Mathematics Intervention Research Articles

A scaled-up mathematics intervention in preschool classes

ABSTRACT We report on a scaled-up mathematics intervention in preschool classes (children age six) in Sweden. In the intervention, teachers at seven schools in four municipalities implemented the Thinking, Reasoning and Counting in Preschool Class (TRC) teacher guide in their teaching of 254 students. Results are compared to a previous randomized experimental small-scale intervention based on TRC showing a significant positive effect on students’ learning. Pre- and post-test scores for the present scaled-up intervention indicate even higher learning gains compared to the original small-scale intervention. Low-performing students were given extra tutoring time in the scaled-up intervention, but the learning gains for this group cannot be shown to be significantly higher compared to the treatment group in the small-scale study.

The impact of intervention modality on students' multiplication fact fluency

AbstractWhile an abundance of evidence‐based mathematics interventions are available to support students’ mathematics fluency, research suggests that they are not often implemented within schools. Moreover, national data suggests that most students in the United States are not meeting grade level expectations in mathematics. This underperformance coupled with limited implementation of evidence‐based practices emphasizes the need to provide schools with effective, efficient, and resource friendly interventions to support students’ mathematics achievement. The purpose of this study was to compare the effects of reciprocal peer tutoring, iPad delivered flashcards, and a combined intervention condition on the multiplication fluency of 72 third grade students enrolled in two public schools in the midwestern region of the United States using a randomized pretest–posttest design. Students received 10 min of intervention after their core instruction 4 days per week for 5 weeks. Results suggest that there were few differences between treatment groups on both proximal and distal measures. Moreover, all groups demonstrated significant growth from pre‐ to posttest on proximal measures. Assessment response rates across modalities and student engagement are discussed along with implications for research and practice.

Development of a Week-Long Mathematics Intervention for Incoming Chemistry Graduate Students.

A student-led mathematics bootcamp has been designed and implemented to help foster community building, improve confidence in mathematical skills, and provide mathematical resources for incoming physical chemistry doctoral students. The bootcamp is held immediately before the start of the first semester of graduate school and uses an active learning approach to review and practice undergraduate-level mathematics problems over 5 days in small student groups. This work includes the development and presentation of a new, publicly available mathematics curriculum for the bootcamp on select mathematics topics, including calculus, linear algebra, functions, differential equations, statistics, and coding in Python, aiming at improving students' confidence and learning experiences in graduate quantum mechanics and statistical physics courses. Surveys before and after the bootcamp showed an increase in students' confidence in problem-solving in key mathematical areas and social aspects of peer-led group learning. Qualitative and quantitative analyses demonstrate that the bootcamp reduced prior inequities in students' confidence metrics based on gender and mathematical background.

Reporting Quality of Single–Case Research Published in Learning Disabilities Journals

Single–case research designs are useful for learning disability researchers interested in refining novel interventions (e.g., new mathematics intervention) before scaling, small n populations (e.g., students with comorbid learning and emotional and behavioral disabilities), and testing unique conditions (e.g., remote locales). Much attention has been devoted to developing research quality standards, which is essential for replication and implementation fidelity; however, little is known about the reporting quality of single–case design studies. To gain insight into the quality of learning disability single–case research design study reporting, we analyzed 72 articles published between 2010 and 2021 in six learning disability–focused journals using the Single–Case Reporting Guideline In BEhavioral interventions (SCRIBE) standards. Findings suggest that reporting quality has remained stagnant, and none of the studies reviewed met all of the reporting standards. Alignment with standards ranged from 33% to 77%. Implications for researchers and practitioners are discussed.

