Mindset as a potential link between family background and high-school achievement

The link between students’ family background and their school achievement is well documented. The recent literature has also investigated how social and emotional skills and mindsets relate to educational outcomes. Here I examine how mindset—that is, whether students believe more in that intellectual abilities are fixed or capable of growth—is related to family background and school achievement in Norway. I find that students with higher-educated parents have lower levels of a fixed mindset on entering high school. I also estimate heterogeneity in this association using multilevel modeling. The predicted level of students’ fixed mindset is low for higher-performing middle-school students, irrespective of parents’ education. Furthermore, low middle-school performance predicts higher levels of a fixed mindset, particularly for students with lower-educated parents. A higher level of fixed mindset on entering high school is related to lower achievement after the first year. The results suggest that students’ belief in “natural talent” is a mechanism worthy of further investigation as it is more malleable than the mechanisms traditionally used to explain differences in academic performance according to family background.


Introduction
In a knowledge economy with a rapidly changing labor market, education is increasingly important for people's opportunities. The persistence of inequality in school performance according to family background remains a policy concern. In sociology, the mechanisms used to explain differences in academic performance often relate to properties of individuals, families, and societies that are difficult to change (Jackson, 2013). However, the recent literature has also investigated how social and emotional skills and mindsets (also known as soft or noncognitive skills) relate to educational performance and life outcomes (Jackson et al., 2020). Several studies suggest that noncognitive skills are more malleable than cognitive skills in later childhood (Carneiro et al., 2013;Cunha and Heckman, 2008). It has also been established that mindsets can be taught (Haimowitz and Dweck, 2017). Research indicates that social and emotional skills or traits such as determination, perseverance, and tenacity are fundamental for success in school (Heckman, 2006). For example, a person with high perseverance will stay focused on challenging tasks, will work hard, and will not give up-all of which are critical for learning (Bettinger et al., 2018).
A growing literature proposes that the relationship between family background and academic achievement is mediated in part by psychological mechanisms (Bernardo, 2021;Destin et al., 2019;King and Trinidad, 2021). One such mechanism is a belief in "natural talent"-that only certain people can be successful in school. In mindset theory, people lean toward a "fixed mindset," according to which attributes such as intelligence or personality are simply fixed, or a "growth mindset," according to which such attributes are instead capable of being shaped and developed (Dweck and Yeager, 2019). However, the socioeconomic dimension of students' mindset has not been extensively explored (Destin et al., 2019).
In this article, I investigate how students' beliefs about the nature of intelligence-whether they believe more that intellectual abilities are fixed or that they are capable of growth )-relate to family background and performance in middle and high school. I investigate two questions. First: How are family background and middle-school grade-point average (GPA) related to the level of fixed mindset when students enter high school? Second: Is there a relationship between the level of fixed mindset when students enter high school and their achievement after the first year, and does this relationship vary across family backgrounds?
I study this in the context of Norway. Family background and grades in 10th grade (the final year of middle school) are strong predictors of high-school graduation in Norway (Grøgaard and Arnesen, 2016;Markussen et al., 2017). There is also a strong relationship between family background and middle-school and highschool grades (Andersen and Hansen, 2012). Achievement gaps attributable to socioeconomic status (SES) have grown over the past 50 years in many countries, and Norway is one of those where this gap has grown the most (Chmielewski, 2019). The main challenge when it comes to ensuring that Norwegian young people obtain a high-school education is not to make middle-school students go to high school, because they nearly all do. Instead, the challenge is to make them stay there and leave with a qualification. This suggests that social and emotional competencies might be a factor worth exploring. One type of social and emotional competency that may be of particular importance is students' mindset.
I use a large dataset from multiple data sources pertaining to students in public high schools in two counties in Norway (Rege et al., 2020). The dataset consists of survey data, registry data on parents' education, and administrative data from the students' last year of middle school and their first year of high school. Very few studies have investigated how students' mindset relates to learning in Norway, and to my knowledge no studies have examined its relationship to family background. The relationships I study have previously been investigated in a U.S. context by Destin et al. (2019). In a sample of 4828 ninthgrade students in public high schools, they found that, on average, students with a university-educated mother had fewer fixed beliefs about academic ability. Further, they found student's mindset to be a significant but small factor in explaining the relationship between SES and achievement among high-school students. My analyses extend these results by exploring how family background interacts with prior performance in predicting the level of fixed mindset, and I also examine the interaction between family background and mindset in predicting high-school GPA in an additional model.

