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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 that 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. [This paper was published in "Exceptional Children" v85 n1 p46-65 2018 (EJ1192718).]

Ratio and proportional relationships, along with the interrelated topics of fractions,decimals, and percent, provide a critical foundation for algebra (National Mathematics Advisory Panel, 2008). Proportional reasoning, which not only requires understanding the concept of ratios and that two or more ratios are equal, also requires the ability to extract relevant information to develop a representation of the problem situation and is challenging for many children and adolescents, especially students with mathematics difficulties (Özgün-Koca & Altay, 2009).The intervention investigated in this study represents an approach to proportional problem solving via schema-based instruction (SBI). Jitendra, Harwell, Dupuis, and Karl (2017a)examined the effectiveness of SBI for a subsample of students with mathematics difficulties (MD) selected from a randomized cluster study (Jitendra et al., 2015). The findings raise an important question: What is the range of proportional reasoning skills and general mathematical proficiencies for which SBI enhances student performance? The present study uses a regression discontinuity approach to identify the boundaries of the effectiveness of SBI for students with and without MD. Using a regression discontinuity approach provides evidence SBI is effective for a wide range of proportional reasoning skills and general mathematical proficiencies and thus broadens the population of students SBI can be used effectively with. Standardized slopes for the treatment effect also provide evidence the magnitude of the SBI effect is non-negligible. [SREE documents are structured abstracts of SREE conference symposium, panel, and paper or poster submissions.]

Ratio and proportional relationships, along with the interrelated topics of fractions, decimals, and percent provide a critical foundation for algebra (National Mathematics Advisory Panel, 2008). Solving even simple proportion problems is challenging for many children and adolescents. A small number of studies have examined the efficacy of schema-based instruction (SBI), a multicomponent approach to teaching proportional problem solving. The studies of SBI, with roots in schema theory of cognitive psychology and cognitive models of mathematical problem solving, have provided evidence of its promise in improving student learning. However all of these studies relied on data from the Upper Midwest of the U.S, and what is needed is evidence that the efficacy of SBI generalizes to a range of students and teachers located throughout the country. In this study, the authors pooled data from the three SBI studies by Jitendra et al. (2015, 2017a, 2017b) and asked a single research question: Is SBI effective in improving students' proportional problem solving at posttest and nine to 11 weeks later at delayed posttest (PPS), and in improving general problem solving (GMADE posttest) and, if so, is it equally effective for classroom/teacher and student characteristics such as teacher gender, percentage of students receiving special education services in a classroom, years of teaching experience, and student race and gender across three U.S. states? 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, teachers with more experience tend to be associated with higher performing classrooms, and increasing concentrations of FRL and students receiving special education services are generally associated with weaker performances. These and other findings provide an empirical adjudication of results from individual studies and represent an opportunity to enhance generalizability of the effectiveness of SBI. [SREE documents are structured abstracts of SREE conference symposium, panel, and paper or poster submissions.]

This randomized controlled study investigated the efficacy of a Tier 1 intervention, schema-based instruction (SBI), designed to help students with and without mathematics difficulties (MD) develop proportional reasoning. Twenty seventh-grade teachers/classrooms were randomly assigned to a treatment (SBI) or control (business-as-usual) condition. Participants included 373 students of whom 253 demonstrated MD. A measure of proportional problem solving (PPS) was administered at pre- and post-testing, and at 11 weeks following treatment, along with a general mathematical problem solving measure at pre- and post-testing. 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. [This paper was published in "Exceptional Children" (EJ1151254) and "Journal of Learning Disabilities" v83 n4 p340-358 2017.]

The purpose of this study was to replicate and extend the study of the schema-based intervention (SBI) conducted by Jitendra et al. (2015) that demonstrated impact in proportional problem solving for a homogeneous sample of Upper Midwest students and teachers who were predominantly White and middle class. This study was replicated in two geographically diverse locations (Northern Rocky Mountains and Southeast U.S.). The following research question was explored: What are the effects of the SBI intervention compared to business-as-usual instruction on students' proportional problem solving at immediate posttest and after 11 weeks as well as on students' general mathematical problem solving? Students from 52 seventh-grade classrooms (N = 1,379) and their teachers (J = 52) from 30 middle schools in four school districts participated in the study. The study used a randomized cluster design with longitudinal data. Students' proportional problem solving (PPS) performance was tested on three occasions (pre, post, delayed posttest given 11 weeks after the intervention). Results indicated statistically significant differences between treatment and control groups on the total score for fidelity-of-implementation items, with treatment teachers implementing SBI elements with more fidelity than topics implemented by control teachers (t(50) = 7.98, p < 0.001, g = 2.21). [SREE documents are structured abstracts of SREE conference symposium, panel, and paper or poster submissions.]

