The analysis of PISA 2012 and 2015 data reported in this paper provided some insights into potential predictors of high achievement in mathematics and science among 15-year-old students in Ireland. In light of earlier findings in the area, the most consistent findings of this study and their implications for policy and practice are discussed.
Overall, the findings of this study indicate that students’ families might play a crucial role in enhancing students’ chances of being high achievers in mathematics and science. Hence, it seems reasonable to suggest that further efforts to enhance collaboration between teachers, schools, and parents are needed, while there is also a need for educational policy to focus teaching and public awareness on the value of non-cognitive factors and wellbeing as well as of appropriate leisure activities for improving achievement. Along these lines, preschool practitioners, teachers, and school principals could raise parents’ awareness of their important role as learning partners in shaping their children’s learning on an ongoing basis from the early years. Broadly speaking, greater attention could be placed on initial preschool practitioner and teacher education and continuing professional development programmes to preparing these professionals as well as school principals to work in partnership with parents. Specific ways of how these could be materialised with reference to student- and family-level factors that were found to predict high achievement in mathematics and science in this study are discussed below. In the interest of clarity, the discussion of findings mirrors the approach adopted in the model-building process (see Fig. 1).
Student and family demographics
Student sex
In comparison with sex differences noted in overall achievement in mathematics and science in Ireland (e.g., Clerkin et al., 2015; Shiel et al., 2016), sex differences in high achievement in the two subjects at the bivariate level, as identified by this study, were larger. In general terms, this corroborates earlier findings in the area (e.g., Ellison & Swanson 2010; Gilleece et al., 2010; Stoet & Geary, 2013) indicating that the sex gap in mathematics and science among high-achieving students favouring males is consistently larger compared to the respective gaps in overall achievement in the two subjects. After taking other variables into account, though, sex differences in high achievement remained relatively small, following the unsystematic patterns found in research studies on overall achievement (e.g., Zhou et al., 2017).
These findings do not necessarily undermine the practical significance of sex differences in the context of high achievement; rather, they point towards potential factors on which the Irish education system could focus to address these differences. In the mathematics model, the gap between males and females in high achievement was no longer significant after student self-beliefs, dispositions, drive, and engagement were considered. This suggests that these variables may have accounted for sex differences among high achievers, indicating that males and females with equivalent self-beliefs, dispositions, drive, and engagement tended to be equally likely to be high achievers in mathematics. Based on these findings, it seems that one possible way to deal with sex differences in high achievement in mathematics in Ireland would be to focus on students’ non-cognitive attributes, especially those of females.
It is also noteworthy that although sex differences were not large or systematic, they were in favour of males in both mathematics and science, suggesting that female students may be lagging behind in high achievement in the two subjects. Given that high achievement in these areas during schooling is associated with higher participation in STEM-related courses at third level, a way of bridging this sex gap would be for schools to assure that all students but, especially, females are aware of the range of STEM courses and careers that are available to them from an early age. However, as it was highlighted in the STEM Education Review Group report, “one key barrier in this regard [under-representation of females in the STEM workforce in Ireland] arises from the fact that, while parents are the main influencers when it comes to advising their daughters on how to define educational and career paths, they generally lack information about career options.” (The STEM Education Review Group, 2016, p. 8). Hence, schools could cooperate with parents to make sure that the latter are in a position to make STEM careers and their associated benefits more desirable for female students, in particular, without, of course, neglecting male students in these efforts. Making STEM careers more desirable for all students but, especially, females falls under the key priorities of the current STEM Education Policy in Ireland (DES, 2017b). This study highlights the importance of such policies and of closely monitoring sex differences in high and overall achievement in all the subjects, as an important aspect of educational equity.
Socioeconomic status
One factor that yielded large differences between the two performance groups in both subjects was students’ family socioeconomic status. Prior to and even after accounting for a range of variables, students coming from households with higher socioeconomic status were more likely to be high achievers in mathematics and science. This finding suggests that aspects of post-primary students’ lives pertaining to their home possessions (e.g., books at home), and their parents’ occupation and education are particularly important when it comes to their probabilities of belonging to the high-achieving groups in mathematics and science.
This finding corroborates those of the few studies that have examined high achievement in mathematics and science. For instance, studies by Gilleece et al. (2010) and Tourón et al. (2018) have shown that higher socioeconomic status is associated with higher chances of high achievement. Further, it echoes findings from a body of research that investigated the relationship between family socioeconomic status and overall achievement in a range of subjects, including mathematics and science (e.g., Reardon, 2011). This is an important finding in the context of educational equity, especially when the relationship is examined while other variables are taken into account, as it indicates that over and above anything else that is going on in students’ lives as well as in their classes and schools, the socioeconomic status of their family is still an important predictor of their academic outcomes even at the highest levels of performance. This is despite significant efforts that have been made by the Department of Education in Ireland over the years to support the more socioeconomically disadvantaged (e.g., Delivering Equality of Opportunity in Schools [DEIS] initiative). Consequently, this finding begs questions for policymakers and teachers alike about what more can be done to deal with this important aspect of equity in education.
