Assessment for Effective Intervention

Incremental rehearsal (IR) has consistently led to effective retention of newly learned material, including math facts. The number of new items taught during one intervention session, called the intervention set, could be used to individualize the intervention. The appropriate amount of information that a student can rehearse and later recall during one intervention session is called the acquisition rate (AR). The current study taught single-digit multiplication facts with factors of 6, 7, and 8 to 55 third- and fourth-grade students. Each student was randomly assigned to be taught two multiplication math facts, eight multiplication math facts, or a set size determined by each student’s AR. The average AR was 4.05 (SD = 0.71). Set size led to a significant and large effect on retention, percentage of multiplication math facts retained, and efficiency as computed by math facts retained per minute of intervention time. IR appeared to be an effective intervention when AR data were used to determine the intervention set size, and it was more efficient to do so.

This article describes the development and initial validation of a measure of middle school students’ perspectives of culturally responsive teaching practices. The Student Measure of Culturally Responsive Teaching (SMCRT) was developed by modifying items on the Culturally Responsive Teaching Self-Efficacy (CRTSE), which measures teachers’ self-efficacy beliefs regarding their culturally responsive teaching practices. Data obtained from a sample of 748 seventh-grade students (63.9% Latino/as) were used to conduct exploratory and confirmatory factor analyses that yielded three factors: Diverse Teaching Practice, Cultural Engagement, and Diverse Language Affirmation. The three-factor model was compared with two competing models, yielding a second-order factor model as the final model. Initial validity of the SMCRT was demonstrated through tests of measurement invariance across subgroups of gender, immigrants, and Latino/as versus non-Latino/as and correlational analyses with SMCRT, teacher support, and school belonging. Internal consistency was also tested using Cronbach’s alpha. Results of the data analyses suggest that SMCRT is a psychometrically sound measure of seventh-grade students’ perceptions of their teachers’ culturally responsive teaching practices.

The present study examines an ecological model for intervention use to explain student vocabulary performance in a multi-tiered intervention setting. A teacher self-report measure composed of factors hypothesized to influence intervention use at multiple levels (i.e., individual, intervention, and system level) was administered to 54 teachers and 48 interventionists conducting vocabulary interventions with different levels of instructional intensity with 553 kindergarten students. The reliability and validity of the measure in the context of a specific multi-tiered intervention was explored. Of particular interest was the potential explanatory power of system-level factors, over and above intervention-specific measures of fidelity, to explain student performance in a multi-tiered context. Results indicate that the climate of the school system predicted student performance in the Tier 1 context, and intervention feasibility predicted student performance in Tier 2. However, the intervention-specific fidelity measure was not a significant predictor. This research provides supporting evidence for the use of ecological models of intervention implementation to capture factors that influence intervention use and performance in multi-tiered settings.

Receiver operating characteristic curve (ROC) analysis was used to investigate the ability of early numeracy curriculum-based measures (EN-CBM) administered in preschool to predict performance below the 25th and 40th percentiles on a quantity discrimination measure in kindergarten. Areas under the curve derived from a sample of 279 students ranged from .65 to .82. Optimal cut scores were associated with sensitivity ranging from .44 to .79, specificity ranging from .49 to .91, and classification accuracy ranging from .60 to .79. Among a validation sample of 140 students, sensitivity ranged from .36 to .83, specificity ranged from .46 to .89, and classification accuracy ranged from .57 to .79. Results indicate that EN-CBM administered in preschool predicts math performance in kindergarten and can be a valuable component of an evidence-based decision-making process.

The purpose of the current study was to evaluate the importance of growth in math fact skills within the context of overall math proficiency. Data for 1,493 elementary and middle school students were included for analysis. Regression models were fit to examine the relative value of math fact fluency growth, prior state test performance, and a fall administration of a computer adaptive test for predicting performance on a year-end state math test. Across all grades, the largest effect sizes were observed for student performance on the fall computer adaptive assessment (β = .43–.56). Fact fluency growth accounted for unique variance in each regression model, with the largest effect size observed for students in Grade 4 (β = .20) and the smallest effect sizes observed for students in Grades 7 and 8 (β = .11). Results provide insight into the potential role of math fact fluency across late elementary and middle school. In particular, the observed results indicate that math facts may retain predictive value for math proficiency despite their absence from the formal curriculum in later grades.