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The objective of this study is to examine the characteristics of PSTs' selection of real-life examples for discussion, the aspects they attended to during the discussion, and their reflection on facilitating the discussion. A total of 46 elementary PSTs in the US joined in the study. We gathered data from a three-phase task using an online course management platform and restricted the real-life contexts using percent. The collected data were analyzed using enumerative and ethnographic content analysis. The findings revealed that while we detected some shifting features in PSTs' selection of real-life contexts compared to prior studies, we found their static preference of contexts around consumer practices over others (e.g., contexts related to science and critical literacy). The findings also revealed that PSTs tended to pay attention to the contexts with critical views when the context was not straightforward and direct computations were not readily feasible to get the final answer. Moreover, the vague contexts helped encourage PSTs to view the situations critically, but they had difficulties having meaningful mathematical discussions in such contexts. We provided suggestions and implications for future research based on these findings.

Word problems are frequently used in school mathematics to offer students the opportunity to explore mathematical relationships and structure. However, previous studies have reported that word problems are misused or abused in ways that overlook the original intent of exploring mathematical structure and relationship. This study aims to share a series of a small group of third-grade students' explorations while debating the mathematical relationships in solving a word problem with representations over several days. Although the exploration took longer than planned, it was worthwhile. It offered students a space to express confusion, showcase their knowledge, test conjectures, and imagine alternative contexts. Ultimately, these explorations helped students recognize multiple relationships within the context of specific problems while bringing their attention to real-world related applications. The retrospective analysis of class episodes offers insight into learning opportunities to support students in exploring mathematical structure and relationships while discussing and debating the word problem context.

This study performed a scoping review of the literature concerning the use of technology in mathematics education published between January 1981 and March 2022 to explore research trends. After the defined filtering process, we retrieved 2,433 articles from "Web of Science," "ERIC," and "PsycInfo" databases and employed Latent Dirichlet Allocation (LDA) topic modeling to extract key terms and topics from the selected articles. The analysis focused on the four aspects: (a) evolution of research trends of technology use in mathematics education, (b) frequently used words, (c) latent research topics, and (d) research trends for particular topics. The findings revealed a steady increase in research interest, and the combination of frequently used words in the article abstracts suggests popular research topics that have been studied during the set period. The results of LDA identified seven research topics that were not precisely aligned with those identified in prior studies on mathematics education or educational technology. This implied technology integration into mathematics education as a distinctive research area. Over time, the seven topics showed different research trends (stable, fluctuating, increasing, and decreasing). We discussed plausible reasons for these varied patterns and proposed implications based on the research findings.

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.

The relationship between students' attitudes toward mathematics and mathematics achievement has garnered tremendous attention from researchers. However, there is a degree of inconsistency in the findings regarding this relationship. Therefore, this study aimed to identify the profiles of students' attitudes toward mathematics and examine their relationship with mathematics achievement. Using latent profile analysis, we examined data from the Trends in International Mathematics and Science Study conducted in Singapore in 2019. We identified four profiles of attitudes toward mathematics, namely very negative (5.44%), negative (41.38%), neutral (38.77%), and positive (14.41%). We also confirmed the literature describing students' attitude toward mathematics as a multidimensionally integrated construct, comprising 'like mathematics,' 'value mathematics,' and 'confidence in mathematics.' Moreover, we discovered a positive relationship between students' attitudes toward mathematics and mathematics achievement. These results showed that the following students are more likely to have high mathematics achievement: (a) those who like to study mathematics and pursue mathematics-related activities, (b) those who believe that learning mathematics will result in a positive outcome (e.g., success in school and job opportunities), and (c) those who trust in their mathematical abilities. Therefore, educators need to examine students' attitudes toward mathematics and provide appropriate support to stimulate the development of a positive attitude toward mathematics.

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.

Patterned Mg2Si structures can be attractive for use in optoelectronic, thermoelectric, and other devices. Such structures can be fabricated as conformal Mg2Si films on patterned Si substrates via direct reaction of these substrates with Mg vapor at modest temperatures and ambient pressure. Here, we report the kinetic mechanism (rate-limiting step and associated rate law) that controls such vapor/solid reactive formation of conformal Mg2Si films. To avoid oxidation during silicide formation, experiments were conducted within metal ampoules that were sealed in an argon atmosphere. Upon heating each sealed ampoule to 600 °C, Mg vapor (generated from solid Mg sealed within the ampoule) underwent reaction with a Si single-crystal plate (located a fixed distance from the solid Mg within the ampoule). Kinetic data were obtained by evaluating the change in thickness of the product Mg2Si film, and the specimen mass change per area, with reaction time at 600 °C. The changes in mass and in film thickness were both found to follow parabolic kinetics, with the rate constants obtained from both types of measurements in good agreement. Changes in the diffusion distance of the Mg vapor to the reacting Si single-crystal plate, and in the crystal orientation of the plate, were found to have negligible influences on the reaction kinetics. Such data were consistent with solid-state diffusion through the Mg2Si product layer as the rate-limiting step. An inert marker experiment was used to determine the predominant interface at which Mg2Si formed, and to evaluate the rate-limiting species controlling such formation. [ABSTRACT FROM AUTHOR]