Browsing by Author "Tolar, Tammy D."
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Item Predicting development of mathematical word problem solving across the intermediate grades(Journal of Educational Psychology, 2012-11) Tolar, Tammy D.; Fuchs, Lynn S.; Cirino, Paul T.; Fuchs, Douglas; Hamlett, Carol L.; Fletcher, Jack M.This study addressed predictors of the development of word problem solving (WPS) across the intermediate grades. At beginning of 3rd grade, 4 cohorts of students (N = 261) were measured on computation, language, nonverbal reasoning skills, and attentive behavior and were assessed 4 times from beginning of 3rd through end of 5th grade on 2 measures of WPS at low and high levels of complexity. Language skills were related to initial performance at both levels of complexity and did not predict growth at either level. Computational skills had an effect on initial performance in low- but not high-complexity problems and did not predict growth at either level of complexity. Attentive behavior did not predict initial performance but did predict growth in low-complexity, whereas it predicted initial performance but not growth for high-complexity problems. Nonverbal reasoning predicted initial performance and growth for low-complexity WPS, but only growth for high-complexity WPS. This evidence suggests that although mathematical structure is fixed, different cognitive resources may act as limiting factors in WPS development when the WPS context is varied.Item Reading skill components and impairments in middle school struggling readers(Reading and Writing, 2013-08) Cirino, Paul T.; Romain, Melissa A.; Barth, Amy E.; Tolar, Tammy D.; Fletcher, Jack M.; Vaughn, SharonThis study investigated how measures of decoding, fluency, and comprehension in middle school students overlap with one another, whether the pattern of overlap differs between struggling and typical readers, and the relative frequency of different types of reading difficulties. The 1,748 sixth, seventh, and eighth grade students were oversampled for struggling readers (n = 1,025) on the basis of the state reading comprehension proficiency measure. Multigroup confirmatory factor analyses showed partial invariance among struggling and typical readers (with differential loadings for fluency and for comprehension), and strict invariance for decoding and a combined fluency/comprehension factor. Among these struggling readers, most (85 %) also had weaknesses on nationally standardized measures, particularly in comprehension; however, most of these also had difficulties in decoding or fluency. These results show that the number of students with a specific comprehension problem is lower than recent consensus reports estimate and that the relation of different reading components varies according to struggling versus proficient readers.Item Teaching Efficacy and Knowledge of Algebra for Teaching Among Secondary Mathematics Teachers(2016-12) Warren, Ashley; Fan, Weihua; Tolar, Tammy D.; Copur-Gencturk, Yasemin; Benzon, MariaResearch has revealed the importance of identifying specialized content knowledge essential for teaching mathematics (Ball, Thames, & Phelps, 2008), the significance of assessing mathematics teacher’s teaching efficacy and outcome expectancy beliefs (Enochs, Smith, & Huinker, 2000) and the necessity for all students to have access to algebra within an elementary and secondary mathematics curriculum (National Council for Teaching Mathematics, 2014b). Previous literature, however, has failed to address the relation of teaching efficacy, outcome expectancy, and teacher’s algebra content knowledge. The primary aim of the present study is to determine if scores on a knowledge of algebra for teaching assessment can be predicted by teachers’ levels of mathematics teaching efficacy and outcome expectancy. The secondary aim of the study is to investigate the factors accounting for secondary mathematics teacher’s teaching efficacy, outcome expectancy, and knowledge of algebra for teaching. Data from an algebra content knowledge assessment, teaching efficacy and outcome expectancy beliefs survey, and demographic questionnaire were collected from a sample of 100 pre-service, in-service, and former secondary mathematics teachers. Quantitative data analysis methods including multiple regression, hierarchical regression, and mediation were employed to address the aims of the study. Additionally, principal components analysis was conducted to assess the psychometric properties of the mathematics teaching efficacy beliefs instrument (MTEBI) and knowledge of algebra for teaching (KAT) scales. The results indicated that each measure had satisfactory reliability. Multiple regression analyses were used to determine if individual teacher characteristics were