Journal of Learning Disabilities, Ahead of Print.
This study investigated the extent to which domain-general and domain-specific antecedents contributed to pre-algebra’s initial level and growth rate among students who experience word-problem difficulty (WPD). We examined if such a profile differs for English-language learners (ELLs; n = 75) and non-ELLs (n = 55) with WPD. We assessed 130 students at the beginning of Grade 3, end of Grade 3, and middle of Grade 4. The latent growth curve analyses revealed only word-problem solving emerged as a predictor of pre-algebraic growth across ELLs and non-ELLs. English-language learners’ stronger computational skills, along with their cognitive flexibility, potentially enabled them to effectively leverage working memory and nonverbal reasoning in acquiring pre-algebraic knowledge.

Journal of Learning Disabilities, Ahead of Print.
Both vocabulary skill and morphological complexity, or whether words can be broken down into root words and affixes, have a significant impact on word processing for adults with low literacy. We investigated the influence of word-level variables of morphological complexity and root word frequency, and the sentence-level variable of context strength on word processing in adults with low literacy, who differed on levels of vocabulary depth skills, which was a participant-level variable. Our findings demonstrate that morphological complexity, root word frequency, and context strength are all related to how adult learners process words while reading, but their effects are dependent on participants’ vocabulary depth. Participants with higher levels of vocabulary depth were able to more quickly process morphologically complex words and make better use of supportive sentence context as compared to individuals with lower levels of vocabulary depth. These findings suggest that both morphological complexity and vocabulary depth are important for word processing and reading comprehension in adults with low literacy.

Journal of Learning Disabilities, Ahead of Print.
For decades, there have been competing visions of how and where to educate students with disabilities (SWDs) in America’s K-12 schools. One conception is that general classrooms can accommodate the learning needs of virtually all children. A second approach calls for multiple placement options. Over the years, the context in which this disagreement has played out has changed as educators have shifted from a reliance on special classes to trust in general classes to enthusiasm for intensive instruction beyond the general class. Such variation in practice has influenced how researchers have explored relations between SWDs’ placement and their academic performance. Some of this research has been weak, producing unreliable findings. Some has generated more trustworthy results. All stakeholders would benefit from distinguishing the weaker studies from the stronger ones. Yet, to date, there has been an absence of such effort. In this paper, we provide a concise history of placement-achievement research and then review evidence spanning 50 years, bearing on how and where to educate SWDs. We conclude that the research on where to teach has generally been weak and inconclusive; the research on how to teach, stronger and more certain. Implications for educating SWDs are discussed.

Journal of Learning Disabilities, Ahead of Print.
Learning disabilities are challenging to characterize because they evolve throughout development, frequently co-occur, and have varying domain specificity. Addressing these challenges, we analyzed longitudinal patterns of growth, co-occurrence, and specificity manifesting in the math and reading skills of children with and without learning disabilities. With a sample of 498 Grade 1 children followed for 5 years, we used linear mixed-effects models to explore group-level differences among children with math disability (MD), reading disability (RD), co-occurring disability, and no disability. Findings revealed: Math and reading trajectories of children with learning disabilities parallel those of children without disabilities. Skill growth slows over time, regardless of skill level, suggesting disability-related impairments will not resolve without intervention. Impairment levels and growth trajectories of children with co-occurring disabilities match the within-domain patterns of children with isolated disabilities, supporting a longitudinally maintained additive model of co-occurrence. MD and RD show varying specificity. MD impairments are domain-specific and become more pronounced over time. RD impairments impact both domains early, become more domain-specific over time, but maintain curriculum-contingent math deficits. Findings suggest early math intervention should balance linguistic and conceptual support, as the source of a child’s math difficulties may not be clear until well into elementary school.

Journal of Learning Disabilities, Ahead of Print.
Evidenced-based mathematics interventions are critical for supporting students with mathematics difficulties. In research and practice, collecting implementation fidelity is important for ensuring that all the core components of the intervention are implemented as designed. Historically, implementation fidelity has been defined as multifaceted, including examinations of adherence, instructional quality, and student engagement, though mathematics intervention studies rarely report on fidelity components outside of adherence. The current study examined the relationships between these different components of fidelity and whether they are associated with student mathematics outcomes and intervention group size within the context of a first-grade mathematics intervention. Findings revealed relationships between components of fidelity with student’s initial mathematics skill; however, no relationship was observed between fidelity components and student mathematics growth. Findings for group size were mixed. Limitations, implications for research and practice, and future directions are discussed.

Journal of Learning Disabilities, Ahead of Print.
Graduates of special education teacher education programs can teach in a range of special education settings, raising the potential that their training can occur in very different settings than where they find their first jobs. We follow 263 completers of Moderate Disabilities programs in Massachusetts from their field placements to their early-career teaching positions and study the characteristics of their field placements and the degree to which these are aligned with their early-career teaching positions. We also assess the degree to which alignment is associated with early-career teacher turnover. We found that many of these teachers student taught in an inclusive setting but were hired into a self-contained special education setting and vice versa, and teachers who experienced this misalignment were more likely to leave the workforce early in their careers. Teachers who student taught with a supervising practitioner without a special education license were also more likely to leave early. Findings suggest that teachers training to educate students with learning disabilities should student teach in a setting that is aligned with where they are likely to be hired and with a supervising practitioner who is trained in special education.

Journal of Learning Disabilities, Ahead of Print.
We examined how generalized and mathematics-specific language skills predicted the word-problem performance of students with mathematics difficulty. Participants included 325 third-grade students in the southwestern United States who performed at or below the 25th percentile on a word-problem measure. We assessed generalized language skills in word reading, passage comprehension, and vocabulary knowledge. In addition, we measured mathematics-specific vocabulary knowledge. To explore variation within the mathematics-difficulty population, we utilized unconditional quantile regression to determine how each of these skill sets predicted word-problem performance when controlling for computation and emergent bilingual status. Results revealed that mathematics-vocabulary knowledge significantly predicted word-problem performance at all but two quantiles (p < .001), with strongest predictive relations at the highest quantiles. Passage comprehension had an overall significant relation to word-problem performance (p < .05) that was also reflected in multiple quantiles. Neither word-reading accuracy nor generalized-vocabulary knowledge demonstrated a significant predictive relation to word-problem performance. Given the consistent relation between mathematics-vocabulary knowledge and word-problem performance across quantiles, researchers and practitioners should prioritize evidence-based mathematics-vocabulary instruction to support students’ word-problem-solving skills.

Journal of Learning Disabilities, Ahead of Print.
Youth with attention-deficit/hyperactivity disorder (ADHD) often exhibit impairments in mathematics, but long-term math development into adulthood, particularly in females, is underexplored. We characterized trajectories of math achievement in girls with ADHD and an age- and ethnicity-matched comparison sample from childhood through early adulthood across four waves and examined childhood cognitive predictors (global executive functioning, working memory, processing speed) of trajectories. The ethnically and socioeconomically diverse sample comprised 140 girls with carefully diagnosed ADHD and 88 neurotypicals, ages 6 to 12 years at baseline. Using latent growth curve models, we examined predictors of 16-year math achievement trajectories. In both the ADHD and neurotypical groups, scores declined over time; rates of change did not differ significantly. Yet in the ADHD sample, math difficulties (defined as scores at least 1 SD below the national average) increased notably over time, with many such difficulties emerging after childhood. By adulthood, nearly half of women with ADHD exhibited clear math difficulties. Worse baseline global executive functioning predicted slower math growth over time. Girls with ADHD may benefit from math supports before concerns emerge or worsen after childhood. Additional research on preventive interventions for math difficulties, including investigation of executive functioning, is warranted.