A Synthesis of Technology-Mediated Mathematics Interventions for Students With or at Risk for Mathematics Learning Disabilities

Abstract

With the increasing availability of technology and the emphasis on science, technology, engineering, and mathematics education, there is an urgent need to understand the impact of technology-mediated mathematics (TMM) interventions on student mathematics outcomes. The purpose of this study was to review studies on TMM interventions that target the mathematical outcomes of K–12 students with or at risk for mathematics learning disabilities (MLDs). A review of the literature revealed 19 studies (9 single-case and 10 group/quasi experimental designs) published between 2000 and 2016. Results suggest that TMM interventions had mainly positive results on the mathematics outcomes of students with or at risk for MLD. This study also examined the extent to which principles of explicit instruction were integrated in TMM interventions. While many of the interventions provided frequent practice opportunities with academic feedback, few complemented such practice opportunities with overt demonstrations and explanations of mathematical content. Implications for designing TMM interventions are discussed.

Keywords

technology-mediated intervention mathematics learning disabilities explicit instruction computer-assisted instruction

The expectation that all students will develop a robust and lasting understanding of mathematics has begun to shed light on technology-mediated mathematics (TMM) interventions as potentially important mechanisms for improving the mathematical outcomes of students with or at risk for mathematics learning disabilities (MLDs). Currently, there are major efforts to incorporate technology into the mathematics instruction delivered in U.S. classrooms (Atkins et al., 2010). Despite this increased interest, the empirical research behind TMM interventions for improving student mathematics outcomes is woefully thin (Dynarski et al., 2007). The capacity of TMM interventions to increase mathematics outcomes is likely dependent on the extent to which they include empirically validated principles of instruction. Comparable to the literature that has evaluated the instructional features of print-based mathematics interventions (Doabler, Fien, Nelson Walker, & Baker, 2012; Bryant et al., 2008), there is an urgent need to examine not only the level of evidentiary basis of TMM interventions but also the extent to which such interventions incorporate the instructional principles that have been found to positively benefit students with or at risk for MLD (Gersten et al., 2009). Collectively, these areas of research may have strong appeal, given the growing interest in bringing technology into the classroom (Atkins et al., 2010). To this end, the purpose of this study is to examine the overall effectiveness of TMM interventions in mathematics for students with or at risk for MLD and investigate the degree to which these interventions incorporate principles of explicit mathematics instruction (Gersten et al., 2009). Based on this focus, the next section reviews two relevant research literatures: explicit mathematics instruction and prior syntheses of TMM interventions for struggling learners.

Effective Mathematics Instruction for Students With or at Risk for MLD

Intervention research provides a preponderance of evidence that explicit mathematics instruction results in positive gains for students with or at risk for MLD (Gersten et al., 2009; Sood & Jitendra, 2013). Explicit mathematics instruction is defined as a systematic methodology for teaching critical mathematics concepts and skills to mastery. When teachers implement explicit mathematics instructional practices, they provide students with a structured opportunity to gain conceptual understanding and procedural fluency of mathematics. For example, to introduce new mathematical topics, teachers will deliver overt demonstrations and clear explanations. Teachers will also facilitate guided and independent student practice opportunities and provide academic feedback to extend learning opportunities and address potential misconceptions (Gersten et al., 2009).

While the value of explicit instruction in print-based interventions has been quantitatively demonstrated in recent meta-analyses (Baker, Gersten, & Lee, 2002; Gersten et al., 2009), the extent to which principles of this instructional approach are incorporated in TMM interventions is not as clear. However, given the capacity of TMM interventions to differentiate mathematics instruction for students with or at risk for MLD, it is reasonable to believe that such interventions can provide features of explicit instruction effectively and efficiently (Nelson, Fien, Doabler, & Clarke, 2016). Soundly designed TMM interventions, for example, can offer engaging and vivid demonstrations of mathematical concepts and skills. TMM interventions can also overtly articulate how to solve mathematical problems through virtual teacher think alouds. Moreover, TMM interventions can provide students with frequent, individualized opportunities to engage in interactive mathematical tasks and activities. Finally, TMM interventions that include features of explicit instruction can illuminate student misconceptions and provide teachers with real-time performance information to inform instructional decision-making. In the current study, therefore, we sought to determine the extent to which TMM interventions included one or more of the following principles of explicit mathematics instruction: (a) opportunities for students to receive overt demonstrations and explanations of targeted mathematical content, (b) opportunities for students to participate in guided and independent practice activities, and (c) opportunities for students to receive timely, specific academic feedback based on their mathematical performance.

