COMMUNITY SUPPORTED MATH INTERVENTION 1 

Evaluation of a Math Tutoring Program Implemented with Community Support: A Systematic 

Replication & Extension 
 

 

 

 

 

COMMUNITY SUPPORTED MATH INTERVENTION 2 

Abstract 

The current study evaluated the impact of a math tutoring program delivered in 20 schools to 

students in 4th through 8th grades by community members over one academic year. Students 

were randomly assigned to treatment and control groups. Linear and logistic regression were 

used to evaluate group differences in post-test scores and the probability of attaining the spring 

proficiency benchmark on each of three outcomes. Intent-to-treat analyses revealed higher 

achievement scores and a higher probability of meeting the end-of-year proficiency benchmark 

for the fact fluency and computer-adaptive tests among students assigned to treatment. No 

statistically significant effects were observed on a state proficiency test. Implications for 

significant and null findings are discussed within the context of intervention content and 

delivery. 

Keywords: mathematics intervention, tutoring, community-supports, RCT, tier 2 
 

 

 

 

 

 

COMMUNITY SUPPORTED MATH INTERVENTION 3 

Evaluation of a Math Tutoring Program Implemented with Community Support: 

A Systematic Replication & Extension 

According to the most recent National Assessment of Educational Progress (NCES, 

2017), only 40% of fourth graders and 34% of eighth graders in the United States are proficient 

in mathematics and performance declined for students at or below the 25th percentile. 

These data suggest that a large number of students experience difficulties with mathematics in 

school. As many as 17% of school-age children experience substantial mathematics difficulties, 

7% of children will be diagnosed as having a mathematics learning disability, and an additional 

5% to 10% experience persistent low achievement (Berch & Mazzocco, 2007; Geary et al., 2007; 

Shalev et al., 2005). Collectively, students that struggle with mathematics in school face several 

negative outcomes. These students are not as likely as their peers to succeed in or even complete 

high school and they lack the quantitative literacy necessary for a variety of careers (Claessens & 

Engel, 2013; Parsons & Bynner, 1997). Unfortunately, mathematics difficulties begin as early as 

pre-school and, without intervention, persist through intermediate grades (e.g., Duncan et al., 

2007; Morgan et al., 2011). Such realities for math education in the United States illustrate the 

need to provide students who are at-risk for mathematics failure with supplemental school-based 

supports. 

Evidence-based Math Intervention 

Schools are increasingly turning to educational frameworks that focus on prevention and 

early intervention (Jimerson, Burns, & VanDerHeyden, 2016), because such frameworks 

represent a promising and systematic approach to address the needs of more students with 

academic difficulties sooner than traditional frameworks of service-delivery. Often referred to as 

response to intervention or multi-tiered systems of support, such frameworks are comprehensive 
 

 

 

 

 

COMMUNITY SUPPORTED MATH INTERVENTION 4 

approaches to improving educational systems. They prescribe high-quality, research-based core 

instructional practices for all students; intervention and progress monitoring for students who are 

low-achieving; and individualized, high-intensity support for students requiring special education 

(Burns, Jimerson, VanDerHeyden, & Deno, 2016). Data are used within these frameworks to 

inform decisions and supplemental interventions are provided to students who demonstrate risk 

for academic failure based on screening measures or minimal progress in response to core 

instruction (Gersten et al., 2009). Although every state has an initiative to promote and expand 

these frameworks (Jimerson, Burns, & VanDerHeyden, 2016), only about 59% of elementary 

schools and 48% of middle schools report implementation in math (Spectrum K-12, AASA, 

CASE, NASDSE, 2010). 

One of the most significant implementation barriers for such frameworks is the lack of 

intervention resources (Long et al., 2016; Spectrum K-12, AASA, CASE, NASDSE, 2010), 

which is particularly problematic for math. Intervention delivery for prevention and early 

intervention frameworks has been conceptualized as either an individualized problem-solving 

approach or a standard protocol approach, with standard protocol approaches having advantages 

both logistically and evidentiary for at-risk students not yet identified for special education 

(Fuchs & Vaughn, 2012). For math, there are a limited number of evidence-based standard 

protocol mathematics interventions designed to target foundational mathematics skills for 

students beyond third grade. According to What Works Clearinghouse (WWC, 2016), when 

filtering by grade and either supplemental or small group intervention, there are only two 

interventions that have received a rating of potentially positive or positive that provide math 

intervention for students in grades four through eight. Other evidence summaries report a similar 

state for math interventions. The National Center on Intensive Intervention includes 10 
 

 

 

 

 

 

COMMUNITY SUPPORTED MATH INTERVENTION 5 

individual or small group intervention programs or strategies directed toward the elementary or 

middle school levels as offering convincing or partially convincing evidence of effectiveness. 

Further, although there are many peer-refereed articles published on mathematics intervention 

outcomes, in 51.5% of these studies researchers, rather than school professionals, were the 

implementers, suggesting that these interventions might be in the development phase and 

therefore not widely available for practitioner use (DeFouw, Codding, Collier-Meek, & Gould, 

2018). Finally, the majority of these intervention studies addressed whole number knowledge 

and skills appropriate for students within the early elementary school grades. Interventions with 

strong evidence for improving rational number skills for older students are comparatively rare. 

Even when evidence-based standard protocol interventions are available, teachers report 

that finding time and resources to integrate the intervention within existing routines is a 

substantial barrier, and almost 89% indicated a need for additional implementation support 

(Long et al., 2016). These data correspond with other surveys suggesting that time is a powerful 

constraint for school personnel when it comes to providing students with additional academic 

supports outside of core instruction (e.g., Bosworth et al., 1999; Bambara et al., 2009; Durlak & 

Dupre, 2008). Unfortunately the persistence of these barriers impacts the integrity with which 

prevention and early intervention frameworks are successful. In one national evaluation of the 

frameworks, nearly 40% of schools neglected to administer intervention supports as intended 

resulting in an overall failure to observe positive effects of the framework (Balu et al., 2015; 

Fuchs & Fuchs, 2017). 

