Introduction: Ever since the Second World War, knowledge and skills in the STEM (Science, Technology, Engineering, and Mathematics) area have been the key to economic progress (Ritz & Fan, 2015). However, many countries today are facing a shortage of workforce in STEM sectors (European Centre for the Development of Vocational Training, 2016; President’s Council of Advisors on Science and Technology, 2012). This problem cannot be considered separately from the problems and specificities associated with the STEM education. Even early educational experiences in primary school can determine the later educational and professional path of an individual (Tai, Qi Liu, Maltese, & Fan, 2006). Because of this, it is important to identify as many determinants of student educational outcomes in the STEM domain. Parents, along with teachers, have been recognized as crucial socializing factors in this area (Chouinard, Karsenti, & Roy, 2007). It has been shown that in empirical research STEM should be conceptualized as a heterogeneous domain. For example, prior research found that there is a differentiation in student motivational beliefs in different STEM school subjects (Simpkins, Price, & Garcia, 2015) and that gender segregation is not equal across STEM fields (Mann & DiPrete, 2013). The heterogeneous conceptualization of the STEM domain is even more needed in research that is embedded in the educational contexts such as Croatian, in which there is no integrated teaching of STEM. In the present study, we thus focused on two STEM educational domains – mathematics and technical education. These are the only two STEM school subjects in Croatia that all students take through all upper grades of elementary school (5th through 8th grade). Focusing on mathematics is of additional importance since student outcomes in mathematics are crucial for later educational and career trajectories in STEM (Sadler, Sonnert, Hazari, & Tai, 2012). Regarding technical education, although similar types of courses are taught in primary and secondary schools in other countries, we have found very little research on parenting influences in this domain. Thus, focusing on technical education in the present study presents a contribution to existing findings on the parent socialization in the STEM education. This research is guided by the two models proposed by Eccles and her colleagues – the expectancy-value model (Eccles, 2005; Eccles et al., 1983; Eccles & Wigfield, 2002) and the parent socialization model (Eccles, 1993; 2007). The expectancy-value model outlines the expectations for success and the subjective task value as the two key constructs that influence achievement, perseverance, effort, and activity choices in different areas (Eccles & Wigfield, 2002). Among competency beliefs, in addition to the expectations for success, the model outlines the self-concept of ability. While the expectation for success is defined as a person's belief in how successful they will be in a task in the near or far future, the self-concept of ability refers to an individual's assessment of their current competence in a particular area of activity (Eccles et al., 1983). However, research has shown that the self-concept of ability and expectation for success are saturated with the same factor and therefore can be treated as the same construct in research (Eccles, 2009; Eccles & Wigfield, 1995). According to the expectancy-value model, the subjective task value has four components (Eccles, 2005; Eccles & Wigfield, 2002). Attainment value can be defined as the personal meaning that an individual attaches to being successful in an activity. Interest or intrinsic value is defined as the enjoyment of engaging in an activity, while utility value refers to the extent to which the achievement domain is related to a person's present or future goals. In the empirical research, items measuring utility and attainment value are often combined into one measure called importance value (e.g., Viljaranta, Lazarides, Aunola, Räikkönen, & Nurmi. 2015; Simpkins, Fredricks, & Eccles, 2012; Watt et al., 2012). Finally, the perceived cost refers to the individual's perception of what they have to give up, and how much they have to invest to engage in an activity (Eccles, 2005). Eccles’ parent socialization model is embedded in the expectancy-value model. This model describes how family, and in particular parents, shape children's activity choices and achievement, primarily through influencing children's motivational beliefs (Simpkins, Fredricks, & Eccles, 2015). The model outlines several groups of parental influences and a number of direct, indirect, and moderating relationships between these groups of variables (Eccles, 1993; Simpkins et al. 2015a). The distal mechanisms of parental influence are parental sociodemographic characteristics, such as parental education, financial status, occupation, and parental gender. According to the model, parental distal characteristics influence student outcomes primarily through their influence on parental beliefs and behaviours (Eccles, 2005). Research has found that children from families of lower socio-economic status (SES) achieve lower scores in the STEM school area (OECD, 2007) and are less likely to choose the advanced math and science courses (Bozick & Ingels, 2008). The next set of constructs in the model are parental general beliefs and behaviours, such as gender stereotypes, efficacy beliefs, general and specific values, and educational styles. These beliefs are expected to directly influence parental child-specific beliefs (Wigfield et al., 2015). Parental distal characteristics and general practices may also act as moderators in the model. For example, it can be expected that because of the reduced financial and social resources, parents of lower SES