Self-determination theory (SDT) states that all human beings have basic psychological needs (BPN) for autonomy, competence, and relatedness (Deci and Ryan, 2000; Ryan and Deci, 2017, 2020). Autonomy is volitional action toward a goal that people embrace as consistent with their sense of self and purpose in life. Competence is the feeling of being self-confident, knowledgeable, skilled, and capable of mastering challenging tasks (Di Domenico and Ryan, 2017). Relatedness is the sense of caring about others and being cared for by others. The fulfillment of these basic psychological needs positively influences motivation, psychological health, vitality, wellbeing, and quality of life (Van den Broeck et al., 2016; Avsec et al., 2021; Schutte and Malouff, 2021; Martela et al., 2023).

In education, the fulfillment of the students' BPN is essential to developing their agency and resilience as learners (Reeve et al., 2020). Studies have shown that adolescent engagement in school typically decreases over time, but satisfaction of BPN can play an important role in maintaining student engagement in learning (Earl et al., 2023). Alternatively, frustration of BPN has a negative association with student satisfaction and engagement in learning (Hughes et al., 2023).

SDT holds that human motivation is expressed along a continuum from autonomous to controlled (Deci and Ryan, 2000; Ryan and Deci, 2017). Autonomous motivation is that which individuals perceive as volitional and consistent with their sense of self, while they perceive controlled motivation as forced upon them and incongruent with their identity (Deci and Ryan, 2000; Ryan and Deci, 2017). The degree to which individuals feel that their actions are autonomous or controlled affects how they self-regulate their thoughts and actions. The highest level of autonomous motivation in education arises from learning that is inherently interesting and enjoyable (Bureau et al., 2022). Throughout the course of formal education, autonomy support by teachers predicts student autonomous motivation, engagement, conceptual understanding, academic performance, and psychological wellbeing (Reeve and Jang, 2006; Reeve, 2009; Ryan and Deci, 2017). In this context, autonomous motivation influences student academic performance through its positive impact on critical thinking, which is the only cognitive process that has a positive, significant impact on academic performance (Manganelli et al., 2019). By contrast, controlled motivation has a negative direct impact on student academic performance. It promotes the use of surface-level cognitive strategies of rehearsal and organization but has a negative influence on elaboration and critical thinking, both deep-level cognitive processes (Manganelli et al., 2019).

Self-efficacy is a construct of social cognitive theory and its perspective on human agency (Bandura, 1986, 1997, 2001). Self-efficacy is the “metacognitive capability to reflect upon oneself and the adequacy of one's thoughts and actions” (Bandura, 2006, p. 165) and influences all other aspects of human agency. Those with more developed competencies, self-regulatory skills, and stronger self-efficacy beliefs are more successful in accomplishing desired outcomes than those whose agentic skills and beliefs are less developed (Bandura, 1986, 1997).

Within the sphere of education, self-efficacy is students' beliefs about their own ability to influence academic achievement (Bong and Skaalvik, 2002; Er et al., 2022). It has been found that students' self-efficacy beliefs influence their motivation to learn, their ability to self-regulate, and their academic performance (Usher and Pajares, 2006, 2008). Students' self-efficacy beliefs arise from four sources (Bandura, 1986, 1997): mastery experiences where students evaluate their competence from results of their own learning efforts; vicarious experiences from observing social models such as classmates who master or fail an academic task; verbal and social persuasions, such as encouragement from parents, teachers, and peers; and emotional and physiological states such as anxiety, mood, and stress.

Most important to the development of self-efficacy is students' success in academic tasks. Students with high self-efficacy beliefs have positive mastery experiences, while students with low self-efficacy beliefs have experienced failure (Yildiz and Özdemir, 2019). Although psychological states such as anxiety have the least impact, studies indicate that they can undermine self-efficacy because students interpret anxiety as evidence of low ability (Yildiz and Özdemir, 2019).

