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Mathematics growth trajectory plays a significant role to predict future outcomes and careers. We examined the existence of different growth trajectories in mathematics during the late elementary-school period (from Grades 4 to 6) and the relationship between the trajectory group classification and later mathematics achievement (Grade 8). Then, this study examined the moderating effects of mathematics teachers' teaching styles. Two thousand six hundred eighty students participated in a 5-year longitudinal study in South Korea. Growth mixture modeling provided four distinctive classes of growth trajectories in elementary mathematics achievement, and all classes significantly predicted later achievement in Grade 8. Furthermore, the student's perception of teaching styles revealed different associations with mathematics achievement depending on growth trajectory groups. While direct teaching is positively associated with the high and the average performing groups, dialogic teaching is positively associated with the low performing group. The findings highlighted the growth trajectory is a critical component in predicting later academic achievement and students need appropriate instructional supports.

Developing textbooks of optimal quality is crucial for enriching the students' learning and understanding. This study examined fraction addition and subtraction problems in the U.S. and South Korean mathematics textbooks according to the types of denominators. In particular, we investigated Everyday Mathematics (EM) and South Korean mathematics (KM) textbooks revised in 2015 and developed an analytic framework encompassing horizontal and vertical dimensions to examine the learning opportunities presented to students by the textbooks. We assessed their topic sequence and frequency of fraction addition and subtraction contents with regard to the former and examined their contextual features, cognitive demands, and mathematical activities with regard to the latter. We observed that EM provided inadequate learning opportunities for fraction subtraction problems, representation problems, and high-order cognitive abilities. However, KM provided more even learning opportunities for fraction addition and subtraction problems, various contextual features, and high and low thinking skills. Moreover, we found that EM emphasized understanding and resolving activities, whereas KM underscored exploring and explaining activities. The findings of this study suggested updating fraction addition and subtraction contents in the U.S., South Korea, and other countries by considering horizontal and vertical dimensions.

Professional development (PD) has been widely implemented to shift mathematics instruction practices from teacher-centered (traditional practice) to studentcentered. As such, a study examining mediating factors on the relationship between PD and student-centered instruction is of great importance in enhancing the effectiveness of PD and shifting teacher practice. Although studies examining the mediating effects of contextual factors (e.g., administrative support) on the relationship between PD and instruction abound, studies exploring the effects of teachers' psychological factors on this relationship are relatively scarce. In this study, we examined the mediating effects of mathematics teachers' self-efficacy beliefs and classroom stress on the relationship between PD and student-centered instruction. We used a secondary data set collected for the 2015 Trends in International Mathematics and Science Study (TIMSS). For this data set, 317 teachers of eighth-grade mathematics, selected from 150 schools in Korea, were surveyed, and an analysis was conducted using structural equation modeling. Our findings revealed significant mediating effects of self-efficacy beliefs on the relationship between PD and student-centered instruction. However, the mediating effects of classroom stress were not significant. Moreover, we found significantly positive direct effects of PD and self-efficacy on student-centered instruction.

This study aimed to examine the effect of early numeracy activities at home on children's mathematics achievement in fourth grade. It also examined the mediating effects of early numeracy competencies and self-efficacy beliefs in mathematics on this relationship. The study used Trends in International Mathematics and Science Study (TIMSS) 2015 Korean data, selecting nationally representative samples of fourth-grade elementary students (N = 4 669) and their parents. A confirmatory factor analysis (CFA) and structural equation modeling (SEM) were used to analyze the study data. The study findings revealed that students who engage in more early numeracy activities at home are more likely to have high mathematics achievement in fourth grade. Early numeracy competencies and self-efficacy beliefs positively mediate this relationship. Moreover, the findings of the study revealed that sequential mediating effects of early numeracy competencies and self-efficacy beliefs on this relationship. Based on the findings of the study, several implications have been proposed.