Mathematics Intervention Research Articles

Alignment of K‐8 mathematics interventions with strands of mathematical proficiency in meta‐analytic research

AbstractThe purpose of this paper was to examine current mathematics interventions designed for students in kindergarten through eighth grade to determine how often they incorporated the five strands of mathematical proficiency identified by the National Research Council (2001). The five strands are conceptual understanding, procedural knowledge, strategic competence, adaptive reasoning, and productive disposition. A systematic review of the literature resulted in 13 meta‐analyses of that studied a total of 19 unique interventions. The five strands of mathematical proficiency were then compared to each intervention to determine with which strand(s) the intervention aligned. None of the 19 interventions contained all five strands, but interventions could be combined to enhance math proficiency. The strands of mathematics proficiency could provide a framework with which to meaningfully combine intervention components.

Concrete-Representational-Abstract–Integrated as a Tier 2 Instruction to Teach Addition

Mathematics is crucial to the educational and vocational success of students. The concrete-representational-abstract (CRA) approach is a method to teach students mathematical concepts. The CRA involves instruction with manipulatives, representations, and numbers only in different lessons (i.e., concrete lessons include manipulatives but not pictures or numbers only). Researchers are exploring integrating the phases of CRA, referred to as concrete-representational-abstract–integrated (CRA-I), because it may be a more efficient method of instruction. The CRA-I integrates all phases starting with the first lesson (e.g., Lesson 1 includes manipulatives, pictures, and numbers only) and then fades concrete and representational instruction. The purpose of this article is to provide information about a CRA-I Tier 2 mathematics intervention on additive reasoning for second-grade students in a rural school in the southeastern United States. The researchers describe CRA-I, the lessons implemented, and implications for teacher use.

How to Structure and Intensify Mathematics Intervention

Many students who experience difficulty with mathematics may also require behavioral support. We suggest educators create an appropriate scope and sequence for mathematics intervention by focusing on the critical mathematics content. Educators can then design the intervention with a common session structure. Finally, educators can embed and intensify supports for a student by increasing the dosage, focusing on the alignment of the intervention, and attending to transfer.

How early mathematics interventions support mathematics vocabulary learning: A content analysis

AbstractWhile there is a strong research base that supports intervening early in mathematics, research investigating the importance of mathematics vocabulary is still emerging. Practitioners and researchers may benefit from understanding how mathematics interventions support mathematics vocabulary acquisition, particularly for students who struggle with learning mathematics. Thus, the purpose of this study was to conduct a mathematics vocabulary content analysis across seven kindergarten and first‐grade mathematics interventions. Across the intervention lessons, we recorded suggested teacher and student actions related to mathematics vocabulary instruction. The results indicated the most common instructional strategies used to teach mathematics vocabulary include: providing students with the opportunity to apply the meaning of the vocabulary term (94.7%), using representations (66.4%), and asking students to respond to teacher prompts using the term (44.7%). Overall, 29.7% of lessons clearly defined vocabulary terms, and 5.8% of lesson objectives addressed teaching the definition of the term. We discuss implications for researchers and practitioners to supplement interventions with opportunities for students to learn, practise, and apply mathematics vocabulary.

A Systematic Review of Research Syntheses on Students with Mathematics Learning Disabilities and Difficulties

AbstractThe purpose of the systematic review of mathematics intervention syntheses was to identify patterns and gaps in content areas, instructional strategies, effect sizes, and definitions of learning disabilities (LD), mathematics LD (MLD), and mathematics difficulty (MD). Using rigorous inclusion criteria, we evaluated 36 syntheses that included 836 studies with 32,495 participants. Although each synthesis stated a focus on LD, MLD, or MD, few students with LD or MLD were included, and the authors’ operational definitions of disability and risk varied. Syntheses predominantly focused on word‐problem solving, fractions, computer‐assisted learning, and schema‐based instruction. Wide variation in effectiveness, content areas, and instructional strategies was reported. Finally, our results indicate the majority of syntheses included achievement outcomes, but very few reported on other outcomes (e.g., social validity, strategy use). We discuss how the results of this comprehensive review can guide researchers in expanding the knowledgebase on mathematics interventions.

A Synthesis of the Conceptualization and Measurement of Implementation Fidelity in Mathematics Intervention Research

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.