Encouragingly, recent research shows that K-5 validated math intervention programs 

delivered by either teachers or paraprofessionals produced the strong effects, particularly for low 

achieving students and students from low income backgrounds (Pelligrini, Lake, Inns, & Slavin, 
 

 

 

 

 

 

 

COMMUNITY SUPPORTED MATH INTERVENTION 6 

2018). This suggests that licensed professionals may not be required to deliver evidence-based 

intervention programs in order to produce positive outcomes for students. The status of the 

research base suggests more research is necessary to identify math interventions with evidence 

for effectiveness in typical school settings, as opposed to efficacy evidence produced with strong 

involvement of research teams, particularly for intermediate elementary and middle school 

students. Further, given the high numbers of students that need additional mathematics supports 

and the limited time and support presently available in schools to provide students with 

evidence-based interventions, it also appears necessary to identify feasible delivery mechanisms 

for such interventions. Community-based tutoring might be a reasonable alternative. 

Community-supported Tutoring 

The idea of using community-based volunteers or non-educators to provide substantive 

academic supports in schools is neither novel nor without evidence. Most schools have access to 

multiple community- or business-based volunteers, and these volunteers can make a significant 

positive impact on student learning outcomes (Ritter, Barnett, Denny, & Albin, 2009; Slavin, 

Lake, Davis, & Madden, 2011). Moreover, some community organizations offer fully-developed 

interventions that align with educational best practices and closely resemble standard protocol 

interventions (Jacob, Armstrong, Bowden, & Pan, 2016; Markovitz et al., 2014). The potential 

for such programs is particularly promising in the context of the logistical and knowledge 

barriers many schools face when attempting to deliver educational interventions. Early 

intervention is often a paradigm-shift in educational settings that rely on conventional “wait-tofail” models for educational service delivery (Fuchs & Fuchs, 2006). The experience and 

knowledge required for effective resource reallocation can be a considerable challenge (Noell & 

Gansle, 2016). Moreover, few practitioners appear adequately familiar with the concepts and 
 

 

 

 

 

 

 

 

 

COMMUNITY SUPPORTED MATH INTERVENTION 7 

practices necessary for successful intervention within prevention and early intervention 

frameworks (Vujnovic et al., 2014). These knowledge barriers are exacerbated by basic resource 

demands for providing evidence-based interventions, which in math require schools to provide 

each struggling student up to 90 minutes of intervention support per week (Gersten et al., 2009). 

Community-based organizations help address these barriers by providing schools with 

resources, time, and expertise. Such organizations also have the advantage of being able to 

specialize their topic area. In math, this translates to knowledge about evidence-based math 

interventions and technically adequate and instructionally informative data-based decisionmaking practices, as well as being able to generate resources necessary for implementation. 

Community-based organizations that develop specialized expertise in an educational area can 

form inter-organizational partnerships with schools that facilitate effective implementation of 

math interventions (Aarons, Hulburt, & Horwitz, 2011). In other academic domains, such as 

reading, inter-organizational partnerships using community support have also proven to be costeffective ways to deliver intervention supports within the school context (Hollands et al., 2016). 

Math Corps 

The ecology of student development includes macro-level structures that influence 

student outcomes (Bronfrenner, 1987). Within this broader ecology, public policy is inherently 

designed to influence issues of the broader public interest, and the federal AmeriCorps program 

is an example of a policy initiative that translates to increased local community-based resources 

for implementing educational interventions. The AmeriCorps program helps generate nearly 

seven billion hours of community service annually (Corporation for National and Community 

Service, 2018), and a portion of that time has been allocated to educational programs that exist to 

deliver standard protocol interventions for struggling students. The Math Corps program is an 
 

 

 

 

 

COMMUNITY SUPPORTED MATH INTERVENTION 8 

intervention program for students in grades four through eight that uses AmeriCorps members to 

deliver math intervention support to struggling students. It provides schools with materials for 

implementing evidence-based interventions, recruits and trains tutors and school staff, and 

engages in ongoing coaching (see Method section for details). 

Previously, a wait-list randomized control trial of the Math Corps program was 

conducted with 550 students in grades four through eight who were at-risk for mathematics 

failure over the course of one semester (AUTHOR, 2018). Results on a computer-adaptive, 

comprehensive measure of mathematics performance indicated that students receiving Math 

Corps tutoring outperformed the control group, yielding a small positive effect size (d = .17). 

Effect sizes were larger (d = .24) when the designated optimal dose of the intervention was 

achieved. This study represents initial research in the area of mathematics regarding the promise 

of community-supported delivery of evidence-based interventions. However, the prior study did 

not examine outcomes on other measures of interest, such as math skills more proximal to the 

intervention focus or distal outcomes of policy importance like state math tests. Given that 

mathematics is hierarchical and builds upon core foundational skills, analysis of the extent to 

which other math skills improve would be useful. Previous research has indicated that the 

amount of exposure to and the number of opportunities to practice any given mathematics 

subskill can be substantial before mastery occurs across both basic (Burns, Ysseldyke, Nelson, & 

Kaive, 2015; Stickney et al., 2012) and complex (Nelson, Parker, & Van Norman., 2018) tasks. 

In particular whole number fact fluency appears to be a central underpinning of overall 

mathematics proficiency, permitting greater access to higher level content including more 

complex whole and rational number operations and understanding (Bailey, Seigler, & Geary, 

2014; Jordan, Resnick, Rodrigues, Hansen, & Dyson, 2017). Such considerations reflect 
 

 

 

 

COMMUNITY SUPPORTED MATH INTERVENTION 9 

increasingly important aspects of replication studies for intervention research (Travers, Cook, 

Therrien, & Coyne, 2016). 