Although schools alone might not be able to decrease socioeconomic inequalities per se, their role in preventing such inequalities from shaping students’ learning and outcomes is crucial. Along with existing initiatives that primarily target socioeconomically disadvantaged schools, efforts could also be made at the individual level. Specifically, to support learning among disadvantaged students, schools need to target their efforts to improve communication with parents in the most disadvantaged homes, and help develop home environments conducive to learning in mathematics and science. Parents from socioeconomically disadvantaged families should be made aware of the importance of the availability of adequate educational resources at home (e.g., books and appropriate space to study) for their children’s learning as well as of useful resources that they could use at home. Additionally, they should be supported by teachers and schools in getting involved in their children’s learning, and in encouraging their children to take part in extracurricular activities related to mathematics and science that are organised by the school or other bodies. Such practices could contribute towards mitigating the impact of inequalities on students’ outcomes. Alongside such efforts, there must also be a stronger emphasis on identifying and nurturing talent of all students but especially of those coming from socioeconomically disadvantaged backgrounds. This could involve a stronger role for special education teachers in Irish schools, who currently seem to focus on addressing the needs of at-risk low-achieving students.
Student self-beliefs, dispositions, drive, and engagement
A range of variables related to students’ self-beliefs, dispositions, drive, and engagement emerged as important predictors of high achievement in mathematics and science. This is not surprising given cognate research, such as Bandura’s (1997) work on the importance of such non-cognitive constructs and, especially, self-beliefs in the context of the social-cognitive theory as well as Stankov’s (2013) predictability gradient hypothesis. Such non-cognitive student attributes are likely malleable and responsive to change through appropriate schooling and interventions and, thus, merit consideration.
Overall, more positive self-beliefs and dispositions and greater drive and engagement were linked with higher chances of high achievement in mathematics and science. Student self-beliefs and, more specifically, domain-specific self-beliefs were among the strongest predictors of high achievement in mathematics and science in both the bivariate and the multilevel binary logistic regression analysis, with self-efficacy yielding the largest differences. The bivariate analysis indicated that self-efficacy yielded larger effect sizes for high achievement in mathematics compared to high achievement in science. Lee and Stankov (2018), who analysed, amongst others, PISA data to investigate the role of non-cognitive factors in overall mathematics achievement, rather than high achievement, also indicated that students’ self-efficacy was the strongest predictor of achievement, even after accounting for home possessions and parental education as proxies for students’ socioeconomic status. This study echoed and extended this finding to high achievement in both mathematics and science. This highlights the importance of retaining and, potentially, increasing the current emphasis on initiatives that purport to enhance these students’ self-beliefs in mathematics and science, such as those established following the Junior Cycle wellbeing guidelines in Ireland (National Council for Curriculum and Assessment [NCCA], 2017).Footnote 7
There were also variables related to students’ self-beliefs, dispositions, drive, and engagement (e.g., enjoyment of science, expected occupational status) that yielded particularly large differences between the two performance groups in mathematics and science in a bivariate context but, when examined in a multiple regression context, were no longer significant predictors of high achievement. Given that most of the existing studies examined the relationships of these variables with high achievement in mathematics and science in a bivariate context (see, for example, Tourón et al., 2018), the findings of the current study extend existing research by taking into account other important student- and school-level variables in a multiple and multilevel regression context.
There were also a small number of instances where differences between the two performance groups in each subject in the bivariate analysis were in favour of one group but, when examined in a multiple regression context, were in favour of the other. Tourón et al. (2018) showed that, in a bivariate context, high-achieving students had higher levels of environmental awareness compared to their low-achieving peers, which was also the case in this study. However, when students’ environmental awareness was included in the multilevel model of the PISA 2015 data in this study, it was found to be a negative predictor of high achievement in science. This suggests that students who were identical in all of the other examined variables but had a more thorough understanding of environmental issues were less likely to be high achievers in science. It is plausible that students with high knowledge of science have a greater awareness of the difficulties associated with reversing environmental problems. In any case, this is a finding that raises more questions than it answers, prompting further investigation of the underpinning mechanisms behind this relationship.
These findings provide a strong rationale for the current emphasis that the Irish education system has placed on students’ self-beliefs and other non-cognitive attributes, as integral parts of their wellbeing. They also suggest that preschool practitioners, primary and post-primary teachers, and schools along with parents could work together to help students develop and strengthen such self-beliefs, which, in turn, are expected to work positively towards raising students’ chances of becoming high achievers in mathematics and science.
