Academic journal article School Psychology Review

Preliminary Evaluation of a Tier 2 Mathematics Intervention for First-Grade Students: Using a Theory of Change to Guide Formative Evaluation Activities

Academic journal article School Psychology Review

Preliminary Evaluation of a Tier 2 Mathematics Intervention for First-Grade Students: Using a Theory of Change to Guide Formative Evaluation Activities

Article excerpt

Abstract. This pilot study examined the efficacy of a Tier 2 first-grade mathematics intervention program targeting whole-number understanding for students at risk in mathematics. The study used a randomized block design. Students (N = 89) were randomly assigned to treatment (Fusion) or control (standard district practice) conditions. Measures of mathematics achievement were collected at pretest and posttest. Treatment and control students did not differ on mathematics assessments at pretest. A series of random-effects models were estimated to compare gains between treatment and control conditions. Gain scores of intervention students were significantly greater than those of control peers on a proximal measure of mathematics achievement. The role of a strong theory-of-change model in the development and evaluation of mathematics interventions is articulated. Implications for researchers and educators designing and delivering instruction for at-risk students in a response-to-intervention model are discussed.

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The critical importance of mathematics has garnered increased attention in the past decade (National Mathematics Advisory Panel [NMAP], 2008; National Research Council [NRC], 2001). The most recent National Assessment of Educational Progress (NAEP) results classified 58% of fourth-grade students as failing to reach proficiency in mathematics and 17% as falling below basic achievement patterns on the NAEP; the results are even more disconcerting when examined by income, ethnicity, and disability status (National Center for Education Statistics, 2013). Young students without a deep understanding of mathematics risk losing access to more advanced mathematics including algebra (NMAP, 2008) and long-term career opportunities available in the fields of science, technology, mathematics, and engineering (National Science Board, 2008). The National Council of Teachers of Mathematics (2013) noted that "an economically competitive society recognizes the importance of mathematics learning to adult numeracy and financial literacy, and it depends on citizens who are mathematically literate" (p. 1). With recognition of the negative impact of low mathematics achievement at both the individual and national level, urgent calls from the highest levels of the federal government have been made for an increased focus on improving the mathematics outcomes of our nation's students (Obama, 2013).

Occurring simultaneously with lower than desired levels of mathematics achievement is a growing recognition that a successful start in mathematics is critical in ensuring long-term success. Morgan, Farkas, and Wu (2009) analyzed longitudinal data from the Early Childhood Longitudinal Study database and found that of the students who entered and exited kindergarten below the 10th percentile, 70% remained below the 10th percentile in fifth grade. In contrast, of the students who entered kindergarten below the 10th percentile but exited above the 10th percentile, only 30% were below the 10th percentile in fifth grade. In other words, those students who came into kindergarten at an elevated risk for math difficulties but grew substantively over the course of the year were markedly less likely to be at risk up to 5 years later. These trends found in longitudinal data sets of mathematics achievement mirror those found for the development of reading trajectories (Juel, 1988). Such findings in the area of reading development spurred a focus on prevention of reading difficulties through the use of screening systems to identify at-risk students (Good, Gruba, & Kaminski, 2002) and the development of curriculum materials targeting foundational reading skills (Wanzek & Vaughn, 2010). A similar system, based on the idea of preventing mathematics difficulties before they fully develop by identifying at-risk students and providing early intervention services targeting key foundational skills, has been advocated in mathematics (Fuchs, Fuchs, & Compton, 2013). …

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