Conceptual framework
Mindset as a potential link between family background and high-school achievement I propose a conceptual framework (Figure 1) that can help us understand the interrelationships between family background, achievement, and mindset by combining sociological and psychological theories and building on prior empirical research. The expected relationships are visualized in the figure. Some of them have been extensively studied in the literature-for instance, how family background predicts performance in middle and high school, and how prior performance predicts future performance (arrows 1a, 1b, and 2). Regarding the remaining relationships (arrows 3, 4, 5, 6a, and 6b), we have limited evidence; those relationships reflect the key hypotheses that will be investigated in this article. The two dependent variables in the present study are level of fixed mindset and grades after the first year of high school. The study will investigate whether and how parents' education and students' prior performance predict the level of fixed mindset when students enter high school (arrows 4 and 5), and whether and how students' mindset, parents' education and students' prior performance predict grades after the first year of high school (arrows 3, 6a, and 6b).

Family background and achievement
Family background is a strong predictor of educational achievement (Chmielewski, 2019;Jackson, 2013) (arrows 1a, 1b in Figure 1). When it comes to explaining why family background causes inequality in achievement, von Hippel et al. (2018) outline that an enduring research tradition assumes that much of this inequality is caused by schools while an equally venerable tradition argues that the bulk of the inequality is due to nonschool influences, especially the family. Jaeger and Breen (2016) claim that cultural reproduction is among the most influential explanations for why inequalities in educational and socioeconomic outcomes persist over generations. In recent years, some scholars have argued that schools also help to compensate for inequality (Downey and Condron, 2016;von Hippel et al., 2018).
A starting point for the conceptual model is that family background is indeed related to performance in middle and high school (arrows 1a and 1b). Several studies confirm that these relationships exist in a Norwegian context as well. For example, Anderson and Hansen (2012) found that the higher social classes tend to perform best in both middle and high school, and Markussen and Grøgaard (2020) identified a slight tendency for grade differences by family background to increase in high school but found that the large differences are established in compulsory education. Numerous explanations for why these differences exist have been proposed, and Heggen et al. (2013) conclude that explanations related to students' Figure 1. Conceptual model: mindset as a potential link, alongside prior achievement, between family background and achievement. Arrow numbers represent relationships discussed in the Conceptual Framework section. environment (family and school), abilities, and motivation all have some explanatory power when it comes to explaining performance differences and that it is likely that many mechanisms are at play at the same time. However, few studies have examined how students' beliefs about the nature of intelligence and about what it takes to do well in school may relate to their family background and performance.
It is also well known from the literature that educational experiences as manifested in prior performance are related to future performance (arrow 2). Cunha et al. (2006) argue that skills beget skills via complementarity and self-productivity. This implies that skills produced at one stage raise productivity at later stages, and that skills produced at one stage augment skills attained at subsequent stages (Cunha et al., 2006).

Mindset and achievement
People form beliefs based on their experiences, and various theories try to explain how, in turn, beliefs can guide motivation and behavior (arrow 3 in Figure 1). Dweck suggests that mindsets create meaning systems (Dweck and Yeager, 2019) (Figure 1. Mindsets might organize goals, attributions, and helplessness into one meaning system. To these variables, she adds the concept of "effort beliefs"-believing that effort is a positive thing that helps grow your ability, or a negative thing that demonstrates deficient ability. All these variables may be ascribed different importance or meaning depending on whether a person has a fixed or growth mindset. When people view ability as fixed, validating their own ability (by pursuing performance goals or by avoiding challenges) may take on more importance, high effort may indicate low ability, and setbacks are more easily attributed to low ability. This may reduce persistence. By contrast, when people view ability as something that can be improved, developing their ability (by taking on challenging learning goals) may become more important, effort may be seen as a tool in this process, and setbacks are more readily seen as providing information about the learning process. This may strengthen persistence (Dweck and Yeager, 2019).
For the sake of convenience, researchers often refer to people with a fixed mindset and people with a growth mindset as two distinct groups, but data are typically analyzed as a continuum (Plaks, 2017). Mindsets tend not to be clearly developed and articulated in people's minds (Plaks, 2017): they are not fixed entities but are continually influenced by messages and experiences in a person's context (Haimovitz and Dweck, 2016). Indeed, Yeager et al. (2019) found that a growth-mindset intervention teaching students that intellectual abilities are capable of development improved grades, more so among lower-achieving students. Several other studies also show that holding a growth mindset correlates with better learning and higher grades over time, compared with holding a fixed mindset (Claro et al., 2016;Yeager and Dweck, 2012). Destin et al. (2019) characterize the negative relationship between a fixed mindset and lower academic achievement as well documented. The mechanisms at work are that students with more of a fixed mindset tend to avoid challenges and relent when faced with academic difficulty, leading to lower academic achievement relative to students with more of a growth mindset. In the conceptual model, this relationship is marked by arrow 3 in Figure 1.
Lately, mindset theory has also been criticized. In a meta-study, Sisk et al. (2018) found that the association between mindset and school achievement was inconsistent across studies. For studies using GPA as an achievement measure, they found an average correlation between growth mindset and academic achievement of r = 0.08, 95% confidence interval (CI) = (0.05, 0.11), p < 0.001. Because of these inconsistent findings, the present study in a Norwegian context represents a highly relevant contribution to our knowledge about mindsets and their (potential) relationship with academic achievement.

