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Mastery measurement in mathematics and the goldilocks effect
Benjamin G Solomon1, Amanda M VanDerHeyden2, Emily C Solomon2
1Division of School Psychology.
School Psychology (Washington, D.C.)
|January 20, 2022
Summary
This study confirms the reliability of math curriculum-based measurement (CBM) mastery measures. Short assessments (1-4 minutes) provide dependable data for student screening and educational support.
Area of Science:
- Educational Measurement
- Psychometrics
- Mathematics Education
Background:
- Curriculum-based measurement (CBM) is vital for educational decision-making, yet its reliability in mathematics requires further investigation, especially using advanced methods like generalizability (G) theory.
- Existing research on math CBM reliability is limited, particularly concerning mastery measures and diverse student populations.
- This study addresses the need for rigorous reliability analysis of math CBM, focusing on mastery measures across various grade levels.
Purpose of the Study:
- To investigate the generalizability and dependability of math mastery measure CBMs using rigorous methods.
- To extend prior research by including new grade levels, advanced math content, and novel methodological approaches.
- To evaluate the impact of different scoring methods and examine potential biases related to race and sex.
Main Methods:
- Conducted 17 concurrent generalizability (G) and dependability studies using a partially crossed design.
- Assessed 263 students in Grades K, 1, 3, 5, and 7, employing generated math measures.
- Analyzed score variance, probe form effects, replication across days, and reliability coefficients (G coefficients).
Main Results:
- Student-level variance was the primary contributor to overall score variance.
- Probe form effects explained less than 5% of the variance for most measures, with results showing consistency across days.
- Generalizability (G) coefficients surpassed .75 on the first trial for 14 out of 17 measures, indicating high reliability.
- Reliability thresholds were met with assessments as short as 1-4 minutes.
Conclusions:
- Math CBM mastery measures demonstrate strong reliability and dependability.
- The findings support the use of math CBM mastery measures as a precise tool for screening and multi-tiered systems of support.
- Short assessment durations are sufficient to achieve acceptable reliability levels for math CBM.
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