Research on TMM Interventions for Struggling Learners

A review of the literature on technology and mathematics for students with or at risk for MLD shows that the topic of technology and mathematics instruction is not new. In fact, technology has been incorporated in mathematics instruction for students with and without MLD as far back as the 1970s (Woodward & Reith, 1997). In more recent years, major stakeholders have continued to shed light on the role of instructional technologies in students’ learning experiences. The National Education Technology Plan (Atkins et al., 2010), for example, charged the field of education to develop an actionable plan to embrace the potential of technology in today’s classrooms. The literature from the field of special education has also continuously promoted the potential of TMM interventions to improve the mathematics outcomes of students with or at risk for MLD (e.g., Allsopp, McHatton, & Farmer, 2010). Much of this has been summarized in six recent literature reviews, which we examine below and discuss how our current study expands from this existing literature base.

Maccini, Gagnon, and Hughes (2002) reviewed 10 studies conducted between 1970 and 2001. The studies included participants enrolled in Grades 6 through 12 identified with learning disabilities. The authors examined the treatment effects of various technology-based practices (i.e., computer-assisted instruction [CAI], multimedia software, videodisc instruction, hypertext and hypermedia software programs, and verbatim text recordings). Of the 10 studies, 9 were found to improve student mathematics outcomes. Specifically, increases in students’ fluency with facts and completion of word problems were noted. Effect sizes reported ranged for CAI (d = 1.2–15.6), multimedia software and videodisc instruction (d = 0.1–2.1), hypertext study guides (d = 4.3–6.1), hypermedia study guides (d = 0.6), and verbatim text recordings (d = 0.9).

Fitzgerald, Koury, and Mitchell (2008) conducted a review of the literature from 1996 to 2006 on TMM interventions in the areas of reading, writing, and mathematics. Participants included in 34 reviewed studies were students with high-incidence disabilities. In mathematics, they reviewed seven TMM intervention studies. In the area of mathematical problem-solving, Fitzgerald found mostly positive effects of TMM interventions. However, in the area of fact fluency, they reported inconclusive results, citing potential research design flaws in the studies reviewed. For the mathematical problem-solving interventions, findings suggested particular design features of the computer software, such as instructional scaffolding and feedback, as being beneficial to students’ mathematical learning.

More recently, Bouck and Flanagan (2009) conducted a meta-analysis of 17 studies (1996–2007) on the effects of assistive technology on students’ mathematics learning. Participants were K–12 students identified with high-incidence disabilities. The authors focused on two forms of technology relevant to the current study: CAI and anchored instruction. Results suggested that anchored instruction had the largest impact on students’ mathematics outcomes. Conversely, effects of CAI were mixed, with no significant impact on students’ subtraction and word problem-solving skills. Bouck and Flanagan did not report effect sizes.

In 2010, Li and Ma conducted a meta-analysis (1990–2006) of 46 studies focused on the effects of computer technology on the mathematics learning of K–12 students. Participants in the studies were students drawn from general education classrooms. Li and Ma reported that, on average, TMM interventions resulted in positive effects on mathematics achievement (d = 0.71). They also highlighted that TMM interventions had varied effects across grade levels and instructional settings. For instance, Li and Ma found computer technology had greater effects for students identified with special needs and students in the elementary grades. Results further suggested that the four types of technology targeted in the studies (i.e., tutorial, communication media, exploratory environment, and tools) led to similar effects on students’ mathematics achievement.

Weng, Maeda, and Bouck (2014) examined the effectiveness of cognitive skills–based CAI on learning outcomes for students with disabilities. The review included 21 U.S. and international studies conducted between 1975 and 2013. Participants were pre-K–12 students with disabilities, excluding students identified as deaf-blind, and with hearing impairments, visual impairments, and physical impairments. It is important to note that of the 21 studies, only 2 focused on mathematics skills. One study showed negative effects of CAI (d = −0.15) in favor of teacher-directed instruction for high school students with learning disabilities. The second study found moderate effects (d = 0.66) on students’ solving of multiplication facts.

Most recently, Cozad and Ricommini (2016) conducted a synthesis (1998–2016) of eight studies of digital-based interventions with a specific focus on fact fluency. The studies included elementary and middle school-aged participants with mathematics difficulties. Cozad and Ricommini reported that in all of the studies, CAI led to students’ improvement in fact fluency. While effect sizes were not reported, various components of CAI, including wait time, correction procedures, and feedback, were found to impact mathematics outcomes.

Purpose of the Study

Although these previous syntheses of TMM interventions represent significant contributions to the field (Bouck & Flanagan, 2009; Cozad & Ricommini, 2016; Fitzgerald, Koury, & Mitchell, 2008; Li & Ma, 2010; Maccini, Gagnon, & Hughes, 2002; Weng, Maeda, & Bouck, 2014), we extend this work in several ways. First, based on the increasing proliferation of technology use in today’s classrooms, we included more recently published studies. Second, the previously conducted syntheses included students with a wide range of disabilities. Because accumulating research suggests that a considerable number of U.S. students are struggling to reach adequate levels of mathematical proficiency (Kena et al., 2015), we targeted existing studies that focused specifically on TMM interventions designed for K–12 students with or at risk for MLD. Additionally, whereas the previous syntheses focused on specific areas of mathematical learning (e.g., mathematics fact fluency), we included more recently published studies that investigated the effects of TMMs across mathematics concepts and skills. By expanding our review to include a host of important student mathematics outcomes, we sought to provide a broader picture for how TMM interventions influence the mathematics achievement of K–12 students with or at risk for MLD.

