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1

Running head: MATH INTERVENTIONS

EDUC 841:

A Review of Literature on Middle School Math Interventions

Anne Brawand

George Mason University

MATH INTERVENTIONS 2

Abstract

Eleven investigations pertaining to math interventions used in the middle school setting

for students with and without disabilities were part of an integrative review utilizing meta-

analytic research integration techniques. All of these studies appeared in eight different journals

published from 2001-2010. Effect sizes were calculated on all study outcomes. Regarding

disability type in relationship to setting, the effects of math interventions for students with

learning disabilities (LD) were most successful when they took place in a room in the school by

the researcher. The highest effect size was evident in the 7th grade for math interventions having

greater than 30 sessions, and lasting more than 76 minutes for each session. Additionally,

interventions with less than 20 students in the multiple baseline comparison had a strong effect.

Enhanced Anchored Instruction (EAI) and math fluency were the most effective interventions.

However, the Explicit Inquiry Routine (EIR) intervention had the highest effect size for students

with LD. Additionally, math fluency was the most effective intervention for students with mild

intellectual disabilities and self-regulation strategy in math had the highest effect size for

students without disabilities.

Keywords: math, intervention, students with disabilities, middle school


A Review of Literature on Middle School Math Interventions

Mathematics is essential for daily living needs that require such skills as budgeting, time

management, and cooking, as well as for educational and occupational opportunities which

reflect an increasingly technological society that necessitates problem solving and reasoning

skills (Maccini, Mulcahy, & Wilson, 2007). The No Child Left Behind Act of 2001 (NCLB)

frameworks a national initiative to improve the link between elementary and secondary

education and high-stakes testing. In response to this legislation, the National Council of

Teachers of Mathematics (NCTM, 2000) has called for standards that range beyond skills of

basic procedural competency. According to Miller and Hudson (2007), it’s important to provide

balanced instruction across mathematics standards and to address conceptual, procedural, and

declarative knowledge within a comprehensive math curriculum. General strategies for

addressing achievement problems in secondary mathematics include organizing explicit teaching

of important concepts, providing numerous examples of new concepts that address the overall

range of the concepts, direct teaching of relevant cognitive routines, and systematically teaching

of prioritized objectives (Montague & Jitendra, 2007).

Many students with learning disabilities may exhibit difficulties in the area of memory

and general strategy use, literacy and communication, specific processes and strategies

associated with math problems, and low motivation and affect (Bryant & Bryant, 2008). A

number of students may also have difficulty with the English language and communication

aspects of mathematics (Lang & Pagliaro, 2007). Rao and Mallow (2009) expressed concern

that a lack of knowledge of basic math facts is a common impediment to learning higher-level

math for all students including those with disabilities and that students with this deficiency in

knowledge may learn neither math computation nor higher order mathematics. Additionally,


students who are taught math skills until they achieve fluency tend to maintain their skills (Axtell

et al., 2009).

In 2007, Maccini et al. extended a previous review by Maccini and Hughes (1997) on

math interventions for secondary students with LD in order to determine the nature and focus of

current math interventions that were effective for assisting secondary students with LD. Maccini

et al. found that many practices produced significant gains for secondary students with a learning

disability in math including: mnemonic strategy instruction, graduated instructional approach,

cognitive strategy instruction involving planning, schema-based instruction, and contextualized

videodisc instruction. They also concluded that the nature and focus of many math interventions

at the secondary level tended to favor remedial interventions, neglecting to address middle

school and high school curriculum standards. However, compared to Maccini and Hughes

(1997); the percentage of studies targeting secondary math content increased from 35% to 57%.

Finally, Maccini et al. (2007) also suggested that future math interventions include more detailed

descriptions of participants, include larger sample sizes, and examine effects of math

interventions in the general education classroom.

A preliminary literature search was conducted to obtain a count of math intervention

studies that appear to be elementary vs. secondary, which yielded 73% elementary level and only

27% at the secondary level. The purpose of this paper is to review research involving effective

math interventions for students with and without disabilities in the middle school setting.

Specific questions to explore include: 1) Are math interventions more effective when participants

are identified as LD, mild intellectual disability, or non-disabled, in a specific setting with a

specific intervener? 2) Do math interventions work best for middle school students for a certain

comparison type (experimental vs. control, A vs. B, multiple baseline) and sample size? 3) How


do design and group delivery size of the intervention influence the outcome? and 4) What impact

do study validity and quality have on the strength of the intervention?

