The number line has been proposed as a central construct used by students to solve a range of mathematics problems. Given the capacity of number lines to represent all real numbers and to be used in ...a variety of contexts, there have been calls to increase the use of number lines in mathematics instruction. However, due to the recency of these recommendations coupled with the myriad ways in which number lines can be used, little hands-on guidance has been provided how best to leverage number lines in mathematics instruction. This special series details five areas in which teachers can use number lines to support acquisition of critical mathematics concepts and skills.
Abstract Effective classroom management is critical to supporting student learning and success in school. However, little research has focused specifically on the impact of classroom management on ...student mathematics achievement, especially in the early elementary grades or in a small group (i.e., Tier 2) context. To address this need we investigated the relationship between classroom management and student mathematics achievement within the context of ROOTS, a validated Tier 2 kindergarten mathematics intervention taught by paraprofessionals. Results show that the quality of classroom management within the ROOTS intervention predicted gains in student mathematics achievement from pretest to posttest. These findings have critical implications for practitioners, including the importance of integrating effective classroom management techniques into Tier 2 mathematics intervention groups and supporting paraprofessionals' knowledge and use of effective classroom management.
Practitioner points Gains in student mathematics achievement in a Tier 2 kindergarten mathematics intervention were significantly associated with the quality of interventionists' classroom management. Effective small group management techniques may be more important in intervention groups with smaller student‐to‐teacher ratios. School psychologists and other personnel involved in schoolwide processes such as Multi‐tiered Systems of Support should intentionally support instructors to use effective classroom strategies while delivering mathematics instruction, across instructional tiers of support.
Explicit Mathematics Instruction Doabler, Christian T.; Fien, Hank
Intervention in school and clinic,
05/2013, Letnik:
48, Številka:
5
Journal Article
Recenzirano
This article describes the essential instructional elements necessary for delivering explicit mathematics instruction to students with mathematics difficulties. Mathematics intervention research ...indicates that explicit instruction is one of the most effective instructional approaches for teaching students with or at risk for math difficulties. Explicit instruction is a systematic approach that facilitates important instructional interactions between teachers and students around critical math content. This article describes a framework for delivering explicit math instruction in the early grades. Although the explicit framework is relevant across the range of early math content (i.e., measurement, geometry), the focus is on explicit instruction in the context of teaching place value concepts in kindergarten and first grade classrooms. Place value is a critical component of whole-number understanding and a necessary concept for students to develop mathematical proficiency. Key questions associated with explicit math instruction are also addressed.
Rational number proficiency is predictive of later mathematics achievement, especially for rigorous mathematics courses, such as Algebra I. Students with learning disabilities (LD) in mathematics ...struggle to make adequate progress on rational number concepts and skills that lay the foundation for successfully completing secondary mathematics courses. However, recent research has demonstrated that utilizing effective instructional design, such as the use of a number line with systematic and explicit instruction, can result in academic progress for students with LD in mathematics. This article presents teachers with a four-step teaching sequence utilizing the number line and effective strategies for teaching students with LD in mathematics to introduce fraction-to-decimal relationships in upper elementary, a prerequisite for middle school mathematics.
The effectiveness of Tier 2 interventions may depend on the variability of student skills within an intervention group. We investigated the effect of pretest variability within intervention groups ...using data from a large-scale study of ROOTS, a Tier 2 kindergarten mathematics intervention. Our research questions were as follows: Does mathematics pretest variability within ROOTS groups predict student gains from the intervention, and is this relationship moderated by (a) intervention group size (two- vs. five-student groups), (b) quality of explicit instruction, or (c) group-level initial skill? We found that ROOTS groups with greater pretest variability on a closely aligned mathematics measure experienced smaller gains from the intervention. This association was more impactful in larger intervention groups (i.e., five-student groups compared with two-student groups) and in groups with higher quality of explicit instruction. We unpack these findings and conclude with recommendations for practice and future research.
