Exploring dropout risk in higher education in Croatia: an empirical analysis

IN ENGLISH: The study examines the association of social background, academic-related and institution-related factors with indicators of higher education dropout risk, i.e. students' perceived probability of graduating and their consideration of leaving their studies. Bivariate analysis and multilevel logistic models were used to analyse data from 1533 students from 25 study programs of the University of Zagreb, Croatia. The results confirmed the assumption that higher education dropout risk may be associated with different factors (i.e. social background, academic and institution-related characteristics), but also that there may be differences regarding the two indicators of perceived dropout risk. Moreover, the analysis revealed that perceived dropout risk may be viewed as part of a process of self-selection in which a combination of different factors leads a student to withdraw from higher education. Accordingly, the impact of the covariates of dropout risk should not be viewed only relative to each other, but should be evaluated in the context of educational decision-making net of academic ability. --------------- IN CROATIAN: U radu se ispituje povezanost društvenog podrijetla te različitih akademskih i institucionalnih čimbenika s pokazateljima rizika od napuštanja visokog obrazovanja (tj. sa studentskom procjenom vjerojatnosti diplomiranja i razmišljanjem o napuštanju studija). Bivarijatna analiza i višerazinski logistički modeli korišteni su u analizi podataka prikupljenih na 1533 studenata s 25 studijskih programa Sveučilišta u Zagrebu. Rezultati potvrđuju pretpostavku o povezanosti rizika od napuštanja visokog obrazovanja i različitih čimbenika (tj. društvenog podrijetla, akademskih i institucionalnih varijabli), ali i da postoje određene razlike u vezi dva korištena pokazatelja percipiranog rizika. Nadalje, analiza ukazuje da se percipirani rizik od napuštanja studija može promatrati kao dio procesa samoselekcije u kojem kombinacija različitih čimbenika vodi studenta k napuštanju visokog obrazovanja. Sukladno tome, upućuje se da nije dovoljno samo procjenjivati relativne doprinose različitih korelata rizika od napuštanja studija, nego je potrebno i sagledati te doprinose u kontekstu donošenja obrazovnih odluka neovisno o akademskom postignuću

Comparison of results of candidates from different dialectal regions on items related to the texts written in Čakavian dialect in Croatian language state final examination

Jedan od suvremenih izazova u području konstrukcije pismenih provjera znanja je razumijevanje razlika u uspjehu različitih skupina ispitanika na pojedinim zadacima. Razumijevanje ovih razlika je od posebne važnosti na ispitima visokog rizika kao što su ispiti državne mature. Cilj ovog rada bio je ispitati razlike u uspješnosti rješavanja zadataka državne mature iz Hrvatskoga jezika vezanih uz polazne tekstove pisane čakavskim narječjem među pristupnicima iz različitih dijalektalnih regija (čakavske, kajkavske i štokavske). Usporedbom prosječne riješenosti zadataka vezanih uz čakavske tekstove te analizama diferencijalnoga funkcioniranja zadataka (engl. differential item functioning) i diferencijalnoga funkcioniranja čvora zadataka (engl. differential bundle functioning) pronađene su vrlo male razlike u rezultatu u korist pristupnika iz čakavske regije u odnosu na pristupnike iz kajkavske i štokavske regije. Na temelju ovih rezultata, u stručnoj raspravi donesena je preporuka o nastavku uporabe izvornih tekstova na čakavskom, kajkavskom i štokavskom narječju na ispitima državne mature iz Hrvatskog jezika, pri čemu trebaju biti podjednako zastupljena sva narječja kako pristupnici ne bi bili u neravnopravnom položaju zbog pripadnosti svojega razgovornog jezika jednomu narječju.One of the modern challenges in the field of written examination construction is the understanding of the difference in the success of different groups of examinees on individual items. Understanding these differences is of particular importance in high-stakes examinations such as the state final examinations. The aim of this study was to examine the differences in the results between examinees from different dialectal regions (Čakavian, Kajkavian and Štokavian) on the Croatian language state final examination items which were related to the texts written in the Čakavian dialect. Based on a comparison of the average results on items related to Čakavian texts and an analysis of differential item functioning and differential bundle functioning, very small differences were found in favor of examinees from the Čakavian region in comparison to examinees from the Kajkavian and Štokavian region. Based on these findings, the professional discussion on the Croatian language examination resulted in a recommendation to continue using authentic texts in Čakavian, Kajkavian and Štokavian dialects in Croatian language state final examinations in which all dialects should be equally represented to ensure equal treatment of all candidates regardless of their native dialect

