming a longitudinal trend. Additionally, some of the periodic measurements are linked at the individual level, creating a true longitudinal panel. The agency did not collect data for scientific purposes, but for educational administration purposes. Therefore, the quality of the collected data was checked by means of psychometrics.</p> <p>The researchers standardised and normalised the aggregated data. All test scores were transformed into two types of scales: (<reflink idref="bib1" id="ref39">1</reflink>) the standard normal distribution <emph>Z</emph>‐scale and (<reflink idref="bib2" id="ref40">2</reflink>) percentile scale. This was necessary because the agency used scales of different types where the maximum score is, for example, 28, 30, 50 or 100 points. There were precedents for using a scale common in TIMSS‐PISA projects, where the mean is equal to 500 and the standard deviation is 100. Therefore, below in this text, in all tables and graphs, it is mainly the <emph>z</emph>‐scores or percentiles that are explained. The latter quantity is used in addition because not all empirical distributions of test scores correspond perfectly to the normal distribution.</p> <p>Due to the unpredictability of test content, not all sample test items were publicly available. However, estimates of individual subscales or total scales for individual subtopics of mathematics and verbal achievement were already available to the researchers. In grade four, the verbal achievement index consisted of the writing and reading subscales. In higher grades, the index of the analogous name is already formed from the subscales 'Lithuanian Language', 'Literature' and 'Foreign Language'.[<reflink idref="bib1" id="ref41">1</reflink>] The mathematics test in fourth, sixth and eighth grade lasts up to 1 h and includes 30–40 primary tasks. In the 10th grade, the test lasts up to 2 h and includes 30–40 tasks. The central state matriculation examination in grade 12 lasts up to 3 h and includes up to 25 tasks. The researchers who took the data did not have the option of calculating the item characteristic curve for each task. They were also precluded from calculating the Item to total correlation. However, given the sufficient length of the tests, it was possible to justify the good psychometric quality. The units of analysis were aggregated test scores of subscales. Minding a fact that the reliability of a test is nothing more than a function of the length of a test this study used the long tests to ensure content reliability. The verbal test in grades 10 or 12 consists of three different school subjects. It is a mother tongue, literature and a foreign language. Thus, the summative result of the three tests is based on a derivative verbal index, which consists of at least 60–100 primary items in each of these three tests.</p> <p>For example, in grade 4, the factorisation of the eight subscales of the mathematics subject, conducted using the principal component method, yields the following factor weights: <emph>L</emph><subs>mean</subs> = 0.865; <emph>L</emph><subs>min</subs> = 0.738; <emph>L</emph><subs>max</subs> = 0.934. The variance explained by the model is 75.25%. Accordingly, the seventh subscales of the fourth‐grade reading test yield the following factor weights: <emph>L</emph><subs>mean</subs> = 0.823; <emph>L</emph><subs>min</subs> = 0.723; <emph>L</emph><subs>max</subs> = 0.900 and the variance explained by the model is 68.00%. Analogous favourable factorisation indicators were found in all five age cohorts of the pupils studied.</p> <p>It turned out to be appropriate to combine not only the subscales of the same subject but also the scales of different subjects—'Mathematics', 'Lithuanian', 'Literature', 'English'. By further factoring the test results of the above four school subjects in the 12th grade, a model is obtained that explains 65% of the variance. The values of the factor weights are, respectively, as follows: <emph>L</emph><subs>mean</subs> = 0.810; <emph>L</emph><subs>min</subs> = 0.780; <emph>L</emph><subs>max</subs> = 0.84.</p> <p>Thus, on the basis of 'mathematical' and 'verbal' achievement tests, an aggregate 'general educational achievement index' of the third order can be derived with good reason. The correlation between 'mathematical' and 'verbal' achievement was relatively high in all five age cohorts (classes): <emph>r</emph><subs>mean</subs> = 0.627; <emph>r</emph><subs>min</subs> = 0.617; <emph>r</emph><subs>max</subs> = 0.656.</p> <p>The interpretation of the results of the primary and tertiary factorisation is associated with the well‐known Ch. Spearman's 'G‐factor' theory, whose main postulates remain unrefuted even in modern psychology and neuroscience (Jensen [<reflink idref="bib19" id="ref42">19</reflink>]). The 'mathematical' and 'verbal' achievement indices constructed in the study represent a kind of equivalence of mathematical intelligence and verbal intelligence, although one should not put a sign of complete equality between school tests and IQ tests.</p> <p>Favourable values for criterion validity and predictive validity were found. Standardised test scores correlate with grades in the same academic subjects. With the exception of grade 4, where no quantitative classroom assessment in Lithuanian schools, the validation values are favourable in the other age cohorts of pupils. In the area of mathematical achievement, <emph>r</emph><subs>mean</subs> = 0.686; <emph>r</emph><subs>min</subs> = 0.599; <emph>r</emph><subs>max</subs> = 0.747; in the area of verbal achievement, <emph>r</emph><subs>mean</subs> = 0.745; <emph>r</emph><subs>min</subs> = 0.667; <emph>r</emph><subs>max</subs> = 0.791. Most importantly, estimates of standardised tests as a whole make it possible to predict the future results of standardised tests (after 3 years). The correlation coefficients take the following values: (<reflink idref="bib1" id="ref43">1</reflink>) in the area of mathematics achievement when predicting from sixth grade to eighth grade—<emph>r</emph> = 0.535; from 10th grade to 12th grade <emph>r</emph> = 0.793. In the area of verbal achievement, the following coefficients apply: when predicting from sixth grade to eighth grade—<emph>r</emph> = 0.615; from 10th grade to 12th grade—<emph>r</emph> = 0.648.</p> <p>It should be noted that after several years of schooling, the measurement can no longer be carried out with the same test. Thus, although the purpose of testing remains the same in higher grades, the content and difficulty of the exam questions change. Therefore, the values estimated of the validation coefficients to be considered as high.</p> <p>The indicators presented here show an overall favourable psychometric quality of the aggregated indices used in all achievement domains investigated and in all age cohorts studied.</p> <p>Due to the extremely large number of subjects, inferential statistics and statistical tests, both parametric and nonparametric, lose their usual significance in the context of the research conducted. The highest occurring standard error of an index fulfilled the condition SE ≤ 0.0066 on the <emph>z</emph>‐scale. Thus, the largest occurring full length of the confidence interval for the mean is only 0.04 <emph>z</emph>‐scale points for <emph>α</emph> = 0.01 or 0.06 <emph>z</emph>‐scale points for <emph>α</emph> = 0.001. In general, there is talk about even shorter confidence intervals, as the smallest standard error only reached the value 0.0033. In 10 indices, the average standard error mentioned is only 0.0049 points.</p> <p>A typical age cohort (class) in Lithuania usually consists of about 20,000 pupils. By gender, as already mentioned, they are distributed about 50%:50%. The size of the sampling error can be calculated using the VARIMAX method. This size is only 0.2% in the subpopulations, for example, for fourth or sixth graders, when <emph>α</emph> = 0.01. When the target population is roughly halved by gender, it results in up to 10,000 pupils. The formally calculated sampling error in that case is 0.3%. With <emph>α</emph> = 0.001, the error sizes correspondingly reach only 0.3% and 0.4%age points. A difference of 3%–4%, which is often recorded in a typical sampling study with <emph>N</emph> ≈ 1000, should be neglected. In the case of this big data study, such a difference may already represent a proper statistical regularity.