Extending Responsiveness to Intervention to Mathematics at First and Third Grades

Responsiveness to intervention (RTI) is an innovative approach to the identification of learning disabilities (LD). The central assumption is that RTI can differentiate between two explanations for low achievement: poor instruction versus disability. If the child responds poorly to validated instruction, then the assessment eliminates instructional quality as a viable explanation for poor academic growth and instead provides evidence of a disability. For children who do respond nicely, RTI serves a critical prevention function. Most of RTI research has been focused on early reading. In this article, we describe two ongoing programs of research on RTI in the area of mathematics: one on a comprehensive mathematics curriculum at first grade and the other focused on word problems at third grade. For each research program, we describe the sample, explain how students are identified as at risk for mathematics disability, provide an overview of the interventions to which responsiveness is gauged, and describe some results to date.     

Considering Identification and Service Provision for Students with Autism Spectrum Disorders within the Context of Response to Intervention

The Response to Intervention (RTI) framework, a preventive model of universal screening, tiered interventions, and ongoing progress monitoring, poses an interesting consideration for identification and service delivery for children with autism spectrum disorders (ASD). Upon examination of the existing literature, paucity exists regarding how RTI might guide identification and service delivery for students with ASD; however, the authors consider core tenets of RTI and how they are relevant for students with ASD given what is known about this unique population. Due to the importance of early identification and interventions for individuals with ASD, the RTI framework could be problematic if used to delay education eligibility. Thus, two routes of identification are outlined by the authors, one of which expedites evaluation based on pervasive symptomatology, while the other route uses a form of universal screening to assist in moving toward evaluation for those suspected of ASD. The use of tiered interventions for prevention or service delivery could cause potential complications given the need for early identification and individualized intensive programming. However, there is a clear match for several instructional RTI components and ASD, specifically for evidence-based interventions that are implemented with fidelity and monitored frequently, and other aspects such as family involvement, which could improve programming for students with ASD.     

Response to intervention with secondary school students with reading difficulties

The authors summarize evidence from a multiyear study with secondary students with reading difficulties on (a) the potential efficacy of primary-level (Tier 1), secondary-level (Tier 2), and tertiary-level (Tier 3) interventions in remediating reading difficulties with middle school students, (b) the likelihood of resolving reading disabilities with older students with intractable reading disabilities, (c) the reliability, validity, and use of screening and progress monitoring measures with middle school students, and (d) the implications of implementing response to intervention (RTI) practices at the middle school level. The authors provide guidance about prevailing questions about remediating reading difficulties with secondary students and discuss future directions for research using RTI frameworks for students at the secondary level.     

On the importance of a cognitive processing perspective: an introduction

Children with learning problems require early intervention. If it is evidence based and implemented with integrity and intensity, it will accelerate the academic progress of many students. This is the hope and expectation of the many supporters of responsiveness-to-intervention (RTI). A minority of children, however, will not respond sufficiently to such intervention because of learning disorders like specific learning disabilities (SLD). Some RTI models do not include research-backed methods to identify these children, nor do RTI practitioners often produce the data necessary to develop individualized instruction for them. The authors suggest practitioners go beyond typical RTI assessment data documenting responsiveness/ unresponsiveness to conduct comprehensive evaluations of these most difficult-to-teach students and to include in their evaluations carefully chosen cognitive measures. This special issue presents the work of teams of researchers, which suggests that cognitive and neuropsychological assessments can provide information to further understand SLD, which in turn can guide development of promising interventions.     

The Insufficiency of Response to Intervention in Identifying Gifted Students with Learning Disabilities

Many states are implementing response‐to‐intervention (RTI)–based assessment as the sole means of identifying students with specific learning disabilities (SLDs). Although RTI is often hailed as an improved model of identification, concern for the possibility of this model elevating false positives has been examined. The risk of RTI producing a second form of diagnostic error, however, has received relatively little attention, namely, false negatives. The widespread implementation of RTI necessitates an analysis of its ability to identify students who are most vulnerable to be inaccurately judged as responsive to instruction, namely, students with coexisting intellectual talent and SLDs.     

Response-to-intervention (RTI) as a model to facilitate inclusion for students with learning and behaviour problems

Many students with learning and behaviour problems are routinely excluded from regular education. Although calls have been made to educate students with these problems in the same settings as their typically developing peers, it remains unclear how best to support their needs for academic and behavioural support. We address this question first by describing response-to-intervention (RTI), a specific model of prevention and early intervention for learning and behaviour problems. A comprehensive summary of the RTI literature is provided. Second, we will discuss the feasibility and applicability of RTI as one approach to facilitate inclusion of students with learning and behaviour problems. Specifically, we will demonstrate how RTI can be used to address at least four barriers to inclusion by (1) providing a clear implementation strategy for inclusion practices; (2) clearly defining the roles, responsibilities and collaboration of general and special education teachers; (3) enabling the allocation of resources for instruction and intervention; and (4) avoiding early and unnecessary labelling of students with learning and behaviour problems. Third, limitations of RTI as a model to facilitate inclusion will be discussed.     