Self-efficacy changes as students have new experiences and gain new information in the transition from one grade to the next (Usher and Pajares, 2008; Kontaş and Özcan, 2022). Learning conditions that foster positive relationships and student belonging are conducive to self-efficacy (Usher and Pajares, 2008; Zysberg and Schwabsky, 2021). Students who experience their classroom environments as more supportive and caring, mastery-oriented, and challenging have higher levels of self-efficacy and competence support (Chang, 2023).

Many studies link the satisfaction and frustration of students' BPN with academic achievement (Ahn et al., 2021; Buzzai et al., 2021; Afzal and Jami, 2023; Vijayakumaran et al., 2023; Wangchuk, 2023; Zhang and Jiang, 2023; Zupančič et al., 2024). Students' perception of satisfaction or frustration in the classroom is influenced by the teacher. Autonomy-supportive teaching practices arise from the teacher's student-focused attitude (Reeve and Jang, 2006) and include three essential instructional behaviors (Jang et al., 2010): the nurturing of students' inner motivational resources, use of non-controlling language that conveys information about the purpose of instructional activities, and overt acknowledgment of student perspective and feelings.

Autonomy supportive teachers listen more to their students, respond to their students' questions, give fewer directives, and converse with students in a way that conveys understanding of students' perspective (Ryan and Deci, 2017; Reeve and Cheon, 2021). They provide optimal learning challenges and present to students interesting and relevant learning activities aligned to meaningful goals (Jang et al., 2010). They do not give in to students but help them understand the importance and requirements of learning tasks (Reeve and Cheon, 2021). Autonomy support that teachers give to students supports students' BPN, which in turn increases student autonomous motivation and is predictive of student achievement (Jang et al., 2012; Bureau et al., 2022). Students' perceived autonomy support is positively associated with perceived competence, relatedness to teachers, vitality in school, contentment with school, and with school performance, while school-related pressure is negatively related (Howard et al., 2021; Bureau et al., 2022; Martinek et al., 2022).

Earl et al. (2023) found that BPN satisfaction is unrelated to school grades at the beginning of the school year, but as the school year progresses, students with more satisfaction of BPN show increasing and higher levels of academic achievement compared to students with less satisfaction of BPN. Fulfillment of BPN is also significantly related to grades and mastery goals (Theis et al., 2020). Support of BPN fosters student intrinsic motivation, which is positively and significantly associated with student wellbeing in learning (Ye et al., 2022) and is the only form of autonomous motivation that is positively associated with academic achievement (Taylor et al., 2014). Taylor et al. (2014) also found a reciprocal relationship between intrinsic motivation and academic achievement, with prior academic achievement also predicting later intrinsic motivation. There have been few studies that incorporate BPN, motivation and achievement besides the ones noted above. Nevertheless, motivation is the connection between students' BPN and achievement.

Overall, the impact of satisfaction of students' BPN and achievement is universally applicable across nations and cultures (Ryan and Deci, 2017, 2020; Wang et al., 2021; Guay, 2022). Nalipay et al. (2020) found positive and significant relationships between satisfaction of student BPN and student achievement across Western and Eastern cultures, with relatedness having the largest association with achievement followed by autonomy. Despite numerous findings associated satisfaction of student BPN with achievement, one meta-analysis (Conesa et al., 2022) found support for the hypothesis that satisfaction of student BPN is associated with student motivation overall but found a lack of studies supporting the hypothesis that BPN satisfaction increases student achievement. This is interesting to note as few studies incorporate both BPN and motivation as predictors of student achievement.