Method

Literature Search Procedures

The database PsychInfo was searched from the years 2001 to the present using the

following descriptors as keywords: math, intervention, students with disabilities, middle school.

Due to a limited number of articles on this topic, the search was expanded to include middle

school students with and without disabilities in the last 10 years. Names of prominent scholars

in this topic were also entered in the same data bases to identify any additional sources. These

authors included Bottge and Jitendra. In addition, an ancestry search was conducted using the

articles identified from the databases.

Criteria for Inclusion and Exclusion

These search procedures identified 36 articles. Articles were examined for relevancy.

Specifically, articles had to be peer-reviewed intervention research studies in math including

middle school students with or without disabilities. Sufficient data had to be provided to

compute effect sizes for group experimental research or percent of non-overlapping data (PND)

for single subject design studies. Studies that measured progress of students, analyzed

perceptions of teachers/students, evaluated a math curriculum school or district wide, or involved

multiple subject areas were excluded.

Final Sample

This resulted in a pool of 11 articles published from 2001-2010 in the following journals:

Remedial and Special Education, Exceptional Children, Journal of Special Education, Learning


Disabilities Research and Practice, Learning Disabilities Quarterly, Education and Training in

Developmental Disabilities, and Psychology in the Schools; that met all inclusion criteria.

Coding Instrument

Sixty-six variables were coded. Basic variable areas included general article identifying

information such as author, year of publication, and name of journal. Information on the

participating sample was also coded. This section included sample size, demographic data on the

sample such as gender, race, age, and grade level. Examples of variables included on the coding

sheet are: type of comparison for effect size, total sample size, grade level, type of disability,

number of sessions, number of minutes per session, type of dependent measures, type of design,

and study quality. For instance, studies coded as “1,” had random assignment of students for

type of design. Coding conventions or rules were developed as coding progressed to assist with

consistent decision making and coding. For example, weighted averages were always computed

when coding sample sizes by grade, age, number of sessions, and minutes per session. So

participants in grades 7 and 8 would have a grade level identified as 7.5. Also for sessions

lasting 20-30 minutes the amount of time recorded for that variable was 25 minutes.

Results

All data from the coding sheets were entered into the Statistical Package for the Social

Sciences (SPSS) computer program for analyses. The overall characteristics of the data set are

presented first. Then, effect sizes and additional study characteristics are presented followed by

overall quality of the studies.

Overall Characteristics of the Data Set

These studies resulted in a sample of 462 middle school students from sixth, seventh, and

eighth grade; with a mean grade level of 7.1. The mean age for the participants sample was


12.97, with a mean IQ of 79.04. In terms of students with disabilities as displayed in Figure 1,

the majority of studies included students with LD (N = 6), and the remaining studies consisted of

students with mild intellectual disabilities (N = 2), and non-disabled students (N = 3). As

displayed in Figure 2, almost half of the studies were published in 2009 (N = 5). In addition, 4

of the 11 studies selected were published in Education and Training In Developmental

Disabilities, and The Journal of Special Education had the next highest amount of studies

included (N = 3). The comparison groups included in the math intervention studies selected

were almost evenly spread across the 3 types of as displayed in Figure 3: experimental vs.

control (N = 3), A vs. B (N = 4), and multiple baseline (N = 4). The range for number of

participants included in the selected of studies was from 2 to 128 students. Thirty–six percent of

the studies included a sample size with less than 20 students, and 36% of the studies had between

forty and sixty students for sample size. Nine out of the 11 studies did not specify

socioeconomic status, and the population density identified was rural, as well as location of the

Midwest yielded the highest amount of studies (N = 4 for both population density, and

geographic location). However, 2 of the 11 studies didn’t specify geographic region and 3

studies did not report population density.

The intervention categories identified in the studies consist of math fluency; the Explicit

Inquiry Routine (EIR); math technology; Enhanced Anchored Instruction (EAI); self-regulated

training in math; problem solving; and concrete, representational, abstract (CRA). The EIR

intervention integrates teaching practices from both general and special education to engage

students in an inquiry process across concrete, representational, and abstract modes to develop an

understanding of the concept (Schuermann, Deshler, & Schumaker, 2009). The math technology

intervention used was a FLY Pentop Computer by Leapfrog (Bouck et. al, 2009), and EAI refers


to the presentation of problems in a multimedia format and then application of what students

learn in a hands-on format (Bottge et al, 2007).