Purpose 

The purpose of the present study was to evaluate the impact of Math Corps as a 

supplemental math intervention delivered by AmeriCorps members across the 2017-2018 

academic year. The study was guided by the overall goal of evaluating the extent to which endof-year math achievement differed for students randomly identified to be served by the program 

or not served by the program. There were three primary math outcomes of interest arranged from 

most proximal to most distal based on the program’s theory of change: basic fact fluency, broadbased math achievement as measured by a computer adaptive test, and end-of-year performance 

on the state test. The following research questions framed the study: (1) to what extent do 

students assigned to Math Corps demonstrate higher test scores on a basic fact fluency measure 

relative to students assigned to a control group ? (2) to what extent do students assigned to Math 

Corps demonstrate higher posttest scores on a computer adaptive measure of math achievement 

relative to students assigned to a control group? (3) to what extent do students assigned to Math 

Corps demonstrate higher posttest scores on the end-of-year state achievement test relative to 

students assigned to a control group? In addition to addressing the above research questions by 

comparing the performance of students in both groups on each measure, we also compared the 

performance of students in each group to criterion-based levels of proficiency for each measure. 

Method 

Participants 
 

 

 

 

 

 

 

COMMUNITY SUPPORTED MATH INTERVENTION 10 

Twenty schools across the state of Minnesota participated, including six middle schools, 

one intermediate school, and 13 elementary schools. Nine schools in the sample were suburban 

(45%), five were urban (25%), and six were rural (30%). All schools that received Math Corps 

services in the 2017-2018 school year and served enough struggling students to support a 

treatment and control group were invited to participate, resulting in the 20 schools that 

volunteered. All students meeting eligibility criteria within those schools were included in the 

randomization process (detailed below). The sample student distribution across elementary and 

middle schools was generally commensurate with the overall distribution of students served by 

Math Corps. There were slightly more female students relative to male students in the sample. 

Across both groups, a majority of students were White (53.4% and 52.9%) followed by Black 

(24.5% and 23.3%), Hispanic (10.6% and 12%), Asian (8.9% and 6.9%), American Indian (1.2% 

and 0.5%), and Other (0.7% and 2.3%). 

Intervention Overview 

The instructional focus of Math Corps is on improving whole and rational number 

understanding. It uses evidence-based intervention strategies that target specific skills (e.g., 

adding fractions with like and unlike denominators) required to effectively work with whole and 

rational numbers. In the present study, Math Corps was implemented by full-time AmeriCorps 

members who operated as tutors embedded within each school. Math Corps tutors had no 

preexisting professional preparation in evidence-based standard protocol interventions for math. 

Each tutor attended a three-day training session in late summer, two additional days of training in 

the fall (October and November), and received monthly coaching sessions from a school-based 

(internal) coach and a program (master) coach, both of whom were fully-trained in the Math 

Corps program model. 
 

 

 

 

 

COMMUNITY SUPPORTED MATH INTERVENTION 11 

Tutors were observed monthly between September and March or April by internal and/or 

master coaches, resulting in six observations by the internal coaches and five from the master 

coaches. In September tutors were observed administering the STAR assessment but during the 

remaining observations tutors were observed delivering specified lessons. During all 

observations, coaches used a standardized observation form in which implementation fidelity 

was assessed using a checklist with 19 items aligned with various components of the 

intervention. In addition, coaches assigned an engagement quality rating and instructional 

delivery quality rating to tutors after each observation. Both ratings were scaled from one to five 

with five representing the highest quality rating. In the present study, tutors tended to implement 

the intervention as intended with average adherence equal to 91%, delivery quality equal to 4.32 

(SD = 0.75), and engagement quality equal to 4.44 (SD = 0.56). 

Math Corps content. Math Corps delivers intervention in the form of instructional 

lessons, which varied across grade levels. In fourth grade 22 lessons were delivered across 

approximately 17 weeks, in 5th grade 25 lessons were delivered across 21 weeks, in 6th grade 31 

lessons were delivered across 21 weeks, in 7th grade 27 lessons were delivered across 22 weeks, 

and in 8th grade 20 lessons were delivered across 18 week. Lessons used one of four intervention 

components to improve targeted subskills required to work effectively with whole and rational 

numbers. The first component included conceptual-based instruction using the Concrete, 

Representational, Abstract (CRA) approach (e.g., Witzel et al., 2003). The second component 

focused on procedural accuracy and includes direct instruction followed by supervised practice 

with Cover, Copy, and Compare (CCC; Skinner, Turco, Beatty, & Rasavage, 1989). The third 

component used Cognitive Strategy Instruction to support development of the skill for word 

problem solving (Montague, 1997). Intervention components were applied in a sequence for each 
 

 

 

 

 

 

COMMUNITY SUPPORTED MATH INTERVENTION 12 

skill. For example, students first received CRA to better develop the conceptual basis for adding 

fractions with dissimilar denominators; then received CCC to become efficient at accurately 

applying the corresponding computational strategies; and then received CSI to be able to solve 

word problems involving fractions with unlike denominators. Students were required to 

demonstrate mastery—defined as 85% correct on a brief informal assessment of intervention 

content—before advancing among the intervention components. Tutors also delivered short 

duration fact fluency practice using Explicit Timing (e.g. Van Houten & Thompson, 1976) at the 

end of intervention sessions. 

All intervention support was provided during the school day to groups of two students, 

consistent with standard Math Corps program procedures. Student pairs were determined by 

performance on a brief pretest as well as the scheduling constraints of the school. Tutors worked 

with school staff to provide student pairs either three 30-min or two 45-min intervention sessions 

per week. Across the academic year, and accounting for short weeks and interventionist or 

student absences, the average min per week for students was equal to 69.33 (SD = 18.93) over an 

average of 21.89 weeks (SD = 10.34). This dosage information relates only to students that were 

assigned to receive Math Corps and actually received the intervention. An additional 59 students 

did not have any treatment time recorded, but were included in analyses. 

Control. Students assigned to the control group in the present study did not receive Math 

Corps interventions but were allowed to receive other school-based services. Surveys were sent 

to school staff two times during the study to determine the frequency and type of other 

mathematics services throughout the school year. Approximately 43% of control group students 

received more than 30 minutes per week of supplemental support for at least one month during 

the year. The nature of additional support varied between sites, but most frequently took the form 
 

 

 

 

 

COMMUNITY SUPPORTED MATH INTERVENTION 13 

of supplemental small-group pre-teaching/re-teaching activities with a teacher or teaching 

assistant; no evidence-based practices were reported. 