Self-efficacy has a large effect on students' use of deeper learning strategies and their ability to transfer learning to novel contexts (Karaman et al., 2019; Schunk and DiBenedetto, 2021). It is one of several positively correlated agentic processes that are predictive of academic achievement (Code, 2020). Academic self-efficacy is associated with academic performance in reading literacy (Yang et al., 2018; Ocak and Tiraki, 2020; Zysberg and Schwabsky, 2021; Zorlu and Ünver, 2022), mathematics (Kitsantas et al., 2011; Xu and Qi, 2019; Ugwuanyi, 2020; Zysberg and Schwabsky, 2021; Er et al., 2022; Kontaş and Özcan, 2022; Muhtadi et al., 2022), and the sciences (Aurah, 2017; Oyelekan et al., 2019; Gao et al., 2020; Adjei et al., 2023; Dever, 2024) and is positively associated with overall academic achievement (Asakereh and Yousofi, 2018; Akturk and Ozturk, 2019; Olivier et al., 2019; Usher et al., 2019; Zysberg and Schwabsky, 2021; Luo et al., 2023; Salvo-Garrido et al., 2023; Al-khresheh and Alkursheh, 2024; Bozzato, 2024).

Low academic self-efficacy causes maladaptive behaviors such as procrastination (Katz et al., 2014). There is also a negative correlation between students' homework stress and their self-efficacy (Katz et al., 2012). High self-efficacy predicts perseverance through difficulties and anxieties (Usher and Pajares, 2008). Students with high self-efficacy beliefs are more likely to engage in school and persist in learning until they have achieved their learning goals (Hong et al., 2021; Zorlu and Ünver, 2022; Nong et al., 2023). It affects how students believe they can apply the skills and abilities they have to learning tasks (Bong and Skaalvik, 2002). But academic efficacy can also be negatively associated with academic achievement when students are overconfident or underconfident of their abilities (Alafgani and Purwandari, 2019). Some studies also indicate reciprocal effects between prior achievement and self-efficacy (Olivier et al., 2019), with prior achievement having a stronger effect (Talsma et al., 2018; Ansong et al., 2019; Sorjonen and Melin, 2023), and few studies have found weak effects of self-efficacy on student achievement (Ansong et al., 2019; Li et al., 2023). Recent studies have also revealed that fluctuations in students' self-efficacy and perceptions of academic burden are negatively associated with academic achievement (Vongkulluksn et al., 2024).

There are a growing number of studies that use both social cognitive theory and self-determination theory to understand sources of academic motivation. For example, Katz et al. (2014) noted that support for students' autonomy, competence, and relatedness may reduce student procrastination by increasing autonomous motivation and self-efficacy through support of the need for competence. A study involving postsecondary students found a significant, positive relationship between self-efficacy and autonomous motivation (Azila-Gbettor et al., 2021). Another study found that autonomous motivation in prospective 1^st year university students was predictive of academic achievement, but academic self-efficacy was not (Fokkens-Bruinsma et al., 2021). Raven and Pels (2021) found that self-efficacy was significantly and positively associated with satisfaction of BPN and performance. Macakova and Wood (2022) found that satisfaction of BPN of college students was positively and directly related to self-efficacy, and indirectly related to academic achievement via self-efficacy. Satisfaction of BPN has also been associated with increased academic self-efficacy of undergraduate vocational students (Chen, 2024). In their longitudinal study of Chinese secondary students studying English as a Foreign Language, Li et al. (2024) found significant reciprocal relationships between self-efficacy, autonomous motivation, and academic achievement.

In summary, we have found many studies of the relationship between student BPN and motivation, and between student BPN and achievement, with some contradictory evidence for the relationship between BPN and achievement. There are also numerous studies which support the relationship between student self-efficacy and achievement. To the best of our knowledge, however, there are few studies that investigate the associations between BPN, motivation, self-efficacy, and academic achievement and there are even fewer studies on these concepts at the middle or elementary grade levels and across academic subjects. Consequently, we put forth the following hypotheses:

Further, we were interested in which variable would have the largest impact on student achievement and the relationship among all the variables. The next section discusses the methodology used to investigate these questions.