</p> <p>A separate aspect in justifying the methodology of the study is the empirical distributions obtained from big data that reflect pupils' mathematical and verbal achievement. Characteristic examples of the dominant distribution type are shown in the graph (see Figure 1). The median, mode and skewness values of all 10 distributions are close to zero, indicating the symmetry of the distributions, which is characteristic of all bell‐shaped curves. However, the kurtosis value of the distributions was negative in all cases, fluctuated around one and had an average value of −1.123. Therefore, the curves are compressed at their sides and their peaks are raised. In that case, one can only speak of the normality of the distributions to a limited extent. It must be hypothetically assumed that we are confronted here with a phenomenon called mixture model and compound probability distribution in statistical theory (Améndola, Engström, and Haase [<reflink idref="bib2" id="ref44">2</reflink>]; Röver and Friede [<reflink idref="bib32" id="ref45">32</reflink>]).</p> <p> <img src="https://imageserver.ebscohost.com/img/embimages/rdk/EJE/01mar25/ejed12802-fig-0001.jpg?ephost1=dGJyMNXb4kSepq84yOvqOLCmsE6epq5Srqa4SK6WxWXS" alt="ejed12802-fig-0001.jpg" title="1 Verbal and mathematical achievement: Empirical distributions of the total index, typical examples, sixth grade; N ≈ 23,000." /> </p> <p></p> <p>Two statistical strategies were triangulated in the analysis. (<reflink idref="bib1" id="ref46">1</reflink>) Analysis of mixed data from the point of view of learning achievement and gender differences was carried out throughout the statistical mass. (<reflink idref="bib2" id="ref47">2</reflink>) Using K‐mean cluster analysis, existing learning achievement types in mathematics and verbal learning achievement are identified. Only then does the search for correlations between achievement type and gender begin. If the inductively recorded learning achievement types and the gender of the pupils are not related to each other, then within each type (cluster) the distribution by gender (%) must be symmetrical. It is the same objectively in the whole pupil population. For the data in this study, this ratio is 49.6% (boys) and 50.4% (girls). A clear deviation from the expected ratio mentioned above indicates that the corresponding type of learning achievement is relatively more 'boyish' or more 'girlish'.</p> <p>In the course of the K‐mean cluster analysis, the six‐cluster model was chosen. There are concrete arguments for this. (<reflink idref="bib1" id="ref48">1</reflink>) The model is interpreted fluidly. (<reflink idref="bib2" id="ref49">2</reflink>) The model retains its structural‐typological stability in all the school classes (age cohorts) studied, of which there were actually five (see Figures 3–5). (<reflink idref="bib3" id="ref50">3</reflink>) Checking the purity and homogeneity of the isolated clusters using the method of one‐factor ANOVA showed that the achievement types in the selected model are clearly differentiated. The distances between the groups on the <emph>z</emph>‐scale are sufficiently large. In individual cases, when there is no significant difference between the group means, this fact is interpreted in a theoretically reasonable way. (<reflink idref="bib4" id="ref51">4</reflink>) Detected clusters—pupil's types by achievement—have an optimal size of about 16.66% each (100:6 ≈ 16.666). The observed variation series of the percentage prevalence of all discovered achievement types (6 types × 5 age groups = 30) forms a Uniform distribution oscillating around the expected value (Kolmogorov–Smirnov <emph>Z</emph> = 1.240, asymp). Sig. (2‐tailed) = 0.092. 5. The six‐cluster model possesses predictive validity. In its typological structure, the model complies with the statistical regularities of the education system, the existence of which in Lithuania is objectively known from other sources (Zabulionis [<reflink idref="bib42" id="ref52">42</reflink>]). In the case of learning achievement, there are significant contrasts between urban and rural schools also between private and state/municipal schools in Lithuania. These contrasts are becoming more significant every year and are detrimental to rural schools and public schools. The socioeconomic status of the family is also a factor indicating significant contrasts of learning results. It indicated that students from the lower social class performed significantly weaker in all tests in this study. The discovered model of the six clusters clearly displays this in its internal structure. The above regularities occur in all studied age cohorts of students. In the clusters with higher achievements, the proportion of private schools, city schools and pupils from socially advantaged families is significantly higher. A reverse regularity also been observed. In the clusters with the lower performance, there are almost no private schools and the proportion of urban schools is extremely low. On the contrary, the proportion of pupils from the lower class and from neglected rural places of residence is clearly overrepresented in the less favourable clusters. For all the reasons mentioned, can certainly speak of the logical validity, construct validity and predictive validity of the chosen six‐cluster model.</p> <hd id="AN0183654302-5">Results</hd> <p>The results are presented according to two different statistical approaches: (<reflink idref="bib1" id="ref53">1</reflink>) calculations from the entire (mixed) dataset; (<reflink idref="bib2" id="ref54">2</reflink>) preliminary stratification of pupils into homogeneous types according to mathematical and verbal achievement using K‐mean cluster analysis, followed by a search for gender differences.</p> <p>When calculating the mixed data (see Table 2), gender differences only show up in the area of verbal achievement. There are no gender differences in mathematical achievement. The distances between the group averages in the standard <emph>z</emph>‐scale for verbal achievement are as follows: diff<subs>mean</subs> = 0.436; diff<subs>min</subs> = 0.237; diff<subs>max</subs> = 0.702. The observed differences in verbal achievement indicate higher achievement by girls and lower achievement by boys in the target population. Both statistical regularities found replicate systematically across all age cohorts of the pupils studied. The statistical purity of the empirical findings is illustrated by the curves of cumulative frequencies, which are noncrossing, 'quiet' and very uniform (Figure 2). A slightly higher variance in achievement is observed in the subgroups of boys, but the effect is minimal here.</p> <p>2 TABLE Verbal and mathematical achievement: descriptive statistics; differences in group means by gender; N tot pupil = 248,664.</p> <p> <ephtml> <table><thead valign="bottom"><tr><th align="left">Grades</th><th align="center">Achiev. subject</th><th align="center">GIRLS</th><th align="center">BOYS</th><th align="center">Mean diff. (<italic>z</italic>)</th><th align="center">Mean diff. (PR)</th></tr><tr><th align="center">Mean <italic>z</italic></th><th align="center">Mean PR</th><th align="center">SD <italic>z</italic></th><th align="center">SD PR</th><th align="center">Mean <italic>z</italic></th><th align="center">Mean PR</th><th align="center">SD <italic>z</italic></th><th align="center">SD PR</th></tr></thead><tbody valign="top"><tr><td align="left">4</td><td align="center">Math.</td><td align="center">−0.021</td><td align="center">49.40</td><td align="center">0.990</td><td align="center">28.55</td><td align="center">0.020</td><td align="center">50.59</td><td align="center">1.01</td><td align="center">29.13</td><td align="center">0.041</td><td align="center">1.184</td></tr><tr><td align="center">Verbal</td><td align="center">0.172</td><td align="center">56.12</td><td align="center">0.970</td><td align="center">26.94</td><td align="center">−0.169</td><td align="center">46.66</td><td align="center">1.00</td><td align="center">27.78</td><td align="center">0.341</td><td align="center">9.451</td></tr><tr><td align="left">6</td><td align="center">Math.</td><td align="center">−0.036</td><td align="center">48.97</td><td align="center">0.991</td><td align="center">28.59</td><td align="center">0.036</td><td align="center">51.04</td><td align="center">1.01</td><td align="center">29.08</td><td align="center">0.072</td><td align="center">2.075</td></tr><tr><td align="center">Verbal</td><td align="center">0.294</td><td align="center">57.44</td><td align="center">0.952</td><td align="center">25.10</td><td align="center">−0.292</td><td align="center">42.00</td><td align="center">0.96</td><td align="center">25.34</td><td align="center">0.586</td><td align="center">15.441</td></tr><tr><td align="left">8</td><td align="center">Math.