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This formative study of a multiplicative reasoning (MR) intervention explored the intervention's potential for improving the ability of third-grade struggling students' ability to reason with multiplicative concepts and procedures. The feasibility of the study was examined in a school setting before a randomized control trial was conducted. Students who scored between the 10th and 35th percentile on a district-administered math screening test received the MR intervention from their teachers. We developed intervention units to build a conceptual foundation in a student-centered approach to Tier 2 instruction that included opportunities for students to engage in critical thinking as they generalized big ideas, participated in classroom discourse, and modeled multiplicative relationships with multiple representations. Preliminary data demonstrate the potential of the intervention to promote students' MR skills. Instructional implications are discussed in terms of opportunities for these students to engage in grade-level mathematics content.

Data analysis is a significant methodological component when conducting quantitative education studies. Guidelines for conducting data analyses in quantitative education studies are common but often underemphasize four important methodological components impacting the validity of inferences: quality of constructed measures, proper handling of missing data, proper level of measurement of a dependent variable, and model checking. This paper highlights these components for novice researchers to help ensure statistical inferences are valid. We used empirical examples involving contingency tables, group comparisons, regression analysis, and multilevel modelling to illustrate these components using the Program for International Student Assessment (PISA) data. For every example, we stated a research question and provided evidence related to the quality of constructed measures since measures with weak reliability and validity evidence can bias estimates and distort inferences. The adequate strategies for handling missing data were also illustrated. The level of measurement for the dependent variable was assessed and the proper statistical technique was utilized accordingly. Model residuals were checked for normality and homogeneity of variance. Recommendations for obtaining stronger inferences and reporting related evidence were also illustrated. This work provides an important methodological resource for novice researchers conducting data analyses by promoting improved practice and stronger inferences.

Proportional reasoning is the cornerstone of many higher-level mathematics topics. We evaluated the sustainability effects of schema-based instruction (SBI) on proportional reasoning and the impact of professional development (PD) on the instructional practices of two cohorts of seventh-grade teachers (i.e., SBI-experienced-teacher implementers, who taught SBI in a previous study; SBI-novice-teacher implementers, who taught SBI for the first time with PD) and mathematics outcomes of students with mathematics learning difficulties. SBI was implemented for 6 weeks by 49 teachers in two distal states. Despite the cessation of PD provided to SBI experienced-teacher implementers, teachers in both cohorts demonstrated similar levels of fidelity. Results indicated no SBI experience effect on the immediate and 11-week retention tests of proportional problem solving, on a general measure of problem solving, and on an end-of-year mathematics achievement test, suggesting that the effectiveness of SBI generalizes over time to different cohorts of teachers and students.

The present study used a regression discontinuity approach to test whether schema-based instruction (SBI) was effective for students identified with varying levels of mathematics difficulties (MD) who received Tier-1 instruction. The performance of these students was compared to similar students who received business-as-usual Tier-1 instruction. Results indicated SBI on average raised scores regardless of whether a student was categorized as having MD on outcome measures of mathematics problem solving, suggesting that SBI is effective for a wide range of proportional reasoning skills and general mathematical proficiency, which broadens the population of students who could benefit from SBI. Standardized slopes for the treatment effect also provide evidence of the effectiveness of SBI. Implications for practice and research are discussed.

Variance heterogeneity is a common feature of educational data when treatment differences expressed through means are present, and often reflects a treatment by subject interaction with respect to an outcome variable. Identifying variables that account for this interaction can enhance understanding of whom a treatment does and does not benefit in ways that can inform and improve the treatment. Even in the absence of a treatment effect expressed through means studying variance heterogeneity offers insight into a treatment by identifying subject characteristics related to heterogeneity. This study illustrates four methods of modeling variance heterogeneity for data from a study of the impact of an engineering design-based STEM curriculum on student achievement with a focus on multilevel models.

