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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.

In this study, the authors assessed the contribution of engagement (on-task behavior) to the mathematics problem-solving performance of seventh-grade students after accounting for prior mathematics achievement. A subsample of seventh-grade students in four mathematics classrooms (one high-, two average-, and one low-achieving) from a larger intervention study assessing improvement in middle school students' proportional reasoning was assessed on initial mathematics achievement, on-task behavior, and mathematics problem-solving performance. Results suggested that engagement uniquely predicted mathematics problem- solving performance after controlling for prior mathematics achievement. Furthermore, the authors found differential rates of engagement for the three achievement groups. Based on an analysis of engagement by instructional lesson, the authors offer suggestions for addressing engagement when designing instruction. [This article was published in "Preventing School Failure" (EJ1090266).]

This study compares undergraduate student exam performance of classroom and online course sections that have nearly identical instructional designs. The sections differed only in lecturing and peer discussion activities that are typical differences of classroom and online instruction. Classroom discussion activities were synchronous speech and online discussion were asynchronous text. Composite mean exam scores show a large effect size difference that is statistically significant. Results suggest that asynchronous peer-to-peer discussion is more effective than traditional classroom lecture-discussion for undergraduate students.

When classifying the evidence base of practices, special education scholars typically appraise study quality to identify and exclude from consideration in their reviews unacceptable-quality studies that are likely biased and might bias review findings if included. However, study quality appraisals used in the process of identifying evidence-based practices for students with learning and other disabilities have not been empirically validated (e.g., studies classified as unacceptable quality shown to have different, and presumably more biased, effects than high-quality studies). Using Gersten et al.'s (2005) approach for appraising the quality of group experimental studies in special education, we examined whether (a) studies classified as unacceptable quality and high quality had meaningfully different effects and (b) unacceptable-quality studies were more likely to have outlying effects than high-quality studies among 36 group experimental studies that investigated the effectiveness of instructional practices for students with learning disabilities. Our preliminary analyses found that the effects of unacceptable-quality studies were not meaningfully different from the effects of high-quality studies. We discuss implications of these findings and call for more research to be conducted in this area.

In this study, the authors assessed the contribution of engagement (on-task behavior) to the mathematics problem-solving performance of seventh-grade students after accounting for prior mathematics achievement. A subsample of seventh-grade students in four mathematics classrooms (one high-, two average-, and one low-achieving) from a larger intervention study assessing improvement in middle school students' proportional reasoning was assessed on initial mathematics achievement, on-task behavior, and mathematics problem-solving performance. Results suggested that engagement uniquely predicted mathematics problem-solving performance after controlling for prior mathematics achievement. Furthermore, the authors found differential rates of engagement for the three achievement groups. Based on an analysis of engagement by instructional lesson, the authors offer suggestions for addressing engagement when designing instruction.

This study examined the effect of schema-based instruction (SBI) on the proportional problem-solving performance of students with mathematics difficulties only (MD) and students with mathematics and reading difficulties (MDRD). Specifically, we examined the responsiveness of 260 seventh grade students identified as MD or MDRD to a 6-week treatment (SBI) on measures of proportional problem solving. Results indicated that students in the SBI condition significantly outperformed students in the control condition on a measure of proportional problem solving administered at posttest (g = 0.40) and again 6 weeks later (g = 0.42). The interaction between treatment group and students' difficulty status was not significant, which indicates that SBI was equally effective for both students with MD and those with MDRD. Further analyses revealed that SBI was particularly effective at improving students' performance on items related to percents. Finally, students with MD significantly outperformed students with MDRD on all measures of proportional problem solving. These findings suggest that interventions designed to include effective instructional features (e.g., SBI) promote student understanding of mathematical ideas.

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 7th-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 purpose of this study was to examine the reliability and validity of a curriculum-based measure of word problem solving (CBM-WPS) as an indicator of performance and progress in a sample of 136 third-grade students at risk for mathematics difficulties (MDs) instructed in a standards-based mathematics curriculum. Students completed the CBM-WPS measure every 2 weeks across 12 school weeks. Results indicated that the CBM-WPS measure was reliable and significantly correlated with measures of arithmetic WPS, number combinations fluency, and a standardized test of mathematics achievement. Results of growth modeling indicated that students showed significant growth on the CBM-WPS measure, with an average increase of 0.33 problems correct per week. Additional analyses revealed that students identified as high at-risk demonstrated similar growth as students identified as low at-risk. Furthermore, the CBM-WPS growth slopes were a significant predictor of students' spring performance on a standardized test of mathematics achievement, demonstrating their predictive validity. Implications for practice and future research for assessing mathematics skill development are discussed.

