Bayesian latent change score modeling (LCSM) was used to compare models of triannual (fall, winter, spring) change on elementary math computation and concepts/applications curriculum–based measures. Data were collected from elementary students in Grades 2–5, approximately 700 to 850 students in each grade (47%–54% female; 78%–79% White, 10%–11% Black, 2%–4% Hispanic/Latino, 2%–4% Asian, 2–4% Native American or Pacific Islander; 13%–14% English learner; 10%–14% had special education individualized education plans). Results converged with common nonlinear growth patterns from the assessment norms and prior independent findings. However, Bayesian LCSMs captured practically relevant sources of change not observed in prior studies. Practical and methodological implications for screening and data–based decision–making in multitiered systems of support, limitations, and future directions are discussed.
Get full access to this article
View all access options for this article.
References
1.
ChristT. J., SilberglittB., YeoS., & CormierD. (2010). Curriculum–based measurement of oral reading: An evaluation of growth rates and seasonal effects among students served in general and special education. School Psychology Review, 39(3), 447–462.
2.
CoddingR. S., MercerS., ConnellJ., FiorelloC., & KleinertW. (2016). Mapping the relationships among basic facts, concepts and application, and common core curriculum–based mathematics measures. School Psychology Review, 45(1), 19–38. https://doi.org/10.17105/SPR45–1.19–38
3.
DawidA. P. (1984). Present position and potential developments: Some personal views: Statistical theory: The prequential approach. Journal of the Royal Statistical Society Series A, 147(2), 278–292.
GartlandD., & StrosniderR. (2020). The use of response to intervention to inform special education eligibility decisions for students with specific learning disabilities. Learning Disability Quarterly, 43(4), 195–200. https://doi.org/10.1177/0731948720949964
6.
GelmanA., CarlinJ. B., SternH. S., DunsonD. B., VehtariA., & RubinD. B. (2014). Bayesian data analysis (3rd edn.). CRC Press.
7.
GloverT. A., & AlbersC. A. (2007). Considerations for evaluating universal screening assessments. Journal of School Psychology, 45, 117–135. https://doi.org/10.1016/j.jsp.2006.05.005
8.
GraneyS. B., MissallK. N., MartinezR. S., & BergstromM. (2009). A preliminary investigation of within–year growth patterns in reading and mathematics curriculum–based measures. Journal of School Psychology, 47, 121–142.
9.
HendricksE. L., & FuchsD. (2020). Are individual differences in response to intervention influenced by the methods and measures used to define response? Implications for identifying children with learning disabilities. Journal of Learning Disabilities, 53(6), 428–443. https://doi.org/10.1177/0022219420920379
10.
JitendraA., SczesniakE., & Deadtline–BuchmanA. (2005). An exploratory validation of curriculum–based mathematical word problem–solving tasks as indicators of mathematics proficiency for third graders. School Psychology Review, 34(3), 358–371.
11.
KaplanD. (2014). Bayesian statistics for the social sciences. Guilford.
12.
Keller–MargulisM. A., MercerS., & ShapiroE. S. (2014). Seasonal differences in growth on math curriculum–based measures using tri–annual benchmarks. Assessment for Effective Intervention, 39, 146–155. doi:10.1177/1534508412452750
13.
Keller–MargulisM. A., ShapiroE. S., & HintzeJ. M. (2008). Long–term diagnostic accuracy of curriculum–based measures in reading and mathematics. School Psychology Review, 37(3), 374–390. https://doi.org/10.1080/02796015.2008.12087884
14.
KettlerR. J., GloverT. A., AlbersC. A., & Feeney–KettlerK. A. (Eds.). (2014). Universal screening in educational settings: Evidence–based decision making for schools. American Psychological Association.
15.
KlingbeilD. A., Van NormanE. R., & NelsonP. M. (2021). Using interval likelihood ratios in gated screening: A direct replication study. Assessment for Effective Intervention, 47(1), 14–25.
O'HaganA., BuckC. E., DaneshkhahA., EiserJ. R., GarthwaiteP. H., JenkinsonD. J., OakleyJ. E., & RakowT. (2006). Uncertain judgements: Eliciting experts’ probabilities. Wiley.
23.
Pearson. (2012). AIMSweb technical manual.
24.
R Core Team. (2021). R: A language and environment for statistical computing. R Foundation for Statistical Computing.
25.
Rittle–JohnsonB., SchneiderM., & StarJ. R. (2015). Not a one–way street: Bidirectional relations between procedural and conceptual knowledge of mathematics. Educational Psychology Review, 27, 587–597. https://doi.org/10.1007/s10648–015–9302–x
26.
RubinD. B. (1987). Multiple imputation for nonresponse in surveys. Wiley.
27.
SieglerR. S., & BraithwaiteD. W. (2017). Numerical development. Annual Review of Psychology, 68, 187–213. doi:10.1146/annurev–psych–010416–044101
28.
ThurberR. S., ShinnM. R., & SmolkowskiK. (2002). What is measured in mathematics tests? Construct validity of curriculum–based mathematics measures. School Psychology Review, 31(4), 498–513.
29.
Van NormanE. R., & NelsonP. M. (2019). The influence of trend estimation method on forecasting curriculum–based measurement of reading performance. Journal of School Psychology, 74, 44–57. https://doi.org/10.1016/j.jsp.2019.04.001
30.
Van NormanE. R., & NelsonP. M. (2021). An evaluation of the use of seasonal goal lines to improve the accuracy of curriculum–based measurement of reading decision rule recommendations. Assessment for Effective Intervention, 46(3), 167–177. https://doi.org/10.1177/1534508419872249
31.
Van NormanE. R., & ParkerD. C. (2016). An evaluation of linearity of curriculum–based measurement of oral reading (CBM–R) progress monitoring data: Idiographic considerations. Learning Disabilities Research & Practice, 31(4), 199–207. https://doi.org/10.1111/ldrp.12108
32.
van BuurenS., & Groothuis–OudshoornK. (2011). Mice: Multivariate imputation by chained equations in R. Journal of Statistical Software, 45(3), 1–67.
33.
VehtariA., GelmanA., & GabryJ. (2017). Practical Bayesian model evaluation using leave–one–out cross–validation and WAIC. Statistics and Computing, 27(5), 1413–1432. https://doi.org/10.1007/s11222–016–9696–4