Word problems were the most prominent dependent measure (N = 4), and algebra

concepts were the least (N = 1). The other types of dependent variables were math achievement

(N = 3), and fractions (N = 3). The special education classroom was utilized the most for the

middle school math interventions studied (N = 5), and the general education teacher delivered

the intervention in the majority of studies (N = 6). The group delivery size ranged from 1 to 4

students, with a mean total of 2.73 students. The mean number of experimental sessions is 30.2,

with a mean amount of 51 minutes for each session. Finally, the overall effect size for the

selection of studies included is significant (ES = .86), as well as an overall percent of non-

overlapping data (PND) result of 84.3%.

Effect Sizes by Disability, Setting and Teacher

As displayed in Table 1, math interventions in the experimental condition were most

effective when they took place in a room in the school by the researcher for students with LD

(ES = 2.32, PND = 93%). Students with mild intellectual disabilities also yielded strong results

when the intervention was implemented by the researcher in a separate room in the school (PND

= 100%). Students with LD who received the treatment in a regular class, with a regular teacher,

were close behind these outcomes, ES = 1.27. Finally, students without disabilities also had high

effect sizes after treatment in a regular class with the regular teacher conducting the intervention,

ES = .61.

Effect Sizes by Type of Comparison and Sample Size

Math interventions implemented utilizing a multiple baseline comparison had the

strongest effect sizes (ES = 2.32, PND = 84%). The comparison of A vs. B also yielded high


effects, ES = .69, followed by experimental vs. control, ES = .55. A breakdown analysis to study

sample size in relation to these results had the highest effect size for the smallest sample size

range of less than 20 students in the multiple baseline comparison (ES = 2.32). The sample size

values of 2 to 128 students were recoded to reflect these ranges of effect sizes in Table 2.

Additionally, a sample size of 21 to 40 students for the experimental vs. control comparison type

had the next highest effect (ES = 1.2), followed by a sample size of more than 41 students in the

A vs. B comparison type (ES = .68).

Effect Sizes by Disability and Intervention

Overall, EAI was the most effective intervention (ES = 2.32, PND = 93%), followed by

math fluency (ES = 1.2, PND = 100%). Table 3 displays a breakdown analysis to detail the most

effective math interventions by disability type. The EIR intervention had the highest effect size

for students with LD (ES = 2.32, PND = 93%). Math fluency was the most effective

intervention for students with mild intellectual disabilities (PND = 100%), and self-regulation

strategy in math had the highest effect size for students without disabilities, ES = .51.

Effects by Grade, Intensity and Duration

Grade 7 had the highest effect sizes for math interventions overall, ES = 1.04, and PND =

97%. Further analysis was conducted including intensity and duration to attempt to explain this

data. The only 6th grade study did not include number of minutes so only 7th grade effects by

duration and intensity are reported in Table 4. The highest effect size is evident in the 7th grade

for math interventions having greater than 30 sessions, and lasting more than 76 minutes for each

session, ES = 2.16.


Effect sizes by Design and Group Delivery Size

There was not a significant effect between the types of design implemented in the studies,

as they were both identified as having high significance. The random assignment design resulted

in an effect size of .76, and non-random/relevant matching design yielded and effect size equal to

.76. Effect sizes for group delivery size were pretty evenly spread, with small groups of 2 to 8

students having the most significant effect, ES = 1.16. Interventions implemented individually

resulted in a strong PND of 91%, followed by whole class group delivery size, ES = .76.

Effect Sizes by Validity and Quality of Study

Overall study quality was coded in two ways by validity and quality. If the study

included randomization it was classified as having “high” validity if 2 or more classes to each

condition it was of “medium” validity, and “low” validity was identified as just 1 class per

condition. A quality coding rubric was also used to rate the overall quality of the study in

relation to 9 key components consisting of: participant/setting descriptions, ability to be

replicated, random assignment, detailed intervention procedure, appropriate design for research

questions, technique used for data analysis, fidelity of implementation, effect sizes given, and

reliability measured (see Appendix). Studies that included all 9 of these aforementioned

components were coded as “high” quality, at least 6 components were “medium” quality, and at

least 3 components were identified as “low” quality. Studies with high validity/random

assignment and high quality had the highest effect, ES = 1.2. Studies with medium validity and

medium quality had the next strongest effect, ES = 1.09. Finally low validity and low quality

studies yielded an effect size of .51.