This study compared the effects of delivering a supplemental, small-group tutoring intervention on the mathematics outcomes of third-grade students at risk for mathematics difficulties (MD) who were randomly assigned to either a schema-based instruction (SBI) or control group. SBI emphasized the underlying mathematical structure of additive problems. All students at risk for MD identified through screening received a mathematics intervention in groups of 2-4 for 12 weeks across the school year. Results revealed that students in the SBI group outperformed students in the control group on a word problem solving (WPS) posttest ("g" = 0.46). The effect of SBI proved to be equivalent for students in both high and low at-risk subgroups. On a district-administered mathematics achievement test, SBI students scored significantly higher than control students (g = 0.34); however, there were no significant effects on the WPS retention test (8 weeks later). (Contains 3 tables and 1 figure.)

This study examined the relationship between high school mathematics curricula and student achievement and course-taking patterns over 4 years of college course taking for a sample of over 10,000 students from 32 postsecondary 4-year institutions. Three types of curricula were studied: National Science Foundation (NSF) funded curricula, the University of Chicago School Mathematics Project curriculum, and commercially developed curricula. The major result was that high school mathematics curricula were unrelated to college mathematics achievement or students' course-taking patterns for students who began college with precalculus (college algebra) or a more difficult course. However, students of the NSF-funded curricula were statistically more likely to begin their college mathematics at the developmental level. Implications of these results for research and practice are discussed.

The purposes of this study were (a) to evaluate differences in arithmetic word problem solving between high and low at-risk students for mathematics difficulties (MD) and (b) to assess the influence of attention, behavior, reading, and socio-economic status (SES) in predicting the word problem solving performance of third-grade students with MD. Participants ("n" = 127) were assessed on arithmetic word problem solving, as well as on reading. In addition, we collected teacher ratings of attention and behavioral strengths. One-way analysis of variance indicated significant differences between high at-risk and low at-risk students on word problem solving skill. The unique predictors of word problem solving skill were attention, reading, and SES; behavior was not a significant predictor. (Contains 2 tables.)

This study explored the extent to which domain-specific knowledge predicted proportional word problem-solving performance. We tested 411 seventh-grade students on conceptual and procedural fraction knowledge, conceptual and procedural proportion knowledge, and proportional word problem solving. Multiple regression analyses indicated that all four domain-specific knowledge variables (i.e., conceptual and procedural fraction knowledge, conceptual and procedural proportion knowledge) significantly predicted proportional word problem-solving performance. Conceptual fraction and procedural proportion knowledge contributed the most unique variance (10.0 and 6.7%, respectively, of the total variance) to proportional word problem solving. Procedural fraction and conceptual proportion knowledge each also contributed significant unique variance to proportional word problem solving explaining 5.6 and 2.8%, respectively. The results support the notion that both conceptual fraction and proportion knowledge and procedural fraction and proportion knowledge play a major role in understanding individual differences in proportional word problem-solving performance to inform interventions.

This study examined the effect of schema-based instruction (SBI) on 7th-grade students' mathematical problem-solving performance. SBI is an instructional intervention that emphasizes the role of mathematical structure in word problems and also provides students with a heuristic to self-monitor and aid problem solving. Using a pretest-intervention-posttest-retention test design, the study compared the learning outcomes for 1,163 students in 42 classrooms who were randomly assigned to treatment (SBI) or control condition. After 6 weeks of instruction, results of multilevel modeling indicated significant differences favoring the SBI condition in proportion problem solving involving ratios/rates and percents on an immediate posttest (g = 1.24) and on a 6-week retention test (g = 1.27). No significant difference between conditions was found for a test of transfer. These results demonstrate that SBI was more effective than students' regular mathematics instruction. (Contains 7 tables.)

In this study we examined the effects of prior mathematics achievement and completion of a commercially developed, National Science Foundation-funded, or University of Chicago School Mathematics Project high school mathematics curriculum on achievement in students' first college statistics course. Specifically, we examined the relationship between students' high school mathematics achievement and high school mathematics curriculum on the difficulty level of students' first college statistics course, and on the grade earned in that course. In general, students with greater prior mathematics achievement took more difficult statistics courses and earned higher grades in those courses. The high school mathematics curriculum a student completed was unrelated to statistics grades and course-taking. (Contains 5 tables.)

The first college mathematics course a student enrolls in is often affected by performance on a college mathematics placement test. Yet validity evidence of mathematics placement tests remains limited, even for nationally standardized placement tests, and when it is available usually consists of examining a student's subsequent performance in mathematics courses. This study expands on existing literature by considering whether a nationally standardized college mathematics placement test (ACCUPLACER) contributes to the prediction of enrollment and success in developmental and nondevelopmental mathematics courses above and beyond prediction associated with the ACT mathematics test. Results for a sample of more than 1,300 students from 20 postsecondary institutions suggest that ACCUPLACER does not contribute to either the prediction of enrollment or subsequent success in such courses, and that comparable information is provided by using the ACT mathematics score alone. Implications of these findings are discussed. (Contains 4 tables and 3 figures.)