Our aim in synthesizing this literature base, therefore, was twofold. First, we sought to gain a deeper understanding of the evidentiary basis of TMM interventions for increasing the mathematics achievement of K–12 students with or at risk for MLD. Second, the value of TMM interventions to increase mathematics outcomes is likely dependent on the manner in which they are instructionally designed and thus incorporate the instructional features shown important for students who struggle with mathematics. Thus, we examined the extent to which interventions prioritized empirically validated principle of explicit mathematics instruction. Two research questions were addressed:
What are the effects of TMM interventions on mathematics outcomes for K–12 students with or at risk for MLD as investigated in single-case and group/quasi-experimental research?

To what extent do TMM interventions incorporate principles of explicit mathematics instruction?

Method

Search Procedures and Inclusion Criteria

In 2000, the National Council of Teachers of Mathematics [NCTM] recommended the use of technological tools during mathematics instruction, referring to technology as essential. They posited that a strategic use of technology can increase student access to critical mathematics content (NCTM, 2000). Therefore, we used 2000 as our cutoff year for the studies to include in this synthesis.

To identify studies, we first searched Academic Search Complete, Education Source, and PsycINFO and Teacher Reference Center. The following search terms were used: math, mathematics, mathematics difficulties, mathematics disabilities, learning disabilities, computer, computer assisted instruction, technology, K-12, elementary school, or high school. Additionally, we conducted a hand search of the following six journals: Exceptional Children, Journal of Research on Educational Effectiveness, Journal of Special Education, Journal of Special Education Technology, Learning Disability Quarterly, and Remedial and Special Education. We targeted these journals because they have previously published research on mathematics interventions, including TMM interventions, for students with or at risk for MLD.

A total of 1,339 articles were identified through the search processes. We applied additional criteria as a way to further screen the identified articles. First, the studies had to be published in peer-reviewed journals, conducted in the United States between 2000 and 2016, and include a sample where more than 50% of the participating K–12 students were considered with or at risk for MLD. We included only studies that employed single-case research, quasi-experimental, and group research designs. Finally, studies had to investigate TMM interventions as the independent variable and target mathematics achievement as the dependent variable.

A total of 19 studies met the inclusion criteria and were included in this synthesis. It is important to note that we excluded studies that investigated the effects of low-tech technology, such as calculators, on student mathematics outcomes. We considered this type of technology as an instructional accommodation rather than a TMM intervention with anticipated purpose to improve student mathematics outcomes. Of the 19 identified studies, 9 employed single-case design and 10 used group- or quasi-experimental designs.

Coding Procedures

To review key features of the 19 identified studies, we developed a standardized coding protocol, which focused on the following six features: (a) participants, (b) TMM intervention, (c) information on the treatment and control conditions, (d) outcome measures, (e) results, and (f) effect sizes. Two trained coders used the protocol to review the 19 studies. To calibrate the coders’ interpretation of the protocol, the coders concurrently applied the protocol to one study. Coding discrepancies were resolved through discussion between the two coders. To gauge the coders’ consistency with the protocol, all of the studies were coded by a third coder. Interrater reliability was 100%.

Effect Size Calculation

For the nine single-subject design studies, studies reported percentage of nonoverlapping data (PND) points to determine the effects of the intervention.

For the 10 studies that employed group- and quasi-experimental research designs, we calculated a Hedges’s (1981) g effect size for further interpretation of the TMM intervention effects. Hedges’s g, recommended by the What Works Clearinghouse (2014), represented the difference between the means of the treatment conditions divided by the pooled weighted standard deviation. For studies that had more than one dependent variable, we report the range of effects including the most conservative and strongest effect sizes. For each Hedges’s g effect size, we calculated 95% confidence intervals.

Results

The 19 studies were evaluated for their effectiveness to increase student mathematics achievement and inclusion of explicit mathematics instructional principles. Table 1 summarizes the 9 single-case studies included in this synthesis, while Table 2 offers information on the 10 group- and quasi-experimental studies. Both tables provide general information on the studies’ samples, targeted interventions, and dependent variables. In Table 1, we include effects based on findings reported in the single-case design studies. Table 2 provides Hedges’s g effect sizes and 95% confidence intervals for each group- and quasi-experimental design study. For the group- and quasi-experimental design studies that incorporated more than one outcome measure, we offer the most conservative and strongest Hedges’s g effect sizes calculated. Table 3 summarizes findings from our second research question.