</td><td align="center">−0.002</td><td align="center">50.69</td><td align="center">0.987</td><td align="center">27.89</td><td align="center">0.002</td><td align="center">50.81</td><td align="center">1.01</td><td align="center">28.61</td><td align="center">0.004</td><td align="center">0.119</td></tr><tr><td align="center">Verbal</td><td align="center">0.117</td><td align="center">54.76</td><td align="center">0.980</td><td align="center">27.61</td><td align="center">−0.120</td><td align="center">48.08</td><td align="center">1.01</td><td align="center">28.38</td><td align="center">0.237</td><td align="center">6.687</td></tr><tr><td align="left">10</td><td align="center">Math.</td><td align="center">0.076</td><td align="center">52.19</td><td align="center">0.997</td><td align="center">28.55</td><td align="center">−0.076</td><td align="center">47.82</td><td align="center">0.10</td><td align="center">28.57</td><td align="center">0.152</td><td align="center">4.373</td></tr><tr><td align="center">Verbal</td><td align="center">0.351</td><td align="center">60.01</td><td align="center">0.940</td><td align="center">26.78</td><td align="center">−0.351</td><td align="center">39.10</td><td align="center">0.93</td><td align="center">26.60</td><td align="center">0.702</td><td align="center">20.012</td></tr><tr><td align="left">12</td><td align="center">Math.</td><td align="center">0.006</td><td align="center">50.17</td><td align="center">0.999</td><td align="center">28.66</td><td align="center">−0.007</td><td align="center">49.80</td><td align="center">1.00</td><td align="center">28.75</td><td align="center">0.013</td><td align="center">0.381</td></tr><tr><td align="center">Verbal</td><td align="center">0.144</td><td align="center">52.20</td><td align="center">1.013</td><td align="center">25.94</td><td align="center">−0.171</td><td align="center">44.13</td><td align="center">0.96</td><td align="center">24.49</td><td align="center">0.315</td><td align="center">8.074</td></tr></tbody></table> </ephtml> </p> <p>2 Abbreviations: Mean <emph>z</emph>, mean of the test values on the <emph>z</emph>‐scale (<emph>z</emph>‐score); Mean PR, mean of the test values on the percentile scale; SD <emph>z</emph>, standard deviation of the test values on the <emph>z</emph>‐scale; SD PR, standard deviation of the test values on the percentile scale; Mean diff. (<emph>z</emph>), difference of the group means on the <emph>z</emph>‐scale; Mean diff. (PR), difference of the group means on the percentile scale.</p> <p> <img src="https://imageserver.ebscohost.com/img/embimages/rdk/EJE/01mar25/ejed12802-fig-0002.jpg?ephost1=dGJyMNXb4kSepq84yOvqOLCmsE6epq5Srqa4SK6WxWXS" alt="ejed12802-fig-0002.jpg" title="2 Mathematic and verbal achievement, sixth grade; gender differences: cumulative curves, N = 22,774." /> </p> <p></p> <p>Using the K‐Means method, a six‐cluster model was developed. The theoretical (abstracted) model is shown in Figure 3. Empirical (observed) types of the model are shown in Figures 4 and 5. Table 3 presents descriptive statistics of the model. It explains: (a) the name of the cluster (in other words, a brief interpretation of the pupils' achievement type); (b) the age cohort of the pupils examined; (c) prevalence (%) of the achievements type in the target population; (d) Group mean values of each achievements group on the percentile scale and <emph>Z</emph> scale; (e) the distance between the average values of the mathematical and verbal achievements within cluster; (f) Distribution of pupils (%) by gender within the achievement type.</p> <p> <img src="https://imageserver.ebscohost.com/img/embimages/rdk/EJE/01mar25/ejed12802-fig-0003.jpg?ephost1=dGJyMNXb4kSepq84yOvqOLCmsE6epq5Srqa4SK6WxWXS" alt="ejed12802-fig-0003.jpg" title="3 Verbal and mathematic achievement: A six‐cluster model, systematically repeated in the 4th–6th–8th–10th–12th grades (age cohorts). Schematic representation of the cluster model. z score, test values on the z‐scale (z‐score); PR, test values on the percentile scale. (A–F) 6 different statistical types of students according to their mathematical and verbal achievement." /> </p> <p></p> <p> <img src="https://imageserver.ebscohost.com/img/embimages/rdk/EJE/01mar25/ejed12802-fig-0004.jpg?ephost1=dGJyMNXb4kSepq84yOvqOLCmsE6epq5Srqa4SK6WxWXS" alt="ejed12802-fig-0004.jpg" title="4 Empirical configuration of clusters. Mathematic and verbal achievements: A six‐cluster model, repeated in 8th and 12th grades; N8th graders = 35,722; N12th graders = 28,736." /> </p> <p></p> <p> <img src="https://imageserver.ebscohost.com/img/embimages/rdk/EJE/01mar25/ejed12802-fig-0005.jpg?ephost1=dGJyMNXb4kSepq84yOvqOLCmsE6epq5Srqa4SK6WxWXS" alt="ejed12802-fig-0005.jpg" title="5 Empirical configuration of clusters. Mathematic and verbal achievements: A six‐cluster model, repeated in sixth grades; N = 22,774." /> </p> <p></p> <p>3 TABLE Mathematic and verbal achievement: a six‐cluster model; Group means within the cluster and distribution by gender within the cluster (%). All school classes, N  = 248,664.</p> <p> <ephtml> <table><thead valign="bottom"><tr><th align="left">Cluster: type of achievement</th><th align="center">Grade/class</th><th align="center">Prevalence %</th><th align="center">Mean of percentiles within cluster</th><th align="center">Mean of <italic>z</italic>‐scores within cluster</th><th align="center">Gender (%) within cluster</th></tr><tr><th align="center">Verbal</th><th align="center">Math.</th><th align="center">Verbal</th><th align="center">Math.</th><th align="center">Boys</th><th align="center">Girls</th></tr><tr><th align="left">1</th><th align="center">2</th><th align="center">3</th><th align="center">4</th><th align="center">5</th><th align="center">6</th><th align="center">7</th><th align="center">8</th><th align="center">9</th></tr></thead><tbody valign="top"><tr><td align="left">A</td><td align="center">The very high achievers (a homogeneous group)</td><td align="center">4</td><td align="center">19.7</td><td align="center">86.16</td><td align="center">84.53</td><td align="center">1.25</td><td align="center">1.20</td><td align="center">44.3</td><td align="center">55.7</td></tr><tr><td align="center">6</td><td align="center">18.9</td><td align="center">83.68</td><td align="center">86.01</td><td align="center">1.29</td><td align="center">1.25</td><td align="center">39.7</td><td align="center">60.3</td></tr><tr><td align="center">8</td><td align="center">20.7</td><td align="center">85.72</td><td align="center">85.62</td><td align="center">1.22</td><td align="center">1.23</td><td align="center">46.6</td><td align="center">53.4</td></tr><tr><td align="center">10</td><td align="center">25.8</td><td align="center">84.74</td><td align="center">79.66</td><td align="center">1.22</td><td align="center">1.04</td><td align="center">31.2</td><td align="center">68.8</td></tr><tr><td align="center">12</td><td align="center">20.2</td><td align="center">84.57</td><td align="center">86.12</td><td align="center">1.41</td><td align="center">1.26</td><td align="center">36.6</td><td align="center">63.4</td></tr><tr><td align="left">B</td><td align="center">The higher achievers (a nonhomogenous group, verbal achievers)</td><td align="center">4</td><td align="center">14.4</td><td align="center">76.73</td><td align="center">42.83</td><td align="center">0.91</td><td align="center">−0.25</td><td align="center">35.0</td><td align="center">65.0</td></tr><tr><td align="center">6</td><td align="center">15.7</td><td align="center">72.44</td><td align="center">50.23</td><td align="center">0.86</td><td align="center">0.01</td><td align="center">29.0</td><td align="center">71.0</td></tr><tr><td align="center">8</td><td align="center">14.5</td><td align="center">77.34</td><td align="center">49.81</td><td align="center">0.92</td><td align="center">−0.03</td><td align="center">38.2</td><td align="center">61.8</td></tr><tr><td align="center">10</td><td align="center">8.4</td><td align="center">75.01</td><td align="center">29.27</td><td align="center">0.88</td><td align="center">−0.72</td><td align="center">21.0</td><td align="center">79.0</td></tr><tr><td align="center">12</td><td align="center">13.2</td><td align="center">71.67</td><td align="center">44.34</td><td align="center">0.90</td><td align="center">−0.20</td><td align="center">30.6</td><td align="center">69.4</td></tr><tr><td align="left">C</td><td align="center">The higher achievers (a nonhomegeneous group, mathematic achievers)</td><td align="center">4</td><td align="center">16.8</td><td align="center">57.32</td><td align="center">76.10</td><td align="center">0.22</td><td align="center">0.90</td><td align="center">56.3</td><td align="center">43.7</td></tr><tr><td align="center">6</td><td align="center">15.2</td><td