Family background and mindset
The mindset literature hypothesizes that many students are socialized into believing that only certain people can be successful academically (Dweck, 2017) (Figure 1). Messages fostering a growth or fixed mindset can come from parents, teachers, or coaches (Dweck, 2017).
There are several possible mechanisms through which parents may influence their children's mindset in response to academic failure (arrow 4 in Figure 1). An important one is communication about family traits, such as "nobody in our family ever understood math." This can push children into a fixed mindset. Haimovitz and Dweck (2016) found that parents' beliefs about failure as motivating or demotivating, and their responses to their children's failures, predicted their children's mindsets. Parents who saw failure as enhancing were less likely to worry that their child did not have enough ability and more likely to respond with a focus on the process of learning-by engaging the children in discussions about what they could learn from the experience, how they could study their mistakes to improve, and how they might consider asking for help from their teacher (Haimovitz and Dweck, 2017).
This can also be aligned with Bourdieu, who gave an example of how we would expect family background to affect mindset in an interview where he exemplified "doxa" (what people take for granted): "When you ask a sample of individuals what the main factors of achievement at school are, the further you go down the social scale the more likely they believe in natural talent and gifts-the more they believe that those who are successful at school are naturally endowed with intellectual capacities. And the more they accept their own exclusion, the more they believe they are stupid, the more they say 'Yes, I was no good at English, I was no good at French, I was no good at mathematics'" (Eagleton and Bourdieu, 1992: 114). Bourdieu and Passeron (1979: 72) describe how a mother from the lower classes imposes damaging influence in three different ways when she says for instance "He's no good in French" in front of her son: " First, (…) she makes an individual destiny out of what is only the product of education and can still be corrected, at least in part, by educative action. Secondly, (…) she uses simple test scores as the basis of premature definitive conclusions. Finally, (…) she intensifies the child's sense that he is this or that by nature." This is tantamount to suggesting that having fewer socioeconomic resources will be associated with a tendency to develop more of a fixed mindset when encountering educational struggles. In other works, Bourdieu (1998) finds that students with high levels of cultural capital are the most inclined to invoke natural talent to account for their success and hence have a fixed mindset. Nonetheless, a key point is that individuals' explanations for their own success or failure differ by social position. While Bourdieu is often associated with embodied cultural capital acquired in the home environment, Bourdieu and Passeron (1979: 73) also point to the fact that the techniques and habits of thought required by school could have been taught where the most disadvantaged could acquire them, that is, in school.

Prior educational outcomes and mindset
In the conceptual model, it is hypothesized that students' achievement in middle school may be related to their mindset at the start of high school (arrow 5 in Figure 1). Several studies find that mindset predicts performance (Yeager and Dweck, 2020), but fewer address how prior achievement predicts mindset. Bettinger et al. (2018) note that the presence of a growth mindset in baseline data from the first year of high school seems significantly more likely for students with a high GPA. Snipes and Tran (2017) found that students' level of growth mindset varied significantly by prior academic achievement: students with lower prior achievement had lower levels of growth mindset. The authors suggest that the differences in growth mindset can be the result of differences in prior academic experiences and outcomes. For instance, if low-achieving students have had more difficult or less rewarding academic experiences, they may have grown discouraged and developed beliefs that are more consistent with a fixed mindset. A study of undergraduate college students in Georgia, USA (Limeri et al., 2020), found that those who struggled with the course taken tended to shift toward viewing intelligence as a stable trait, that is, toward a fixed mindset.