Responsiveness‐to‐Intervention: Definitions,Evidence, and Implications for the Learning Disabilities Construct

Longstanding concern about how learning disabilities (LD) are defined and identified, coupled with recent efforts in Washington, DC to eliminate IQ‐achievement discrepancy as an LD marker, have led to serious public discussion about alternative identification methods. The most popular of the alternatives is responsiveness‐to‐intervention (RTI), of which there are two basic versions: the “problem‐solving” model and the “standard‐protocol” approach. The authors describe both types, review empirical evidence bearing on their effectiveness and feasibility, and conclude that more needs to be understood before RTI may be viewed as a valid means of identifying students with LD.     

Promoting basic arithmetic competence in early school years–using a response to intervention model

This study investigated whether mathematics education based on a multi-tiered response to intervention (RTI) model can support students' arithmetic competence in primary schools in Sweden. The intent was to identify and support students at risk of failure. In this study, 113 students participated in the intervention, and 30 students participated in the control group. Both groups were followed from Grade 1 to the end of Grade 2 and compared. During the first semester in Grade 1, all students were taught basic addition and subtraction with explicit instructions in Tier 1. Those who did not respond to Tier 1 after one semester were provided support within Tier 2 during the second semester. The same was repeated in grade 2 and the students that did not respond to Tier 2 were supported within Tier 3. At the end of Grade 2, students in the intervention group performed significantly higher on the basic arithmetic competence in the number range 1–9 than the control group. No significant difference was found in a test measuring basic arithmetic competence in the number range 10–19. This study shows that using multi-tiered RTI might be sufficient to identify and support students at risk in early arithmetic competence.     

中日两国小学生数学学力的比较研究

促进中小学生数学学力发展是数学教育的重要任务。本文选用了日本"全国学力调查"小学六年级数学试卷,对中国五省部分六年级学生的数学基本知识的掌握情况和灵活应用的能力进行测试,并与日本同龄小学生进行比较,分析两国小学生数学学力的异同,对我国数学课程与教学改革进行一些思考。     

Long-Term Effects of First-Grade Multitier Intervention

Abstract

The purpose of this study was to compare the long-term effects of 2 first-grade Response to Intervention (RTI) models (Dynamic and Typical RTI) on the reading performance of students in second and third grade. Participants included 419 first-grade students (352 in second grade and 278 in third grade after attrition). Students were classified based on first-grade screeners as at risk or not at risk and then based on their RTI (no risk [NR], relative easy to remediate [ER], and requiring sustained remediation [SR]). Students in the dynamic RTI condition had higher reading comprehension scores at the end of third grade. At the end of second grade, ER and SR students had lower reading scores than NR students. At the end of third grade, there were no differences in reading skills between ER and NR students, but SR students had lower scores than NR students. ER students in the dynamic RTI condition had higher reading scores at the end of second grade than those in the typical RTI condition. Limitations and directions for future research are discussed.     

Response to intervention for reading difficulties in the primary grades: some answers and lingering questions

The purpose of this article is to describe the current research base and identify research needs related to response to intervention (RTI) frameworks in primary-grade reading. Research is reviewed on early reading instruction and intervention, the implementation of multitiered reading interventions, and the determination of intervention responsiveness. Areas identified as in need of research include (a) the conditions under which early reading interventions are most effective in RTI contexts, (b) multitiered interventions for students with limited English proficiency, (c) reading instruction for students who make limited progress in Tier 3 intensive interventions, (d) criteria for determining intervention responsiveness, and (e) the effects of fully implemented RTI frameworks. Although RTI research may be expensive and difficult to implement, it may contribute to improved reading outcomes for many students who are otherwise at risk of serious negative life consequences.     

Mental-Physical Relationships during the preschool period

Little is known about the development of mathematics anxiety in elementary school students. To address this gap in knowledge, the authors evaluated students in Grades 3 and 6 on measures of mathematics anxiety, school test anxiety, and attitudes toward mathematics to determine (a) whether different forms of mathematics anxiety exist, (b) whether mathematics test anxiety differs from school test anxiety, and (c) whether mathematics anxiety is related to different attitudes toward mathematics. Evidence was found for two distinct forms of mathematics anxiety: test and problem-solving anxiety. Mathematics test anxiety increased with age relative to mathematics problem-solving anxiety; this result demonstrated that children become more anxious about mathematics testing situations as they progress through school. Mathematics test anxiety was related, but not identical, to school test anxiety, and students in both grades were less anxious about math tests than about academic testing generally. Finally, older students tended to show more positive attitudes toward mathematics than did younger students, and relations between these attitudes and the two forms of mathematics anxiety also changed between Grades 3 and 6.     