align="center">51.24</td><td align="center">77.72</td><td align="center">0.06</td><td align="center">0.96</td><td align="center">64.6</td><td align="center">35.4</td></tr><tr><td align="center">8</td><td align="center">15.9</td><td align="center">54.24</td><td align="center">74.17</td><td align="center">0.10</td><td align="center">0.83</td><td align="center">54.9</td><td align="center">45.1</td></tr><tr><td align="center">10</td><td align="center">13.0</td><td align="center">49.43</td><td align="center">79.51</td><td align="center">−0.02</td><td align="center">1.03</td><td align="center">61.6</td><td align="center">38.4</td></tr><tr><td align="center">12</td><td align="center">17.0</td><td align="center">58.08</td><td align="center">74.14</td><td align="center">0.37</td><td align="center">0.84</td><td align="center">56.7</td><td align="center">43.3</td></tr><tr><td align="left">D</td><td align="center">A lower achievers (inhomogeneous group, verbal achievers)</td><td align="center">4</td><td align="center">16.5</td><td align="center">45.45</td><td align="center">27.32</td><td align="center">−0.21</td><td align="center">−0.79</td><td align="center">43.2</td><td align="center">56.8</td></tr><tr><td align="center">6</td><td align="center">15.2</td><td align="center">50.06</td><td align="center">23.54</td><td align="center">0.01</td><td align="center">−0.92</td><td align="center">32.9</td><td align="center">67.1</td></tr><tr><td align="center">8</td><td align="center">15.7</td><td align="center">48.46</td><td align="center">28.69</td><td align="center">−0.11</td><td align="center">−0.78</td><td align="center">42.1</td><td align="center">57.9</td></tr><tr><td align="center">10</td><td align="center">19.3</td><td align="center">48.64</td><td align="center">42.83</td><td align="center">−0.05</td><td align="center">−0.25</td><td align="center">50.2</td><td align="center">49.8</td></tr><tr><td align="center">12</td><td align="center">16.6</td><td align="center">48.12</td><td align="center">19.87</td><td align="center">−0.02</td><td align="center">−1.05</td><td align="center">39.2</td><td align="center">60.8</td></tr><tr><td align="left">E</td><td align="center">A lower achievers (inhomogeneous group, mathematic achievers)</td><td align="center">4</td><td align="center">13.0</td><td align="center">29.14</td><td align="center">56.80</td><td align="center">−0.80</td><td align="center">0.24</td><td align="center">65.7</td><td align="center">34.3</td></tr><tr><td align="center">6</td><td align="center">15.4</td><td align="center">28.49</td><td align="center">50.49</td><td align="center">−0.80</td><td align="center">0.02</td><td align="center">71.3</td><td align="center">28.7</td></tr><tr><td align="center">8</td><td align="center">12.8</td><td align="center">26.84</td><td align="center">52.86</td><td align="center">−0.87</td><td align="center">0.07</td><td align="center">59.0</td><td align="center">41.0</td></tr><tr><td align="center">10</td><td align="center">11.8</td><td align="center">14.64</td><td align="center">46.03</td><td align="center">−1.24</td><td align="center">−0.14</td><td align="center">78.2</td><td align="center">21.8</td></tr><tr><td align="center">12</td><td align="center">15.8</td><td align="center">33.39</td><td align="center">53.28</td><td align="center">−0.59</td><td align="center">0.11</td><td align="center">56.7</td><td align="center">43.3</td></tr><tr><td align="left">F</td><td align="center">An extreme low achievers (crisis homogenous group)</td><td align="center">4</td><td align="center">19.7</td><td align="center">14.61</td><td align="center">14.38</td><td align="center">−1.32</td><td align="center">−1.23</td><td align="center">58.7</td><td align="center">41.3</td></tr><tr><td align="center">6</td><td align="center">19.6</td><td align="center">16.54</td><td align="center">14.09</td><td align="center">−1.26</td><td align="center">−1.24</td><td align="center">61.4</td><td align="center">38.6</td></tr><tr><td align="center">8</td><td align="center">20.4</td><td align="center">15.31</td><td align="center">14.99</td><td align="center">−1.28</td><td align="center">−1.27</td><td align="center">55.3</td><td align="center">44.7</td></tr><tr><td align="center">10</td><td align="center">21.6</td><td align="center">19.69</td><td align="center">13.50</td><td align="center">−1.06</td><td align="center">−1.27</td><td align="center">61.2</td><td align="center">38.8</td></tr><tr><td align="center">12</td><td align="center">17.2</td><td align="center">18.55</td><td align="center">16.72</td><td align="center">−1.17</td><td align="center">−1.16</td><td align="center">50.2</td><td align="center">49.8</td></tr></tbody></table> </ephtml> </p> <p>Clusters 'A' and 'F' (see Figure 3) reflect two extreme (contrasting) types of achievement. Cluster 'A' is characterised by very high achievement and is concentrated in the 85th percentile rank. The very low achievement cluster 'F' includes pupils whose achievement is concentrated at the 15th percentile rank. The distance between the group means on the <emph>z</emph>‐scale here is about 2.5 standard deviations. The identified contrasting pupils' types have one essential fact in common: the achievement after the blocks of both school subjects is homogeneous—very high or very low.</p> <p>The remaining four types of pupil achievement are heterogeneous in terms of their internal structure. The mathematical achievement of a part of pupils is relatively higher, while the verbal achievement indicator is relatively lower (see clusters 'C' and 'E'). Here, the regularity of inversion can also be observed. The verbal achievement of the pupils is relatively high but the mathematical achievement is relatively low (see clusters 'B' and 'D'). The distance between the means of mathematical and verbal achievements within the same cluster in inhomogeneous groups is about 0.85 of the standard deviation. According to Cohen's effect size, such a difference is large. On this basis, the concepts of 'inhomogeneous' and 'homogeneous' achievement groups are introduced in the interpretation of the results. Furthermore, the relative concepts of the 'mathematicians' group and the 'verbalists' group are introduced. The characteristic 'X'‐shaped cut lines reflect a rather pronounced effect of subject profiling of achievement (mathematics vs. verbal achievements): see Figure 3, clusters 'B', 'C' and 'D', 'E'.</p> <p>The six‐cluster model discussed clearly differentiates the types of pupils according to their general learning achievement level (hierarchy). It clearly distinguishes four levels of achievement: (<reflink idref="bib1" id="ref55">1</reflink>) 'A' cluster—type 'very high achievement'; (<reflink idref="bib2" id="ref56">2</reflink>) type 'higher achievement' ('B' and 'C' clusters); (<reflink idref="bib3" id="ref57">3</reflink>) type 'lower achievement' (clusters D and 'E') and (<reflink idref="bib4" id="ref58">4</reflink>) type 'very low' (cluster F). Clusters A and F are 'opposite' in terms of the achievement hierarchy. From a social and pedagogical[<reflink idref="bib2" id="ref59">2</reflink>] point of view, the clusters (types of achievement) 'A', 'B' and 'C' can be considered 'favourable' and the clusters 'D', 'E', 'F' 'unfavourable'.</p> <p>From Table 3, columns 4–5 and 6–7, it can be seen that within the inhomogeneous clusters ('B', 'C', 'D', 'E') the differences in the group means are large and indicate the fundamental contrast between mathematical and verbal achievements. On the percentile scale, the mean difference—mean<subs>diff</subs> = 24.67; and on the <emph>z</emph>‐scale, the difference between the group means is mean<subs>diff</subs> = 0.87. Thus, the mentioned distance within inhomogeneous clusters occupies a full quartile, and on the <emph>z</emph>‐scale, this distance is approximately equal to one standard deviation. According to the concept of the Cohen size effect, such a difference can be considered large. In contrast, within the homogeneous clusters ('A' and 'F', see Figure 3), the differences between the group averages of the mathematical and verbal achievements index are minimal. On the percentile scale, these differences are as follows: mean<subs>diff</subs> = 2.171; On the <emph>Z</emph>‐scale, the group mean differences are: mean<subs>diff</subs> = 0.077. Both values converge towards zero and this shows that there are no differences between mathematical and verbal achievements within the clusters mentioned.