Randomization 

Students who are eligible for Math Corps must (1) score below proficiency on the state 

test from the previous year and (2) score below a grade-level benchmark on the fall 

administration of STAR Math (Renaissance Learning, 2018). In the current study, a total of 924 

students were identified as eligible for Math Corps at the 20 participating schools. Of those 

students, 750 were randomly assigned to treatment (n = 484) and control (n = 266) groups. An 

additional 174 students were assigned to a waitlist group to ensure interventionist caseloads 

would remain full if treatment students moved or withdrew consent from participating. Data for 

waitlist students were not retained for the current study. Following randomization, 37 students 

(34 from treatment and three from control) withdrew consent and four students (three from 

treatment and one from control) were determined ineligible due to receipt of special education 

math services. Demographic data separated by group assignment are displayed in Table 1. 

A series of analyses were conducted on the resulting sample to establish baseline 

equivalence. Chi-square analyses revealed no statistically significant differences between groups 

on the distribution of grade, gender, or ethnicity. Further, a paired t-test examining state test 

scores from the previous year revealed no significant differences between groups. However, tests 

for baseline equivalence conducted on STAR Math pretest scores revealed a significant 

difference between groups (t(693) = 2.79, p = .005). The mean fall STAR Math score for 

students in the treatment group was equal to 646.77 (SD = 102.91) and the mean score for 

students in the control group was equal to 667.70 (SD = 83.79). An analysis of the distribution of 
 

 

 

 

COMMUNITY SUPPORTED MATH INTERVENTION 14 

fall STAR Math scores revealed a disproportionate number of students in the treatment group 

with scores far below the mean in each grade level. 

After examining potential reasons for this difference, it was discovered that although 

assignment to treatment condition was random, aspects of the randomization process resulted in 

disproportionate assignment across conditions in which more students with very low STAR Math 

scores were assigned to the treatment condition. This occurred because the evaluation team 

established two blocks of students by median score within a school, rank-ordered the scores 

lowest-to-greatest within block, assigned random numbers to each case within the block, reordered lowest-to-greatest, and then made condition assignments starting with treatment. For 

this process, a single fixed ‘seed order’ of random numbers was assigned across all blocks that—

by chance—had more lower values earlier in the seed order, which meant more students with 

low STAR Math scores were assigned to treatment. A number of potential solutions were 

explored to address this issue, including re-randomization and propensity score weighting; 

however, the most effective approach included trimming potential outliers from the data file (i.e, 

STAR pre-test scores outside of two standard deviations from the mean). This resulted in the 

exclusion of 31 students originally assigned to the treatment group and one student originally 

assigned to the control group. After trimming the data file for potential outliers, there were no 

significant differences in baseline STAR scores between groups. The resulting file for analysis 

included 416 students assigned to Math Corps and 259 students assigned to the comparison 

group (N = 675). 

Measures 

Minnesota Comprehensive Assessment (MCA). Students completed the MCA in math 

at the end of the academic year. The MCAs are the statewide accountability tests used by the 
 

 

 

COMMUNITY SUPPORTED MATH INTERVENTION 15 

state of Minnesota. Beginning in the third grade and extending to eighth grade, students in 

Minnesota complete the MCA in math. The MCA is a standards-based assessment—the items on 

the test are constructed to align with the curricular standards for the state of Minnesota. Thus, 

students’ scores on the MCA are interpreted as the degree to which students have mastered grade

level content. MCA scores for math and reading range from 0-100, with scores of 50 and above 

signifying proficiency. The MCA-III has adequate evidence for internal consistency (r = .78 to 

.95; Minnesota Department of Education, 2017). Because the MCA is a standards-based 

assessment, validity evidence is primarily derived from content-related evidence (e.g., test 

blueprint aligned with standards, expert item writers) and construct-related evidence (e.g., interscale correlations, high functioning items). In the present study, MCA testing was conducted by 

trained test officials at school sites in accordance with state guidelines. 

STAR Math. Students completed STAR Math at the beginning and end of the academic 

year. STAR Math is a computer-adaptive test (CAT) with scaled scores ranging from 0-1400. 

The vendor reported split-half reliability estimate for grades 1-12 is equal to .94 (Renaissance 

Learning, 2013). In a recent evaluation, concurrent validity correlations between STAR Math 

and the Minnesota state test were equal to .74 (grade three) and .73 (grade five). Predictive 

validity coefficients (fall to spring) were equal to .60 (grade three) and .75 (grade five). The 

publisher for STAR Math provides spring benchmarks for performance that were derived using 

diagnostic accuracy analyses using MCA proficiency as the criterion. Those benchmarks are 

used to identify students as on-track for proficiency or below proficiency. In the present study, 

we used those benchmarks as the metric of interest in the proficiency analyses. Pre-test STAR 

Math data were obtained by tutors, prior to randomization, in accordance with program 

guidelines for screening—those data are used to identify students for Math Corps support. Post-
 

 

 

 

 

COMMUNITY SUPPORTED MATH INTERVENTION 16 

test STAR Math data were obtained by research assistants who were blind to group assignment; 

with one exception. One school district regularly used STAR Math as part of their universal 

screening procedures and therefore collected these data outside of the Math Corps procedures. In 

that case, school officials oversaw post-test data collection using their standard school-wide 

procedures. 

