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Background In this cross-national study, Spanish, Finnish, and Swedish middle and high school students’ procedural flexibility was examined, with the specific intent of determining whether and how students’ equation-solving accuracy and flexibility varied by country, age, and/or academic track. The 791 student participants were asked to solve twelve linear equations, provide multiple strategies for each equation, and select the best strategy from among their own strategies. Results Our results indicate that knowledge and use of the standard algorithm for solving linear equations is quite widespread across students in all three countries, but that there exists substantial within-country variation as well as between-country variation in students’ reliance on standard vs. situationally appropriate strategies. In addition, we found correlations between equation-solving accuracy and students’ flexibility in all three countries but to different degrees. Conclusions Although it is increasingly recognized as an important construct of interest, there are many aspects of mathematical flexibility that are not well-understood. Particularly lacking in the literature on flexibility are studies that explore similarities and differences in students’ repertoire of strategies for solving algebra problems across countries with different educational systems and curricula. This study yielded important insights about flexibility and can push the field to explore the extent that within- and between-country differences in flexibility can be linked to differences in countries’ educational systems, teaching practices, and/or cultural norms around mathematics teaching and learning.

For school-age adolescents, teacher justice plays an important role in their learning and social outcomes. The present study examined the relation between teacher justice and students’ class identification in 1735 Chinese school-age adolescents by considering belief in a just world (BJW) and teacher–student relationship as mediators. Structure equation modeling (SEM) was used to reveal the direct and indirect effects. The analyses showed that all the direct and indirect effects were significant. These findings indicated that teacher justice had a positive effect on students’ class identification. In addition, teacher justice impacted students’ class identification through students’ just-world belief and teacher–student relationships. These results suggested that for adolescents, teacher justice played an important role in shaping their just-world belief system and their interpersonal relationships with teachers, which in turn affected their sense of belonging and values in relation to their class. Thus, it is important for teachers to be aware that their injustice may negatively impact their relationships with students, students’ belief systems, and their psychological engagement at school. There is a need to develop teacher-training programs to help teachers to establish classroom reward-punishment systems with the consideration of social justice, to communicate with students through an unbiased approach, and to increase student participation in the important decision making of the whole class.

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Recent studies have suggested a link between bullying victimization and passive bystander behaviors, such as more outsider behaviors and fewer defender behaviors. However, little is known about the internal mechanism underpinning this relation. The present study aimed to examine the direct and indirect relationships between bullying victimization and two types of bystander behaviors (defender behavior and outsider behavior), considering the possible mediator role of bullying sensitivity and moral disengagement among Chinese adolescents. Participants were 435 primary school students aged from 11 to 13 years ( M = 12.27, SD = 0.69) who completed measurements of bullying victimization, bullying sensitivity, moral disengagement, and bystander behaviors. The results of the total effect model indicated that bullying victimization was positively related to outsider behavior and negatively related to defender behavior. The results from the structural equation modelling (SEM) analysis showed that bullying sensitivity mediated the relationship between bullying victimization and defender behavior. The relationship between bullying victimization and outsider behavior was mediated by moral disengagement, as well as the multiple mediation of bullying sensitivity and moral disengagement. These results highlight the roles of bullying sensitivity and moral disengagement in explaining the relation between bullying victimization and bystander behavior among adolescent students. The findings provide important implications for developing intervention programs aiming at school bullying prevention.