Table 1.
Summary Table of Single-Case Design Studies.

Study Sample Intervention Description Dependent Variables Percentage of Nonoverlapping Data

Participants Design

Bryant et al. (2015) N = 6 fourth-grade students with LD Alternating treatment Students received practice on multiplication facts in one of the three conditions: (a) teacher-directed activity, (b) iPad applications (Math Drills and Math Evolve), and (c) combined instruction for 30-min sessions, 5 days per week for 3 weeks Researcher- developed assessments 100%

Cihak and Bowlin (2009) N = 3 high school students with LD Alternating probe Students received practice on the concept of perimeter via a handheld computer with video clips for 20 sessions Researcher-developed assessments 100

Gross and Duhon (2013) N = 3 elementary students at risk for MLD Nonconcurrent multiple baseline Students received practice on addition and multiplication facts via computers for 32-min sessions, 4 days per week, for 16 sessions Researcher-developed assessments 41–100

Nordness, Haverkost, and Voldberding (2011) N = 3 second-grade students with LD Multiple baseline Students received practice on two-digit subtraction facts in 10-min sessions, 3 times a week for 14 weeks Researcher-developed assessments 75; 80

Ok and Bryant (2015) N = 4 fifth-grade students with LD Multiple probe Students received practice on multiplication facts via iPads in 30-min sessions for 5 days a week for 3 weeks Researcher-developed assessments 93–100

Satsangi and Bouck (2014) N = 3 9th- and 11th-grade students with MLD Alternating treatment Students received practice on concepts of area and perimeter via VM in 40-min sessions Researcher-developed assessments 100

Satsangi, Bouck, Taber-Doughty, Bofferding, and Roberts (2016) N = 3 11th- and 12th-grade students with LD Alternating treatment Students received practice on linear equations in three conditions: (a) VM, (b) CM, or no treatment. Each condition lasted 10 sessions Researcher-developed assessments 100

Seo and Bryant (2012) N = 4 second- and third-grade students MLD Multiple probe across subjects Students received practice on add/sub word problems via Math Explorer in 20- to 30-min sessions, 5 times per week for 18 weeks Researcher-developed assessments 100

Shin and Bryant (2016) N = 4 second- and third-grade students with MLD Multiple baseline with multiple probes Students received practice on fraction word problems via fun fraction in 20-min sessions, 2 times per week for 13 weeks Researcher-developed assessments 56–100

Note. MLD = mathematics learning disability; LD = learning disability; VM = virtual manipulatives, CM = concrete manipulatives.

Table 2.
Summary Table of Group- and Quasi-Experimental Studies.

Study Sample Intervention Description Dependent Variables Hedges’s g [95% CI]

Participants Assignment

Fien et al. (2016) N = 250 first-grade students (n = 125 Tx and n = 125 Ctl). Of the 250 students, 151 scored ≤ 25th percentile on easy CBM-CCSS-M and thus at risk for MLD Matched in pairs based on pretest scores, students were randomly assigned within classrooms to Tx or Ctl Students in the Tx condition received the NS1 intervention, which targeted whole number concepts and skills, 4 days per week in 15-min sessions for a total of 48 sessions (12 hr). Ctl students received BAU Tier 2 math instruction supports easyCBM Math; easyCBM-NCTM^a; Group-Admin MN and QD; NS1 mastery tests (2, 4, and 6 weeks); ProFusion-Revised^b −0.13 [−0.38, 0.12]^a to 0.30 [0.05, 0.55]^b

Bos (2007) N = 95 11th-grade students (n = 48 Tx and n = 47 Ctl) from 10 Tx classes and 9 Ctl classes. All students at risk for MLD No random assignment In the Tx classes, students received six lessons from Texas Instruments InterActive program delivered across eight 55-min sessions and focused on quadratic functions. Students in Ctl received BAU instruction on quadratic functions Objective 5—quadratic functions—Texas assessment of knowledge and skills exit level mathematics test 0.65 [0.23, 1.05]

Bottge, Rueda, Grant, Stephens, and Laroque (2010) N = 54 sixth-, seventh-, eighth-grade students (n = 29 Tx and n = 25 Ctl). Students with MLD Randomly assigned within classrooms to Tx or Ctrl Students in the Tx condition received fraction computation practice via computer-based enhanced anchored instruction in 50-min sessions for 24 days. Ctl students received teacher-delivered EAI Researcher-developed problem-solving^a; fraction Computation.^b ITBS computation and data analysis 0.11 [−0.42, 0.64]^a to 1.05 [0.49, 1.62]^b