Math fact fluency. Students completed a timed (1-min) test of fact fluency in the fall 

(administered by Math Corps tutors) and spring (administered by research assistants blind to 

group assignment) of the academic year. Parallel eighty-item mixed computation measures 

(Foegen, 2000; Foegen & Deno, 2001) were used to assess fluency with basic facts. The fact 

fluency probes required students to solve single-digit combinations (0-9) in addition, subtraction, 

multiplication, and division. All probes were scored as the number of problems correct in one 

min. Math Corps uses a fluency proficiency goal of 30 problems correct in one min, which 

approximates the rate at which previous research using the fact fluency probes provides 

sufficient reliability evidence (internal consistency r = .91-.92; test-retest r = .85; alternate forms 

r = .82). In the present study, the correlation between students’ fall fact fluency scores and STAR

Math was .57, which is generally consistent with studies examining the relationship between 

basic computation skills and broad measures of achievement (Foegen, 2000; Jitendra, Sczesniak, 

& Deatline-Buchman, 2005; Thurber, Shinn, & Smolkowski, 2002). In the present study, fact 

fluency data were obtained immediately before STAR Math testing. 

Analysis Procedures 

Missing data. Missing data differed by posttest outcome. The largest instances of 

missing data were observed for pre (12%) and post (13%) fact fluency tests. Approximately 10% 

of cases were missing MCA data. Lower levels of missing data were observed for STAR Math at 
 

 

COMMUNITY SUPPORTED MATH INTERVENTION 17 

pre-test (2%) and post-test (8%). There were no differences in missing data across group 

assignment for STAR Math or MCA data; however, students assigned to the control group were 

more likely to have missing fact fluency data at post-test (22%) relative to students assigned to 

receive Math Corps (7%). This was largely due to a small number of sites that opted to oversee 

STAR Math testing, but failed to uniformly administer the fact fluency test. Regardless it is not 

likely that data were missing completely at random (MCAR) and instead were missing based on 

factors known in the data set (MAR). To account for missing data in the analytic models we used 

multiple imputation to simulate 40 additional data sets with estimated values for missing data 

(Graham, Olchowski, & Gilreath, 2007; Rubin, 2004). The multiple imputation procedure was 

run using SPSS (v. 25) and included multivariate normal regression paired with an iterative 

Markov chain Monte Carlo simulation process. To facilitate accurate estimation, imputation 

models included a series of predictors including STAR Math data, MCA data, fact fluency data, 

gender, ethnicity, grade level, site, and group assignment. Estimates from each simulated data set 

were pooled to provide a single estimate. Results from analytic models using the pooled 

estimates were compared to identical models in which listwise deletion was used. No differences 

were observed in the statistical significance or magnitude of effects between models that used 

imputed data and those that used listwise deletion. 

Analytic models. As discussed, the three outcomes of interest in the present study were 

evaluated on continuous and dichotomous (criterion-referenced) scales. Thus, both linear 

regression and logistic regression models were used to evaluate the impact of Math Corps on 

student achievement. In addition to a dichotomous variable indicating treatment assignment, 

each model included students’ pre-intervention scores and dichotomous variables for gender and 

race. Linear regression models included a series of dichotomous variables for each site to adjust 
 

 

 

COMMUNITY SUPPORTED MATH INTERVENTION 18 

for site-based clustering. The variance observed between sites was non-significant when 

evaluating the log-odds of meeting proficiency on any of three outcomes. All analyses followed 

an intent-to-treat framework in which all students were included in the analysis according to their 

original group assignment regardless of their experiences during the school year. 

Results 

Descriptive 

Means and standard deviations for outcomes across time and groups are displayed in 

Table 2. On average, students in both groups tended to answer between 16 and 17 problems 

correct on the timed fact fluency pre-test. All students increased their fact fluency scores across 

the academic year; however, the average number of problems answered correctly at post-test was 

slightly larger for students assigned to receive Math Corps (M = 23.29) compared to students in 

the control group (M = 19.46). Likewise, a larger percentage of students assigned to Math Corps 

met the proficiency criterion for fact fluency (23%) relative to students in the control group 

(11%). 

As discussed, students assigned to Math Corps had slightly lower STAR Math scores 

(approximately 10 points) at pre-test relative to students in the control group. At post-test, the 

average score for students in Math Corps was 11.22 scaled score points higher than the average 

score for students in the control group. Similar to the fact fluency results, a greater percentage of 

students assigned to Math Corps met the end-of-year benchmark for STAR Math (27%) relative 

to students in the control group (15%). There were small descriptive differences between groups 

on the Minnesota state test in math—the average MCA score for students assigned to Math 

Corps was 0.72 points higher than control students. Likewise, the percentage of students meeting 

proficiency criteria on the MCA was 4% higher for Math Corp students. 
 

 

 

 

 

 

COMMUNITY SUPPORTED MATH INTERVENTION 19 

Linear Regression 

The first set of research questions was related to student outcomes on a continuous scale. 

That is, to what degree did student scores on the fact fluency test, STAR Math test, and state test 

differ as a function of group assignment? Results from the three linear regression models of 

interest are displayed in Table 3. All models controlled for students’ prior achievement (mean 

centered), grade level, gender, race, and school. The referent for grade was always fourth grade 

and the referent for race was always White. 

In regard to fact fluency, statistically significant and positive associations with post-test 

fact fluency scores were observed for pre-test fact fluency scores (B = 0.69), sixth grade 

enrollment (B = 2.94), eighth grade enrollment (B = 3.21), and Asian students (B = 2.91). 

Assignment to Math Corps was associated with a statistically significant and positive effect on 

post-test fact fluency scores. Specifically, assignment to Math Corps was associated with a 3.16 

increase in the number of problems correct on the fact fluency post-test relative to students 

assigned to the control group (B = 0.16). 

When examining STAR Math scores, statistically significant and positive effects were 

observed for fifth through eighth grade. That is, students in later grades had significantly larger 

scores, which is generally consistent with the scaling of STAR Math. In addition, being a male 

student was associated with a 12.81 scaled score increase in post-test STAR Math scores. 

Assignment to Math Corps was associated with a statistically significant and positive impact on 

post-test scores equivalent to an advantage 15.78 scaled score points (B = 0.08). 

