Precision of Single-Skill Math CBM Time-Series Data: The Effect of Probe Stratification and Set Size

Abstract

Comparatively little research exists on single-skill math (SSM) curriculum-based measurements (CBMs) for the purpose of monitoring growth, as may be done in practice or when monitoring intervention effectiveness within group or single-case research. Therefore, we examined a common variant of SSM-CBM: 1 digit × 1 digit multiplication. Reflecting how such measures are often used in contemporary research and practice, we examined the comparative reliability of three representative SSM-CBM set sizes of 8, 16, and 32 unique problems. In a separate study, we investigated the possible benefit of stratifying problems within operation and probe relative to random assignment. Findings suggest that SSM-CBM slope reliability benefits from explicit stratification and that set size is a relevant consideration. Implications for the selection and interpretation of SSM-CBMs when engaging in practice and research are discussed.

The impact of intervention modality on students' multiplication fact fluency

“…On the two CBM measures no groups reached a ROI of 12.96 DC2M or higher. Therefore, while the results of the present study resulted in higher ROIs than would be expected for students who are not receiving intervention, the ROIs were not as high as results found in Solomon et al (2020). The lower ROIs observed in the present study could be due to many factors relating to student characteristics or levels of initial fluency or the large set size used in the included interventions.…”

“…On the two CBM measures no groups reached a ROI of 12.96 DC2M or higher. Therefore, while the results of the present study resulted in higher ROIs than would be expected for students who are not receiving intervention, the ROIs were not as high as results found in Solomon et al (2020).…”

“…Additionally, the ROI on the measure for all groups surpassed the expected growth of 0.72 on the math computation measures with no intervention (Pearson, 2011). Solomon et al (2020) found higher average math fluency growth rates per session (1.62 digits correct per minute). In the present study, students received four sessions per week and the dependent variable was digits correct per 2 min (DC2M) which means that a rate of improvement of approximately 12.96 DC2M would be consistent with the results of other interventions targeting math fact fluency (Solomon et al, 2020).…”

“…Solomon et al (2020) found higher average math fluency growth rates per session (1.62 digits correct per minute). In the present study, students received four sessions per week and the dependent variable was digits correct per 2 min (DC2M) which means that a rate of improvement of approximately 12.96 DC2M would be consistent with the results of other interventions targeting math fact fluency (Solomon et al, 2020). On the two CBM measures no groups reached a ROI of 12.96 DC2M or higher.…”

Mastery measurement in mathematics and the goldilocks effect.

“…Emerging data suggest that mastery measures, which briefly sample (e.g., 2 min) computational fluency across generally equivalent problems umbrellaed under a narrowly conceptualized skill (e.g., 1 × 1 addition), can yield highly reliable scores (Hintze, Christ, et al, 2002; Solomon et al, 2020; VanDerHeyden & Broussard, 2020). As one example of this research, VanDerHeyden and Broussard (2020) investigated delayed alternate form reliability of scores on generated mastery measures in Grades K, 1, 3, 5, and 7 using fall and winter screening measures from the commercial tool sampled presently ( SpringMath ; Education Research & Consulting, Inc, 2013).…”