The Effect of Addition and Subtraction Practice within a Word–Problem Intervention on Addition and Subtraction Outcomes

This study examined the influence of addition and subtraction practice embedded within a word–problem intervention for Grade 3 students experiencing word–problem difficulty. Students ( N = 448) were randomly assigned to one of two variants of a word–problem intervention or a business–as–usual comparison condition. Within the word–problem interventions, students participated in targeted addition and subtraction fact and computation practice for approximately 3 minutes of each 30–minute session across 47 intervention sessions, but also continually practiced addition and subtraction through word–problem solving. At posttest, students who participated in the intervention demonstrated improved single–digit addition and subtraction performance as well as improved double–digit addition and subtraction performance. At follow–up in Grade 4, persistence of effects was only identified for double–digit addition. Considering addition and subtraction are foundational to many other mathematics skills, addition and subtraction practice serves as an important component of mathematics intervention.

Magnitude representation of preschool children with autism spectrum condition.

The mathematical abilities of children with autism spectrum condition have been understudied. Magnitude representation (e.g. presenting the number of a collection of objects) is a fundamental numerical ability presented since early infancy and is correlated with children's later learning of formal mathematics. It remains unclear about whether children with autism spectrum condition differ from their peers without autism spectrum condition in precision of magnitude representations. This study compared preschool children with and without autism spectrum condition in their precision of magnitude representation with an approximate number comparison task, in which children compared two sets of dots without counting and chose the set with more dots. Children with autism spectrum condition exhibited the lower numerical comparison accuracy (i.e. the weaker magnitude representation) than their peers without autism spectrum condition. This difference existed even when multiple general cognitive abilities (working memory, inhibitory control, and nonverbal intelligence) and language abilities were statistically controlled. Moreover, the individual difference of the numerical comparison accuracy was larger in children with autism spectrum condition than without autism spectrum condition. These findings suggest that children with autism spectrum condition are at risk of weaker magnitude representation from an early age, emphasizing the need for specialized mathematics education or interventions to support their learning. In addition, the large variance in the precision of their magnitude representation suggests that individualized mathematics interventions are needed for children with autism spectrum condition.

Four Best Practices for Meta-Analysis: A Systematic Review of Methodological Rigor in Mathematics Interventions for Students With or at Risk of Disabilities

Meta-analysis methodology has evolved with the development of more robust statistical techniques; however, few reviews in special education have focused specifically on methodological rigor in meta-analyses. In this study, we examined 29 meta-analyses of mathematics interventions published from 2000 to 2022 to determine the extent to which researchers have applied four best practices in meta-analyses focused on mathematics interventions for students with disabilities. Our findings were (a) studies used three primary moderator techniques: meta-regression ( k = 10), subgroup analysis ( k = 8), analysis of variance ( k = 3), and both subgroup analysis and meta-regression ( k = 1); (b) only one study considered small sample corrections for hypothesis tests; (c) few researchers handled the dependence between multiple effect sizes ( k = 3); and (d) the funnel plot was commonly used to detect publication bias ( k = 8). Based on our findings, we make recommendations for methodological considerations for future meta-analyses.

The effects of a whole-class mathematics intervention on students’ fraction knowledge in primary school

ABSTRACT The intention of the study was to examine the effects of a fraction intervention in a whole-class environment. The intervention aimed to enhance students’ conceptual fraction knowledge, with a major focus on fraction magnitude understanding. This study included 120 fifth-grade students in standard classroom settings. Utilizing a cluster randomized controlled trial design, students were divided into either an intervention group (n = 64) or a control group (n = 56). Students in the intervention condition received a series of seven 35-minute lessons. Students in the control condition received “treatment as usual”. Both post-test and delayed post-test results revealed that students in the intervention group performed significantly better than those in the control group on fraction concepts, with a stronger effect in measurement aspects compared to part–whole aspects. The intervention group also outperformed the control group on fraction arithmetic on both post-tests, while no significant difference was observed on fraction word problems.