考研高等数学的重点内容和常见题型

依照考研数学考试大纲[1],对考研高等数学的重点内容和常见题型进行归纳、整理和总结,使其所涉及的各知识点之间相互关系清晰明了,可供学生考研复习高等数学以及教师进行高等数学课程教学时参考。     

Role of teacher characteristics and school resources in early mathematics learning

The authors investigated the degree to which school-level teacher characteristics and resources are related to the mathematics learning of kindergarten children using a sample drawn from a large US database. Kindergarten-level teacher characteristics were operationalised as collective teacher efficacy, teacher experience and teacher preparation; kindergarten resources were operationalised as efforts that schools make to reach out to parents, classrooms with mathematics manipulatives, and classroom technology. Kindergarten students learned more in mathematics over a year in schools where teachers’ collective efficacy was high. School resources yielded a range of significant yet mixed results in young children’s mathematics achievement. Notably, younger students and students entering kindergarten with lower levels of mathematical skills benefited greatly from classroom resources. Overall, the presence of classroom technology as a school-level resource was positively related with older kindergarten students’ learning. Based upon the findings, organisational and policy implications are discussed.     

Examining a Grade-Level Math CBM Designed for Persistently Low-Performing Students

Students with disabilities participate in two major measurement systems. The Individuals with Disabilities Education Act emphasizes working within a Response to Intervention (RTI) framework to identify and monitor the progress of low-performing students. Persistent low-performing students also may be eligible for some form of an alternate assessment for accountability purposes. Working within these two systems, educators need technically sound measures to inform decision making. This study presents scaling results from a Curriculum Based Measurement tool designed within an RTI framework and specifically for persistently low-performing students. We use the phrase “persistently low-performing students” to refer to a specific group of students who have been identified with a nonsevere learning disability and who perform well below grade-level expectations. Key findings indicate that items appear to function well in the lower tail of the distribution of students' estimated ability level. Further, the distribution of items is positively skewed, resulting in many accessible items that are most informative for low-performing students. Results provide initial validity evidence for the measurements as one source of data for progress monitoring within an RTI framework and the identification of persistent low-performing students who may be eligible for a large-scale assessment option other than the general grade-level assessment.     

New Look at a Persistent Problem: Inequality,Mathematics Achievement,and Teaching

ABSTRACT

The authors examined the relation of school-year teaching practices to SES and race/ethnic score gaps in mathematics by fitting an individual growth model with a representative sample drawn from the Early Childhood Longitudinal Study Kindergarten Cohort data. There were mixed findings. Teaching practices had uniform effects for all students, increasing their scores equally during the school year. Teaching mattered in maintaining proficiency during summer, although modestly. Specifically, practices emphasizing analytical and reasoning skills, thought among mathematics reformers to be most effective, were positively associated with summer learning among low-SES students. The authors explore possible reasons for the weak association between teaching practices and mathematics scores.     

Tiers of intervention in responsiveness to intervention: prevention outcomes and learning disabilities identification patterns

Response to Intervention (RTI) models have attracted great attention as an alternative to traditional methods used for identifying students with learning disabilities. A major feature of this approach is the implementation of academic interventions in general education and measuring the student's response to those interventions. A common question that needs to be addressed is the number of stages or tiers of intervention necessary in the Response to Intervention model. This article reviews three studies of RTI that investigate the RTI tiers. Sharon Vaughn and Rollanda O'Connor report on studies using the Standard Protocol approach to RTI. David Tilly reports on using the Problem Solving Model as an RTI model. This article summarizes the results of these three investigations.     

Self-Study of a Teacher's Journey toward Standards-Based Mathematics Teaching

The authors describe a journey of self-study during which one author shifted from traditional, teacher-driven approaches to a more problem-based inquiry approach to teaching mathematics. He videotaped a series of lessons taught to sixth-grade students over a semester and analyzed his teaching during discussions with his mentor at the university. The shared analysis helped him learn to involve his students more directly in their own learning. A major lesson learned was that understanding the potential value of a problem-solving approach to teaching mathematics does not guarantee corresponding changes in the classroom. Two vital elements of lesson development emerged as focal points for self-study. After first learning how to prepare worthwhile mathematical tasks, the teacher also learned the importance of implementing effective questioning strategies to help students think more deeply about the mathematics they were learning.