This article reports results from a study investigating the efficacy of a proportional problem-solving intervention, schema-based instruction (SBI), in seventh grade. Participants included 806 students with mathematical difficulties in problem solving (MD-PS) from an initial pool of 1,999 seventh grade students in a larger study. Teachers and their students in the larger study were randomly assigned to an SBI or control condition and teachers in both conditions then provided instruction on the topics of ratio, proportion, and percent. We found that students with MD-PS in SBI classrooms scored on average higher than their counterparts in control classrooms on a posttest and delayed posttest administered 9 weeks later. Given students' difficulties with proportional problem-solving and the consequences of these difficulties, an important contribution of this research is the finding that when provided with appropriate instruction, students with MD-PS are capable of enhanced proportional problem-solving performance.

This study used integrative data analysis (Curran & Hussong, 2009), which allows combining data from different studies, to examine the generalizability of a research-based mathematics program, schema-based instruction (SBI), with a focus on proportional reasoning. Data were pooled from existing SBI studies spanning three U.S. states in which teachers and their classrooms were randomly assigned to either a SBI or control condition. Results of a series of multilevel (i.e., two-level, students within teachers) models indicated the effectiveness of SBI in improving students' mathematical problem-solving performance. The pooled data findings clarify that SBI improves students' mathematical problem solving more so for proximal than distal measures. These findings also show Black and Hispanic students continue to lag behind White students, that teachers with more experience tend to be associated with higher performing classrooms, and that increasing concentrations of students eligible for free or reduced price lunch and students receiving special education services are generally associated with weaker performances. Implications of these findings are discussed.

This meta-analysis synthesized the available empirical evidence on the impact of interventions on the development and enhancement of mathematical word problem solving skills for K-12 students with learning disabilities (LD) and those with mathematics difficulties (MD). A total of 33 studies met inclusion criteria for this meta-analysis. After removing 2 influential data points, 31 true-experimental or quasi-experimental studies (34 independent effect sizes) contributed effect sizes for this meta-analysis. Results of a random effects model showed that word problem solving interventions yielded a moderate positive mean effect size (g = 0.56, 95% confidence interval [0.40, 0.72]). The relation between word problem solving interventions and student learning was moderated by grade level, year of publication, type of measure, intervention model type, and implementer. On average, intervention effects were larger for (a) elementary grades than secondary grades, (b) studies published between 2000 and 2009, (c) researcher-developed than norm-referenced measures, (d) researcher implementers than teacher implementers. Results also showed intervention effects for schema-based transfer instruction were larger than those for schema-based instruction, strategy instruction, and other. These results support mathematics word problem solving interventions for students with LD and/or MD. We conclude by discussing directions for future research and implications for practice.

Accurate and consistent reviews of documents describing research studies are essential to valid and generalizable inferences in a meta-analysis. Traditionally a small number of reviewers screen studies using the title, abstract, and possibly the full text to determine a study's eligibility for a meta-analysis. This study explores whether reviewing loads and resources to support accurate and consistent reviewing have increased over time. A survey of N = 193 meta-analyses published between 1980-2019 showed that the average number of documents reviewed has increased, especially since 2010, but the typical number of reviewers has not changed over the past 40 years. The importance of meta-analysts providing information about reviewers and the review process to help readers evaluate the validity and generalizability of inferences is emphasized. This information would typically include the number of reviewers and their qualifications, number of titles, abstracts, and full-text documents reviewed, time spent reviewing documents, evidence of the accuracy and consistency of reviews, and the role of software in facilitating reviewing.

The purpose of this replication study was to provide replication evidence not currently available of the effects of a research-based mathematics program, schema-based instruction, on the mathematical problem-solving performance of 7th-grade students. The replication was implemented in 36 schools in 5 districts; 59 mathematics teachers and their students (N = 1,492) participated in the study. Multilevel hierarchical linear analyses revealed statistically significant differences between conditions on proximal and distal measures of mathematics problem solving, with effects sizes similar to those reported in Jitendra et al. (2015).

Commercial data analysis software has been a fixture of quantitative analyses in education for more than three decades. Despite its apparent widespread use there is no formal evidence cataloging what software is used in educational research and educational statistics classes, by whom and for what purpose, and whether some programs should be recommended over others. This paper argues that the rise of the R data analysis software has intensified the need for rigorous evaluations of these programs to identify their strengths and weaknesses in ways that provide educators with guidance in choosing programs. Examples of research activities to produce a literature to guide these choices are described.