In regard to students’ state test scores, statistically significant and negative effects were

observed for all grades relative to fourth grade. In other words, students tended to score lower on 

the state test if they were in fifth (B = -5.54), sixth (B = -7.27), seventh (B = -7.77), or eighth 
 

 

COMMUNITY SUPPORTED MATH INTERVENTION 20 

grade (B = -7.41) relative to fourth grade. Black students were also associated with lower state 

test scores relative to White students (B = -2.75). Unlike the models examining fact fluency and 

STAR Math, group assignment was not a significant predictor of students’ MCA scores. 

Logistic Regression 

Each of the three outcomes of interest was also examined in dichotomous terms—

students either met (1) or did not meet (0) a predefined criterion of proficiency on each outcome 

measure. Results from the three logistic regression models of interest are displayed in Table 4. 

All effects are expressed as the log-odds of attaining proficiency. 

The observed results for fact fluency proficiency—defined as 30 problems correct in one 

min—were generally consistent with those observed for linear regression; however, the 

probability of meeting the proficiency criterion did not differ across grades. Thus, the only 

significant effects were observed for the fall fact fluency score and assignment condition. More 

specifically, an increase of one problem correct was associated with a log odds increase of 0.15 

and assignment to Math Corps was associated with a log odds increase of 1.00. To facilitate 

interpretation, log-odds can be converted to predicted probabilities. For example, the predicted 

probability of meeting the fact fluency proficiency criterion was approximately .05 among 

students in the control group and .12 among students in Math Corps. 

In regard to STAR Math, the log odds of meeting the grade-level spring benchmark 

significantly increased for every scaled score unit increase above the fall grade-level mean. 

Relative to fourth grade students, students in fifth (-0.72), seventh (-1.33), and eighth grade (-

0.97) had a lower log-odds of meeting the end-of-year benchmark for proficiency. For example, 

the predicted probability of success among fourth grade students assigned to the control group 

was 0.15, compared with .08 among fifth grade students, .05 among seventh grade students, and 
 

 

COMMUNITY SUPPORTED MATH INTERVENTION 21 

.07 among eighth grade students. The predicted probability of success for sixth grade students 

assigned to the control group was .18, which, based on the observed results using fourth grade as 

the referent, was significantly different from students in fifth, seventh, and eighth grade. The 

predicted probability of meeting the end-of-year benchmark was higher among students assigned 

to Math Corps. Among sixth grade students assigned to Math Corps, the predicted probability of 

success was .35, followed by fourth grade (P = .32), fifth grade (P = .18), eighth grade (P = .15), 

and seventh grade (P = .11). Thus, when examining STAR Math proficiency, assignment to 

Math Corps was associated with an increase in predicted probability of success between .17 and 

.06. 

When examining MCA proficiency (i.e., scores at or above 50), an increase of one fall 

STAR Math scaled score above the grade-level mean was associated with a small increase in the 

log-odds of meeting MCA proficiency (.01). Further, students in fifth grade had a lower log odds 

of meeting the MCA benchmark relative to fourth grade students. Black students also had a 

lower log odds of success relative to White students. For example, the predicted probability of a 

White fourth grade student with an average fall STAR Math score meeting MCA proficiency 

was equal to .21, which was higher than the predicted probability of a Black student with the 

same STAR Math score (P = .12). Similar to the linear regression results, the impact of group 

assignment on the probability of meeting the MCA benchmark was non-significant. 

Discussion 

In the present study we evaluated the impact of Math Corps, a community-supported 

supplemental math intervention program, on three outcomes aligned with the program’s 

instructional focus. All analyses adopted an intent-to-treat approach in which students were 

included in the analysis regardless of their exposure to Math Corps. Statistically significant and 
 

 

 

 

COMMUNITY SUPPORTED MATH INTERVENTION 22 

positive results were observed for Math Corps’ impact on the two more proximal outcomes of 

interest—fact fluency performance and STAR Math performance. Yet state test scores for 

students assigned to receive Math Corps were not statistically different from those of students 

not assigned to Math Corps. These effects are discussed in detail below. 

Math Corps and Student Math Achievement 

Fact Fluency. Of the three outcomes considered in the present study, fact fluency 

performance was most closely aligned with Math Corps support. That is, tutors were trained to 

deliver 3-5 min of explicit fact fluency support as part of each session. In the present study, 

assignment to Math Corps was associated with an unstandardized effect size of 3.16 problems. 

The effect of Math Corps on fact fluency scores is particularly notable when contextualized by 

the average growth rate of control students across the full year—3.09 problems. In other words, 

the effect size observed for Math Corps was larger than the average annual growth of control 

students in the present study. The impact of Math Corps on students’ fact fluency performance

was also evident when considering the proportion of students reaching the mastery criterion for 

fluency as Math Corps students were twice as likely to reach that benchmark by the end of the 

year. Yet it is also worth noting that an overwhelmingly large proportion of students across 

groups failed to correctly answer 30 or more fact fluency problems within one minute. This is 

relevant because automatic retrieval of basic math facts is generally considered to hold value for 

more complex math operations as well as a variety of tasks outside of school (Fuchs et al., 2014; 

Nelson, Parker, & Zaslofsky, 2016). The relatively low levels of automaticity among the students 

included in the present study generally conforms to findings that students who struggle on gradelevel math assessments may also struggle with foundational skills (Jordan et al. 2013; Vukovic et 

al., 2014). 
 

 

COMMUNITY SUPPORTED MATH INTERVENTION 23 

STAR Math. STAR Math covers a full range of grade-level standards, many of which 

fall outside the scope of the Math Corps intervention which focuses on whole and rational 

number understanding. The underlying assumption of Math Corps is that advancing whole and 

rational number skills will confer benefits to the those skills, but also other skills that rely on 

whole and rational number understanding (e.g., geometry; Gersten et al., 2009; NMAP, 2008). 

Although STAR Math assesses a broad range of content, the test is vertically scaled and grade 

independent, making it a useful broad-based measure of student growth. 