can experience difficulties in translating their beliefs, values, and educational goals into appropriate educational practices (Eccles, 1993). A prominent role in the model is given to parental child-specific beliefs, such as expectations for a child's achievement, perceptions of the child's abilities and interests, and perceptions of the value of a particular domain for the child. Studies have shown that parental evaluations of children's abilities in the STEM area predict students' motivational beliefs (Bhanot & Jovanovic, 2009; Bleeker & Jacobs, 2004; Frome & Eccles, 1998; Jacobs & Eccles, 1992) in this area. Parental child-specific beliefs have also been found to predict student achievement in STEM school subjects (Aunola, Nurmi, Lerkkanen, & Rasku-Puttonen, 2003; Gill & Reynolds, 1999). The model postulates that this relationship is primarily realized through the influence of parental child-specific beliefs on student motivation (Eccles, 2007). The power of parental child-specific beliefs in predicting student motivation and achievement is retained even when other relevant variables that may explain these associations are taken into account, such as student past achievement (Simpkins et al., 2015a). The model also assumes that through their child-specific beliefs, parents act as the “interpreters of reality”. This means that children significantly rely on parental interpretations of the child’s past performance as a relevant source for the self-assessment of their current abilities (Jacobs & Eccles, 2000). Finally, the model outlines different parenting behaviours, including role modelling, encouragement of a child’s interests, provision of activity-related experiences, and parent–child coactivity (Simpkins et al., 2012). Research has found that all of these behaviours in the STEM domain can predict student outcomes related to STEM (e. g., Berkowitz et al., 2015; Jacobs & Bleeker, 2004; Simpkins, Davis-Kean, & Eccles, 2005). According to the parent socialization model, through their behaviours and practices, parents communicate to the child their values, beliefs, and goals in a certain activity domain (Eccles, 1993). Accordingly, two important mediational hypotheses emerge from the model: parenting behaviours should mediate the relationship between parental beliefs and children's motivational beliefs, and children's motivational beliefs should play a mediating role in the relationship between parents’ and children's behaviours in a given area of activity (Simpkins et al., 2012). Integrating student constructs from the expectancy-value model and parent constructs from the parent socialization model offers a wide view of parental influences in specific activity domains such as mathematics and technical education. Accordingly, in this research, we explored how parents shape student achievement and activity choices but also student academic motivation in these fields. This is important since the socialization of achievement motivation in specific activity domains has not been studied enough (Wigfield et al., 2015). Research aims and problems: The aim of this research was to examine the parental determinants of students' motivational beliefs, out-of-school activities, and achievement in mathematics and technical education, using theoretical assumptions and constructs specified in the expectancy-value model (Eccles et al., 1983; Eccles & Wigfield, 2002) and the parent socialization model (Eccles, 1993; Simpkins et al., 2015a). The research attempted to address two broader problems. The first research problem was to test the conceptual model of parental determinants of student educational outcomes in mathematics and technical education. In the scope of this problem, we wanted to examine the direct and indirect relationships between distal and proximal parental influences and student educational outcomes in these two educational areas. The second research problem was to examine whether the relations assumed by the conceptual model differ with regard to the student gender and parental educational level. Methods:Participants A total of 1064 sixth- and seventh-grade students from 16 elementary schools in Zagreb and the surrounding area participated in this study. For each student, we also obtained the data from one of their parents or guardians. Thus, 1064 parents/guardians also participated in the study. In the student sample, there was an approximately equal number of girls (48%) and boys (52%) and sixth- (49%) and seventh-grade (51%) students. In the parental sample, 76.4% of parents were mothers and 19.1% of parents were fathers, while for 48 parents (4.5%) the information on gender was missing. Measures Bearing in mind the theoretical framework, the operationalization of the constructs in this study largely followed the empirical work of Eccles and colleagues and most of the measures were adopted from the "Childhood and Beyond Study (CAB)" project (Eccles, Wigfield, & Blumenfeld, 1984). Among parental variables, we measured parental educational level, parental child-specific beliefs in math and technical education, and parental behaviours in math and technical domain. To capture parental child-specific beliefs, parents had to report on their perceptions of a child’s ability in the subject, their perception of the value of the subject for the child, and their perception of a child’s effort and interest in the subject. Among parental behaviours, we measured parental role modelling in math and technical domains, parental encouragement of a child’s interests in these domains, parents’ involvement in student educational activities at home (i. e. homework assistance in math/technical education), and parental provision of STEM-related materials for the child. Among student motivational beliefs, we measured student self-concept of