Populacijska perspektiva - visokoškolski odabiri hrvatskih srednjoškolaca u razdoblju od 2010. do 2017. godine

IN CROATIAN: U ovom se poglavlju na populacijskim podacima analiziraju i razmatraju učestalosti odabira i upisa studijskih programa učenika iz različitih srednjoškolskih programa, s posebnim naglaskom na razlike među generacijama koje su srednju školu završile 2010., 2015. i 2017. godine. Učenici u najvećem broju biraju i upisuju studijske programe unutar onih znanstvenih i umjetničkih polja koja po profilu u najvećoj mjeri odgovaraju srednjoškolskom programu koji su završili. Takav obrazac očekivano najviše dolazi do izražaja kod učenika iz strukovnih programa. Ovaj nalaz o vertikalnoj prohodnosti sustava za učenike iz srednjih strukovnih škola poželjan je te upućuje na visoku razinu povezanosti i sljedivosti strukovnih srednjoškolskih programa i studijskih programa u određenim znanstvenim područjima i poljima. Nalazi upućuju na veću divergentnost odabira i upisa učenika gimnazijskih programa nego što je to slučaj kod učenika strukovnih škola. Aspiracije učenika za upisom studijskih programa iz različitih znanstvenih i umjetničkih područja i polja relativno su stabilne među generacijama, a jednako tako i raspodjele učenika upisanih u određene studijske programe prema područjima i poljima. Ustvrđene su neznatne do male razlike među generacijama u čestoći odabira i čestoći upisa studijskih programa iz različitih znanstvenih područja i polja te različitih vrsta studija (redovni i izvanredni studij), tipova studija (sveučilišni i stručni studij) i nositelja studija (javna sveučilišta, javna veleučilišta i visoke škole, privatna visoka učilišta). Broj upisnika privatnih visokih učilišta vrlo je malen i nije se uvelike mijenjao tijekom godina, iz čega proizlazi kako u Hrvatskoj javna visoka učilišta i dalje ostaju dominantan tip visokih učilišta. Učenici gimnazija su u prosjeku nešto češće upisivali studijske programe koji su im bili prvi izbor nego učenici strukovnih škola. Rezultati pokazuju da većina učenika želi nastaviti svoj obrazovni put na visokoškolskoj razini u području srednjoškolskog obrazovanja koje su pohađali. --------------- IN ENGLISH: In this chapter, selection and enrolment rates of higher education programs are analysed and discussed for students from different upper secondary school programs using the population data, with particular emphasis on differences between the generations who graduated from upper secondary school in 2010, 2015, and 2017. In most cases, students choose and enrol in higher education programs within those fields of science and art that correspond most closely to the upper secondary school program they have completed. As expected, this pattern is most prominent among graduates from vocational upper secondary programs. This finding of the vertical passability of the system for secondary vocational students is desirable and indicates a high level of coherence and traceability between vocational upper secondary school programs and higher education programs in specific scientific areas and fields. The findings indicate a greater diversity of selected and enrolled higher education programs for gymnasium students than for vocational school students. Students' aspirations for enrolment in various scientific and artistic areas and fields are relatively stable across generations, as well as the distributions of students enrolled in specific areas and fields. Differences between generations in the frequency of selection and enrolment of higher education programs from different scientific areas and fields, as well as different types of programs (full-time/part-time; university/professional; public universities/public polytechnics and schools of professional higher education/private institutions of higher education) were negligible or small. The number of students who enrolled in private institutions of higher education is very small and has not changed much over the years, indicating that public institutions of higher education remain the dominant type of institutions of higher education in Croatia. Gymnasium students, on average, were slightly more likely to enrol in higher education programs that were their first choice than students from vocational schools. The results show that the majority of students wants to pursue higher education in the area that corresponds to the area of upper secondary school program they have attended

Kompetencija učiti kako učiti u Hrvatskoj

