Proficiency with mathematics requires an understanding of mathematical language. Students are required to make sense of both spoken and written mathematical terms. An essential component of mathematical language involves the understanding of the vocabulary of mathematics in which students connect vocabulary terms to mathematical concepts or procedures. In this brief psychometric report, we developed and tested a measure of mathematics vocabulary for students in the late middle-school grades (i.e., Grades 7 and 8) to determine the reliability of such a measure and to learn how students answer questions about mathematics vocabulary terms. The vocabulary terms on the measure were those terms determined as essential by middle-school teachers for success with middle-school mathematical language. Analysis indicates the measure demonstrated high reliability and validity. Student scores were widely distributed and students, on average, only answered two-thirds of vocabulary terms correctly.
Assessment results are used to investigate relations between performance on a fraction number line estimation task and a circular area model estimation task for students with LD in Grades 6–8. Results indicate that students’ abilities to represent fractions on number lines and on circular area models are distinct skills. In addition, accurate fraction magnitude estimation using number lines was more strongly related to other fractions skills (e.g., fraction magnitude comparison) than accurate fraction magnitude estimation using circular area models. Our findings call for greater integration of the number line into early fractions instruction, and highlight the importance of explicitly teaching students to make connections between different visual representations of fractions. Implications for research and practice are presented.
Communicating with peers often poses challenges for individuals with autism spectrum disorder (ASD); these social interactions, however, can be especially difficult during the teenage years. For many adolescents with ASD, peer interaction is often limited or nonexistent, even for those taught in general education settings. The purpose of this meta-analysis was to investigate social interaction interventions for adolescents with ASD within public school settings, with a focus on studies that utilized single-case design. Studies were evaluated per the What Works Clearinghouse guidelines. This meta-analysis includes 24 studies with participants with ASD ranging in ages from 13 to 21 years. The effects of social skill interventions were evaluated using visual analysis, Tau- U, and a parametric effect size ( d-Hedges–Pustejovsky–Shadish [DHPS]). Combined effect sizes were calculated and compared. Results provide evidence that interventions can produce positive change in social behavior of adolescents with ASD. Effect sizes were generally large. Interpretations and implications are discussed.
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