A multiple linear regression model of students’ performance in calculus in the new normal

The Philippines launched an educational reform in 2012, adding two years of senior high schools (SHS) with strands that aim to prepare students for work or pursue college degrees. The STEM strand was designed for those wishing to enroll in Science, Technology, Engineering, and Mathematics-related degree programs. This study investigates the performance in Calculus and the University admission examination of a random sample of 234 enrolled students for the First Semester of 2021-2022 at Caraga State University taking Differential Calculus. It tries to identify the socio-economic predictors of students' performance in Calculus. Results revealed that age, gender, SHS strand, enhancement program, and admission scores in English, Mathematics, and Abstract Reasoning correlate with students' Calculus performance. Also, the students who graduated from the SHS strand performed better in Calculus than those who did not. Nonetheless, Calculus student performance is regardless of the type of community, SHS type, and family monthly income. Among the socio-economic correlates, the SHS strand and calculus enhancement program are the main predictors of student performance in Calculus using multiple linear regression. Other significant predictors of Calculus student performance are the students' admission scores in Mathematics and Abstract Reasoning. This means that students who performed well in the Mathematics and Abstract Reasoning admission scores, along with SHS STEM strand enrolment and provision of the Calculus enhancement program, are indicators of students' performance in Calculus, implying the importance of mathematics interventions for the students' performance. Furthermore, an appropriate senior high school strand for college degree program preference is a necessary pre-requisite.

Incremental Rehearsal for Math Fact Fluency Improvement: An Implementation Guide

More research attention and implementation support are needed for mathematics intervention as student achievement in this area continues to fall below desirable levels. Incremental rehearsal is an intervention to help students build reading, vocabulary, and math fluency. Research supports the use of incremental rehearsal for improving math fact fluency. However, this intervention is more complicated than the traditional flashcard intervention. Therefore, an implementation guide is needed to increase its use with students who need to improve math fact fluency. This article will provide step-by-step instructions for implementing incremental rehearsal plus helpful implementation aids such as a chart demonstrating the proper presentation sequence and a treatment integrity checklist.

Examining heterogeneity of education intervention effects using quantile mixed models: a re-analysis of a cluster-randomized controlled trial of a fluency-based mathematics intervention

ABSTRACT Traditionally, cluster randomized controlled trials are analyzed with the average intervention effect of interest. However, in populations that contain higher degrees of heterogeneity or variation may differ across different values of a covariate, which may not be optimal. Within education and social science contexts, exploring the variation in magnitude of treatment effect at different points in the population can indicate where the intervention is most effective rather than assuming an average effect. Data from [Owen, K.L., et al., 2021. Implementation support improves outcomes of a fluency-based mathematics strategy: A cluster-randomized controlled trial. Journal of research on educational effectiveness, 14 (3), 523–542.] were reanalyzed using three modeling approaches: conditional mean-modeling reporting the average treatment effect using linear mixed models, and two quantile regression-based methods. Quantile regressions report the quantile treatment effects at different percentiles: 10th, 25th, 50th, 75th and 90th. For the Quantile approaches, a significant intervention effect in the median to upper quantiles was found and linear quantile mixed model showed improved fit over the other approaches. An improved picture of intervention effects may be apparent using quantile regression methods when analyzing cluster randomized trials that have heterogeneous error variance. In particular, the linear quantile mixed model shows improved model fit allowing a multilevel framework to include random effects. There is considerable scope to extend this framework to incorporate more complex RCT designs.

Extent and Effectiveness of Mathematics Intervention Strategies: Their Relationship to the Academic Performance of Students

Extent and Effectiveness of Mathematics Intervention Strategies: Their Relationship to the Academic Performance of Students

Exploring the Relationship Between Initial Mathematics Skill and a Sixth-Grade Fractions Intervention

This study explored whether initial skill moderated outcomes of Promoting Algebra Readiness, a Tier 2 sixth-grade mathematics intervention targeting conceptual and procedural knowledge of fractions. The study analyzed data from a quasi-experimental pilot study in which at-risk students ( N = 198) from Oregon middle schools were assigned to the treatment or control condition at the school level. Proximal and distal measures of math proficiency were collected in the fall (pretest) and spring (post-test). Analyses examined initial student achievement as a moderator of mathematics outcomes. Results indicated that intervention outcomes were not moderated by initial skill. Implications for tiered mathematics instruction and future mathematics intervention research are discussed.