In total, we surveyed 35 middle schools, and 2,359 students completed the questionnaire. In Germany, students take both math and German each year. Therefore, this questionnaire consisted of three parts: demographic data, items related to math courses, and items related to German. The items in the Math and German parts were identical, but worded to be subject specific. The mean age of the students responding to the questionnaire was about 13 years of age (SD = 1.74) and varied between nine and 18 years old. It is possible for students in Germany to be in 9^th grade and be 18 years old if they start school late and are held back a grade, but there were only two students who were 18 years of age. About 51 percent of the sample were female (SD = 0.50), 79 percent of the sample were living in a two-parent household (SD = 0.40), and 42 percent had at least one parent that was born in another country (SD = 0.49).

In Germany, at the end of fourth grade students are assigned to one of three school tracks based on their school performance. When students move from elementary to secondary school in the fourth grade, the teacher recommends the track in which the student should be placed. In some states, parents also have input on the track. There are three different tracks: Gymnasium (13 years of school attendance) reserved for the highest performing students headed for college, Realschule (10 years of school attendance) for the middle tier, and Hauptschule (9 years of school attendance) for the bottom tier that prepares students for vocational training.

By the age of 10 years, most students in Germany have been placed on one of the tracks. While students have their track set by fourth grade, some schools serve students from combined tracks (integrative track called Gesamtschule) where students with high, average, and low achievement levels attend school together (Lohbeck et al., 2022). Students who were on the integrative track were excluded from the analysis (n = 743) which equated to 23 percent of the original sample. While we were hesitant to exclude a large percentage of students, we removed these students because we did not know the individual students' recommended track, only that they attended an integrative school. Consequently, we conducted a similar analysis on just the students who were enrolled in an integrative school. While we did not find substantive differences in the results, the findings from this study may not be generalizable to students who attend integrative track schools. The discussion section will review generalizability in more detail. The next section describes the measures and the methods used in the study.

This section describes the outcome measure, independent, and control variables. Response categories ranged from 1 to 5 on a Likert scale (1 = not true to 5 = very true) for all scales excluding the outcome measures (math and German self-reported grades). We incorporated four independent variables in the models including perceived BPN support, motivation (both autonomous and controlled), and self-efficacy. Items for each of the measures were combined into a scale and we used both Cronbach's alpha and McDonalds Omega to gauge reliability and subsequent measurement error. The reliability standard aims to set principles for maximum allowable measurement error. Cronbach's alpha of 0.6 is considered the minimum reliability threshold in education sciences (United States Department of Education, 2022). Conversely, the Omega takes into account the strength of association between items and constructs as well as item-specific measurement errors in addition to the latent factor loading to estimate reliability (Revelle and Zinbarg, 2009). An Omega of 0.7 is considered the minimum reliability threshold (Nunnally, 1978). Furthermore, Murphy and Davidshofer (1998, p. 89) state that reliability >0.6 and ≤ 0.7 is considered low. To this end, the minimum reliability thresholds are highly debated, often contextual, and researchers have even argued that Cronbach and Omega have the same standards (Lance et al., 2006; Dunn et al., 2014). To this end, we report both the alpha and Omega to assess reliability because, in some cases, it may provide more realistic estimates of the true reliability of a scale (Malkewitz et al., 2023).

For brevity, we provide examples of items within the following narrative. For replication, all items are reported in the Supplementary material. Next, we describe each construct in greater detail beginning with the dependent variables.

We used Pearson's correlation coefficients to assess the magnitude and direction of the relationships between the dependent and independent variables. Correlation analyses were performed to assess the predictability, strength, and direction of the observational instruments and to investigate multicollinearity. Due to the nested nature of the data collection mode, we used Hierarchal Linear Modeling (HLM) to adjust for clustering of students within buildings (Raudenbush and Bryk, 2002). If we did not adjust for clustering, statistical significance could be inflated. We used SPSS version 29 with the Advanced Statistics module using the mixed methods command to calculate the estimates. We chose HLM as opposed to other methods because data were collected in clusters of schools, and data were cross-sectional, so we could not infer causality.