Effects of early mathematics intervention for low-SES pre-kindergarten and kindergarten students: a replication study

ABSTRACT A socioeconomic status (SES)-related achievement gap in mathematics emerges prior to school entry, and increases in elementary school. This gap makes implementation of demanding mathematics standards (e.g., the Common Core State Standards) an ongoing challenge. Early educational intervention is a strategy for addressing this challenge. A randomised controlled trial was conducted in public American preschools to (1) replicate the efficacy of an intervention, Pre-K Mathematics, for low-SES children, and (2) test the combined impact of this intervention and a Common-Core-aligned kindergarten intervention, Early Learning in Mathematics. Forty-one clusters of pre-kindergarten and kindergarten classrooms, containing a sample of 389 low-SES children from an agricultural region, were randomly assigned to treatment and control conditions. The original impact findings were replicated: Child mathematics outcomes in pre-kindergarten were positive and significant. Gains were maintained in kindergarten. Thus, the gap can be reduced and gains maintained by sustained early intervention.

Heterogeneity in Mathematics Intervention Effects: Evidence from a Meta-Analysis of 191 Randomized Experiments

Since the standards-based education movement began in the early 1990s, mathematics education reformers have developed and evaluated many interventions to support students in mastering more rigorous content. We conducted a systematic review and meta-analysis of U.S. PreK-12 mathematics intervention effects from 1991 to 2017 to study sources of heterogeneity. From more than 9,000 published and unpublished study reports, we found 191 randomized control trials that met our inclusion criteria, with 1,109 effect size estimates representing more than a quarter of a million students. The average effect size on student mathematics achievement was 0.31, with wide heterogeneity of most effects ranging from −0.60 to 1.23. Two modeling approaches—meta-regression and machine learning—provided converging evidence that outcome measure type (researcher-created vs. standardized) and technology delivery (vs. teacher or interventionist delivery) were predictors of effect size. Intervention type, intervention length, grade level, and publication year were also identified as potentially explanatory factors.

Video Lessons via YouTube Channel as Mathematics Interventions in Modular Distance Learning

Modular distance learning is a new learning delivery modality implemented by most public schools in the Philippines. However, as seen on the summative test result for the first grading period, students struggled in Grade 7 Mathematics using the self-learning modules. Hence, mathematics concepts were hard to understand and not explained well in the module. To address the problem, the teacher made video lessons and uploaded them to the YouTube channel Direct to the Point by DM as interventions. A YouTube channel as an avenue to upload educational videos has been used before the pandemic. This platform’s advent can be used in delivering mathematics interventions since the students preferred to watch videos. This study aimed to assess the Mathematics video lessons via a YouTube channel for modular distance learning. This was a practical action research design following the PDSA model that utilized the participants’ pretest and the posttest scores. Also, open-ended surveys and interviews were conducted to elicit qualitative data to support the quantitative findings. The result reveals that video lessons help the students understand the mathematics concepts complementing lessons on the modules. Moreover, they enjoyed watching the teacher-made videos since they see the teacher explaining the lesson. However, the students suggested having regular posting of videos with more examples and explanations having clear and loud voice of the teacher.

The Effects of a Computer-Based Mathematics Intervention in Primary School Students with and Without Emotional and Behavioral Difficulties

Mathematics difficulties (MD) affect about 20% of the students in German schools. Almost half of them also exhibit emotional and behavioral difficulties (EBD). While a growing number of mathematics interventions target children with MD separately, there is a lack of evidence for the effectiveness of these interventions for children with combined MD and EBD. This study aims to investigate the differential effects of an evidence-based mathematics intervention on children with and without EBD. This single-case study examined 11 children with internalizing and externalizing EBDs from grades 3 and 4 using a staggered AB-Design. A computer-based mathematics intervention was provided for 5 weeks, during which the mathematical performance of the students was measured using a learning progress assessment in A- and B-phases. Data were analyzed using (a) overlap indices, (b) piecewise linear regression (PLM) models for each student, and (c) a multilevel PLM across all children. The results suggest different effectiveness for children with and without EBD, indicating a small direct influence of the severity of the EBD. Thus, the effectiveness of mathematics interventions might not be generalizable for children with combined EBD and MD. Further research is necessary to better understand the differential effectiveness of mathematics interventions for these children.

Domestic and foreign literature analysis on the types and effectiveness of Edu-Tech based smart learning for students subject to learning support: focusing on experimental research