Interaction between family background, mindset and achievement?
In the conceptual model, two possible interactions are proposed. The first (arrow 6a in Figure 1) is an interaction between family background and middle-school grades in predicting the level of fixed mindset.
In the literature examining school-continuation decisions, a widespread finding is that students from different family backgrounds respond differently to previous school performance when making educational transitions. Holm et al. (2019) conclude that signals about academic ability, communicated via GPAs, matter for educational decision making such as enrolling in and completing upper-secondary education in Denmark. The effect of such signals is stronger for students from low socioeconomic status (SES) backgrounds than for those from high-SES ones. Bernardi and Triventi (2020) found that students with poor previous grades were more likely to complete high school and enroll in university if their parents were highly educated. Similarly, regarding higher education, Herbaut (2021) found that students from low-SES backgrounds were more likely to drop out after academic failure than students from more advantaged backgrounds.
On the analysis presented in those studies, the inequality-generating mechanism operates mainly among the upper-class students, who move on despite poor educational performance in order to avoid downward mobility (Bernardi and Triventi, 2020;Holm et al., 2019). According to the compensatory-advantage framework, higher-educated parents of students in academic difficulty will mobilize more resources than lower-educated ones (Bernardi and Triventi, 2020;Herbaut, 2021). However, another explanation, in line with mindset theory, could be that students with a low-SES background more often have a fixed mindset and so relent when faced with academic difficulty. I will investigate whether there is an interaction between students' previous school performance and parents' level of education in predicting students' mindset.
The second possible interaction proposed (arrow 6b in Figure 1) is between family background and level of fixed mindset in predicting high-school GPA. It could be that a fixed mindset at the start of high school is more negatively associated with achievement after the first year among low-SES students. In a study from Chile, Claro et al. (2016) found evidence that students from lower-income families were less likely to hold a growth mindset than their wealthier peers, but that low-income students who had a growth mindset were buffered against the deleterious effects of poverty on achievement. Further, Jia et al. (2021), studying a subsample from PISA 2018 of 79 countries with information on students' expressed mindset, found that mindset interacted with SES to predict academic achievement for science and reading scores, and that the effect of a growth mindset was stronger among low-SES than high-SES students. However, a recent study from the United States (King and Trinidad, 2021) found that a growth mindset positively predicted mathematical achievement only among high-SES students. By contrast, Sisk et al. (2018) analyzed SES as a moderator variable, finding that academic-risk status and SES did not moderate the relationship between mindset and academic achievement in the studies reviewed in their meta-study. Similarly, Destin et al. (2019), in their US study, found a negative association between a fixed mindset and achievement regardless of SES.
These inconsistencies may be due to the use of different analytic strategies or outcome measures. While Claro et al. (2016), Jia et al. (2021), and King and Trinidad (2021) examined the relationship between mindset and performance at the same timepoint, Destin et al. (2019) analyzed the relationship between mindset and performance across time and conditioning on prior achievement. I reconcile some of these differences by examining the relationship across time with and without conditioning on prior achievement.

Context
Compulsory education in Norway starts at the age of 6 and covers 10 years of education, with years 8 to 10 constituting middle school. Young people who have completed their compulsory education are entitled to receive up to 4 years of either vocational or academic upper-secondary education and training in high school. Nine-tenths of Norwegian high-school students are enrolled in public high schools (Norwegian Directorate for Education and Training, 2019). Vocational education and training usually consists of 2 years spent in school followed by 1 year worth of in-service training. Since in-service training as an apprentice at a training establishment is usually combined with productive work, in which case the apprenticeship lasts for 2 years, vocational high-school programs tend to cover 4 years (Eurydice, 2020/21). Academic programs last for 3 years and provide general eligibility for admission to university. Students who have completed at least the first 2 years of a vocational program may complete a supplementary 1-year program to obtain general eligibility for admission to university. The high-school completion rate is lower in Norway than in similar countries, especially for vocational programs (OECD, 2020). In fact, only 67.7% of students entering high school in 2015 completed it within the standard timeframe while another 12.7% completed it within 2 years of their expected graduation date (Statistics Norway, 2020).