Bottge et al. (2015) N = 134 sixth-, seventh-, eighth-grade students (n = 72 Tx and n = 62 Ctl). Students with MLD Randomly assigned within schools to Tx or Ctrl Students in the Tx condition received fraction word problem practice via computer-based enhanced anchored instruction in 45–75 sessions for 66 days. Ctl students received BAU district math curriculum ITBS computation^a and data analysis. Researcher-developed problem-solving; fraction computation^b −0.23 [−0.57, 0.11]^a to 0.64 [0.30, 0.99]^b

Burns, Kanive, and DeGrande (2012) N = 442 third- and fourth-grade students. Third grade (n = 139 Tx, n = 142 Ctl). Fourth grade (n = 77 Tx, n = 84 Ctl). Scored ≤ 25th percentile on Star Math. Students with MLD No random assignment. Extant data analysis Students in the Tx condition received A/S/M/D fact fluency practice via CBMFF program in 5- to 15-min sessions, 3 days per week for 8–15 weeks. Ctrl students received CBMFF approximately 1 day per week for < 8 weeks Star Math third grade^a; Star Math fourth grade^b 0.36 [0.12, 0.59]^a; 0.48 [0.17, 0.80]^b

Fede, Pierce, Matthews, and Wells (2013) N = 32 fifth-grade students (n = 16 Tx and n = 16 Ctl). Scored ≤ 30th percentile on the process and application subtest of the GMADE Randomly assigned within classrooms to Tx or Ctrl Students in the Tx condition received A/S/M/D word problem practice via the GO Solve Word Problems program in 45-min sessions, 2 days per week for 16 weeks GMADE^a; Massachusetts comprehensive assessment system^b 0.36 [−0.33, 1.03]^a; 0.76 [−0.33, 1.03]^b

Fuchs, Fuchs, Hamlett, and Appleton (2002) N = 38 fourth-grade (n = 28 Tx, n = 10 Ctl) students with MLD Randomly assigned within classrooms to one of four conditions; 10 students in each condition Students randomly assigned to (a) word problem-solving tutoring + computer-assisted practice, (b) computer-assisted practice only, (c) word problem-solving or (d) control. Computer sessions consisted of 24 sessions, 2 times per week for 12 weeks Story problems^a; transfer story problems; real-world problem-solving^b 0.58 [−0.33, 1.48]^a to 0.88 [−0.07, 1.80]^b

Kanive, Nelson, Burns, and Ysseldyke (2014) N = 85 fourth- and fifth-grade students (n = 28 Tx, n = 29 Ctl, n = 29 conceptual). Scored ≤ 25th percentile on the measures of academic progress subtest Two levels of randomization: (1) random assignment to one of three conditions and (2) random assignment to multiplication facts Students in the Tx condition received multiplication facts practice via computers in two 15-min sessions (30-min total). Students in the conceptual condition received explicit instruction of single-digit multiplication facts Single-digit multiplication word problem^a; fact fluency CBM^b 0.14 [−0.38, 0.65]^a; 0.59 [0.06, 1.11]^b

Mendiburo and Hasselbring (2014) N = 67 fifth-grade students (n = 34 Tx and n = 33 Ctl). All students at risk for MLD Randomly assigned within classrooms to Tx or Ctrl Students in the Tx condition received practice fraction magnitude via laptops. Ctl students received teacher-facilitated fraction magnitude instruction with concrete manipulatives Researcher-developed assessments 0.31 [−0.17, 0.78]^a to 1.55 [0.99, 2.08]^b

Stultz (2013) N = 58 10th-grade students with LD (n = 29 Tx and n = 29 Ctl) Randomly assigned within classrooms to Tx or Ctrl Students in the Tx condition received BMCSB instruction, 90 min for 10 sessions. Ctl students received BAU teacher-directed activities Brigance Comprehensive Inventory of Basic Skills—Revised −0.15 [−0.65, 0.36]

Note. MLD = mathematics learning disability; LD = specific learning disability; Tx = treatment condition; Ctl = control condition; BAU = business as usual; BMCSB = basic math competency skill building program; CBM = curriculum-based measure; ITBS = Iowa test of basic skills; CI = confidence interval; CCSS-M = Common Core State Standards for Mathematics; NS1 = NumberShire Level-1; CBMFF = computer-based math fact fluency; NCTM = National Council of Teachers of Mathematics; EAI = enhanced anchored instruction; GMADE = group-math assessment and diagnostic evaluation; MN = missing number; QD = quantity discrimination; A = addition; D = division; M = multiplication; S = subtraction.

^aConservative effect size calculated. ^bLargest effect size calculated.

Table 3.
Summary of Principles of Explicit Instruction Incorporated in Technology-Mediated Mathematics Interventions.