IN CROATIAN: U obrazovnoj se politici u novije vrijeme koristi pojam kompetencije učiti kako učiti, kojom su, među ostalim, obuhvaćeni i različiti konstrukti samoregulacije učenja. Kompetencija učiti kako učiti u Republici Hrvatskoj proučava se duže od desetljeća te je bila u središtu interesa nekoliko istraživačkih projekata. Povećana svijest o važnosti kompetencije učiti kako učiti među znanstvenicima i odgojno-obrazovnim radnicima također je rezultirala i naporima za njezinom sustavnijom implementacijom u odgojno-obrazovni sustav. S obzirom na tradiciju domaćih istraživanja kompetencije učiti kako učiti, cilj ovog poglavlja bio je dati kratak pregled dosadašnjih postignuća hrvatskih istraživača vezanih uz ovu temu. Također, predstavljena je konceptualizacija i elaboracija prijedloga kurikuluma međupredmetne teme učiti kako učiti, jednog od prvih kurikulumskih dokumenata u svijetu u čijem je fokusu razvoj ove kompetencije u formalnom sustavu odgoja i obrazovanja. --------------- IN ENGLISH: Competence learning to learn as a term has been used in recent years in education policy. It includes, among other things, different constructs of self-regulated learning. The competence learning to learn has been studied in Croatia for more than a decade and has been the focus of several research projects. Increased awareness of the importance of this competence among scholars and educators has also resulted in efforts to implement it more systematically in the educational system. Given the tradition of home-based research on competence learning to learn, the aim of this chapter was to give a brief overview of the achievements of Croatian researchers on this topic. In addition, conceptualization and elaboration of the curriculum of a cross-curricular theme learning to learn was presented. This is one of the first curriculum documents in the world focusing on the development of the competence learning to learn in the formal education system

Konfirmatorni pristup istraživanju rodnih razlika u uspješnosti rješavanja matematičkih zadataka: doktorska disertacija

IN CROATIAN: U ovom radu ispitane su postavke taksonomije svojstava matematičkih zadataka koja dovode do rodnih razlika u uspješnosti njihovog rješavanja (TSMZ; Gallagher, 1998; Gierl i sur., 2003), temeljene na psihobiosocijalnom modelu (npr. Halpern, 1997; 2000). Pri tome su korištene sljedeće metodologije čija kombinacija omogućuje konfirmatorni pristup ispitivanju hipoteza o smjeru rodnih razlika: 1) ispitivanje rodnih razlika u riješenosti zadataka ispita državne mature iz Matematike za višu razinu (usporedba postotnih riješenosti zadataka te ispitivanje rodnog diferencijalnog funkcioniranja zadataka i skupova zadataka), 2) usporedba nastavničke klasifikacije zadataka u kategorije TSMZ i klasifikacije nastale na temelju učeničkih iskaza za vrijeme rješavanja zadataka, 3) usporedba rodnih razlika između različitih gimnazijskih programa i 4) pokušaj replikacije rodne razlike te smanjenja razlike modifikacijom zadataka u eksperimentalnom nacrtu na novom uzorku. Nalazi ukazuju na zanemarive rodne razlike u prosječnim ukupnim rezultatima na ispitima, što je u skladu s rezultatima novijih meta-analiza (De Lisi i McGillicuddy-De Lisi, 2002; Lindberg, Hyde, Petersen i Linn, 2010). Hipoteze TSMZ samo su djelomično potvrđene. Najveća je razlika utvrđena na verbalnim problemima i to u korist mladića, što je suprotno hipotezama TSMZ. Razlika je replicirana na manjem uzorku studenata ali samo u slučaju kada je u analizu kao kovarijata uvedena zaključna ocjene iz Matematike u srednjoj školi. Vrijednost rodne razlike nije se statistički značajno mijenjala uslijed dodavanja algoritma / pravila za rješavanje u verbalni problem. Nastavnička klasifikacija zadataka u kategorije TSMZ u visokom se stupnju slagala s klasifikacijom na temelju iskaza učenika. Usporedba vrijednosti rodnih razlika u riješenosti zadataka među gimnazijskim programima nije dovela do jednoznačnih nalaza. Nalazi sugeriraju kako u poučavanju Matematike djevojkama treba posvetiti više pažnje pri svladavanju strategija rješavanja verbalnih problema. Prema autorovim saznanjima, ovo je prvo istraživanje rodnih razlika u rješavanju matematičkih zadataka u kojem je korištena opisana kombinacija metodologija te prvo sustavno istraživanje rodnih razlika na ispitima državne mature iz Matematike. --------------- In ENGLISH: INTRODUCTION. In many societies, mathematics is often considered a male domain (Nosek et al., 2009). Males tend to have higher motivation and self-efficacy for mathematics in comparison to females (e.g. Skaalvik & Skaalvik, 2004). On the other hand, gender differences in mathematics achievement are not that unambiguous. While girls usually have higher school grades during the entire education period (Duckworth & Seligman, 2006; Hicks, Johnson, Iacono & McGue, 2008), males have somewhat higher results on standardized mathematics tests (e.g. De Fruyt et al., 2008). However, findings of the meta-analyses indicate that male advantage in mathematics test achievement has decreased or even disappeared in the last decades (De Lisi & McGillicuddy-De Lisi, 2002; Lindberg, Hyde, Petersen & Linn, 2010). Male advantage in test results is more often found in adolescence and in highly selected samples. Furthermore, male results have somewhat larger variability than female results (Hyde, Fennema & Lamon, 1990; Lindberg, Hyde, Petersen & Linn, 2010). The main objective of this study was to explore the taxonomy of mathematics items’ characteristics that are expected to yield gender differences in performance on these items (Gallagher et al., 2000). This taxonomy was based on a