Variables were standardized to discern which variable had the largest impact on achievement. While standardizing dichotomous variables is problematic for linear assumptions and interpretation, we wanted to ensure all variables had the same scale to assess which variable had the largest impact on the outcome. As such, we report standardized Beta coefficients.

To compare measurement models and gauge model fit we used several criteria including the Conditional R-Squared (R²c), Akaike's Information Criterion (AIC), and the Conditional Intraclass Correlation Coefficient (ICC). The Conditional R-Squared is like the R-squared in regression analysis; however, it reflects the proportion of variance explained by both fixed and random effects. In HLM, Akaike's Information Criterion can be used to compare nested models. Models with lower AIC values are considered the best-fitting model. Intraclass Correlation Coefficient is another measure of the proportion of total variance attributable to the group level. It is calculated as the ratio of the between-group variance to the total variance. It is a useful measure for assessing the impact of group-level predictors.

Equation 1 for the full model is listed below. The same model was used for both outcome variables, achievement in math and German.

Final Model

While our findings are supportive of prior research and theory, there are several limitations that should be noted. First, the outcome variable was self-reported student grades. Self-reported grades have been deemed an appropriate method of achievement and it has the benefit of not breaking ethical rules related to student record confidentiality (Shim and Ryan, 2005; Zysberg and Schwabsky, 2021). Although self-reported grades are widely obtained as an operationalization of student achievement in educational contexts (Fryer and Dinsmore, 2020), their validity is sometimes questioned (Kuncel et al., 2005). As such, some scholars have doubted the use of self-reported grades as a valid construct. Somers et al. (2020) found that students' characteristics such as age and school performance impact the accuracy of self-reported grades. It could be that gender also played a role in reporting grades as we found that females fell out of statistical significance in math not German after accounting for self-efficacy. Therefore, future studies should examine this relationship more closely and consider more objective measures of student achievement such as assessment scale scores to confirm the patterns found. Furthermore, areas for future research include replicating the findings by linking student perceptions to assessment scores.

Additionally, teachers' instructional behavior could be assessed more objectively by observational measures instead of student perceptions. When students rate teachers' behavior there is a high variance in responses even though they are rating the same teacher (Katz, 2017). This variability represents an inconsistency among students within one class which could be interpreted as measurement error. Although this points to a more objective approach, there are also empirical findings that support the implementation of student reports when assessing BPN satisfaction in the classroom as determinant of students' motivation. For example, Katz (2017) found that the variance in students' ratings of their teacher's behavior was attributed to differences in students' perception of their teacher's behavior rather than actual differences. Therefore, she assumed that differences in students' motivation were a consequence of differences in their perceived BPN satisfaction in the classroom. Implementing more objective measures such as observations in the classroom could not mirror these important differences in students' perception. As we found students' self-efficacy to have the largest relationship with achievement in math and German, it would be interesting to investigate whether differences in students' perception of their teachers' BPN satisfying behavior similarly predict the differences in students' self-efficacy.

Another methodological limitation addresses the cross-sectional design of this study which limits our inferences on causality, as we found a reciprocal relationship between motivation and self-efficacy. While this study represents the first step of addressing the interrelations of the variables, longitudinal designs would help determine the mediating role of self-efficacy overtime. Moreover, future research should investigate how fostering self-efficacy may change student achievement. While cross-sectional designs are preferable for inquiry of interrelations, longitudinal designs are essential to cross-validate our findings. Indeed, our findings are in line with Nuutila et al. (2020) who found in their longitudinal study that situational interest as a motivational variable had a larger impact on students' self-efficacy than vice versa. However, Du et al. (2021) could not confirm reciprocity. They found that former math achievement and self-efficacy in mathematics to be predictors of later interest in mathematics. Moreover, prior math interest had no impact on students' achievement and self-efficacy.