이 연구는 에듀테크를 기반으로 한 스마트러닝 교수를 학생들에게 직접 적용한 국내외선행연구들을 고찰해 보고, 연구 동향 및 스마트러닝 활용 유형 특성, 그리고 그 효과성을알아봄으로써 후속 연구를 위한 방향 제시 및 이론적 기반을 마련하는 것을 연구목적으로하였다. 분석 대상 논문은 2001년~2021년 5월까지 한국연구재단 등재지 또는 등재후보지에 발표된 논문으로 한정하였다. 연구결과, 학습장애 학생들을 대상으로 한 논문이 가장많았고, 초등학생 대상 연구가 가장 많았으며, 단일대상연구 유형이 가장 많았다. 중재영역별로 살펴보면 수학 중재 논문이 가장 많았다. 스마트러닝 활용 유형은 교육용 프로그램, 인터넷 네트워킹, 가상ㆍ증강현실, 혼합 유형 총 4가지로 분류하여 알아보았는데, 웹기반소프트웨어 활용 논문이 가장 많았고, 모바일 및 애플리케이션 활용 및 ARㆍVR 활용 논문이 그 뒤를 이었다. 스마트러닝 중재 효과성을 랜덤효과모형으로 분석한 결과, 전체 효과크기(0.75)를 비롯하여 모든 중재 영역에 걸쳐 비교적 높은 중간 효과크기~큰 효과크기를나타내고 있음을 알 수 있었다. 본 연구의 후속 작업으로 포스트코로나 시대에 필수적인다양한 에듀테크 기반 스마트러닝 프로그램을 개발하고, 그 효과성을 검증할 수 있는 다방면의 노력이 뒷받침되어야 할 것이다.This study examines domestic and foreign previous studies that directly applied smart learning professors based on Edu-Tech to students, and suggests directions for follow-up research and theoretical The purpose of this study was to lay the foundation. Papers to be a nalyzed were l imited t o papers p ublished i n j ournals registered o r candidates f or registration by the National Research Foundation of Korea from 2001 to May 2021. As a result of the study, the largest number of papers were on students with learning disabilities, the largest number of studies on elementary school students, and the largest number of single-subject research types. Mathematics intervention papers were the most common by intervention area. Smart learning application types were classified into four categories: educational programs, internet networking, virtual/augmented reality, and mixed types. Papers using web-based software accounted for the most, followed by papers using mobile and application and AR/VR. As a result of analyzing the effectiveness of the smart learning intervention with a random effect model, it was found that a relatively high medium to large effect size was shown across all intervention areas including the overall effect size(0.75). As a follow-up of this study, various efforts to develop various Edu-Tech-based smart learning programs essential in the post-corona era and verify their effectiveness should be supported.

Validity and Reliability of Mathematics Intervention Instrument Based on the Learning Style of Students with Learning Disability (IMGAP) Using Rasch Assessment Model

Survey questionnaires have been widely used to measure important outcomes in special education. However, the reliability and validity of these questionnaires are often measured using the Classical Test Theory approach. In the meantime, Rasch Analysis based on Item Response Theory provides a better alternative for examining the psychometric quality of rating scales and informing scale improvements. This article outlines a six-step process for using Rasch Analysis to review the psychometric properties of a rating scale, namely item functional inspection, reliability and item-respondent separation, polarity and suitability of items for construct measurement, and the standard residual correlation values. The questionnaires were distributed to 140 special education (learning disabilities) teachers. The final analysis found that no items were dropped from the questionnaire. Thirty-nine items were deemed suitable for evaluating constructs related to learning styles-based mathematical intervention for students with learning disabilities. The findings from the analysis have statistically proved that the items in this instrument have a high degree of validity and reliability as well as suitable to be used on special education teachers for learning disabilities in determining the importance of considering learning styles as one of the important factors when conducting mathematical interventions of students with learning disabilities.

Measurement Model of Mathematics Intervention Based on the Learning Style of Students with Learning Disability (MIMGAP) Using Exploratory Factor Analysis (EFA)

Measurement Model of Mathematics Intervention Based on the Learning Style of Students with Learning Disability (MIMGAP) Using Exploratory Factor Analysis (EFA)

Reporting Quality in Math Meta-Analyses for Students with or at Risk of Disabilities

Researchers and practitioners alike often look to meta-analyses to identify effective practices to use with students with disabilities. The number of meta-analyses in special education has also expanded in recent years. The purpose of this systematic review is to evaluate the quality of reporting in meta-analyses focused on mathematics interventions for students with or at risk of disabilities. We applied 53 quality indicators (QIs) across eight categories based on recommendations from Talbott et al. to 22 mathematics intervention meta-analyses published between 2000 and 2020. Overall, the meta-analyses met 61% of QIs and results indicated that meta-analyses most frequently met QIs related to providing a clear purpose (95%) and data analysis plan (77%), whereas meta-analyses typically met fewer QIs related to describing participants (39%) and explaining the abstract screening process (48%). We discuss the variation in quality indicator scores within and across the quality categories and provide recommendations for future researchers.