related to KAT and MTEBI scores. Results indicated that individual teacher characteristics (having a math teaching certification, increased years of education, an older age, increased years of teaching experience, being a high school teacher, a public school teacher, and ethnicity) were significant in predicting KAT and MTEBI scores. Hierarchical multiple regression analyses revealed that individual teacher characteristics (having a math teaching certification, increased years of education, an older age, increased years of teaching experience, and being a public school teacher) improved prediction of teaching efficacy and outcome expectancy beliefs while controlling KAT. Additionally, the mediating effects of KAT on teaching efficacy, outcome expectancy, and individual teacher characteristics were addressed using Hayes (2013)’s macro known as PROCESS. Results showed that being a public school teacher, exerted an indirect effect, via knowledge of algebra for teaching on outcome expectancy.Item The Effect of Instructional Program and Phonological Awareness on Reading Outcomes Among Early Elementary Spanish-Speaking English Learners(2020-05) Hilliard, Karrie Aldrich; Gonzalez, Jorge E.; Keller-Margulis, Milena A.; Santi, Kristi L.; Tolar, Tammy D.Background: English Learners (ELs), the majority of whom are Spanish-speaking children, are at risk for academic underachievement in American public schools. Prior research on the effectiveness of instruction designed to support their learning, categorized as bilingual or immersion, is often confounded by selection bias and has not produced definitive conclusions. A recent study suggests that ELs with low English phonological awareness (PA) may benefit more from bilingual than immersion instruction in terms of reading achievement, but selection bias casts doubt on this relationship. Purpose: This study sought to examine if Spanish-speaking EL students with low English PA benefit more from bilingual than immersion instruction while controlling for selection bias using a matched-comparison group design. Preliminary analysis showed, however, that sample size-related challenges required inclusion of ELs of varying PA levels. It was hypothesized that PA would interact with instructional program, and that students with lower English PA would benefit more from bilingual than immersion. Method: From a sample of 689 Spanish-speaking ELs, matched-comparison groups (n = 45 per group) were formed using propensity score matching that improved balance between immersion and bilingual groups on beginning-of-first-grade English and Spanish reading, oral language, and PA. ANCOVA was used to evaluate if instructional program interacted with PA to influence end-of-second-grade reading achievement. Results: Interactions between instructional program and PA were not significant, nor were main effects, except for that of instructional program on Spanish reading, with bilingual students outperforming immersion students. A post-hoc power analysis indicated that the study was largely underpowered. Conclusion: Results suggest that bilingual education more effectively promotes Spanish reading than immersion. Detection of effects in English reading was limited due to power, highlighting the need to take a more methodologically rigorous approach to studying this population, balancing priorities of detecting treatment effects and minimizing selection bias.Item The role of cognitive processes, foundational math skill, and calculation accuracy and fluency in word-problem solving versus prealgebraic knowledge(Developmental Psychology, 2016-01) Fuchs, Lynn S.; Gilbert, Jennifer K.; Powell, Sarah R.; Cirino, Paul T.; Fuchs, Douglas; Hamlett, Carol L.; Seethaler, Pamela M.; Tolar, Tammy D.The purpose of this study was to examine child-level pathways in development of prealgebraic knowledge versus word-problem solving, while evaluating the contribution of calculation accuracy and fluency as mediators of foundational skills/processes. Children (n = 962; mean 7.60 years) were assessed on general cognitive processes and early calculation, word-problem, and number knowledge at start of Grade 2; calculation accuracy and calculation fluency at end of Grade 2; and prealgebraic knowledge and word-problem solving at end of Grade 4. Important similarities in pathways were identified, but path analysis also indicated that language comprehension is more critical for later word-problem solving than prealgebraic knowledge. We conclude that pathways in development of these forms of 4th-grade mathematics performance are more alike than different, but demonstrate the need to fine-tune instruction for strands of the mathematics curriculum in ways that address individual students' foundational mathematics skills or cognitive processes.