</p> <p>Thus, the identified six‐cluster model clearly distinguishes different statistical types (clusters) of pupils according to their learning achievements in mathematical and verbal domains. Moreover, the model maintains its internal structural stability across all age cohorts studied. That is, the model and its identified learning achievement types are systematically repeated in all five age cohorts studied without fundamentally changing their identity and designation (Table 3). The actual prevalence of the identified types in the target population averages 16.666% when <emph>N</emph> = 30, so in this case the observed variable is completely identical to the expected variable.</p> <p>For visualisation, Figure 4 shows the diagrams of the six‐cluster model in 8th and 12th grades and Figure 5 (already on a larger scale) shows the verbal‐mathematical achievements typology model calculated from the total census data in grade 6.</p> <p>Examination of the internal structure of the six‐cluster model revealed a characteristic statistical regularity in all five age cohorts studied. In the set of 30 dichotomous distributions of boys versus girls, there is not a single precedent where the observed distribution by gender within the achievement type (cluster) would have at least approximated the expected 50:50% ratio (see Table 3, its 8th and 9th columns). Thus, all six achievement types found are relatively either more 'girly' or more 'boyish'. There are significant gender effects in both verbal and mathematical achievements.</p> <p>A cross‐tabulation analysis between pupils' gender and the structure of the six‐cluster model in five pupils' age cohorts was conducted. Due to the extremely large samples, the chi‐square significance value is also extremely high—dozens of zeros after the decimal point. A more meaningful measure is the phi coefficient, which is usually considered a measure of the effect size of the chi value. The following coefficients were found: Phi<subs>4th grade</subs> = 0.20; Phi<subs>6th grade</subs> = 0.32; Phi<subs>8th grade</subs> = 0.14; Phi<subs>10th grade</subs> = 0.35; Phi<subs>12th grade</subs> = 0.17.</p> <p>The cluster called 'The very high achievers (a homogeneous group), (Type A)' is, as mentioned, extremely favourable from a social and educational point of view. The average prevalence of this achiever type in the five age cohorts is about 1/5 of the population, with a quantitative dominance of girls (61.1%) within the type. On the contrary, in the most unfavourable cluster from a social and educational point of view, labelled 'An extreme low achiever (crisis homogeneous group), (Type F)', the prevalence of which is also about 1/5 of the population, there is a quantitative preponderance of boys (57.4%).</p> <p>Four clusters with middle achievement remain ('B', 'C', 'D', 'E'), which make up about 3/5 of the pupils' population in grades 4 to 12. The subject profiling—verbal versus mathematical achievement and gender effects become very clear here.</p> <p>For example, in the 'B' and 'D' clusters of the 'verbal' profile, the asymmetry by gender in separate cases is 21% and 79%, with an obvious quantitative advantage on the side of the girls. In the verbal profile clusters of the five age cohorts, boys average 36.1% and girls 63.9%. In the mathematical profile clusters, too, the asymmetry of the dichotomous gender variable is clearly pronounced. In a single case in grade 10, the internal asymmetry of clusters 'C' and 'D' in terms of gender reached 22% and 78%, respectively, in which case the obvious quantitative advantage is on the side of boys. In the five age cohorts within the mathematical clusters, the girls achieved an average of only 37.5%, with the boys clearly prevailing with the value of 62.5%.</p> <hd id="AN0183654302-10">Discussion</hd> <p>According to the authors of the article, the study prioritises 'epistemological findings' rather than 'ontological findings' regarding gender differences. The central methodological inquiry revolves around how to investigate gender differences using large‐scale studies and big data.</p> <p>First, it is appropriate to discuss ontological findings and their nature. That boys and men increasingly remain losers in education, and become a kind of 'weaker gender' in education, is known from many other relevant empirical studies (Schwippert et al. [<reflink idref="bib34" id="ref60">34</reflink>]; Hurrelmann and Schultz [<reflink idref="bib18" id="ref61">18</reflink>]). This becomes particularly clear when it comes not to psychometric cognitive tests, but to learning achievement tests and school grades. The same is evident in the patterns of boys' and men's educational biographies. The conditional delay of boys in reading and thus in verbal achievement is well documented in the PIRLS and PISA studies (Oberleiter et al. [<reflink idref="bib27" id="ref62">27</reflink>]; Steinmann, Strietholt, and Rosén [<reflink idref="bib36" id="ref63">36</reflink>]).</p> <p>By the way, within the historical tradition of research on cognitive achievement and gender differences, a specific approach remains relevant even today. The general level of cognitive achievement of the gender does not differ overall, but in the population of boys and men, mathematical and spatial achievement is more pronounced, in the population of girls and women, verbal achievement is more pronounced. It is not uncommon to try to explain this with the laws of evolutionary psychology. On the other hand, there are studies in which boys' lead in learning mathematics has not been conclusively confirmed empirically or has weakened over the course of history. The studies that have found such facts are not the majority (Perez Mejias et al. [<reflink idref="bib28" id="ref64">28</reflink>]; Schwippert et al. [<reflink idref="bib34" id="ref65">34</reflink>]). The fact that verbal achievement tends to be the domain of girls and mathematical ability tends to be the domain of boys is partially confirmed by our research. In this case, the term 'partially' is used deliberately. Because in the highest achievement group, as the data of our study show, the following can be observed. Girls quantitatively outnumber and demonstrate equally very good mathematics achievements and verbal achievements. Therefore, in the context of this study, the existing traditional view of girls lagging behind in mathematics—whether real or alleged—should not be taken as an undisputed truth.</p> <p>When interpreting the data of the study, a large number of empirical studies are of particular importance, which shows that the natural cognitive development of girls is systematically distorted by social stereotypes, pressure from the social environment, supposedly, in a socially unfavourable direction (Anger, Kohlisch, and Plünnecke [<reflink idref="bib3" id="ref66">3</reflink>]; Breda et al. [<reflink idref="bib8" id="ref67">8</reflink>]; Van Miegroet and Glass [<reflink idref="bib38" id="ref68">38</reflink>]; Ghasemi and Burley [<reflink idref="bib15" id="ref69">15</reflink>]; Baye and Monseur [<reflink idref="bib5" id="ref70">5</reflink>]; Kaiser [<reflink idref="bib20" id="ref71">20</reflink>]). The false stereotype is: 'Mathematics is not a girl's thing'. When discussing the research on gender differences in cognition within the paradigm of neurosciences and other hard sciences on human physiology and brain function, one key point must be noted (Hentzen et al. [<reflink idref="bib17" id="ref72">17</reflink>]; Yuan et al. [<reflink idref="bib41" id="ref73">41</reflink>]). Under the conditions of the rather complicated multilevel causality, it is probably not possible to prove unconditionally what causes the gender‐specific differences in mathematics achievement that are still present in one study or another and that often work to the disadvantage of girls. Was it due to gender hormonal, brain morphological factors, etc.? Such differences are often objective and even trivial. Possibly the causes can be traced back to evolutionary psychological factors? Or, finally, are the observed gender differences in mathematics achievement due to a stereotypical sociocultural environment? It is worth considering a thought experiment: when showering outdoors in a heavy downpour, would it be impossible to distinguish the drops that fell from the clouds and those from the water pipe onto your body?