Study Mathematical Concept/Skill Overt Demonstrations Practice Opportunities Academic Feedback

Fien et al. (2016) Whole numbers concepts X X X

Bos (2007) Quadratic functions X X

Bottge, Rueda, Grant, Stephens, and Laroque (2010) Fractions—computation X X

Bottge et al. (2015) Fractions—word problems X X

Bryant et al. (2015) Fact fluency (M) X

Burns, Kanive, and DeGrande (2012) Fact fluency (A/S/M/D) X X

Cihak and Bowlin (2009) Perimeter X X

Fede, Pierce, Matthews, and Wells (2013) A/S/M/D—word problems X X

Fuchs, Fuchs, Hamlett, and Appleton (2002) Addition—word problems X X

Gross and Duhon (2013) Fact fluency (A/M) X X

Kanive, Nelson, Burns, and Ysseldyke (2014) Fact fluency (M) X X

Mendiburo and Hasselbring (2014) Fraction magnitude X X

Nordness, Haverkost, and Voldberding (2011) Fact fluency (S) X

Ok and Bryant (2015) Fact fluency (M) X X

Satsangi and Bouck (2014) Area and perimeter X

Satsangi, Bouck, Taber-Doughty, Bofferding, and Roberts (2016) Linear equations X X

Seo and Bryant (2012) A/S—word problems X X X

Shin and Bryant (2016) Fractions—word problems X X X

Stultz (2013) Fractions—computation X

Note. A = addition; D = division; M = multiplication; S = subtraction.

Overall Study Characteristics

Grade levels of the participating students in the 19 studies ranged from kindergarten to 12th grade. Of the 19 studies, 6 targeted fluency with basic number combinations, 5 problem-solving, 3 fraction skills, 1 whole number concepts and skills, 1 quadratic functions, 1 linear equations, 1 perimeter problem-solving, and 1 area and perimeter problem-solving. Twelve studies administered only researcher-developed mathematics achievement measures, while the remaining seven used a combination of researcher-developed and standardized, normed-referenced mathematics assessments. Intervention duration varied across the studies, ranging from 30-min to 18 weeks. There was also variation in terms of intervention dosage ranging from 10 to 90 min per session across the 19 studies. Among the 19 studies, only 8 used random assignment, all at the student level. Finally, the TMM interventions were delivered through a variety of technology platforms, including desktop and laptop computers, and handheld technologies (e.g., iPads).

Research Question 1—Single-Case Design Studies

Based on PND results, the nine single-case design studies reported mostly positive results. In four studies, researchers found moderate to strong effects for TMM interventions focused on building automaticity with basic number combinations among students across grade levels. The fact fluency interventions investigated in Gross and Duhon (2013), Nordness, Haverkost, and Voldberding (2011), and Bryant et al. (2015) demonstrated mixed effects for the participating students. However, Ok and Bryant (2015) found that a TMM intervention significantly increased students’ fluency of basic multiplication facts. The intervention, which was delivered via iPads, was provided to students 5 days per week in 30-min sessions for 3 weeks.

Word problem-solving TMM interventions were examined in two studies. Seo and Bryant (2012) found strong, positive effects with the Math Explorer intervention. All four of their participating students demonstrated improvement in their word problem skills on a researcher-developed assessment. Shin and Bryant (2016) reported mixed results of a fraction word problem-solving TMM intervention (fun fraction) for middle school students. In the study, the PND improvement trend (slope) ranged from 56% to 100%. Two students reached mastery level, but their differences from baseline to intervention were not statistically significant.

Three studies focused on areas of mathematics that are rarely investigated in mathematics intervention research. Satsangi and Bouck (2014) examined the effect of an intervention focused on mathematical topics of area and perimeter. Two of the three participating students showed stronger growth in solving area problems than problems on perimeter. Cihak and Bowlin (2009) tested a TMM intervention that provided video clips on the concept of perimeter. Findings from a 10-item assessment showed significant mean improvement among the three middle school students. Finally, Satsangi, Bouck, Taber-Doughty, Bofferding, and Roberts (2016) conducted a study with three high school students to examine the effects of a TMM on the understanding of linear equations. Findings showed significant gains for all three students on a researcher-developed measure.

Research Question 1—Group- and Quasi-Experimental Design Studies

Overall, the results from the 10 group- and quasi-experimental studies showed mostly positive effects of TMM interventions for increasing student mathematics achievement. Fien et al. (2016) conducted a large-scale pilot study to investigate the treatment effects of an explicitly designed, computer-based intervention that targeted the whole number concepts and skills identified in the first-grade Common Core State Standards for Mathematics (CCSS-M, 2010). Students randomly assigned to the treatment condition received a total of 12 hr of whole number instruction and were found to outperform their control peers on six of the seven outcome measures (g = 0.06–0.30). However, Fien et al. (2016) reported a negative effect on a distal measure of whole number understanding (g = −0.13).