psychobiosocial model (Halpern, 1997; 2000), which emphasizes the reciprocal relationships among different types of variables (psychological, biological and social) in the process of learning. According to this taxonomy, males will have higher results on items with multiple solution paths and items that require spatial skills. Females will have higher results on items that require verbal skills and items that require application of routine mathematical solutions (items that require application of routine mathematical solutions to a new unfamiliar situation, items that require application of routine mathematical solutions to a familiar situation, items that require memorization and items that require the use of symbolic processes; Gierl, Bisanz, Bisanz & Boughton, 2003). In exploring this taxonomy, researchers usually compared average scores of males and females on mathematics items (Gallagher, Levin & Cahalan, 2002). This strategy is problematic because it ignores the effects of the Simpson’s paradox (1951). In this study, a confirmatory approach to testing the taxonomy hypotheses was used in the context of the Croatian State Matura exam, based on a combination of different methodologies that are more adequate for this purpose. RESEARCH PROBLEMS. 1. To examine gender differences in mathematical problem-solving performance. 2. To examine the congruence of item classifications in taxonomy categories; the first one made by mathematics teachers, and the second one made based on the students’ remarks while solving individual items. 3. To compare gender differences in mathematical problem-solving performance among general grammar school students and science and mathematics grammar school students. 4. To examine if it is possible to reduce gender difference in mathematical problem-solving performance by manipulating the item characteristics. METHODOLOGY. The data used in this study were obtained from final-year general grammar school and science and mathematics grammar school students who participated in the 2010 and 2011 administrations of the Croatian secondary school final examinations in Mathematics (higher level). In 2010, there were 3425 students from general grammar schools who attended this examination (1361 males and 2064 females) as well as 1577 students from science and mathematics grammar schools (954 males and 623 females). In 2011, 3650 students from general grammar schools (1419 males and 2231 females) and 1531 students from science and mathematics grammar schools (923 males and 608 females) attended the examination. Gender differences in the results on items from every category were analysed using different approaches: the analysis of mean gender differences, differential item functioning (DIF) and differential bundle functioning (DBF) analysis. The DBF analysis has higher statistical power in comparison to analyses conducted on individual items. Therefore, it is more suitable for testing hypotheses about items' characteristics responsible for gender differences in performance on these items. However, it is still relatively rarely used in educational context. In this research, DIF and DBF analyses were performed using Mantel-Haenszel test, SIBTEST / Poly-SIBTEST methodology and empirical curves. Two types of item classifications in taxonomy categories were compared: the first one was made by mathematics teachers, and the second one was made based on the students’ remarks that were recorded after they tried to solve individual items. More specifically, in a small sample of final-year general grammar school students (N = 16; 8 males and 8 females), think aloud protocols were used to inspect students' ways of understanding and solving items. Transcripts were coded according to the descriptions of taxonomy categories. Congruence of the two classifications is necessary if we want to draw conclusions about relationships between values and directions of gender differences on items on the one hand and the belonging taxonomy category on the other hand. Furthermore, gender differences among general grammar school students and science and mathematics grammar school students were compared. Students that attend science and mathematics grammar schools chose to enroll in these schools at least partially based on their motivation for mathematics. On average, these students achieve higher results on the final examinations in Mathematics than students from general grammar schools. The comparison of gender differences within these two groups of students was used to test the hypothesis about larger male advantage in highly selected samples. In order to check if it is possible to reduce gender difference by manipulating the item characteristics, items that require verbal skills (the taxonomy category in which largest gender differences were found) were modified and different versions of the same items were applied on a sample of university students (N = 205; 81 males and 124 females). RESULTS AND DISCUSSION. Gender differences in average total scores on examinations were negligible, which is in accordance with the results