The purpose of this study was to examine the college mathematics achievement and course-taking of students at a large public research university who completed a commercially developed or standards-based (Core-Plus) high school mathematics curriculum, and who subsequently completed at least 2 college mathematics courses of difficulty level at or beyond precalculus mathematics. Mathematics course-taking and achievement data across 8 college semesters were analyzed for a sample of 1,588 students. Findings indicated that students (including science, technology, engineering, and mathematics majors) were equally prepared for intense college mathematics coursework regardless of which high school mathematics curriculum they completed. These findings inform high school mathematics curriculum adoption decisions for college-bound students, and college policies and practices for advising students enrolling in mathematics courses. (Contains 2 tables.)

Bistrategic resource control entails using both coercive and prosocial strategies in competition for resources. The present study sought to clarify whether bistrategic involves more than simply using both strategies some of the time. Examining 88 preschoolers' coercion and prosociality over an entire school year, results showed that coercive resource control was used most frequently at the start of the school year, presumably to access resources and establish social dominance. Rates of prosocial resource control increased over the school year, and socially dominant preschoolers showed higher rates compared with peers, presumably to maintain resource control while keeping peers as allies. Socially dominant preschoolers also used reconciliation more often than peers, resulting in higher rates of affiliation between former competitors and more positive peer regard from fall to spring. Findings are discussed in terms of resource control theory and the importance of situating social behaviors within the behavioral and relationship context in which they are embedded. (Contains 6 tables and 1 figure.)

This retrospective study examined the impact of prior mathematics achievement on the relationship between high school mathematics curricula and student postsecondary mathematics performance. The sample (N = 4,144 from 266 high schools) was partitioned into 3 strata by ACT mathematics scores. Students completing 3 or more years of a commercially developed curriculum, the University of Chicago School Mathematics Project curriculum, or National Science Foundation-funded curriculum comprised the sample. Of interest were comparisons of the difficulty level and grade in their initial and subsequent college mathematics courses, and the number of mathematics courses completed over 8 semesters of college work. In general, high school curriculum was not differentially related to the pattern of mathematics grades that students earned over time or to the difficulty levels of the students' mathematics course-taking patterns. There also was no relationship between high school curricula and the number of college mathematics courses completed. (Contains 9 tables and 1 footnote.)

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. [ABSTRACT FROM AUTHOR]

When classifying the evidence base of practices, special education scholars typically appraise study quality to identify and exclude from consideration in their reviews unacceptable-quality studies that are likely biased and might bias review findings if included. However, study quality appraisals used in the process of identifying evidence-based practices for students with learning and other disabilities have not been empirically validated (e.g., studies classified as unacceptable quality shown to have different, and presumably more biased, effects than high-quality studies). Using Gersten et al.’s (2005) approach for appraising the quality of group experimental studies in special education, we examined whether (a) studies classified as unacceptable quality and high quality had meaningfully different effects and (b) unacceptable-quality studies were more likely to have outlying effects than high-quality studies among 36 group experimental studies that investigated the effectiveness of instructional practices for students with learning disabilities. Our preliminary analyses found that the effects of unacceptable-quality studies were not meaningfully different from the effects of high-quality studies. We discuss implications of these findings and call for more research to be conducted in this area. [ABSTRACT FROM AUTHOR]

This study examined the effect of schema-based instruction (SBI) on the proportional problem-solving performance of students with mathematics difficulties only (MD) and students with mathematics and reading difficulties (MDRD). Specifically, we examined the responsiveness of 260 seventh grade students identified as MD or MDRD to a 6-week treatment (SBI) on measures of proportional problem solving. Results indicated that students in the SBI condition significantly outperformed students in the control condition on a measure of proportional problem solving administered at posttest (g = 0.40) and again 6 weeks later (g = 0.42). The interaction between treatment group and students’ difficulty status was not significant, which indicates that SBI was equally effective for both students with MD and those with MDRD. Further analyses revealed that SBI was particularly effective at improving students’ performance on items related to percents. Finally, students with MD significantly outperformed students with MDRD on all measures of proportional problem solving. These findings suggest that interventions designed to include effective instructional features (e.g., SBI) promote student understanding of mathematical ideas. [ABSTRACT FROM AUTHOR]

In this study, the authors assessed the contribution of engagement (on-task behavior) to the mathematics problem-solving performance of seventh-grade students after accounting for prior mathematics achievement. A subsample of seventh-grade students in four mathematics classrooms (one high-, two average-, and one low-achieving) from a larger intervention study assessing improvement in middle school students’ proportional reasoning was assessed on initial mathematics achievement, on-task behavior, and mathematics problem-solving performance. Results suggested that engagement uniquely predicted mathematics problem-solving performance after controlling for prior mathematics achievement. Furthermore, the authors found differential rates of engagement for the three achievement groups. Based on an analysis of engagement by instructional lesson, the authors offer suggestions for addressing engagement when designing instruction. [ABSTRACT FROM PUBLISHER]