Data
A large randomized controlled trial relating to a mindset intervention was conducted in 2017/2018 (Rege et al., 2020). It covered all but one of the public high schools in two Norwegian counties (N = 58) and all first-year students had to participate. When logging in for the first session of the intervention a few weeks into their first semester, students were asked for their consent to participate in the research project, which 90.8% of them gave. Data from a questionnaire completed during that session were matched with administrative data on tenth-grade GPA retrieved from county records, with data on parents' socioeconomic background obtained from Statistics Norway, and with administrative data on GPAs after the first year of high school.
The final analytic sample consisted of 10,091 students. Out of that sample, 691 students (6.8%) were excluded from this study. To begin with, 394 students were excluded because they quit school during the year and so did not obtain a high-school GPA. Further, 159 were excluded because of missing middleschool grades (they had obtained no grade points from middle school or had completed their lowersecondary education in another country) and 36 were excluded because of missing information on their high-school GPA. In addition, 26 students with missing information on what middle school they had attended, 67 students who were special-education students or were in adapted training over several years, 4 students who changed to a school not in the sample, and 5 students with missing information on the mindset variable were excluded. The 394 students who quit, on average, were lower on middle-school GPA, lower on parents' education, and higher on fixed mindset. However, even if these students are included and their first-year high-school GPA is set to 1.0, the results are very similar to the ones reported here. The above yielded a final analytic sample of 9400 students, of whom 3229 (34.35%) were enrolled on vocational programs and 6171 (65.65%) on academic programs.

Key measures
Level of fixed mindset was calculated using two questionnaire items from the first intervention session. Participants responded on a six-item scale ranging from 1 ("strongly disagree") to 6 ("strongly agree") to two statements: "You have a certain amount of intelligence and you can't really do much to change it" and "Your intelligence is something about you that you can't change very much." The correlation between these two items was 0.7 (Chronbach's alpha: 0.83). An average score was computed for each participant. This type of measure of mindset, based on two or more statements, is used in the international literature (Yeager and Dweck, 2020).
GPA high school: GPA after the first year of high school, which ranges from 2 to 60. Highest education is an indicator of the parents' highest level of education, with a breakdown into four categories. The variable is assigned the value 1 if the highest level of education obtained by a student's mother and father is less than high school. For the values 2 to 4 the highest level of the mother or father is used; 2 indicates that the highest level of education is high school, 3 represents a bachelor's degree, and 4 denotes a master's or PhD degree.
Female: Indicator for gender; 1 represents female. GPA middle school: Tenth-grade GPA, which ranges from 11.6 to 60.
Vocational track: 1 represents vocational track. Students on vocational programs generally have a more positive grade development from middle school to high school than academic-program students, which is why I include this variable in the regression predicting high-school GPA.
Both parents non-Western immigrants: Both parents born in a non-Western country.

Analytic strategy
The aim of the article is to describe the fundamental relationships between the study variables. The study does not detect causal relationships; rather, its purpose is to investigate heterogeneity in descriptive associations. First, I used descriptive analyses to assess correlations between the continuous study variables. Then I used multilevel-regression analysis to predict fixed mindset as measured at the start of high school and GPA after the first year. In the regression focusing on the results from the first year of high school, I control for treatment status. 1 Ringdal (2018) suggests that multilevel modeling should be used if the intraclass correlation coefficient (ICC) of an empty model exceeds 0.05. This is the case here when highschool GPA is the dependent variable (ICC = 0.14), but not when fixed mindset is (ICC = 0.02). To ensure consistency, and because the data have an inherent multilevel structure (middle and high school), I use multilevel modeling in both regression analyses. The continuous independent variables are grand-mean centered. Parents' highest education is used as a categorical variable and not mean centered, as this would change the interpretation of the results. According to Enders (2013), there is a potential for confounding in multilevel models when the interaction between a pair of grand-mean-centered level-1 variables is examined. I have performed additional analyses (in a model using parents' education as a mean-centered continuous variable) for the model with high-school GPA as a dependent variable, as recommended by Enders (2013: 102). The joint significance tests of the additional parameters show that there are no contextual effects or confounded interaction effects when middle-school GPA is included in the model. When GPA is not included, there are such effects; the reason is that much of the variation between high schools (the level-2 variance) is related to the students' grades from middle school. This implies that the validity of the results is lower when GPA from middle school is not included in the models.
In visual presentations of the results, the dependent variable is centered by subtracting the mean. One limitation of the study is that mindset is only measured at a single point in time. Hence the data do not allow investigation of the development of mindset throughout compulsory education or in high school.