of meta-analyses (De Lisi i McGillicuddy-De Lisi, 2002; Lindberg, Hyde, Petersen i Linn, 2010). The taxonomy hypotheses were only partially confirmed. Namely, the results confirmed male advantage on items with multiple solution paths and items that require spatial skills. Females had higher results on items that require application of routine mathematical solutions to a familiar situation. These findings were in accordance with the hypotheses. However, gender differences were ambiguous on items that require memorization and items that require the use of symbolic processes. Furthermore, males had somewhat higher results on items that require application of routine mathematical solutions to a new unfamiliar situation. The largest difference in favour of male students was found on items requiring verbal skills and this finding was contradictory to the hypothesis. This finding was supported with different types of analyses (analysis of mean gender differences, DIF and DBF). These items were also measuring content domain mathematical modelling. Other items from this content domain yield gender differences in the same direction. Gender differences in other categories of taxonomy were rather small and of no practical importance. Based on these findings, further investigation of gender differences in verbal problems was conducted. Gender difference on problems requiring verbal skills was replicated on a sample of university students but only when Mathematics high school grades were used as covariate. The value of gender difference did not change statistically significantly when rule / algorithm for problem solving was explicitly added in the verbal problem. Gender differences were not found in some additional variables that were used in this part of the research (results on the test of verbal series and the inventory of use of mathematics in everyday life). The teachers' classification of items matched the classification that was based on students' statements to a great extent. The comparison of gender differences between general grammar and science and mathematics grammar school students’ results did not give unambiguous results. In other words, the hypothesis of larger male advantage in highly selected samples was not confirmed. CONCLUSION. Different methodologies used in this study led to similar findings regarding the largest gender differences in mathematical verbal problems. Although this research did not yield clear conclusions regarding the reasons behind these differences, the results indicate that more attention should be given to the girls' acquisition of the strategies involved in solving mathematical verbal problems. According to the author's best knowledge, this is the first study that combines the aforementioned methodological approaches in the research of gender differences in performance on mathematics tasks. The confirmatory approach to testing hypotheses about group differences in item performance used in this research can be used in various contexts, e.g. different school subjects. Furthermore, this is the first comprehensive study of gender differences in the context of the Croatian State Matura Mathematics examinations. These examinations are gender-neutral to a great extent

Confirmatory approach in examining gender differences in mathematical problem-solving performance

U ovom radu ispitane su postavke taksonomije svojstava matematičkih zadataka koja dovode do rodnih razlika u uspješnosti njihovog rješavanja (TSMZ; Gallagher, 1998; Gierl i sur., 2003), temeljene na psihobiosocijalnom modelu (npr. Halpern, 1997; 2000). Pri tome su korištene sljedeće metodologije čija kombinacija omogućuje konfirmatorni pristup ispitivanju hipoteza o smjeru rodnih razlika: 1) ispitivanje rodnih razlika u riješenosti zadataka ispita državne mature iz Matematike za višu razinu (usporedba postotnih riješenosti zadataka te ispitivanje rodnog diferencijalnog funkcioniranja zadataka i skupova zadataka), 2) usporedba nastavničke klasifikacije zadataka u kategorije TSMZ i klasifikacije nastale na temelju učeničkih iskaza za vrijeme rješavanja zadataka, 3) usporedba rodnih razlika između različitih gimnazijskih programa i 4) pokušaj replikacije rodne razlike te smanjenja razlike modifikacijom zadataka u eksperimentalnom nacrtu na novom uzorku. Nalazi ukazuju na zanemarive rodne razlike u prosječnim ukupnim rezultatima na ispitima, što je u skladu s rezultatima novijih meta-analiza (De Lisi i McGillicuddy-De Lisi, 2002; Lindberg, Hyde, Petersen i Linn, 2010). Hipoteze TSMZ samo su djelomično potvrđene. Najveća je razlika utvrđena na verbalnim problemima i to u korist mladića, što je suprotno hipotezama TSMZ. Razlika je replicirana na manjem uzorku studenata ali samo u slučaju kada je u analizu kao kovarijata uvedena zaključna ocjene iz Matematike u srednjoj školi. Vrijednost rodne razlike nije se statistički značajno mijenjala uslijed dodavanja algoritma / pravila za rješavanje u verbalni problem. Nastavnička klasifikacija zadataka u kategorije TSMZ u visokom se stupnju slagala s klasifikacijom na temelju iskaza