The relationship between high school mathematics curricula and the likelihood of students who enroll in a developmental (non-credit bearing) course in college taking additional mathematics courses was studied. The results showed that high school mathematics curriculum, years of high school mathematics completed, and ACT mathematics scores were related to developmental mathematics course-taking, but curriculum was not related to the subsequent mathematics course-taking of students who began college with developmental mathematics. The results have important implications for educational researchers and policymakers at the college and high school levels.

The emphasis of reform-oriented science education today focuses on engineering integration in K-12 science classrooms. However, there is little research, particularly longitudinal research, on how different approaches to engineering integration influence student learning and interest. To address this gap in the literature, this study analyzed a middle school life science teacher's enactment of three design-focused life science units and student performances over a 3-year period. Findings indicate that the design and enactment of each unit reflects a unique engineering integration approach: add on, implicit, and explicit. Moreover, the ways the teacher talked about engineering varied among each curriculum unit. Through the analyses of 330 students' pre- and post-content tests and interest surveys as well as videotaped classroom instruction, we found that explicit engineering integration and engineering language use in classroom instruction resulted in higher student learning gains in science and engineering, but they did not have significant effects on students' interest in science and engineering. We explore the implications for curricular materials and discuss a need for long-term professional development and support for teachers.

Measures of socioeconomic status (SES) are widely used in educational research and policy applications in no small part because of a deeply rooted belief of the importance of SES. This paper argues that the usefulness of common SES measures can be undermined by (a) an atheoretical approach to conceptualizing SES and selecting measures, which creates uncertainty about what SES represents; (b) modest correlations between SES measures and outcome variables that limit the effectiveness of SES as a control variable in statistical analyses; and (c) the continued use of the profoundly flawed eligibility for a free/reduced-price lunch variable. These factors can produce biased inferences and speak to an important gap between the perceived impact of SES in educational settings and the usefulness of common SES measures and also can provide a prescription for change that promotes a deeper understanding and more effective use of SES in educational research and policy.

Meta-analytic methods were used to examine the moderating effect of institutional factors on the relationship between high school mathematics curricula and college mathematics course-taking and achievement from a sample of 32 colleges. The findings suggest that the impact of curriculum on college mathematics outcomes is not generally moderated by institutional characteristics such as selectivity and educational profile, providing evidence that the relationships between curriculum and college mathematics outcomes generalize to a range of colleges. The results inform college policies and practices for advising students on mathematics course-taking including enrollment in developmental courses, and high school mathematics curriculum selection. [Note: The title on the PDF is incorrect.]

A scale-up study in education typically expands the sample of students, schools, districts, and/or practices or materials used in smaller studies in ways that build in heterogeneity. Yet surprisingly little is known about the factors that promote successful scaling up efforts in education, in large part due to the absence of empirically supported theories of scaling up. A literature for scale-up studies in education is growing but is years away from providing research-supported practices in planning and conducting these studies. Following the suggestion of Schneider and McDonald (2006) to import relevant knowledge from other fields into the scale-up literature in education, this paper examines the multisite public health and nursing literature in search of a multidisciplinary knowledge base that can inform scaling up efforts in education. Five strategies and practices identified in these literatures as critical to scaling up success are described.

The importance of data analysis software in graduate programs in education and post-graduate educational research is self-evident. However the role of this software in facilitating supererogated statistical practice versus "cookbookery" is unclear. The need to rigorously document the role of data analysis software in students' graduate coursework and research, and in post-graduate educational research studies, is emphasized along with recommendations for obtaining this information.