Due to such inconsistent empirical findings, further research is needed to identify the specific underlying processes. It could be that the relationship of self-efficacy to student achievement varies cross-culturally, with a stronger relationship to achievement in Western cultures and a lesser impact in Eastern cultures (Nalipay et al., 2020). Further, it may be that the relationship between students' academic self-efficacy and student achievement is mediated by other variables such as students' perceptions of teacher support of their BPN (Katz et al., 2010), expectations, beliefs, and emotions concerning the subject area, the skills they are learning, or the value that they assign to learning tasks (Doménech-Betoret et al., 2017; Mete, 2021).

Additional studies should also further examine the impacts of tracking on students' motivation and self-efficacy. Belief in one's own competence stems from social comparisons. In other words, students build their self-efficacy by comparing their competence with other students in their class. After tracking, such social comparisons are limited to students similar in their school performance. According to the Big Fish Little Pond Effect, the assignment of students to tracks in secondary school could inadvertently lower or raise students' academic self-concept and perceived academic self-efficacy when attending schools where the average ability levels of other students are perceived as higher or lower (Marsh and Seaton, 2015; Salchegger, 2016; Basarkod et al., 2023). Furthermore, between-school tracking not only leads to social segregation of students, but also to fewer teaching resources, fewer qualified teachers, lower expectations of students, lower academic rigor of curriculum, and negatively influences learning conditions in lower track (Pomianowicz, 2023). As tracking seems to have such an immense impact on students' self-efficacy, motivation, and achievement, a similar study of integrative tracking would be helpful to determine whether our findings could be replicated. In this context, we investigated the same patterns with the integrative track students that we excluded from our sample, and we found very similar results; however, we did not have a way of determining the students' individual assigned tracks. Furthermore, Germany has one of the largest numbers of tracks within OECD and European school systems (Pomianowicz, 2023). Consequently, results should be cross validated in other countries as these findings may not be generalizable outside of educational systems that incorporate tracking.

Finally, our study included only students' perceived BPN support as relevant predictor of students' academic motivation, self-efficacy, and achievement. Recent models and research within self-determination theory highlight the independent relevance of BPN frustration (Vansteenkiste et al., 2020), assuming BPN frustration to be stronger and more perilous than the mere absence of BPN satisfaction. So far, only very few studies have considered BPN frustration as potential predictor in the educational context (Buzzai et al., 2021; Zhang and Jiang, 2023). Therefore, it would be fruitful to further examine the interplay of BPN satisfaction and frustration as determinants of students' academic motivation, self-efficacy, and achievement in future research.

While we noted several limitations and areas for future research, there are several strengths of this study. The main finding from this study was that self-efficacy had the largest relationship with math and German grades. Furthermore, we found self-efficacy played a mediating role in achievement through perceived BPN support and motivation. Considering the findings, other studies that assess BPN, motivation and achievement that do not account for self-efficacy could have spurious relationships to student achievement. Additionally, most studies only investigated relationships using one subject area at a time. We investigated the impact of perceived BPN support, motivation, and self-efficacy on achievement using a large sample and two different academic subjects and we reached similar findings indicating a potential for generalizations to be made across subjects.

The results also highlight some practical implications for teachers, particularly, the importance of fostering students' self-efficacy. For example, Schunk and DiBenedetto (2021) suggest that teachers can enhance student self-efficacy through teacher or peer modeling, by providing proximal and challenging goals, and by providing feedback linking performance outcomes with student effort. In terms of self-determination theory this would represent need-supportive teaching behavior. Furthermore, this study highlights the need of principals to encourage teachers to be more supportive of students' self-efficacy in the classroom. In this context, Klassen et al. (2012) point out how satisfaction of teachers' own BPN at work supports teachers' emotions and engagement in the classroom. Moreover, it could be that teacher characteristics play a critical role in fostering self-efficacy of students and achievement. Future studies examining these relationships would help educators better understand how practices that support students' BPN, and self-efficacy can improve academic outcomes for all students.