učenika. Usporedba vrijednosti rodnih razlika u riješenosti zadataka među gimnazijskim programima nije dovela do jednoznačnih nalaza. Nalazi sugeriraju kako u poučavanju Matematike djevojkama treba posvetiti više pažnje pri svladavanju strategija rješavanja verbalnih problema. Prema autorovim saznanjima, ovo je prvo istraživanje rodnih razlika u rješavanju matematičkih zadataka u kojem je korištena opisana kombinacija metodologija te prvo sustavno istraživanje rodnih razlika na ispitima državne mature iz Matematike.Introduction In many societies, mathematics is often considered a male domain (Nosek et al., 2009). Males tend to have higher motivation and self-efficacy for mathematics in comparison to females (e.g. Skaalvik & Skaalvik, 2004). On the other hand, gender differences in mathematics achievement are not that unambiguous. While girls usually have higher school grades during the entire education period (Duckworth & Seligman, 2006; Hicks, Johnson, Iacono & McGue, 2008), males have somewhat higher results on standardized mathematics tests (e.g. De Fruyt et al., 2008). However, findings of the meta-analyses indicate that male advantage in mathematics test achievement has decreased or even disappeared in the last decades (De Lisi & McGillicuddy-De Lisi, 2002; Lindberg, Hyde, Petersen & Linn, 2010). Male advantage in test results is more often found in adolescence and in highly selected samples. Furthermore, male results have somewhat larger variability than female results (Hyde, Fennema & Lamon, 1990; Lindberg, Hyde, Petersen & Linn, 2010). The main objective of this study was to explore the taxonomy of mathematics items’ characteristics that are expected to yield gender differences in performance on these items (Gallagher et al., 2000). This taxonomy was based on a psychobiosocial model (Halpern, 1997; 2000), which emphasizes the reciprocal relationships among different types of variables (psychological, biological and social) in the process of learning. According to this taxonomy, males will have higher results on items with multiple solution paths and items that require spatial skills. Females will have higher results on items that require verbal skills and items that require application of routine mathematical solutions (items that require application of routine mathematical solutions to a new unfamiliar situation, items that require application of routine mathematical solutions to a familiar situation, items that require memorization and items that require the use of symbolic processes; Gierl, Bisanz, Bisanz & Boughton, 2003). In exploring this taxonomy, researchers usually compared average scores of males and females on mathematics items (Gallagher, Levin & Cahalan, 2002). This strategy is problematic because it ignores the effects of the Simpson’s paradox (1951). In this study, a confirmatory approach to testing the taxonomy hypotheses was used in the context of the Croatian State Matura exam, based on a combination of different methodologies that are more adequate for this purpose. Research problems 1. To examine gender differences in mathematical problem-solving performance. 2. To examine the congruence of item classifications in taxonomy categories; the first one made by mathematics teachers, and the second one made based on the students’ remarks while solving individual items. 3. To compare gender differences in mathematical problem-solving performance among general grammar school students and science and mathematics grammar school students. 4. To examine if it is possible to reduce gender difference in mathematical problemsolving performance by manipulating the item characteristics. Methodology The data used in this study were obtained from final-year general grammar school and science and mathematics grammar school students who participated in the 2010 and 2011 administrations of the Croatian secondary school final examinations in Mathematics (higher level). In 2010, there were 3425 students from general grammar schools who attended this examination (1361 males and 2064 females) as well as 1577 students from science and mathematics grammar schools (954 males and 623 females). In 2011, 3650 students from general grammar schools (1419 males and 2231 females) and 1531 students from science and mathematics grammar schools (923 males and 608 females) attended the examination. Gender differences in the results on items from every category were analysed using different approaches: the analysis of mean gender differences, differential item functioning (DIF) and differential bundle functioning (DBF) analysis. The DBF analysis has higher statistical power in comparison to analyses conducted on individual items. Therefore, it is more suitable for testing hypotheses about items' characteristics responsible for gender differences in performance on these items. However, it is still relatively rarely used in educational context. In this research, DIF and DBF analyses were performed using Mantel-Haenszel test, SIBTEST / Poly-SIBTEST methodology and empirical curves. Two types of item classifications in taxonomy