In the present study, the impact of assignment to Math Corps was approximately 16 

scaled score points. The expected weekly growth among students in the sample (based on initial 

scaled score and grade level) ranged from .80 to 3.30 with an average of 1.76 (SD = .60). Thus, 

one interpretation of the unstandardized effect of group assignment is to consider the amount of 

additional growth added by the intervention. By this interpretation, the average student who 

received Math Corps demonstrated post-test scores that were the equivalent of 4.85 to 20 weeks 

(M = 9.09 weeks) of additional math growth compared to the average student who did not 

receive Math Corps. The impact on STAR Math scores also translated into an increased 

probability of meeting the end-of-year benchmark among students receiving Math Corps support. 

MCA. Unlike the results observed for fact fluency and STAR Math, the impact on 

students’ state test scores—including the rate at which students met proficiency criteria—was not 

statistically significant. Performance on the state test was the most distal outcome of interest in 

the present study. The Minnesota state test assesses a limited range of content—items are created 

to align with specific grade-level standards and do not explicitly address content that falls above 

or below those standards. Thus, improvements in understanding of precursor concepts (e.g., 

fraction arithmetic among eighth grade students) may be assumed and not directly tested. The 
 

 

 

 

 

COMMUNITY SUPPORTED MATH INTERVENTION 24 

nature of state test construction is relevant because many students who qualify for supplemental 

support are far behind grade-level expectations. For those students, relative to computer adaptive 

tests such as STAR Math, the state test may not be sensitive to gains in math skills outside the 

grade-level standards. As such, the state test is not designed to capture student growth, but 

proficiency on grade-level standards at the conclusion of the academic year (Shapiro & 

Gebhardt, 2012). In the present study, Math Corps resulted in significant improvement in math 

achievement as measured by STAR Math, but not the state test. Thus, although students 

improved their overall math achievement as a result of Math Corps, that improvement was not 

sufficient to produce differences on the state test. Intervention studies do not often evaluate 

impact on distal standardized measures, and thus the current findings are generally consistent 

with other findings that greater effects are typically observed for measures more closely aligned 

to treatment (DeFouw et al., 2018; Gersten et al., 2009; Jitendra et al., 2018). 

As discussed, Math Corps is composed of a series of lessons for each grade level. Those 

lessons were created to align with state standards in the domain of numbers and operations, but 

they were not yoked to a single grade level so as to permit students to receive needed 

intervention on precursor skills. For example, the current sixth grade lesson sequence includes 

31 lessons. Yet only 10 of those lessons are directly aligned with sixth grade content, 9 of which 

are the last lessons in the entire sequence. This progression was by design insofar as many 

students who qualify for Math Corps have deficits on skills that precede grade level content, and 

math learning is generally characterized by progressive skill development that assumes precursor 

skill levels are established for more complex levels to be obtained (NMAP, 2008). Yet because 

Math Corps provides support for precursor skills and has a mastery learning orientation, many 
 

 

 

 

 

 

 

 

 

COMMUNITY SUPPORTED MATH INTERVENTION 25 

students did not receive intervention on grade-level skills. For example, data from the program 

showed that only 10% of sixth grade students reached grade-level content. 

Implications for Community-Supported Educational Intervention 

Overall, these findings add to the literature for community-supported math interventions 

in several ways. First, these findings support the potential for inter-organizational partnerships 

to implement evidence-based interventions in math (Aarons et al., 2011). Math Corps provided 

all training, data collection systems, and materials, but both Math Corps and schools worked to 

identify the community-based AmeriCorps member to serve as an interventionist, acclimate them 

to the local school environment, and ensure they received sufficient coaching support for 

success. The mutual contribution of resources occurred across common phases of 

implementation and serves as a model for how inter-organizational partnerships could feasibly 

implement evidence-based practices in public service settings (Aarons et al., 2011). 

These findings also extend the overall empirical support for service-based educational 

interventions that employ tutoring. When service-based interventions utilize tutoring, they 

employ a form of educational instruction for struggling or at-risk students that has increasingly 

robust evidence. Previous research syntheses identified tutoring as among the most effective 

strategies for reading (Slavin et al. 2011), and updated syntheses have found similar results (Inns, 

Lake, Pelligrini, & Slavin, 2018). The current findings contribute to a smaller but growing 

evidence-base for the promise of tutoring for math outcomes (Pelligrini et al., 2018). Similarly, 

although sufficient research has been conducted on volunteer-based literacy tutoring programs to 

conduct meta-analytic research with positive findings for effects on reading and writing 

outcomes (Ritter et al., 2009), additional individual studies are necessary in math. Relatedly, 

research for community-supported math interventions needs to be conducted with different age 
 

 

 

COMMUNITY SUPPORTED MATH INTERVENTION 26 

and grade levels, including a focus on understanding the role and potential for community-based 

interventions to support early math outcomes (Mazzocco & Myers, 2003). In addition to research 

on the direct effects of community-based interventions on math outcomes, research is necessary 

to better understand the variables and conditions of effective inter-organizational partnerships for 

math interventions (Aarons et al., 2011). Such research holds potential to support efficacious 

implementation as well as identify ways to sustain implementation in a cost-effective manner 

long-term (e.g., Hollands et al., 2016). 

Limitations 

There are a number of limitations to consider when interpreting results from the present 

study. First, the present evaluation was of a specific math intervention program. It is unclear if 

similar programs or subcomponents of Math Corps would produce comparable results. Second, it 

is common for math researchers to include a direct assessment of the set of skills targeted during 

intervention (e.g., Jitendra et al., 2015; Poncy, Skinner, & Jaspers, 2007; Witzel et al., 2003), yet 

no such measure was included in the current study. Math Corps provides support for a wide 

range of skills that vary across grades. Although we might have created an assessment directly 

aligned with the intervention program for each grade, the procedures for test creation were 

considered to be too burdensome and not of long-term relevance to either educator or 

policymaker stakeholders interested on grade-level performance. Further, the use of STAR Math 

and the state test is likely a more rigorous approach to estimating intervention effects than an 

assessment designed to assess the exact content included for intervention. 