A Synthesis on the Impact of Self‐Regulated Instruction on Motivation Outcomes for Students with or at Risk for Learning Disabilities

AbstractIn this synthesis, we examined and assessed the impact of self‐regulated instructional components on the motivation of students with or at risk for learning disabilities (LD) in reading, writing, or mathematics intervention studies. Elements such as goal setting, self‐monitoring for task completion, self‐monitoring for emotions, self‐talk for task completion, self‐talk for emotions, and self‐talk for progress monitoring were identified as relevant constructs, and were further examined to determine their effect on students’ motivation for learning and academic functioning. Results indicated major differences in the application of these self‐regulated instructional components across academic domains. Quantitative analyses also revealed that interventions with self‐regulated instructional components resulted in positive effects on motivation measures such as self‐efficacy, self‐esteem, attributions, value for task, affect, expectancy for success, and intrinsic motivation. Finally, our findings have practical implications for struggling learners, as goal setting and self‐talk, for task completion or for progress monitoring, seem especially likely to improve the likelihood that struggling learners will demonstrate positive gains in motivation.

Examining the Role of Domain‐General Skills in Mathematics Learning and Intervention Response in Kindergarten

AbstractEffective early mathematics instruction is critical to support long‐term mathematics achievement. Given that student response to typical instruction varies, a range of mathematics interventions have been developed to support foundational mathematics development. However, not all students respond to these interventions. To better understand factors associated with intervention response, the current study explored how domain general cognitive skills were associated with intervention response for 621 kindergarten students with or at risk for mathematics difficulties. Results indicated that although domain general skills were associated with mathematics achievement, there was no evidence of differential response to intervention based on cognitive skills. When examining differences while holding initial mathematics skill constant, there was a non‐significant, but potentially important pattern of students with higher domain general skills demonstrating greater mathematics gains as a result of intervention participation. Implications for mathematics intervention and curriculum development, including potentially impactful instructional approaches and cognitive scaffolds are discussed.

Utilizing Facebook and Messenger Groups as Platforms for Delivering Mathematics Interventions in Modular Distance Learning

Modular distance learning is the most implemented learning delivery modality in the Philippines, wherein students learn the lessons through the help of self-learning modules. However, students struggle to learn mathematics lessons independently under this modality based on summative tests and performance tasks’ results from the first grading period using self-learning modules. So, interventions must be placed by using social media platforms preferred by most of the students to reach and help them. The study aimed to assess the utilization of Facebook and Messenger groups as platforms for delivering video lessons and activities, learning materials, administering the test, and answering queries of the students in grade 9 Mathematics following the modified PDSA model. The study employed a practical action research design utilizing surveys, interviews, and test materials as data collection methods validated by master teachers and a head teacher. The pretest was administered before two months of interventions. After that, the posttest, survey, and interview were administered. Based on the results, the pretest scores are statistically different from the posttest scores. It means the interventions via Facebook and Messenger groups help students cope with modular distance learning challenges. The interventions done by the teacher were effective based on the computed effect size so that the students able to learn mathematics competencies despite having in the comfort of their houses. As a result, students better understand the mathematics lessons and enjoy learning at their own pace.

Applying an Individual Word-Problem Intervention to a Small-Group Setting: A Pilot Study’s Evidence of Improved Word-Problem Performance for Students Experiencing Mathematics Difficulty

The purpose of this pilot study was to determine whether positive results from a word-problem intervention implemented one-to-one contributed to similar outcomes when implemented in small groups of three to four students. Third-grade students experiencing mathematics difficulty (N = 76) were randomly assigned to word-problem intervention (n = 56) or business-as-usual comparison (n = 20). Intervention occurred for 13 weeks, 3 times per week, 30 min per session. Multilevel models revealed the intervention condition significantly outperformed the BaU on a proximal word-problem outcome, corroborating results from our prior individual intervention. When comparing student performance in the individual versus small-group intervention, findings suggest students received added benefit from the individual intervention. The word-problem intervention successfully translated to a small-group setting, which holds important implications for educators working with students in supplemental, targeted, or Tier 2 mathematics intervention settings.

Intensifying Instruction to Address Treatment Resistance to Early Mathematics Interventions

Intensifying Instruction to Address Treatment Resistance to Early Mathematics Interventions

A Systematic Review of Mathematics Interventions for Middle‐School Students Experiencing Mathematics Difficulty

AbstractIn this systematic review, we explored mathematics interventions for middle school (Grades 6, 7, and 8) implemented with students who experienced difficulty in the area of mathematics, including students with an identified learning disability in mathematics. A total of 72 single‐subject and group comparison studies met inclusion criteria, with 59 studies demonstrating positive effects on student‐level mathematics outcomes. The majority of mathematics interventions focused on foundational, prealgebraic skills (e.g., operations and problem solving) related to algebraic reasoning. To understand the landscape of effective mathematics interventions and inform instruction within mathematics intervention, we identified six instructional components used with regularity within the effective studies. These components included explicit instruction, multiple representations, problem‐solving instruction, mathematical language, mnemonics, and graphic organizers.