categories were compared: the first one was made by mathematics teachers, and the second one was made based on the students’ remarks that were recorded after they tried to solve individual items. More specifically, in a small sample of final-year general grammar school students (N = 16; 8 males and 8 females), think aloud protocols were used to inspect students' ways of understanding and solving items. Transcripts were coded according to the descriptions of taxonomy categories. Congruence of the two classifications is necessary if we want to draw conclusions about relationships between values and directions of gender differences on items on the one hand and the belonging taxonomy category on the other hand. Furthermore, gender differences among general grammar school students and science and mathematics grammar school students were compared. Students that attend science and mathematics grammar schools chose to enroll in these schools at least partially based on their motivation for mathematics. On average, these students achieve higher results on the final examinations in Mathematics than students from general grammar schools. The comparison of gender differences within these two groups of students was used to test the hypothesis about larger male advantage in highly selected samples. In order to check if it is possible to reduce gender difference by manipulating the item characteristics, items that require verbal skills (the taxonomy category in which largest gender differences were found) were modified and different versions of the same items were applied on a sample of university students (N = 205; 81 males and 124 females). Results and discussion Gender differences in average total scores on examinations were negligible, which is in accordance with the results of meta-analyses (De Lisi i McGillicuddy-De Lisi, 2002; Lindberg, Hyde, Petersen i Linn, 2010). The taxonomy hypotheses were only partially confirmed. Namely, the results confirmed male advantage on items with multiple solution paths and items that require spatial skills. Females had higher results on items that require application of routine mathematical solutions to a familiar situation. These findings were in accordance with the hypotheses. However, gender differences were ambiguous on items that require memorization and items that require the use of symbolic processes. Furthermore, males had somewhat higher results on items that require application of routine mathematical solutions to a new unfamiliar situation. The largest difference in favour of male students was found on items requiring verbal skills and this finding was contradictory to the hypothesis. This finding was supported with different types of analyses (analysis of mean gender differences, DIF and DBF). These items were also measuring content domain mathematical modelling. Other items from this content domain yield gender differences in the same direction. Gender differences in other categories of taxonomy were rather small and of no practical importance. Based on these findings, further investigation of gender differences in verbal problems was conducted. Gender difference on problems requiring verbal skills was replicated on a sample of university students but only when Mathematics high school grades were used as covariate. The value of gender difference did not change statistically significantly when rule / algorithm for problem solving was explicitly added in the verbal problem. Gender differences were not found in some additional variables that were used in this part of the research (results on the test of verbal series and the inventory of use of mathematics in everyday life). The teachers' classification of items matched the classification that was based on students' statements to a great extent. The comparison of gender differences between general grammar and science and mathematics grammar school students’ results did not give unambiguous results. In other words, the hypothesis of larger male advantage in highly selected samples was not confirmed. Conclusion Different methodologies used in this study led to similar findings regarding the largest gender differences in mathematical verbal problems. Although this research did not yield clear conclusions regarding the reasons behind these differences, the results indicate that more attention should be given to the girls' acquisition of the strategies involved in solving mathematical verbal problems. According to the author's best knowledge, this is the first study that combines the aforementioned methodological approaches in the research of gender differences in performance on mathematics tasks. The confirmatory approach to testing hypotheses about group differences in item performance used in this research can be used in various contexts, e.g. different school subjects. Furthermore, this is the first comprehensive study of gender differences in the context of the Croatian State Matura Mathematics examinations. These examinations are genderneutral to a great extent

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