This study investigated the sustainability effects of the schema-based instruction (SBI) program and corresponding PD on the instructional practices of two cohorts of teachers (i.e., SBI experienced-teacher implementers and SBI novice-teacher implementers) and on students' ability to reason with proportions and overall mathematics performance. SBI is a multicomponent program that focuses on recognizing the underlying mathematical problem structure (e.g., ratios, rates, percent) needed to reason with proportions. Results indicated that both experienced- and novice-teacher implementers delivered SBI with similar levels of fidelity; there was an SBI experience effect on the immediate test of proportional problem-solving (PPS), but not on a 11-week retention test of PPS, a general measure of problem solving, or the end-of-year state mathematics achievement tests. [ABSTRACT FROM AUTHOR]

This randomized controlled study investigated the efficacy of a Tier 1 intervention--schema-based instruction--designed to help students with and without mathematics difficulties (MD) develop proportional reasoning. Twenty seventh-grade teachers/classrooms were randomly assigned to a treatment condition (schema-based instruction) or control condition (business as usual). Participants included 373 students, of whom 253 demonstrated MD. A measure of proportional problem solving (PPS) was administered at pre- and posttesting and at 11 weeks following treatment, along with a general mathematical problem-solving measure at pre- and posttesting. For the full sample, posttest differences favoring the treatment group were statistically significant for all measures. For students with MD, posttest differences favored the treatment group for the PPS posttest and PPS delayed posttest but not for general problem-solving posttest.

The new science education reform documents call for integration of engineering into K-12 science classes. Engineering design and practices are new to most science teachers, meaning that implementing effective engineering instruction is likely to be challenging. This quasi-experimental study explored the influence of teacher-developed, engineering design-based science curriculum units on learning and achievement among grade 4-8 students of different races, gender, special education status, and limited English proficiency (LEP) status. Treatment and control students (n = 4450) completed pretest and posttest assessments in science, engineering, and mathematics as well as a state-mandated mathematics test. Single-level regression results for science outcomes favored the treatment for one science assessment (physical science, heat transfer), but multilevel analyses showed no significant treatment effect. We also found that engineering integration had different effects across race and gender and that teacher gender can reduce or exacerbate the gap in engineering achievement for student subgroups depending on the outcome. Other teacher factors such as the quality of engineering-focused science units and engineering instruction were predictive of student achievement in engineering. Implications for practice are discussed.

Measures of socioeconomic status (SES) are routinely used in analyses of achievement data to increase statistical power, statistically control for the effects of SES, and enhance causality arguments under the premise that the SES-achievement relationship is moderate to strong. Empirical evidence characterizing the strength of the SES-achievement relationship and its moderators suggests that this relationship is surprisingly modest, with an average SES-achievement correlation of 0.22, although it appears to have strengthened in the past 3 decades. The modest SES-achievement relationship has important implications for using SES measures in educational data analyses. We provide evidence of this relationship and of the need to use theoretical models to guide the construction and selection of SES measures in analyses of achievement data.

Hierarchical linear models have become a familiar method for accounting for a hierarchical data structure in studies of science and mathematics achievement. This paper illustrates the use of cross-classified random effects models (CCREMs), which are likely less familiar. The defining characteristic of CCREMs is a hierarchical data structure defined by multiple random factors at higher levels. We illustrate CCREMs using data for approximately 10,000 students from more than 250 high schools who attended one of 27 four-year postsecondary institutions. The appropriate use of CCREMs helps to ensure unbiased estimates of effects and credible inferences.

In many countries around the world, there has been an increasing emphasis on improving science education. Recent reform efforts in the USA call for teachers to integrate scientific and engineering practices into science teaching; for example, science teachers are asked to provide learning experiences for students that apply crosscutting concepts (e.g., patterns, scale) and increase understanding of disciplinary core ideas (e.g., physical science, earth science). Engineering practices and engineering design are essential elements of this new vision of science teaching and learning. This paper presents a research study that evaluates the effects of an engineering design-based science curriculum on student learning and attitudes. Three middle school life science teachers and 275 seventh grade students participated in the study. Content assessments and attitude surveys were administered before and after the implementation of the curriculum unit. Statewide mathematics test proficiency scores were included in the data analysis as well. Results provide evidence of the positive effects of implementing the engineering design-based science unit on student attitudes and learning.