</p> <p>The study's findings are presumed to align favourably with the modern theoretical paradigm of gender equality as well as the paradigm of equal opportunities in education and socialisation. The study's results aptly challenge the universality and unconditional nature of the statement, 'girls are always weaker in mathematics'. This is particularly evident in the study's results, which demonstrate that very powerful girls excel equally in solving both verbal and mathematical test items. In the discourses on economic competition, the fourth industrial revolution and the challenges of technological progress, the question is often raised: Where do employers in business and the public sector get talent? Why are young people in general, and girls in particular, in no hurry to choose to study mathematics and science (Anger, Kohlisch, and Plünnecke [<reflink idref="bib3" id="ref74">3</reflink>]; Charles et al. [<reflink idref="bib9" id="ref75">9</reflink>])? As the entire population testing study shows, there are at least 12.2% of girls in the population of Lithuanian schoolchildren aged 9–19 who excel in both mathematical and verbal tasks and have universal interdisciplinary talents. The recommendation to include girls and women more courageously in mathematics and science studies or the corresponding professions is not a half‐empty ideological dream or a humanistic claim that goes beyond reality. All this has an objective basis and a real statistical foundation on which talented girls can be recruited to be motivated to study and choose mathematics and science courses to help the industry and the service sector solve the problem of talent shortage. Of course, in the future, it will be useful to further explore gender differences in cognitive achievement, especially in the subgroup of the most talented pupils.</p> <p>The conditional dominance of girls in a very favourable achievements cluster could hypothetically be explained primarily by social factors. The relatively low proportion of girls in the lowest achievements cluster is also explained in the same way. Gender stereotypes and manifestations of discrimination are always visible in society. On the other hand, in the modern family, school and community, the prevalence and importance of erroneous stereotypes has declined significantly in recent times. It opens up new opportunities for girls in the field of mathematical learning that were previously unreasonably restricted from the point of view of educational history.</p> <p>When talking about intermediate and lower‐achieving pupils, a complicated social mission for education emerges here. It is the search for gender‐specific teaching and learning methods. The social and educational environment must encourage and motivate girls to dive more decisively into mathematics, and boys—into the world of reading and writing.</p> <p>Recently, considerations about the possible dismantling of co‐education have become more frequent. The dismantling of mixed‐gender education is expected to open up better learning opportunities for both genders (Blomberg [<reflink idref="bib7" id="ref76">7</reflink>]; Moya [<reflink idref="bib25" id="ref77">25</reflink>]). There is still a lack of evidence from school experiments on this point. Furthermore, the educational policy vision should also be discussed in relation to the real possibilities of public finances. The small demographically and economically weaker municipalities are possibly at risk. Of course, an alternative educational policy vision can also be formulated. It states that under conditions of gender equality, all educational content and all teaching/learning methods must also be standardised from a gender perspective. As far as the two alternatives or their creative symbiosis are concerned, this opens up a heuristically promising field of discussion for research and educational policy debates.</p> <p>Historically, as far as education and careers are concerned, boys have always been a privileged social group. Why, in a digital age under the conditions of a welfare society, does a significant proportion of young people turn into a socially weaker group of educational losers? Which cultural‐anthropological and psychosocial mechanisms are responsible for this? In the future, more attention has to be paid to this problem.</p> <p>The study carried out also stimulates an epistemological discussion. The question arises as to why contradictory results are obtained in one and the same empirical study based on the entire population testing. In one case, there are no gender‐specific differences in mathematical achievement; in the other case, these differences are not only discernible, they are even quite pronounced. Why and how does this happen? A hypothetical assumption should be made that under the conditions of the entire population testing and working with big data, a mixture model and compound probability distribution naturally emerges. It would be appropriate to test this hypothesis by organising a large meta‐analysis study in the future that would examine the empirical distributions of many large‐scale studies and entire population testing modelling cognitive variables. Indeed, when working specifically with mixture distributions, it may be useful to first identify the basic statistical types of subjects and only then begin to look for gender (or other) differences. This is not a prescriptive instruction, but a creative suggestion to routinely integrate appropriate statistical approaches into the research design. After all, such triangulation, which is fashionable nowadays, may include not only data scanning but also data processing methods and alternative analytical approaches.</p> <p>Is it possible in the status of the hypothesis to present an interpretation of what is objectively happening in the inner structure of the mixture distribution? Again, it is appropriate to use an example in the form of a visual analogy. Ocean water appears to form a single substance. However, at different depths, depending on temperature, oxygen and light content, separate hydro‐layers form, functioning according to different laws, creating different ecosystems and 'inhabiting' different aquatic fauna and flora. If one abandons the subtle hierarchical analysis of the layers, the regularity of all this would be impossible to discern. According to the authors, something similar may happen with those mixture distributions generated from cognitive abilities in big data studies. On the separate level of the achievement hierarchy, there are objective statistical regularities that are different and contradictory to each other. If the basic statistical types of achievement are not discovered at the outset, then these regularities level out when the data are analysed in the general statistical mass, stochastically 'cancelling' each other out and remaining latent, unrecognised by researchers, even though they objectively exist. Perhaps there is a specific bias effect here?</p> <p>K‐mean clustering is not the only method that allows the preliminary analytical classification of subjects into the basic statistical types mentioned above. Latent class analysis and CHAID‐Chi Square automatic interaction detection are worth mentioning. We do not want to emphasise the specific statistical method of typing, but the corresponding analytical‐explorative approach. Its core consists of structuring the data exploratively at the beginning and searching for basic statistical types. This analytical approach could provisionally be called the 'Structural Typing Approach in Large‐scale Studies'. It should be noted that the corresponding analytical approach is particularly applicable in big data and entire population testing studies. In traditional sampling studies, where the number of subjects is usually between 500 and 2000, the proposed approach would probably be much less efficient and would not reveal its heuristic capabilities.</p> <p>It is appropriate to recall the discourse of the philosophy of science, especially the legacy of the classicist Popper ([<reflink idref="bib30" id="ref78">30</reflink>]) and his followers (Albert [<reflink idref="bib1" id="ref79">1</reflink>]). Empirical studies primarily rely on inductive reasoning. Especially in the social and behavioural sciences, the so‐called all‐statements with a kvantor of general validity are not possible. Here, only probabilistic statements apply, whose conditional truth is objectively limited in time and space. Any relative probabilistic truth established in a single empirical study is only valid for a certain limited group, geographical location and time period. It is wrong to say in empirical studies, even in behavioural experiments, 'This study proved ...'