Results
Descriptive statistics relating to the sample studied are presented in Table 1. Girls make up 52%, and 12% have non-Western immigrant parents. The mean fixed-mindset score is 2.65, with a standard deviation of 1.14.
Bivariate correlations between key variables are reported in Table 2. The level of fixed mindset is negatively correlated with grades from both middle and high school.
How are family background and GPA from middle school related to the level of fixed mindset when students enter high school?
To address research question 1, I first look at the bivariate relationship between parents' highest level of education and students' expressed level of fixed mindset. Figure 2 shows levels of fixed mindset by parents' highest education level. On average, students whose parents' highest education is high school or less than high school express levels of fixed mindset above the mean, while students with at least one university-educated parent express levels below the mean.
Next, this association is explored in multilevel models that account for the clustering of students within middle schools (Table 3).
Model 1 in Table 3 shows that students whose parents have at least a high-school education have a significantly lower predicted level of fixed mindset than students whose parents have less than a high-school education. In Model 2, this association weakens when students with similar GPAs are compared: students whose parents have a high-school education do not differ significantly from students whose parents have less than a high-school education. In Model 3, I investigate whether there is an interaction between parents' education and middle-school grades when predicting fixed mindset. The interaction term is significant, and the relationship in question is further illustrated in Figure 3. Finally, Model 4 shows that gender is not a significant predictor of mindset for otherwise similar students, but students with non-Western immigrant parents have a higher predicted level of fixed mindset even when the other predictors are controlled for.
To illustrate the interaction between parents' level of education and students' middle-school GPA, Figure 3 presents predicted means for fixed mindset among students with low, medium, and high middleschool GPAs, respectively, by parents' highest level of education. Among students who were high performing in middle school, the predicted level of fixed mindset is below the mean and there is no difference by family background. Among students who were low performing in middle school, the predicted level of fixed mindset is above the mean, and higher among students with less-educated parents. Hence even students from more privileged backgrounds are predicted to express a higher level of fixed mindset if their performance in middle school was weak, but to a much lower degree than students with low-educated parents.
It should be noted that the proportion of high performers (with GPAs one standard deviation or more above the mean) is 31.3% among students who have at least one parent with a master's or PhD degree but 6.6% among students where both parents have less than a high-school education, while the corresponding proportions of low performers (GPAs one standard deviation or more below the mean) are 5.4% and 39.8%, respectively ( Figure A1 in the Appendix). Hence the comparison of the groups is based on selective samples of, for instance, low-performing students with highly educated parents. Still, this reflects the composition of the students' GPA from middle school, which is strongly related to their parents' level of education.  Is there a relationship between the level of fixed mindset when students enter high school and their achievement after the first year, and does this relationship vary across family backgrounds?
In the next set of analyses, I address research question 2 by investigating whether the level of fixed mindset when students start high school is related to their achievement after the first year. To do this, I perform a series of multilevel models (students nested within high schools) of high-school GPA as a function of mindset, adjusting for the relationship with parents' level of education and students' prior performance (Table 4). First, as suggested by earlier research, relative to the baseline of "less than a high school education," parents' highest level of education is a significant predictor of high-school GPA (Model 1). Next, a higher level of fixed mindset was found to significantly reduce predicted high-school GPA among students with similarly educated parents when introduced in Model 2. In Model 3, students with similar middle-school performance are compared, and this turns out to reduce the coefficients for parents' education and mindset.  Table 3. The x axis shows three GPA categories: high, medium, and low GPA. These categories are constructed based on the following thresholds: low GPA is defined as one standard deviation or more below the mean; average GPA as between one standard deviation below and one standard deviation above the mean; and high GPA as one standard deviation or more above the mean. Using parental education, the average predicted level of fixed mindset within each of these GPA categories is computed (N = 9400).
As mentioned in the Conceptual Framework section, earlier research has yielded inconsistent results when it comes to whether mindset is a stronger predictor of achievement among low-SES than high-SES students. In Models 4 and 5, I include an interaction term between parents' education and fixed mindset to investigate this relationship, and I investigate it without (Model 4) and with (Model 5) conditioning on prior achievement in middle school. Relative to students whose parents have less than a high-school education, the interaction in Model 4 is significant among students with university-educated parents. The interaction term in Model 4 is significant and consistent with the finding in other studies (Claro et al., 2016;Jia et al., 2021) that the positive association between holding less of a fixed mindset and a higher predicted high-school GPA is stronger for students whose parents are less educated. However, consistently with Destin et al. (2019), the interaction term in Model 5 is found not to be a significant predictor when students who performed similarly in middle school is compared. I consider it likely that this difference is due to the strong relationship between the level of fixed mindset and middle-school performance described in Table 3 and Figure 3. 2 The relationships from Models 4 and 5 are illustrated in Figures  A2 and A3 (in the Appendix).
Finally, in Model 6, gender and having parents with a non-Western background are included. Girls are predicted to have a lower GPA in high school than boys who are otherwise similar. A non-Western immigrant background does not predict high-school achievement when the other predictors in the model are controlled for.