A QUANTITATIVE ANALYSIS OF TEACHERS’ AND STUDENTS’ CONTENT KNOWLEDGE IN PHYSICS

This research examined the extent of content knowledge in Physics of teachers and students, as well as its correlation to the contributing factors that affects the extent of content knowledge in Physics among the teachers and students. Based on the computed data, the researcher found a significant relationship between the age, sex, undergraduate specialization, and years in service of teachers profile and the teachers self-evaluation on the extent of content knowledge in Physics. It was also revealed that the teachers self-evaluation on the extent of content knowledge in Physics and the following contributing factors: availability of resources, attendance to trainings and seminars, technological fluency, and research engagement in physics related studies. However, the Peer observation and coaching of Contributing Factors was not observed to have any significant relationship to the teachers self-evaluation on the extent of content knowledge in Physics. The level of students content knowledge in Physics as to test scores has a descriptive equivalent of Satisfactory and verbally interpreted as Average. Moreover, the availability of resources, exposure to practical work, study habits, and teacher factor of contributing factors was observed to have a significant relationship to the test scores based on the computed data. Based on the self-evaluation of the teachers and students, it is recommended to conduct targeted seminar or training in least learned competencies in Physics for various proficiency levels of teachers. There are a lot of trainings implemented on the teaching strategies but only none to few focuses on the mastery of subject content. There should be short-term workshops and trainings on the use of laboratory apparatus and equipment to improve teachers technological fluency. The education sector should also focus on provision of credible and comprehensive learning materials (online or printed) that are aligned with the national standard, appropriate to the level of knowledge of the learners, supplements student learning, and is easy to understand. To bridge learning gaps, it is also recommended to conduct remediation or intervention in Mathematics and English as it has an impact on conceptual understanding of Physics is recommended for students.

A Meta-Analysis and Quality Review of Mathematics Interventions Conducted in Informal Learning Environments with Caregivers and Children

The purposes of this study included conducting a meta-analysis and reviewing the study reporting quality of math interventions implemented in informal learning environments (e.g., the home) by children’s caregivers. This meta-analysis included 25 preschool to third-grade math interventions with 83 effect sizes that yielded a statistically significant summary effect (g = 0.26, 95% CI [0.07, 0.45) on children’s math achievement. Significant moderators of the treatment effect included the intensity of caregiver training and type of outcome measure. There were larger average effects for interventions with caregiver training that included follow-up support and for outcomes that were comprehensive early numeracy measures. Studies met 58.0% of reporting quality indicators, and analyses revealed that quality of reporting has improved in recent years. The results of this study offer several recommendations for researchers and practitioners, particularly given the growing evidence base of math interventions conducted in informal learning environments.

Development of Spatial Abilities of Preadolescents: What Works?

Creation in space and perception of spatial relations are important workplace skills that can be successfully developed in public education through the cooperation of art education, mathematics, and technology, the STEAM model that has been successfully employed in higher education. In a longitudinal school-based experiment, we enhanced the spatial skills of preadolescents through a STEAM-based educational programme. To design our methods of intervention in mathematics, visual arts, and information technology, we used the structure of spatial skills identified in previous studies. Developmental methods involved two- and three-dimensional visualisation tasks in real-life and virtual learning environments. We employed a pre- and post-hoc assessment design using a spatial ability task sequence standardised in Hungary that proved to be valid for assessing Slovak students as well. Authentic assessment tasks included real-life situations when visualisations of spatial relations were used for orientation and creation. Pre-test results showed significant differences between school classes: we identified high achievers and middle-to-low achievers. Our developmental programme was aimed at personalised talent development in the high-achieving classes and the general improvement of the performance of low achievers, raising insufficient pre-test results to an average post-test performance.