. The inductive approach, according to the classics of the philosophy of science, at best only produces a change in the degree of probability of a hypothesis towards its truth or falsity. The inductive approach never guarantees conclusive, irrefutable proof. The concept of epistemology that truth is achieved gradually through trial and error presupposes the exceptional value of some scientific genres for the study of gender differences. There is talk here of large‐scale studies, big data studies, entire population testing and meta‐analyses. Cognitive testing on a national level is extremely rare and complicated from a legal‐administrative and organisational point of view. The condition that all pupils in the respective country are regularly assessed using a valid and unified testing methodology, which is also administered by a single centre, is difficult to implement in reality.</p> <p>Therefore, in the future, the focus should be on cognitive studies based on the comparison of many countries, such as TIMSS, PISA, PIRLS, etc. According to the authors, meta‐analyses based on such studies can be particularly valuable heuristically. In this case, the problem of individual empirical studies and the temporal and spatial limitations of their results is at least partially mitigated. Of course, cross‐country comparative studies are based on a sampling investigation, but large samples taken from many countries at the same time guarantee better ecological validity of the results and better relative universality of the empirical findings, including their generalisability.</p> <p>The research findings obtained in this phase enable the formulation of questions meaningful for future research. (<reflink idref="bib1" id="ref80">1</reflink>) Will the relatively stable model of the six types of pupils found in a single country and in a single large‐scale study be repeated without major variations in the large‐scale studies of populations of other countries and cultures? The latter is, in the opinion of the authors, quite likely. This would confirm the validity and universality of the structural classification regularities discovered in the study. It would make sense to collect data using national large‐scale studies such as the National Assessment of Educational Progress (NAEP), USA, Scottish National Standardised Assessments (SNSAs), the National Educational Panel Study (NEPS) and VERA (an abbreviation for 'comparison work' = 'VERgleichsArbeiten') Germany, as well as TIMSS and PISA. (<reflink idref="bib2" id="ref81">2</reflink>) It would be appropriate to investigate whether the model of the six types of pupils and its gender‐specific effects would also be consistent with the classification models created using alternative statistical methods. The first focus is on the analysis of latent class and CHAID. The multiple replication of the pattern of statistical types, determined using different mathematical methods, would additionally prove the universality of the classification of students determined in the study. (<reflink idref="bib3" id="ref82">3</reflink>) It would make sense to investigate whether the six‐type model of achievement would maintain its stability if verbal and nonverbal subscales of IQ were used instead of school tests.</p> <hd id="AN0183654302-11">Conclusions</hd> <p></p> <ulist> <item> Through traditional calculations, it was found in the general statistical dataset that: (a) there are medium differences between the genders in the area of verbal achievement; in all age groups studied, girls' achievement is significantly better than boys. (b) However, no gender differences were found in mathematical achievement.</item> <p></p> <item> After a preliminary grouping of the entire population testing data into six distinct and theoretically interpretable types of pupils' achievement using the K‐mean method, it became clear that: (a) differences between girls and boys in both verbal and mathematical achievements are consistently present; (b) the differences in achievement are significant; (c) all six types of achievement inductively generated from the entire population testing data are structurally stable and replicated across all age cohorts of pupils studied; (d) each of the six types of pupil achievement found is clearly specific from the point of view by gender of pupils and can be seen as either relatively more 'girlish' or more 'boyish'.</item> <p></p> <item> The six‐cluster model that was established reveals the following statistical patterns in terms of gender differences. (<reflink idref="bib1" id="ref83">1</reflink>) The highest achievement type, concentrated around the 85th percentile and above, showcases exceptionally strong mathematical and verbal pupil achievements. Girls are predominantly represented in this achievement category. (<reflink idref="bib2" id="ref84">2</reflink>) In contrast, the lowest achievement category is characterised by significantly low levels of both mathematical and verbal pupils' achievements. This achievement type is positioned at the 15th percentile rank and below. In this achievement type, boys predominate quantitatively. The remaining four types of middle achievement occupy positions between the 20th and 80th percentile rank. They are characterised by the following statistical regularity: (a) statistical types in which verbal achievement is relatively stronger are quantitatively dominated by girls; boys quantitatively predominate in statistical types in which mathematical achievement is relatively stronger.</item> <p></p> <item> In the form of a hypothesis, a methodological conclusion can be drawn. Various alternative statistical strategies employed and triangulated in this study to identify gender differences were marked by varying levels of analytical and heuristic potential. Sensitivity and precision in detecting gender differences can be enhanced through a statistical approach characterised by appropriate logic and methodology. First, the basic statistical types of pupils according to verbal and mathematical achievement are to be discovered based on big data. Only then is a search made for correlations between the types of achievement and the gender of the pupils. The objective reason why precisely this analytical approach is superior is that the entire population testing data (<emph>N</emph>  ≈ 250,000), which captures learning achievement over several years, presumably forms a mixture distribution. In a traditional approach, whereby the data are only analysed in the total statistical mass, the differences between genders become out and remain latent, although they are, in fact, present.</item> </ulist> <hd id="AN0183654302-12">Conflicts of Interest</hd> <p>The authors declare no conflicts of interest.</p> <hd id="AN0183654302-13">Data Availability Statement</hd> <p>The authors have nothing to report.</p> <ref id="AN0183654302-14"> <title> Footnotes </title> <blist> <bibl id="bib1" idref="ref39" type="bt">1</bibl> <bibtext> In terms of the nationality of the population (and pupils), Lithuania has a very homogeneous population. The mismatch of a child's language of learning with his/her mother tongue (family language) as a factor reducing learning achievement is of little significance for Lithuania. An exception is the case of the children of the few re‐migrants who return to their homeland with little or no knowledge of the Lithuanian language. In Lithuania, there are few pupils whose mother tongue is Polish or Russian and who have the opportunity to learn, be tested and examined in it. Foreign languages such as German, French and Russian are very rarely chosen by pupils as their main foreign language.</bibtext> </blist> <blist> <bibl id="bib2" idref="ref40" type="bt">2</bibl> <bibtext> In 'disadvantaged' clusters, the proportion of rural schools and pupils receiving free meals and support is disproportionately higher compared to the overall population. 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  Label: Title
  Group: Ti
  Data: Differences in Mathematical and Verbal Achievement between Girls and Boys: The Heuristic Potential of the Structural Typing Approach in Large-Scale Studies
– Name: Language
  Label: Language
  Group: Lang
  Data: English
– Name: Author
  Label: Authors
  Group: Au
  Data: <searchLink fieldCode="AR" term="%22Gediminas+Merkys%22">Gediminas Merkys</searchLink> (ORCID <externalLink term="https://orcid.org/0000-0002-9461-8105">0000-0002-9461-8105</externalLink>)<br /><searchLink fieldCode="AR" term="%22Sigitas+Vaitkevicius%22">Sigitas Vaitkevicius</searchLink><br /><searchLink fieldCode="AR" term="%22Daiva+Bubeliene%22">Daiva Bubeliene</searchLink> (ORCID <externalLink term="https://orcid.org/0000-0003-3198-1633">0000-0003-3198-1633</externalLink>)<br /><searchLink fieldCode="AR" term="%22Leonidas+Sakalauskas%22">Leonidas Sakalauskas</searchLink>
– Name: TitleSource
  Label: Source
  Group: Src
  Data: <searchLink fieldCode="SO" term="%22European+Journal+of+Education%22"><i>European Journal of Education</i></searchLink>. 2025 60(1).