In two randomized controlled trials, researchers examined the efficacy of word problem-solving TMM interventions in fourth and fifth grade. Fuchs, Fuchs, Hamlett, and Appleton (2002) investigated an addition word problem-solving intervention for teaching fourth-grade students at risk for MLD how to transfer their problem-solving knowledge, skills, and strategies to novel problems. The study included four conditions: problem-solving tutoring with computer-assisted practice, computer-assisted practice only, problem-solving tutoring only, and control. In general, students in the computer-assisted practice only condition outperformed their control peers on all outcome measures (g = 0.58–0.84). Results also suggested that students in the combined tutoring plus computer-assisted practice condition made stronger gains than students in the computer-assisted practice-only condition. In the other randomized controlled trial, Fede, Pierce, Matthews, and Wells (2013) reported that students in the treatment group showed stronger growth than their control peers on two word problem-solving measures (g = 0.41–0.79).

In two studies, Burns, Kanive, and DeGrande (2012) and Kanive, Nelson, Burns, and Ysseldyke (2014) investigated TMM interventions focused on building fluency with basic math facts. Both interventions offered students with timed fluency building practice. Burns et al. (2012) demonstrated moderate effects for students in third and fourth grades, g = 0.36 and g = 0.48, respectively. Results from Kanive et al. (2014) indicated moderate effects on fact fluency for fourth- and fifth-grade students (g = 0.59). Small effects on single-digit multiplication word problems were also noted in Kanive et al. (g = 0.14).

In four experimental studies, researchers examined the effects of TMM interventions focused on fractions. Findings from Bottge, Rueda, Grant, Stephens, and Laroque (2010) suggested mixed results. Effects indicated strong treatment impact on a researcher-developed measure of fraction computation (g = 1.05), but smaller effects on a distal measure of mathematics achievement (g = 0.18). In a second study on fractions, Mendiburo and Hasselbring (2014) demonstrated moderate to large treatment effects for fifth-grade students who used an intervention with virtual manipulatives (g = 0.31–1.55). In the third fraction study, Bottge et al. (2015) demonstrated mixed effects of a TMM intervention with enhanced anchored instruction. Effect sizes indicated moderate impact on a researcher-developed fraction computation measure (g = 0.64) and a negative impact on a distal measure of mathematics achievement (g = −0.23). Negative effects were also reported in a different TMM intervention on fraction computation (Stultz, 2013).

Finally, a quasi-experiment focused on quadratic functions showed positive effects (g = 0.65) for students who received the Texas Instrument InterActive Environment intervention (Bos, 2007). In all, treatment students received six lessons delivered across eight 55-min sessions.

Research Question 2—Explicit Mathematics Instruction in Studies

Table 3 presents the results of the principles of explicit mathematics instruction. Specifically, the table presents the results of the overt demonstrations, student practice opportunities, and academic feedback incorporated in the TMM intervention studies. We found that all 19 studies provided opportunities for students to practice with targeted mathematical content. Of the 19 studies, 4 were considered practice-only TMM interventions. In three of the four cases, these interventions focused on building fluency with number combinations.

Eight studies complemented student practice opportunities with academic feedback. However, the type of feedback provided in most of these studies was primarily delivered through visuals, such as placing a red X over an incorrect response or a highlighting a text box near the student response. Few studies provided verbal feedback opportunities, such as in Fien et al. (2016) and Gross and Duhon (2013), where student responses were corrected and affirmed through verbal interactions. Three studies provided overt demonstrations to explain the mathematical content that students practiced (Bottge, Rueda, Grant, Stephens, & Laroque, 2010; Bottge et al., 2015; Cihak & Bowlin, 2009). However, we found that these studies did not offer academic feedback to improve student performance on mathematical tasks and activities. Finally, our review revealed that only four studies incorporated all three principles of explicit mathematics instruction (Fede, Pierce, Matthews, & Wells, 2013; Fien et al., 2016; Seo & Bryant, 2012; Shin & Bryant, 2016). These studies investigated TMM interventions that offered students with opportunities to receive overt demonstrations and explanations, participate in guided and independent practice opportunities, and obtain immediate academic feedback.

Discussion

Given the rapid increase of technology in U.S. classrooms, the purpose of this study was to extend the work of previous syntheses by reviewing more recently published studies that focus specifically on TMM interventions designed for K–12 students with or at risk for MLD. Two research questions were addressed. First, we examined the overall effectiveness of 19 TMM intervention studies on the mathematical outcomes of students with or at risk for MLD. Second, because a preponderance of evidence supports the use of explicit mathematics instruction when teaching struggling learners, we investigated the extent to which the TMM interventions included one or more principles of explicit instruction, including (a) overt demonstrations and explanations of targeted mathematical content, (b) guided and independent student practice opportunities, and (c) specific academic feedback based on student mathematical performance during technology-based instruction. Gauging whether TMM interventions fully or partially incorporate principles of explicit mathematics instruction may have implications for the way in which the field designs future TMM interventions. In the next section, we summarize our findings, discuss the study’s limitations, and pose implications for future research.