This study investigated the technical characteristics of four early measurement curriculum-based measures (EM-CBMs) designed to assess concepts related to linear measurement and iteration. The sample ...consisted of 221 first grade students. Data were collected at two time points approximately 10 weeks apart. Reliability and concurrent and predictive validity correlations were in the low to moderate range. We discuss study results related to screening for risk status including limitations to the current work and future directions for research.
Impact Statement
The importance of measurement in mathematics development is garnering increased attention. Exploring measures to screen students for risk status is critical to enable schools to allocate resources to students in need of intervention services. The findings in this manuscript represent a first exploratory attempt to develop screening measures in the area of measurement.
This article introduces the special section on adaptive interventions and sequential multiple-assignment randomized trial (SMART) research designs. In addition to describing the two accompanying ...articles, we discuss features of adaptive interventions (AIs) and describe the use of SMART design to optimize AIs in the context of multitiered systems of support (MTSS) and integrated MTSS. AI is a treatment delivery model that explicitly specifies how information about individuals should be used to decide which treatment to provide in practice. Principles that apply to the design of AIs may help to more clearly operationalize MTSS-based programs, improve their implementation in school settings, and increase their efficacy when used according to evidence-based decision rules. A SMART is a research design for developing and optimizing MTSS-based programs. We provide a running example of a SMART design to optimize an MTSS-aligned AI that integrates academic and behavioral interventions.
In intervention studies, high rates of implementation fidelity are important markers of a study’s success; however, the definition of implementation fidelity is both complex and dynamic. In this ...synthesis, we examined the dimensions of implementation fidelity measured and reported in 99 studies in which researchers utilized a mathematics intervention for elementary students (i.e., Grades 1–5). We examined implementation fidelity following recommendations made by Dane and Schneider (1998), O’Donnell (2008), and DeFouw et al. (2009) to capture a comprehensive representation of the implementation fidelity data collected and reported within mathematics intervention studies. We organized our conceptualization of implementation fidelity into four overarching categories and nine dimensions within those categories: intervention design (i.e., theories of change and logistics), fidelity of implementor (i.e., adherence, quality of delivery, dosage, and implementor knowledge or experience), student engagement, and treatment analysis (i.e., treatment differentiation and analysis of implementation fidelity). Overall, findings indicate many author teams reported adherence data and dosage data, but significantly fewer studies reported quality of delivery data, student engagement data, or treatment differentiation data. In addition, author teams were more likely to report at least one form of logistics, such as implementor support, than theories of change. Implications for research and practice are discussed.
This study utilized a partially nested randomized control design to investigate the impact of Fusion, a first-grade math intervention. Blocking on classrooms, students were randomly assigned to one ...of the three conditions: a Fusion two-student group, a Fusion five student group, or a no-treatment control group. Two primary research questions were examined: What was the overall impact of the Fusion intervention as compared to a business-as-usual comparison condition? and Was there a differential impact on student outcomes between the 2:1 Fusion and the 5:1 Fusion conditions? Analyses found a positive effects on four outcome measures favoring Fusion groups over control with two of the differences statistically significant. Results between Fusion groups found positive effects favoring the Fusion 2:1 group compared to the Fusion 5:1 group on all four outcome measures with two of the differences statistically significant. On a second-grade follow-up measure, no difference was found between Fusion groups and control, but a statistically significant difference was found between Fusion groups favoring the 2:1 Fusion group. Future research directions and implications for practice are discussed.
More than two-thirds of middle school students do not read proficiently. Research has shown that targeted interventions using explicit instruction methods can improve reading outcomes for struggling ...readers. A central feature of explicit instruction is the systematic implementation of instructional interactions, but it is not clear what specific instructional interaction practices lead to stronger outcomes for middle school readers. This study used a regression discontinuity design to compare the frequency and impact of instructional interactions experienced by eighth-grade students who received a targeted reading intervention (
= 1,461) with those who did not (
= 4,292). Results indicated that students who received intervention experienced far more instructional interactions with their teachers than did students who did not. However, the association between rates of interaction and student need in the intervention group was minimal, and the relationship between the rate of instructional interactions and reading growth was mixed. Implications for intervening with struggling students in the middle grades are discussed.
