Mari Strand Cary

Enhancing Core Mathematics Instruction for Students at Risk for Mathematics Disabilities.

CRA) approach (Hudson & Miller, 2006). As part of the CRA approach, a teacher might begin instruction with concrete examples (e.g., counting blocks) and then interweave pictorial representations (e.g., tally marks) and abstract symbols (e.g., numbers) as students grasp conceptual

Examining the Efficacy of a Tier 2 Kindergarten Mathematics Intervention

This study examined the efficacy of a Tier 2 kindergarten mathematics intervention program, ROOTS, focused on developing whole number understanding for students at risk in mathematics. A total of 29 classrooms were randomly assigned to treatment (ROOTS) or control (standard district practices) conditions. Measures of mathematics achievement were collected at pretest and posttest. Treatment and control students did not differ on mathematics assessments at pretest. Gain scores of at-risk intervention students were significantly greater than those of control peers, and the gains of at-risk treatment students were greater than the gains of peers not at risk, effectively reducing the achievement gap. Implications for Tier 2 mathematics instruction in a response to intervention (RtI) model are discussed.

The Science Behind Curriculum Development and Evaluation Taking a Design Science Approach in the Production of a Tier 2 Mathematics Curriculum

The production of an effective mathematics curriculum begins with a scientific development, evaluation, and revision framework. The purpose of this study was to conduct an initial investigation of a recently developed Tier 2 mathematics curriculum designed to improve the outcomes of first grade students at risk for mathematics difficulties (MD). The curriculum, which is anchored to a scientific design framework and a well-specified theory of change, centers on the careful integration of foundational concepts of whole number and validated-design principles of explicit and systematic instruction. Four instructional groups, with each consisting of five first grade students with MD and one interventionist, participated in the study. Data related to the feasibility, usability, and promise of the curriculum to improve student mathematics achievement were collected using multiple methods. Results provide preliminary evidence in terms of these curriculum development and evaluation areas. Implications for instruction and design research are discussed.

Investigating the Efficacy of a Core Kindergarten Mathematics Curriculum to Improve Student Mathematics Learning Outcomes

This study examined the efficacy of a core kindergarten mathematics program, Early Learning in Mathematics (ELM), a 120-lesson program with four content strands: (a) number operations, (b) geometry, (c) measurement, and (d) vocabulary. The study utilized a randomized block design, with 129 classrooms randomly assigned within schools to treatment or control conditions. Measures of achievement were collected in the fall (pretest) and spring (posttest) in kindergarten and in the winter of first grade (follow-up). Although students in ELM classrooms did not differ significantly from students in control classrooms, we expected and found that the effects of ELM depended on students’ initial achievement. Initial achievement moderated condition effects for Test of Early Mathematics Ability (TEMA) scores (p =.0039), but not the Early Numeracy–Curriculum-Based Measurement (p =.1887). We found no effects on follow-up first-grade scores from the Stanford Achievement Test Tenth Edition Problem Solving subtest (p =.9737) or Procedures subtest (p =.6336).

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.

Addressing the Practice-to-Research Gap: A Rigorous Evaluation of Local Education Agency–Based Interventions for Struggling Readers in Sixth Grade

We present the results of a study of local education agency (LEA)-based interventions to improve the reading outcomes of struggling readers in sixth grade. The sample included 1,076 intervention students and 3,644 comparison students. Regression discontinuity was used to evaluate intervention impact. The study contributes to the field by demonstrating (a) the importance of conducting rigorous evaluations of existing school interventions to understand the true impact of evidence-based practices when implemented under local circumstances and constraints, and (b) the use of regression discontinuity as an evaluation design is feasible within typical school settings. Implications for the study are discussed, especially in terms of providing a model for evaluation of LEA-driven interventions in the middle grades.

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.

A Practitioner Implementation of a Tier 2 First-Grade Mathematics Intervention.

We report on a practitioner implementation of Fusion, a first-grade mathematics intervention. Studies such as this evaluation of a loose implementation under realistic conditions are important to curriculum developers’ understanding of how evidence-based programs and tools work under a variety of implementation scenarios. In this quasi-experimental study, first-grade students (n = 253) in 10 schools were assigned to treatment (n = 154) or control (n = 99). Rather than randomly assigning students, schools assigned those students most at risk to treatment and, typically, those less at risk to control. School staff administered pre- and postassessments and led Fusion sessions approximately 30 min per day, 3 days per week. The intervention resulted in a significant positive effect on a researcher-developed first-grade math measure. The implementation of Fusion and feedback from school staff provided insights to guide the curriculum development process.