ability in math/technical education, interest in these school subjects, and attainment and utility value of these subjects. Items measuring attainment and utility value were combined in the measure of student importance value. Students also reported how often they engaged in out-of-school math and technical activities. We also obtained the information on student final grades in math and technical education and information on student gender and age cohort. Procedure The students completed the questionnaires in the paper-pen group testing during their regular classes in their school classrooms. Parental questionnaires were forwarded in open envelopes to parents via participating students. The parental questionnaire was intended to examine only one of the student’s parents or guardians. Parents would send the completed questionnaire back to school in the sealed envelope, which could be opened only by the researchers. We collected two students’ final grades in math and technical education from the school records. The control grades were collected in the school year preceding the student research – at the end of the fifth and sixth grades. As a criterion measure of student achievement, we used student final grades in math/technical education in the school year in which student research was conducted –at the end of sixth and seventh grades. Data analysis Structural equation modelling (SEM) was used to answer the first research problem. Two multigroup SEM analyses were performed to answer the second research problem. Results and discussion: The test of the structural models revealed that the explored parental influences had a different role in explaining students' educational outcomes in mathematics and technical education. We expected that parent educational level will have an indirect effect on student outcomes through parental beliefs and behaviours. We mostly did not confirm these hypotheses. Our results point out that in the period of middle school, parents largely base their child-specific beliefs in math on the external information about the child's past math success, and that parental education does not have an independent contribution in shaping these beliefs. Previous research also shows that school grades are the most prominent source of information on which parents base their beliefs about their child's math abilities (Möller, Zimmermann, & Köller, 2014; Tiedemann, 2000). When students’ past achievement in technical education was taken into account, more educated parents had lower child-specific beliefs in this school subject. Parental education had a completely indirect negative effect on student self-concept of ability in technical education that was mediated through parental beliefs that were positively related to student self-concept. Parental education was also a direct negative predictor of student interest and the importance of technical education. These findings can be explained by the fact that in Croatian primary education, student outcomes in technical education have formal implications solely for the further orientation towards vocational secondary education and this educational path is less appealing to students and parents of higher SES backgrounds than to students and parents of lower SES (Meer, 2007). Parental education positively predicted parental provision of STEM materials but did not predict parental encouragement of a child’s math interest, while in the technical domain this correlation was positive but very low. This result might be attributed to the fact that we did not measure the quality of parental encouragement. Furthermore, previous findings indicate that SES is reflected in parental educational behaviours with young children. For example, more educated parents are more likely to implement practices that develop basic mathematical skills in preschool children (Pan, Yang, Li, Liu, & Liu, 2018). In line with our hypotheses, parental beliefs were confirmed as moderate to strong, positive predictor of all student motivational beliefs in both math and technical education. This was also found in the previous research in the STEM area (e.g., Bhanot & Jovanovic, 2009; Bleeker & Jacobs, 2004). The predictive effect of parental beliefs in explaining student selfconcept of ability in the subject was stronger than the effect of student past achievement. In both subjects, we found a mediating effect of parental beliefs in explaining the link between student past achievement and later self-concept of ability. This finding confirms the role of parents as the "interpreters of reality". Parental beliefs were confirmed as significant predictors of later math achievement, even when student motivation and prior math achievement were controlled for. In technical education, parental beliefs had a marginal positive effect in predicting achievement, which can be attributed to the very low variability in student grades in technical education. Parental beliefs predicted student achievement in both subjects partially thorough higher student self-concept of ability in the subject. Parental beliefs predicted a higher level of parental encouragement in both domains, a higher level of provision of STEM materials, and a lower level of parental assistance in the child's coursework. However, the hypothesis about the mediational role of parental behaviours in explaining the relationship between parental and student beliefs mostly did not find support. This is because parental behaviours were week predictors of student motivation. This is in line with previous examinations of the parent socialization model (Eccles, 1993). Our finding may perhaps be attributed to the fact that we did not include quality measures of parental behaviours. Eccles (2007) argued that the socializing potential of parental behaviours depends on the motivational