Research and relevant initiatives in Ireland and elsewhere acknowledge wellbeing as a key issue in the holistic development of children and young people. The promotion of students’ self-efficacy, as an important aspect of their wellbeing, is among the emphasised areas during early childhood education as well as at primary and post-primary levels in an ever-increasing number of countries around the world, including Ireland; for example, students’ wellbeing is a central aspect within Aistear, the early childhood curriculum framework in Ireland (NCCA, 2009), the proposed revised primary curriculum (NCCA, 2020), and the curriculum frameworks for the Junior and Senior Cycles (i.e., post-primary education) (NCCA, 2011, 2017). This emphasis, which is justified by the findings of this study but also by data from PISA 2018Footnote 8, acknowledges the important role of teachers, schools, and parents in enhancing students’ interest and engagement in learning, by ensuring that students develop positive perceptions about their abilities that, in turn, can help them improve and sustain their gains in achievement.
In Ireland, this emphasis has also led to the creation of a wide range of guidelines, innovative courses, and other resources (for examples, see the NCCA’s website) to assist preschool practitioners, teachers, schools, and parents in their efforts to enhance students’ wellbeing. Specifically, NCCA’s guidelines include relevant information on how preschool practitioners, teachers, and school principals can work together with parents to promote children’s wellbeing, including their self-beliefs. For instance, such a collaboration could be facilitated by individuals who serve as connection points between students’ homes and their schools and who can gain insights into individual students’ home circumstances (such as the Home School Community Liaison Officers within the DEIS initiative in Ireland) and, thus, act as coordinators of action. However, a requirement for parents to be able to support their children in developing and improving their self-beliefs in relation to mathematics and science is that parents themselves have strong self-beliefs in their mathematical and scientific abilities. This highlights that part of the overall efforts in improving students’ self-beliefs may also need to be the corresponding improvement of their parents’ self-beliefs. This is an area, though, that has not been examined by the current study, and one that could be examined by future research.
On the whole, the current emphasis on students’ wellbeing especially within early childhood education in Ireland should be retained and increased, given that these constructs tend to be more malleable during these early years and, thus, positive developments during these early years are likely to have long-term benefits for students.
Student mathematics- and science-related activities and schedule, parent dispositions and support
Students who, according to their parents, were more frequently engaged in science-related activities at the age of 10 were significantly more likely to be high achievers in the subject, again, highlighting the importance of early knowledge about and engagement with materials related to school subjects for future academic success. It is noteworthy that this finding, based on a set of PISA questions about parents’ support for science learning in the middle childhood years, highlights not only the importance of parental encouragement, curiosity, and involvement in their children’s learning, but also how these can contribute to subsequent academic outcomes. The review of the existing literature on high achievement in mathematics and science indicated that previous studies in the area had not explored the role of early skills and engagement with relevant materials in high achievement in either of the two subjects, rendering this one of the first studies to address this topic.
This finding highlights the crucial role of early years and parents’ support in promoting students’ high achievement. On this basis, policymakers and schools should aim to raise parents’ awareness about behaviours and practices that stimulate students’ progress and those that do not. For instance, early interventions and programmes targeted at parents of young children should provide resources and supports to assist parents in enhancing their children’s early knowledge and skills (e.g., literacy, numeracy etc.) and engaging their children in mathematics- and science-related activities during the early years.
In recognition of the usefulness of the resources for mathematics and science education that have already been developed by various Irish educational agencies, including those charged with supporting teachers to implement Project MathsFootnote 9, it is imperative that teachers and parents are made aware of this range of supplementary programmes available for teaching these two subjects and for supporting their children at home, respectively. This is important as solutions to educational issues may not always require newly developed resources but rather awareness and appropriate use of existing ones. Bringing such resources together and organising them thematically, such as efforts being made by scoilnet.ie, sfi.ie, and smartfutures.ie as well as making them readily available for teachers, parents, and students are likely to assist towards this end.
Class and school characteristics
None of the school-level variables that yielded effect sizes large enough to progress to the multilevel binary logistic regression analysis retained their statistical significance in the multilevel models once other variables were accounted for. This does not imply that the role of classes and schools in the context of high achievement should be neglected. In fact, as discussed above, considerable proportions of variance in students’ high achievement in mathematics and science were attributed to between-school differences. The fact that consistent findings about predictors of high achievement in the two subjects at the school level were not detected may be linked with the limited availability of information about these contexts. In light of the findings of this study, though, it appears that teachers and schools can act as mediators and facilitators in tackling differences between high- and non-high-achieving students based on certain characteristics stemming from the students themselves and their families that were found to contribute to the prediction of high achievement in mathematics and science.
At this point, it should be acknowledged that a singular focus on high achievers is highly likely to result in increased variance in performance and, hence, increased inequalities among students (e.g., Ferreira & Gignoux, 2014). Hence, this study advocates that a stronger emphasis on meeting the needs of high achievers, as discussed above, should occur with continuing attention to the needs of low achievers as well. Not only is such an approach expected to enhance Irish students’ achievement across the performance continuum, but it is also expected to improve equity within the Irish education system.