This study examined the effects of a research-based intervention, schema-based instruction (SBI), implemented by experienced- (taught SBI in previous study; Jitendra et al., 2015) and novice-teacher implementers (taught SBI for the first time with professional development) on the mathematics outcomes of seventh-grade students. SBI is a multicomponent intervention that emphasizes the mathematical structure of problems through the use of schematic diagrams and incorporates problem solving and metacognitive strategy instruction. Results indicated that both experienced- and novice-teacher implementers delivered SBI with similar levels of fidelity; there was no SBI experience effect on the immediate and 10-week retention tests of proportional problem-solving, on a general measure of problem solving, or on the end of the year state mathematics achievement test. These results provide evidence that the effectiveness of SBI generalizes over time to different cohorts of teachers and that the impact of SBI on student mathematics outcomes is maintained over time without additional PD. [This article was published in "Learning and Instruction" v44 p53-64 Aug 2016.]

Ratio and proportional relationships are of primary importance during the upper elementary and middle school grades (Kilpatrick, Swafford, & Findell, 2001; National Council of Teachers of Mathematics, 1989, 2000; National Mathematics Advisory Panel [NMAP], 2008). These relationships, along with the interrelated topics of fractions, decimals, and percent provide a critical foundation for algebra (NMAP, 2008). Proportionality involves the concept of ratio and is central to topics in mathematics such as linear functions, scale drawings, similarity, trigonometry, and probability. Proportionality is also at the core of many important concepts in the physical and social sciences. Solving even simple proportion problems is challenging for many children and adolescents when they lack understanding of the problem situation and whether a solution strategy is applicable (Adjiage & Pluvinage, 2007; Fujimura, 2001; Lamon, 2007; Lobato et al., 2010; Miyakawa & Winslow, 2009; NMAP, 2008; Tourniaire & Pulos, 1985; Weinberg, 2002). Although students require instruction that supports the development of underlying concepts and flexible procedures to solve proportion problems (NMAP, 2008; Tourniaire & Pulos, 1985), few intervention studies have been conducted to improve students' learning of ratios and proportions. The purpose of this study was to replicate and extend the study of the schema based instruction (SBI) intervention conducted by Jitendra et al. (in press) that demonstrated impact in proportional problem solving for a homogeneous sample. The following research questions were examined: (1) What are the effects of the SBI intervention on seventh-grade students' proportional problem solving immediately following the intervention and eight weeks following treatment; (2) What are the effects of the SBI intervention on problem solving immediately following the intervention and eight weeks following treatment for students receiving special education services; (3) What are the effects of the SBI intervention on seventh-grade students' general mathematical problem solving; (4) What are the effects of the SBI intervention on general mathematical problem solving for students receiving special education services; and (5) Does the treatment moderate students' learning trajectory over time? The consistent effects in previous randomized studies suggest confidence in the positive effects of SBI in enhancing proportional problem solving (PPS) for all students. This study replicated and extended earlier findings thus enhancing external validity. An SBI effect emerged for the immediate PPS test but unlike the original study (Jitendra et al., in press), participants did not maintain this learning over time for the PPS delayed posttest and the GMADE test. Future research, including a larger sample, is needed to confirm for whom and under what conditions the SBI intervention has positive effects. Tables are appended.

This experimental study evaluated the effectiveness of a research-based intervention, schema-based instruction (SBI), on students' proportional problem solving. SBI emphasizes the underlying mathematical structure of problems, uses schematic diagrams to represent information in the problem text, provides explicit problem solving and metacognitive strategy instruction, and focuses on the flexible use of multiple solution strategies. Eighty-two teachers/classrooms with a total of 1,999 seventh-grade students across 50 school districts were randomly assigned to a treatment (SBI) or control (business-as-usual) condition. An observational measure provided evidence that the SBI intervention was implemented with fidelity. Results of multilevel modeling indicated that the SBI group scored on average significantly higher than the control group on the posttest and retention test (9 weeks later) and also showed significantly more growth in proportional problem solving. There were no treatment effects on the Process and Applications subtest of the Group Mathematics Assessment and Diagnostic Evaluation. These results demonstrate that SBI can be more effective than the control approach in improving students' proportional problem solving. [This paper was published in the "Journal of Educational Psychology," (EJ1082754).]