and emotional climate that parents create in their interactions with the child. Regarding parental behaviours as predictors of student outcomes, significant differences were found depending on the type of behaviour and subject. Parental modelling did not predict any of the student outcomes in math. Parental modelling in the technical area positively predicted student interest in and importance of technical education. Parental modelling also positively predicted student engagement in out-of-school technical activities, through higher student value of technical education. Parents’ technical activities may be more visible within everyday family interactions than math activities since technical activities involve the use of tools, objects, and machines. This would explain the different findings in the two domains. Parental assistance in the student coursework in math was related to lower student interest in math and through lower interest to lower student engagement in math out-of-school activities. Previous research found that parental helping with math homework negatively predicted student achievement (Carmichael & MacDonald, 2016; Robinson, 2014). If this type of parental involvement is motivated primarily by the child's poor performance, parents tend to apply more control which negatively affects the child's motivation (Silinskas & Kikas, 2019). This may explain our findings, as parents were more likely to engage in their child's math coursework if they had lower beliefs about their child in math. This parental behaviour also mediated the relationship between lower parental child-specific beliefs in math and lower student math interest. This implies that this type of parental involvement communicates negative parental beliefs about the child's potential in math which can explain the contra-effect of this type of parental behaviour (Pomerantz, Moorman, & Litwack, 2007). A small positive correlation was found between parental assistance in the student coursework in technical education and student importance value of this subject. This parental behaviour also had a small positive indirect effect on student engagement in technical activities through higher student importance value. This finding can be explained by the fact that parental beliefs were not related to this type of parental involvement in technical education. Thus, it seems that parents do not communicate low beliefs about the child’s potential in technical education when engaging in this type of behaviour with the child. This may be because most students had high grades in technical education. Out of all parenting behaviours, encouragement of a child’s interest was the strongest predictor of student engagement in math and technical activities. According to Eccles (1993), one of the ways in which parental encouragement has a positive effect on student involvement in certain activities is the positive impact that such behaviour has on student motivational beliefs. This assumption was confirmed in our math model since parental encouragement in math predicted student engagement in math activities also indirectly - through a positive effect on student math interest. Parental provision of STEM materials was an insignificant predictor of student outcomes in both subjects. The presence of educational materials in the child’s home does not imply that children actually use these materials in a way that promotes their motivation for the STEM educational domain. Furthermore, parents reported that their children had a relatively small number of STEM materials available at home, which could also explain our findings. Finally, parental provision of STEM materials may be more important for preschool children who still have not encountered educational materials through the regular education. The established socialization mechanisms were equal for male and female children. Regarding the moderating effect of parental education, lower parental beliefs were associated with higher parental assistance in math coursework in both groups of parental education, but this association was stronger among parents who had higher education. Parental beliefs were also more strongly positively correlated with parental encouragement of the child’s interest in mathematics among parents with higher education. Lack of educational, financial, and time resources can make it difficult for parents of lower SES to translate their socialization goals, beliefs, and values into adequate educational practices (Eccles, 1993; Spera 2006). Furthermore, parents who are more educated have stronger beliefs about their active role in their children's education and are more confident in their competencies to contribute to their child's academic achievement (Whitaker & Hoover-Dempsey. 2013; Yamamoto, Holloway, & Suzuki, 2016), which could also explain our findings in math. Conclusion: Parental personal characteristics, beliefs, and behaviours had different roles in explaining student motivation, achievement, and activity choices in math and technical domain. The results indicate that both parent and student mediational mechanisms need to be taken into account to fully understand these processes. Furthermore, the mechanisms of parent socialization may differ depending on the socio-economic background of the family but also depending on the specific STEM discipline. These results reflect the complexity of socialization processes in the STEM area of education in the early adolescence. Thus, it is important to adopt a wide focus on family influences in this domain by examining multivariate models that will integrate multiple parental constructs and student educational outcomes. For a broader understanding of the socialization in the STEM area of education, more comparative research of multiple STEM disciplines is needed.