Summary and Conclusions

A meta-analysis of 11 experimental studies revealed that effect sizes vary for the math

interventions for middle school students with and without disabilities according to specific

variables and areas being measured. As previously mentioned, Maccini et al. (2007) suggested

that math interventions include more detailed descriptions of participants, larger sample sizes,

and examine the effects of math interventions in the general education classroom. It seems that

the majority of studies reviewed adhered to these suggestions as they were able to be coded so

effect sizes could be compared. Regarding disability type in relationship to setting, the effects of

math interventions for students with LD were most successful when they took place in a room in

the school by the researcher. This finding is important because a high percentage of middle

school students with LD are included in co-taught environments, so they may be more successful

working on certain skills in a smaller environment. An additional finding relative to sample size

was that less than 20 students in the multiple baseline comparison had the highest effect size.

So, although in a smaller environment, one-on-one instruction for a math intervention is

preferred.

EAI and math fluency were the most effective interventions. However, the EIR

intervention had the highest effect size for students with LD. This shift to interventions that

measure algebra concepts, fractions and problem solving is of significance because a recent

review by Maccini et al. (2007) concluded that many math interventions at the secondary level

were focused on remedial support, and neglected to address middle school and high school

curriculum standards. Additionally, math fluency was the most effective intervention for

students with mild intellectual disabilities and self-regulation strategy in math had the highest

effect size for students without disabilities. This finding can be attributed to instructional setting


in that math fluency interventions tend to be delivered individually or in a smaller environment

such as a self-contained classroom, and self-regulation is a strategy that can be practiced with a

whole class. It’s necessary to know the math skills that individual students need to develop and

how these individual students may be more successful with certain math interventions according

to the setting utilized. Another factor relative to setting is the duration and time of the

intervention. Highest effects were also evident in 7th grade for math interventions having greater

than 30 sessions, and lasting more than 76 minutes for each session.

Finally, studies with high validity/random assignment and high quality had the highest

effect, and studies with medium validity and medium quality had the next strongest effect. This

verifies that studies that follow quality indicators have a higher success rate. In conclusion,

interventions for students with similar disabilities in small groups have proven to be effective;

however, to generalize that finding to implementations in classroom teaching isn’t always

realistic in today’s larger inclusive settings. Teachers need to do their best to differentiate by

student learning styles or disability characteristics and employ small groups often, especially for

the presentation of new concepts.


References

Axtell, P. K., McCallum, R. S., Bell, S. M., & Poncy, B. (2009). Developing math automaticity

using a classwide fluency building procedure for middle school students: A preliminary

study. Psychology in the Schools, 46, 526-538. doi: 10.1002/pits.20395

Bryant, B. R., & Bryant, D. P. (2008). Introduction to the special series: Mathematics and

learning disabilities. Learning Disability Quarterly, 31, 3-10.

http://www.highbeam.com/doc/1G1-176203759.html

Bottge, B. A., Heinrichs, M., Chan, S., & Serlin, R. C. (2001). Anchoring adoloscents

understanding of math concepts in rich problem-solving environments. Remedial and

Special Education, 22, 299-314. doi: 10.1177/074193250102200505

Bottge, B. A., Heinrichs, M., Mehta, Z. D., & Hung, Y. (2002). Weighing the benefits of

anchored math instruction for students with disabilties in general education classes. The

Journal of Special Education, 35, 186-200.

Bottge, B. A., Rueda, E., Serlin, R. C., Hung, Y., & Kwon, J. M. (2007). Shrinking

achievement differences with anchored math problems: challenges and possibilties. The

Journal of Special Education, 41, 31-49. doi: 10.1177/00224669070410010301

Bottge, B. A., Stephens, A. C., Rueda, E., Laroque, P. T., & Grant, T. S. (2010). Anchoring

problem-solving and computation instruction in context-rich learning environments.

Exceptional Children, 76, 417-437.

Bouck, E. C., Bassette, L., Taber-Doughty, T., Flanagan, S. F., & Szwed, K. (2009). Pentop

computers as tools for teaching multiplication to students with mild intellectual

disabilties. Education and Training in Developmental Disabilties, 44, 367-380.


