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The focus on STEM has centered on knowledge use across multiple disciplines. However, there currently exists limited understanding of the relationship between the cognitive practices utilized across these disciplines as a function of performance on standardized assessments. Focusing on science and mathematics, we investigated the direct and indirect relationships between science and mathematics reasoning practices. The TIMSS 2011 cognitive practices were adopted to establish a hypothesized model representing these relationships. We employed the generalized DINA (deterministic inputs, noisy “and” gate), confirmatory factor analysis (CFA), and structural equation modeling (SEM) to 2287 fourth-graders’ responses to standardized mathematics and science assessments. The findings show positive relationships among science reasoning, mathematics reasoning, and mathematics applying. However, we also found a significant indirect effect from science reasoning to mathematics reasoning through mathematics applying. This result calls for a need to shift the focus of interdisciplinary efforts to emphasize cognitive practices that students use in learning mathematics and science as suggested in the Next Generation Science Standards and the Common Core State Standards for Mathematics.

This research aims to scrutinize the moderating effect of teacher interaction on the relationships between students’ self-efficacy and achievement in mathematics in three countries, Korea, Singapore, and the USA. We analyzed the Trends in International Mathematics and Science Study (TIMSS) 2015 data with hierarchical linear modeling. The findings show that in each country, different types of teacher interaction moderate the relationships between students’ self-efficacy and achievement in mathematics. Also, when moderated relationships are found, Korean students with lower self-efficacy are likely to have higher achievement when teachers interact with each other very often. Singaporean students across all self-efficacy levels are expected to have advantages of high achievement from teachers interacting with other teachers. However, US students have similar achievement although teachers have frequent interaction with other teachers. We suggest several implications: To improve educational systems, it is necessary to consider which type of teacher interaction is common in that specific context as well as to examine how teacher interaction moderates the relationships between students’ self-efficacy and achievement in mathematics.

For a positive integer k, let $$ F (q)^{k}:= \prod_{n \geq 1} \frac{(1-q^{n})^{4k}}{(1+q^{2n})^{2k}} = \sum_{n\geq 0} \frak{a}_{k} (n)q^{n} $$F(q)k:=∏n≥1(1−qn)4k(1+q2n)2k=∑n≥0ak(n)qn be the eta quotients. The coefficients $\frak{a}_{1} (n)$a1(n) can be interpreted as a certain kind of restricted divisor sums. In this paper, we give the signs and modulo values for $\frak{a}_{1} (n)$a1(n) and $\frak{a}_{2} (m)$a2(m) and calculate several convolution sums involving $\frak{a}_{k} (n)$ak(n).

Many efforts have been made to reach educational equity, especially to reduce mathematics and science achievement gaps by students’ socioeconomic status. Across countries, educators strive to reform traditional teacher-centered instructional approaches to more student-centered/inquiry-based instruction to improve equity in education. In this context, this study examines whether relationships between socioeconomic status and scientific or mathematical literacy are moderated by student-centered instruction. Ten countries covering a wide range of achievement levels as well as equity in education are selected for an international comparison. A linear regression analysis is applied to student achievement, equity, and frequency of student-centered instruction data from the PISA 2012 and PISA 2015. We find mixed results: As student-centered instruction is offered more frequently, the gap in mathematical and scientific literacy between low and high socioeconomic status is generally narrowed or maintained. In most countries, students’ mathematical and scientific literacy scores are expected to decrease across all socioeconomic status as student-centered instruction is given more frequently. The findings necessitate further scrutiny of how teachers implement student-centered instruction in various educational systems. This further research need to consider the complexity of implementation related to sociological and pedagogical aspects.

This study compared area lessons from Korean textbooks and US standard-based textbooks to understand differences and similarities among these textbooks, as well as how these textbooks address known learning challenges in area measurement. Several well-known challenges have been identified in previous studies, such as covering, array structure, and linking array structure to area formula. We were interested in knowing if textbooks addressed these issues in their treatments of area measurement and, in doing so, provided students with opportunities to overcome or become familiar with known challenges. The results show that both countries’ textbooks demonstrated similar limitations; only few area and area-related lessons are covered and three important learning challenges in area measurement are not covered well, which need to be informed to practicing teachers.

Compact and dwarfing vining habits in melon (Cucumis melo L.; 2n = 2x = 24) may have commercial importance since they can contribute to the promotion of concentrated fruit set and can be planted in higher plant densities than standard vining types. A study was designed to determine the genetics of dwarfism associated with a diminutive (short internodes) melon mutant line PNU-D1 (C. melo ssp. cantalupensis). PNU-D1 was crossed with inbred wild-type melon line PNU-WT1 (C. melo ssp. agrestis), and resultant F1 progeny were then self-pollinated to produce an F2 population that segregated as dwarf and vining plant types. Primary stem length of F2 progeny assessed under greenhouse conditions indicated that a single recessive gene, designated mdw1, controlled dwarfism in this population. To identify the chromosomal location associated with mdw1, an simple sequence repeat (SSR)-based genetic linkage map was constructed using 94 F2 progeny. Using 76 SSR markers positioned on 15 linkage groups spanning 462.84 cM, the location of mdw1 was localized to Chromosome 7. Using the putative dwarfing-associated genes, fine genetic mapping of the mdw1 genomic region was facilitated with 1,194 F2 progeny that defined the genetic distance between mdw1 and cytokinin oxidase gene, a candidate gene for compact growth habit (cp) in cucumber, to be 1.7 cM. The candidate gene ERECTA (serin/threonine kinase) and UBI (ubiquitin) were also mapped to genomic regions flanking mdw1 at distances of 0.6 and 1.2 cM, respectively.