Discussion
The present study shows that students who were high achievers in middle school express a lower level of fixed mindset when entering high school regardless of their family background. For those who were low Table 3. Estimates from multilevel-regression models predicting level of fixed mindset.  Notes: *p < 0.05, **p < 0.01, ***p < 0.001. Dependent variable: level of fixed mindset. Each column presents a separate regression and reports the estimated coefficient (standard error) for included covariates. The independent variables are mean centered. N = 9400. A test of the interaction term in Models 3 and 4 confirms that it is overall significant (prob<chi = 0.0054 and 0.0036, respectively). GPA, grade-point average.
performers in middle school, the predicted level of fixed mindset is higher when their parents have a low level of education. In high school, a higher level of fixed mindset at the beginning of the first semester is negatively related to achievement after that year even among students who performed similarly in middle school and have similarly educated parents. The article contributes to our understanding of the relationship between family background and achievement in four important ways. First, in line both with the quote from Bourdieu included in the Conceptual Framework section and with findings reported in the international literature (Destin et al., 2019), I have found that Norwegian students with less-educated parents are more likely to believe in natural talent and hence to have higher levels of fixed mindset.
Second, in line with Snipes and Tran (2017) and Bettinger et al. (2018), I find that students who were high performing in middle school have a lower level of fixed mindset when entering high school. My study presents only descriptive patterns and cannot determine whether students were low performing in middle school because they had a higher level of fixed mindset or whether they have a higher level of fixed mindset because they were low performing in middle school. However, it is likely that these aspects mutually reinforce each other. In panel data, DiPrete and Jennings (2012) found that, as children progressed through education, the contribution from noncognitive skills grew smaller as more of this effect became indirect through its impact on intermediate academic outcomes.
These estimates are meaningful in terms of their practical significance. Following Lorah (2018), I standardized the coefficients to investigate the magnitude of the mindset differences in the models not involving interaction. The relationship not conditioning on middle-school GPA (Model 2 in Table 4) shows that an increase of one standard deviation in the fixed-mindset variable is related to an expected decrease of 0.129 standard deviations in high-school GPA, while in the model conditioning on prior performance (Model 3 in Table 4) the same relationship is related to an expected decrease of 0.031 standard deviations in high-school GPA.  Table 4. Estimates from multilevel regression models predicting high-school GPA.  Third, an innovation in this article is the identification of an interaction between family background and middle-school performance in predicting students' expressed level of fixed mindset when entering high school. Specifically, the relationship between low performance in middle school and a higher level of fixed mindset is stronger among students with low-educated parents. If this relationship is present throughout the education system and influences intermediate academic outcomes, it can clearly constitute an inequalitygenerating mechanism. This is an issue that should be further explored.

