Lina Shanley

Evaluating Longitudinal Mathematics Achievement Growth: Modeling and Measurement Considerations for Assessing Academic Progress

Accurately measuring and modeling academic achievement growth is critical to support educational policy and practice. Using a nationally representative longitudinal data set, this study compared various models of mathematics achievement growth on the basis of both practical utility and optimal statistical fit and explored relationships within and between early and later mathematics growth parameters. Common patterns included a summer lag in achievement between kindergarten and Grade 1 and an association between achievement at kindergarten entry and later achievement. Notably, there were no statistically significant relationships between early and later rates of growth, and there was minimal variability in achievement growth in the late elementary and middle school grades. Challenges related to assessing academic achievement in the middle grades and modeling academic skill development are discussed.

Investigating the Incremental Validity of Cognitive Variables in Early Mathematics Screening.

The purpose of this study was to investigate the incremental validity of a set of domain general cognitive measures added to a traditional screening battery of early numeracy measures. The sample consisted of 458 kindergarten students of whom 285 were designated as severely at-risk for mathematics difficulty. Hierarchical multiple regression results indicated that Wechsler Abbreviated Scales of Intelligence (WASI) Matrix Reasoning and Vocabulary subtests, and Digit Span Forward and Backward measures explained a small, but unique portion of the variance in kindergarten students’ mathematics performance on the Test of Early Mathematics Ability—Third Edition (TEMA-3) when controlling for Early Numeracy Curriculum Based Measurement (EN-CBM) screening measures (Rchange2 = .01). Furthermore, the incremental validity of the domain general cognitive measures was relatively stronger for the severely at-risk sample. We discuss results from the study in light of instructional decision-making and note the findings do not justify adding domain general cognitive assessments to mathematics screening batteries.

Validating a Model of Motivational Factors Influencing Involvement for Parents of Transition-Age Youth with Disabilities.

Parent involvement is a predictor of postsecondary education and employment outcomes, but rigorous measures of parent involvement for youth with disabilities are lacking. Hirano, Garbacz, Shanley, and Rowe adapted scales based on Hoover-Dempsey and Sandler model of parent involvement for use with parents of youth with disabilities aged 14 to 23. This study assessed the psychometric properties of the Motivators of Parent Involvement (MPI) scales. A confirmatory factor analysis tested an 11-factor model, three parent involvement factors, and eight motivators of involvement factors for parents of transition-age youth (ages 14–25) with disabilities. Using a sample of 288 parents and caregivers, the model was determined to have acceptable fit. The MPI can be used to assess motivators of parent involvement and guide interventions.

Measuring early mathematics knowledge via number skills and task types

ABSTRACT Early number skills are a critical aspect of early mathematics development. However, the constructs that comprise early number skills differ across assessments, and previous studies have proposed various models of early mathematics skills comprised of formal and informal tasks. This study explored the factor structure of a researcher-developed measure of mathematics administered to a large, geographically diverse sample of kindergarten students at risk for mathematics difficulty (n = 580) in a randomized control trial. Consistent with previous research, factors representing early number skills and task types emerged. Importantly though, the best fitting model was one in which both skill types (e.g., number identification, magnitude comparison) and task types (i.e., informal and formal) were modeled. The inclusion of task type as a factor in early mathematics assessment has many potentially important ramifications. Recommendations for attending to task types when assessing early number skills, and implications for instruction and measurement are discussed.

Exploring the Promise of a Number Line Assessment to Help Identify Students At-Risk in Mathematics

This manuscript presents the results from a study to investigate the technical characteristics of two versions of a number line assessment (NLA 0–20 and NLA 0–100). The sample consisted of 60 kindergarten and 46 first grade students. Both number line versions had sufficient alternate form and test–retest reliability. The NLA 0–20 had low and the NLA 0–100 had low to moderate correlations with math achievement. Results indicated that the NLA 0–100 explained a small, but unique portion of the variance in first grade mathematics performance when controlling for performance on the Assessing Student Proficiency in Early Number Sense (ASPENS) a set of early numeracy screening measures. We discuss study results related to the utility of adding number line assessment tasks to mathematics screening batteries and propose additional areas of research.

Early Number Skills Gains and Mathematics Achievement: Intervening to Establish Successful Early Mathematics Trajectories.

Early number skills, comprised of both informal and formal skills, are associated with later mathematics achievement. Thus, the development of foundational early number skills is an important aspect of early mathematics instruction. This study explored relations between early number skills gains and mathematics achievement for students at risk for mathematics difficulties in a kindergarten intervention study. Results indicated strong relationships between formal number skills gains and mathematics achievement across kindergarten and Grade 1. Intervention participants demonstrated larger informal and formal early number skills gains compared with their control peers, and relations between early number skills gains and first-grade mathematics achievement were moderated by intervention participation. Importantly, these findings suggest that formal and informal number skills gains may be critical components of later mathematics achievement for at-risk students. Implications for special education and intervention in tiered instructional systems are discussed.

Mathematics Fluency—More than the Weekly Timed Test

The purpose of this chapter is to provide an overview of the critical importance of mathematics fluency. We begin by providing an overview of the role of mathematics in today’s society, current shortcomings in the teaching of mathematics, operational definitions of fluency, and the critical role fluency plays in the development of mathematics proficiency. Next, we summarize current interventions designed to promote the development of fluency and assessments designed to measure student acquisition of mathematics fluency. We conclude by noting the potential steps for both researchers and practitioners to take to move the field forward.

What Is Fluency

Fluency is a ubiquitous, but a complicated term. This chapter provides an overview of various conceptions of fluency across a range of disciplines and research contexts as well as discusses implications for research, assessment, and instruction. We include an overview of definitions and exemplars of fluency in language use, reading, and mathematics followed by an exploration of fluency concepts (e.g., automaticity, efficiency, and procedural skill) and considerations for research. The chapter concludes with recommendations for investigations of fluency including attending to measurement issues, explicitly defining and analyzing discrete components of fluency, and leveraging these precise definitions to evaluate the interactions between task and proficiency inherent to fluency exercises.