Butler, F. M., Miller, S. P., Crehan, K., Babbitt, B., & Pierce, T. (2003). Fraction instruction for

students with mathematics disabilties: comparing two teaching sequences. Learning

disabilties Research & Practice, 18, 99-111. doi: 10.1111/1540-5826.00066

Jitendra, A., DiPipi, C. M., Perron-Jones, N. (2002). An exploratory of schema-based word-

problem-solving instruction of middle school students with learning disabilities: An

emphasis on conceptual and procedural understanding. The Journal of Special

Education, 36, 23-38. doi: 10.1177/00224669020360010301

Lang, H. & Pagliaro, C. (2007). Factors predicting recall of mathematics terms by deaf

students: Implications for teaching. Journal of Deaf Studies and Deaf Education, 12,

449-460. doi: 10.1093/deafed/enm021

Maccini, P., Mulcahy, C. A. & Wilson, M. G. (2007). A follow-up of mathematics

interventions for secondary students with learning disabilities. Learning Disabilities

Research and Practice, 22, 58-74. doi: 10.1111/j.1540-5826.2007.00231.x

Miller, S. P., & Hudson, P. J. (2007). Using evidence-based practices to build mathematics

competence related to conceptual, procedural, and declarative knowledge. Learning

Disabilities Research and Practice, 22, 47-57.

doi: 10.1111/j.1540-5826.2007.00230.x

Montague, M. & Jitendra, A. (2007). Teaching mathematics to middle school students with

learning difficulties. New York: Guiliford.

National Council of Teachers of Mathematics. (2000). Principles and standards for school

mathematics. Reston, VA. Author.

No Child Left Behind Act of 2001, 20 U.S.C. 70 § 6301 et seq. (2002).


Perels, F., Dignath, C., & Schmitz, B. (2009). Is it possible to improve mathematical

achievement by means of self-regulation startegies? Evaluation of an intervention in

regular math classes. European Journal of Psychology of Education, 24, 17-31. doi:

10.1007/BF03173472

Rao, S., & Mallow, L. (2009). Using simultaneous prompting procedure to promote recall of

multiplication facts by middle school students with cognitive impairment. Education and

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Table 1

Effects by Disability, Setting, and Intervener

Disability Area Setting Intervener ES PND

LD regular ed class Regular Ed Teacher 1.27

special ed class Special Ed Teacher .37

Regular Ed Teacher 82%

room in the school Researcher 2.32 93%

Mild Intellectual special ed class Special Ed Teacher 62%

room in the school Researcher 100%

Non-disabled regular ed class Regular Ed Teacher .61

special ed class Regular Ed Teacher .26


Table 2

Effect Sizes by Type of Comparison and Sample Size

Type of Comparison Sample Size ES

Exp. vs. Control 21-40 1.2

>40 .39

A vs. B >40 .69

Multiple Baseline <20 2.32


Table 3

Effect Sizes by Disability and Intervention

Disability Intervention ES PND

Learning Disabilities (LD) math fluency 1.2

EIR 2.32 93%

EAI .94

problem solving 82.3%

CRA .15

Mild Intellectual math fluency 100%

technology/math 62%

Non-disabled EAI .49

self-regulation/math .51


Table 4

Effects by Grade, Intensity and Duration

Grade # sessions # minutes ES PND

7 <15 <50 .13

15-30 51-75 1.07 93%

>30 <50 100%

>30 <76 2.16

8 <15 <50 82.3%

<15 51-75 .06


Table 5

Effect Sizes by Validity and Quality of Study

Validity Quality ES

PND

high (random assignment) high 1.2

medium .65

medium (2 or more classes) medium 1.09 88%

low .15

low (1 class per condition) high 62%

medium 100%

low .51


Figure 1


Figure 2


Figure 3


Appendix

Quality Index Coding and Rubric _____________

HIGH QUALITY Score of “1” (9 out of 9 components)

______ Operational definitions of participants/setting

______ Dependent variable allows for replication (observable)

______ Attempt at random participant assignment

______ Intervention clearly described (detailed procedure)

______ Design and technique match research questions

______ Data analysis technique appropriate

______ Fidelity of Implementation described

______ Effect size/PND calculated

______ Interobserver agreement/ reliability measured

MEDIUM QUALITY Score of “2” (6 of above components)

LOW QUALITY Score of “3” (3 of above components)

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mason.gmu.edumason.gmu.edu/~aeichorn//EDSE_841_Brawand_MSMat… · Web viewMany students with learning disabilities may exhibit difficulties in the area of memory and general strategy