– Name: Avail
  Label: Availability
  Group: Avail
  Data: Wiley. Available from: John Wiley & Sons, Inc. 111 River Street, Hoboken, NJ 07030. Tel: 800-835-6770; e-mail: cs-journals@wiley.com; Web site: https://www.wiley.com/en-us
– Name: PeerReviewed
  Label: Peer Reviewed
  Group: SrcInfo
  Data: Y
– Name: Pages
  Label: Page Count
  Group: Src
  Data: 14
– Name: DatePubCY
  Label: Publication Date
  Group: Date
  Data: 2025
– Name: TypeDocument
  Label: Document Type
  Group: TypDoc
  Data: Journal Articles<br />Reports - Research
– Name: Audience
  Label: Education Level
  Group: Audnce
  Data: <searchLink fieldCode="EL" term="%22Elementary+Secondary+Education%22">Elementary Secondary Education</searchLink>
– Name: Subject
  Label: Descriptors
  Group: Su
  Data: <searchLink fieldCode="DE" term="%22Foreign+Countries%22">Foreign Countries</searchLink><br /><searchLink fieldCode="DE" term="%22Elementary+Secondary+Education%22">Elementary Secondary Education</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematics+Achievement%22">Mathematics Achievement</searchLink><br /><searchLink fieldCode="DE" term="%22Verbal+Development%22">Verbal Development</searchLink><br /><searchLink fieldCode="DE" term="%22Standardized+Tests%22">Standardized Tests</searchLink><br /><searchLink fieldCode="DE" term="%22National+Competency+Tests%22">National Competency Tests</searchLink><br /><searchLink fieldCode="DE" term="%22Gender+Differences%22">Gender Differences</searchLink><br /><searchLink fieldCode="DE" term="%22Data+Collection%22">Data Collection</searchLink><br /><searchLink fieldCode="DE" term="%22Sample+Size%22">Sample Size</searchLink><br /><searchLink fieldCode="DE" term="%22Evaluation+Methods%22">Evaluation Methods</searchLink>
– Name: Subject
  Label: Geographic Terms
  Group: Su
  Data: <searchLink fieldCode="DE" term="%22Lithuania%22">Lithuania</searchLink>
– Name: DOI
  Label: DOI
  Group: ID
  Data: 10.1111/ejed.12802
– Name: ISSN
  Label: ISSN
  Group: ISSN
  Data: 0141-8211<br />1465-3435
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: The results of total testing from the years 2015-2022 on the mathematical and verbal achievement of Lithuanian pupils (N [approximately equal to] 250,000) are presented. These are the standardised tests from grades 4 to 12. The K-Means method has discovered six types of achievement. The highest achievement type is dominated by girls (61.1%) who perform well on both mathematical and verbal tasks. The lowest achievement type is dominated by boys (57.4%) who solve both mathematical and verbal tasks extremely poorly. Each of these types makes up 1/5 of the population, and the gap between the means of their groups is about 2.5 standard deviations. The remaining four types of achievement are in the 20th to 80th percentile and make up about 60% of the population. Differences in means within the same type between mathematic and verbal achievement average 0.85 standard deviations or span one quartile. Gender differences are clearly visible in this subgroup: boys solve mathematical tasks better and verbal tasks worse; girls solve verbal tasks better and mathematical tasks worse. Big data may form a mixed distribution. It is appropriate to first discover the basic types of achievement and only then look for gender-specific differences. Such a type-building approach is heuristically superior to the conventional approach of working only with the mixed dataset.
– Name: AbstractInfo
  Label: Abstractor
  Group: Ab
  Data: As Provided
– Name: DateEntry
  Label: Entry Date
  Group: Date
  Data: 2025
– Name: AN
  Label: Accession Number
  Group: ID
  Data: EJ1461238
PLink https://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=eric&AN=EJ1461238
RecordInfo BibRecord:
  BibEntity:
    Identifiers:
      – Type: doi
        Value: 10.1111/ejed.12802
    Languages:
      – Text: English
    PhysicalDescription:
      Pagination:
        PageCount: 14
    Subjects:
      – SubjectFull: Foreign Countries
        Type: general
      – SubjectFull: Elementary Secondary Education
        Type: general
      – SubjectFull: Mathematics Achievement
        Type: general
      – SubjectFull: Verbal Development
        Type: general
      – SubjectFull: Standardized Tests
        Type: general
      – SubjectFull: National Competency Tests
        Type: general
      – SubjectFull: Gender Differences
        Type: general
      – SubjectFull: Data Collection
        Type: general
      – SubjectFull: Sample Size
        Type: general
      – SubjectFull: Evaluation Methods
        Type: general
      – SubjectFull: Lithuania
        Type: general
    Titles:
      – TitleFull: Differences in Mathematical and Verbal Achievement between Girls and Boys: The Heuristic Potential of the Structural Typing Approach in Large-Scale Studies
        Type: main
  BibRelationships:
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      – PersonEntity:
          Name:
            NameFull: Gediminas Merkys
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          Name:
            NameFull: Sigitas Vaitkevicius
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            NameFull: Daiva Bubeliene
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            NameFull: Leonidas Sakalauskas
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          Dates:
            – D: 01
              M: 03
              Type: published
              Y: 2025
          Identifiers:
            – Type: issn-print
              Value: 0141-8211
            – Type: issn-electronic
              Value: 1465-3435
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            – Type: volume
              Value: 60
            – Type: issue
              Value: 1
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            – TitleFull: European Journal of Education
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