Svensen
What is more, this interaction parallels findings in the literature on educational decision making to the effect that students' response to previous school performance differs by family background (Bernardo and Triventi, 2020;Holm et al., 2019). However, those authors' views on the beliefs underpinning students' decisions differ from the theoretical framework of this article. They draw upon the compensatory-advantage framework, in which the assumed mechanism is a desire among high-SES students (and their parents) to avoid downward mobility. Another mechanism that could explain this relationship is that low-achieving students with a low-SES background are more likely than their high-SES peers to have a fixed mindset and therefore to relent when faced with academic difficulty.
The ramifications of a strong belief in "natural talent" could also be investigated in the context of choice effects to further examine whether mindset can be a mechanism relating to primary as well as secondary effects. The probabilistic relationships identified in the present study do not in and of themselves demonstrate that students' beliefs about the nature of intelligence is a mechanism of relevance to the explanation of inequality in achievement. Nonetheless, the subjective beliefs expressed by the students as well as the issue of how they are formed and acted upon are worthy of further investigation. It is clear that what students think about the nature of intelligence when they start high school is strongly related to their middle-school performance. However, it is also clear that their performance level is strongly related to their family background. We need to know more about the processes shaping these fundamental relationships. For instance, further research could investigate how approaches to coping with educational struggles relate to these differences.
Fourth, this study helps to reconcile inconsistencies in the literature on whether there is an interaction between mindset and family background leading to a stronger effect of mindset on achievement among students with lower-SES backgrounds. It does so by suggesting that this matter is related to students' prior educational outcomes. Concretely, I have found that the level of fixed mindset interacts with parents' education in predicting high-school GPA in models without conditioning on prior performance, but not when prior achievement is included in the model. In the literature, the unconditional interaction has been interpreted as evidence of a stronger positive effect of holding a growth mindset among low-SES students. However, the fact that this relationship disappears when similarly performing students are compared suggests that the association with school performance is an important mediating factor.
On the one hand, conditioning on prior performance when analyzing relationships across time more credibly isolates academic processes when the mindset measure was collected, but it may also "control away" influences of SES and mindset on academic performance that operate prior to high school (Destin et al., 2019). On the other hand, not conditioning on prior performance may overestimate the role of mindset and parents' education by not relating them to the students' educational experiences. Longitudinal studies might be the best choice here, but in studies analyzing the interaction at a single timepoint, one solution could be to perform separate analyses on low-performing and high-performing students.
The present study also prompts certain general conclusions about suitable avenues for future research and about appropriate teacher practice. While mindset theory hypothesizes that many students are socialized into believing that only certain people can be successful in school, and that these beliefs guide their motivation and behavior, it devotes little attention to differences by family background. In fact, when social class is measured in psychological studies, it is often relegated to being a control variable instead of a key variable (Diemer et al., 2013). Controlling for social class may reduce the bias of estimates, but it also makes it impossible to draw conclusions about whether the relationships among the study variables are mediated or moderated by social class (Diemer et al., 2013). Insights from sociology could be exploited to add to the mindset-theory literature by examining how mindset relates to family background and educational experiences. This might contribute to a deeper understanding of the fundamental relationships involved.
As stated in the Introduction section, the mechanisms used in the sociological literature to explain differences in performance by family background often relate to properties of individuals, families, and societies that are difficult to change (Jackson, 2013). However, as noted by Heggen et al. (2013), several perspectives taken in the sociological literature have explanatory power in predicting performance inequality by family background and it is likely that many mechanisms are at play at the same time. A shift in focus toward examining presumably more malleable and teachable social and emotional skills and mindsets may be a promising step, especially given that these skills are also more policy amenable.
Teachers can promote a growth mindset by focusing on the learning process instead of on students' performance, and by framing failures and setbacks as opportunities for students to increase their understanding-not as indicative of shortcomings (Haimovitz and Dweck, 2017). DiPrete and Jennings (2012) found that children from high-SES backgrounds have stronger noncognitive skills. However, the same authors also argue that these skills can clearly be taught and that teachers evidently differ in their ability to transmit them to their students (Jennings and DiPrete, 2010). There is a need for further research to examine how teachers and the school environment can teach-low-performing students in particularabout their potential to grow and about how they can handle educational struggles. The findings from such research could be beneficial for the development of better practices in schools and for the targeting of interventions to reduce inequality and help more students fulfill their potential. Figure A3. Predictive margins of parents' highest level of education with 95% confidence intervals from multilevel regression with mean-centered high-school grade-point average (GPA) as dependent variable. The regression is similar to Model 5 in Table 4 (with conditioning on middle-school GPA). Fixed mindset is plotted at one standard deviation below and above the mean. The figure shows that, among students with similar middle-school performance, there is no interaction between parents' level of education and students' level of fixed mindset in predicting high-school GPA.