Finally, it is important to note the issue that the randomization procedures resulted in 

baseline differences in STAR Math scores between students assigned to Math Corps and students 

assigned to the control group. In addition to our final approach to analysis, which included 
 

 

 

 

COMMUNITY SUPPORTED MATH INTERVENTION 27 

trimming cases outside of two standard deviations of the mean, we conducted a series of 

sensitivity tests that included making no modifications to the analytic model, propensity score 

weighting, and fitting a model with no adjustment for pre-test scores (i.e., placing students 

assigned to Math Corps at a disadvantage). These sensitivity analyses showed no substantive 

changes to statistical significance and the corresponding effects and thus we opted to retain the 

trimmed model which eliminated baseline differences. 

Conclusion 

Improved math outcomes are needed for more students to experience math success and 

the accompanying the educational and life benefits. The current study suggests Math Corps can 

improve foundational math skills necessary for working with whole and rational numbers, but 

additional research is needed to extend those benefits to societally-endorsed outcomes like state 

proficiency tests. Nonetheless, this study adds to the general research base for both evidencebased math interventions and the delivery of such interventions via community-based resources. 
 

 

 

 

 

 

COMMUNITY SUPPORTED MATH INTERVENTION 28 

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COMMUNITY SUPPORTED MATH INTERVENTION 36 

Table 1 

Student Demographics across Conditions 

Math Corps Control 

Demographic Category (n = 416) (n = 259) 

Grade 

Fourth 17.5% 17.0% 

Fifth 21.9% 20.5% 

Sixth 29.6% 30.1% 

Seventh 19.3% 19.3% 

Eighth 13.1% 13.1% 

Gender 

Male 48.8% 44.0% 

Ethnicity 

White 53.4% 52.9% 

African American 24.5% 23.2% 

Hispanic 10.6% 12.0% 

Asian 8.9% 6.9% 

American Indian 1.2% 0.5% 

Other/Unknown 0.7% 2.3% 
 

 

 

 

COMMUNITY SUPPORTED MATH INTERVENTION 37 

Table 2. 

Descriptive Outcomes by Assessment Period and Condition 

Fact Fluency STAR Math State Test 

M SD 

Met 

Benchmark 

M SD 

Met 

Benchmark 

M SD 

Met 

Benchmark 

Pre 

Control 

Math Corps 

16.38 

16.99 

7.91 

0.45 

-

-

669.26 

659.47 

81.51 

89.71 

-

-

-

-

-

-

-

-

Post 

Control 

Math Corps 

19.46 

23.29 

8.58 

8.31 

11% 

23% 

716.87 

728.09 

80.43 

90.58 

15% 

27% 

41.47 

42.19 

8.33 

8.73 

15% 

19% 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

COMMUNITY SUPPORTED MATH INTERVENTION 38 

Table 3 

Linear Regression Results across Outcomes 

Fact Fluency STAR Math MCA 

Variable B SE B SE B SE 

Intercept 15.88 ** 1.71 577.76 ** 15.48 48.05 ** 2.09 

Prior Achievement 0.69 ** 0.05 0.54 ** 0.06 0.05 ** 0.01 

Grade Level 

Fifth 0.82 1.02 63.90 ** 8.68 -5.54 ** 1.24 

Sixth 2.94 * 1.18 134.19 ** 9.74 -7.27 ** 1.64 

Seventh 1.16 1.51 144.30 ** 12.32 -7.77 ** 2.02 

Eighth 3.21 * 1.50 153.00 ** 12.11 -7.41 ** 2.14 

Gender 

Male -0.06 0.57 12.81 * 5.21 0.10 0.64 

Race 

American Indian 0.09 3.43 4.04 32.29 -0.88 4.00 

Asian 2.91 * 1.20 15.12 10.76 -1.18 1.30 

Black 0.40 0.81 -11.56 7.41 -2.75 ** 0.91 

Latino -0.44 0.98 -5.02 8.96 -0.83 1.08 

Other 1.39 2.88 -4.01 24.34 -2.38 3.00 

Group Assignment 

Math Corps 3.16 ** 0.62 15.78 ** 5.56 0.90 0.67 

* p < .05, ** p < .01 

Note: Sample sizes for each model equal to those reported in Table 2. Prior Achievement = grade-mean centered fall STAR Math score or mean centered fall fact 

fluency score. Across all three outcomes, model included dichotomous predictors for each of the 20 sites included in the study to adjust for clustering. Fixed 

effects for sites are not displayed in the interest of clarity. 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

COMMUNITY SUPPORTED MATH INTERVENTION 39 

Table 4 

Logistic Regression Results across Outcomes 

Variable 

Intercept 

Prior Achievement 

Grade Level 

Fifth 

Sixth 

Seventh 

Eighth 

Gender 

Male 

Race 

American Indian 

Asian 

Black 

Latino 

Other 

Group Assignment 

Math Corps 

Fact Fluency 

Log-Odds SE 

-3.00 ** 0.67 

0.15 ** 0.02 

0.95 0.67 

0.57 0.65 

-0.09 0.74 

0.85 0.70 

-0.04 0.25 

-18.87 19108.30 

0.24 0.44 

-0.34 0.30 

-0.49 0.46 

0.51 0.98 

1.00 ** 0.29 

STAR Math 

Log-Odds SE 

-1.72 ** 0.31 

0.02 ** 0.00 

-0.72 * 0.30 

0.15 0.30 

-1.33 ** 0.43 

-0.97 * 0.40 

0.40 0.21 

-19.65 19153.08 

0.59 0.34 

-0.38 0.28 

-0.47 0.38 

-16.77 11598.66 

0.92 ** 0.24 

MCA 

Log-Odds SE 

-1.36 0.31 

0.01 ** 0.00 

-0.84 * 0.38 

-0.27 0.32 

-0.34 0.38 

0.40 0.35 

-0.06 0.22 

-19.52 19588.77 

0.05 0.38 

-0.68 * 0.29 

-0.62 0.39 

-17.43 12557.15 

0.34 0.23 

* p < .05, ** p < .01 

Note: Large standard errors are present for “American Indian” and “Other” designations under race due to small samples and no occurrences of students meeting 

benchmark criteria.