Measuring Success: Integrating Number Lines Into Measurement Instruction for Students With Learning Disabilities

Number lines can benefit students in learning an array of mathematical concepts. An area of mathematics where number lines are visibly underused is in teaching measurement concepts. For students in upper elementary grades, accurate measurements require the use of mathematical precision and coordination, including skills in fractions and decimals, operations, and magnitude. A robust knowledge of measurement holds significant value in students’ development of mathematical proficiency, particularly for students with learning disabilities in mathematics. Using number lines to teach and perform mathematical processes involving measurement can build fluency and conceptual understanding for all learners, including those with learning disabilities. This article demonstrates the versatility of integrating number lines into mathematical interventions involving measurement concepts for students with learning disabilities in mathematics. Measurement content discussed includes distance, time intervals, liquid volume, and mass. Scenarios with examples of how to apply number lines to each measurement form are described.

Messenger lectures and video lessons as mathematics interventions for modular distance learning

Providing self-learning modules and other printed materials under modular distance learning in the Philippines does not guarantee the acquisition of learning competencies, particularly in mathematics, wherein explanation and illustration of concepts, principles, and procedures demand the teacher’s clarification. To address this, Facebook Messenger was used as a platform to communicate with the students and deliver interventions like lectures through posting slides with voice clips and video lessons. This study aimed to establish the effectiveness of the said interventions for grade 7 mathematics using practical action research. Test material, questionnaire, and interview guide were the instruments used in collecting data validated by a master teacher and two head teachers in mathematics education. Quantitative data were analyzed using SPSS version 23 and qualitative data were analyzed using thematic analysis. Based on the findings, lectures and video lessons through Facebook Messenger helped students understand the mathematical concepts and procedures for solving mathematical problems. It means that the said interventions via Facebook Messenger were adequate for the students to cope with the learning challenges in mathematics brought by modular distance learning. However, the students suggested that sustain the interventions for a longer time.

App-based mathematical intervention for youth with intellectual disabilities: a randomised controlled trial

ABSTRACT The purpose of the study was to evaluate whether students with intellectual disabilities (ID) can improve their arithmetic skills by participating in an arithmetic intervention programme, theoretically founded on explicit instruction (EI) and administered via an application developed for tablet computers. The intervention study used a randomised controlled trial design (RCT) (n = 30, aged 10-16, 13 females) and lasted for up to 12 weeks. The results show that the intervention group significantly improved in arithmetic fact fluency compared to the controls and the effects remained six months after the intervention. The effects were larger for subtraction than for addition, and this difference remained six months later. These results suggest that mathematics applications based on explicit instruction can be an effective way of teaching arithmetic facts to youth with mild ID.

Ordinal models to analyze strategy sophistication: Evidence from a learning trajectory efficacy study

Investigators often rely on the proportion of correct responses in an assessment when describing the impact of early mathematics interventions on child outcomes. Here, we propose a shift in focus to the relative sophistication of problem-solving strategies and offer methodological guidance to researchers interested in working with strategies. We leverage data from a randomized teaching experiment with a kindergarten sample whose details are outlined in Clements et al. (2020). First, we describe our problem-solving strategy data, including how strategies were coded in ways that are amenable to analysis. Second, we explore what kinds of ordinal statistical models best fit the nature of arithmetic strategies, describe what each model implies about problem-solving behavior, and how to interpret model parameters. Third, we discuss the effect of “treatment”, operationalized as instruction aligned with an arithmetic Learning Trajectory (LT). We show that arithmetic strategy development is best described as a sequential stepwise process and that children who receive LT instruction use more sophisticated strategies at post-assessment, relative to their peers in a teach-to-target skill condition. We introduce latent strategy sophistication as an analogous metric to traditional Rasch factor scores and demonstrate a moderate correlation them (r = 0.58). Our work suggests strategy sophistication carries information that is unique from, but complimentary to traditional correctness-based Rasch scores, motivating its expanded use in intervention studies.