Summary of Results

Research question 1

Overall, findings from our first research question suggest that TMM interventions investigated in single-case and group- and quasi-experimental design research have mostly positive effects on the mathematics outcomes of students with or at risk for MLD. These results are consistent with the findings of previous research syntheses on TMM interventions involving students who face difficulties in mathematics (Bouck & Flanagan, & 2009; Cozad & Ricommini, 2016; Fitzgerald et al., 2008; Li & Ma, 2010; Maccini et al., 2002). In the current study, the beneficial impact of TMM interventions on student mathematics achievement was mostly demonstrated across a range of grade levels and mathematics concepts and skills. In the elementary grades, for example, four studies reported moderate to large effects of TMM interventions to increase students’ fluency with basic number combinations (Burns, Kanive, & DeGrande, 2012; Kanive, Nelson, Burns, & Ysseldyke, 2014; Nordness, Haverkost & Volberding, 2011; Ok & Bryant, 2015). Fuchs et al. (2002) and Fede et al. (2013) demonstrated strong effects for TMM interventions to improve students’ word problem-solving. Additionally, Fien et al. (2016) demonstrated largely positive effects of a TMM intervention on students’ understanding of whole number concepts and skills, with one negative effect found on a distal mathematics achievement measure.

Similar results were found with the studies that involved older students. Shin and Bryant (2016), for instance, showed positive effects of a word problem-solving TMM intervention for 13- and 15-year-old students. Moderate effects were found for an 11th-grade intervention on quadratic functions (Bos, 2007). A strong treatment effect was reported for a TMM intervention that targeted linear algebraic equations for high school students (Satsangi, Bouck, Taber-Doughty, Bofferding, and Roberts, 2016). However, results varied from two group design studies involving middle school students and enhanced anchored instruction (Bottge et al., 2010; Bottge et al., 2015). Bottge et al. (2015) had a negative effect on a distal mathematics outcome measure. Taken together, the findings from our first research question demonstrate the promise of TMM interventions to improve targeted mathematics outcomes.

Research question 2

Results from our second research question suggest that only 4 of the 19 TMM interventions (21%) included all three principles of explicit mathematics instruction. This was surprising because explicit mathematics instruction has a strong evidentiary basis for impacting student mathematics learning. Therefore, we expected more TMM interventions to provide students with vivid demonstrations and explanations of mathematical content and complement practice opportunities with immediate, informational academic feedback. For example, Shin and Bryant (2016) offered students with overt demonstrations and specific academic feedback for how to solve fraction word problem-solving. In the area of whole number concepts and skills, Fien et al. (2016) provided a computer-based TMM intervention with full features of explicit mathematics instruction.

In 8 of the 19 studies, the TMM interventions accompanied student practice opportunities with academic feedback. Although the feedback varied in the way it was presented to students, we found it encouraging that nearly half of the TMM interventions incorporated degrees of this validated instructional principle. Academic feedback is an integral principle of explicit mathematics instruction and vital for supporting students’ development of mathematical proficiency (Gersten et al., 2009). When timely and specific, academic feedback can help students recognize their errors and motivate them to accomplish mathematical tasks successfully. Despite this importance, most of the feedback opportunities in the TMM interventions was offered through visual displays (e.g., message or markings on the screen informing students about the accuracy of their response). Surprisingly, few interventions offered auditory corrections and affirmations. While some level of academic feedback is likely better than none, it is plausible that the visual feedback (e.g., red X over incorrect answer) may have frustrated or confused students. A similar case may be made with verbal feedback offered in TMM interventions (e.g., “the correct answer is”). Therefore, future research is needed to determine which type of academic feedback offered in TMM interventions (i.e., visual vs. verbal) has stronger appeal and beneficial impact for students with or at risk for MLD.

In four studies, we found that the TMM interventions offered practice-only learning experiences. Converging evidence suggests that practice is essential for helping students develop automaticity of mathematical procedures and understanding of mathematical concepts (Gersten et al., 2009). Despite this importance, the impact of the four practice-only TMM interventions on student outcomes was mixed. One study, for example, demonstrated negative effects (Stutlz, 2013), while the remaining three studies showed moderate to strong impact. It may be that for practice-only TMM interventions to reach their full potential, they have to be properly sequenced into students’ ongoing mathematics instruction. In other words, simply receiving sheer amounts of practice without direct linkages to the topics being taught in core mathematics settings may mitigate the impact of practice-only TMM interventions.

Finally, our findings indicate that three TMM interventions provided overt demonstrations prior to offering the student practice opportunities but did not complement student practice with academic feedback (Bottge et al., 2010; Bottge et al., 2015; Fede et al., 2013). It is unclear as to why these TMM interventions did not incorporate academic feedback. One plausible reason is that the TMM interventions, such as enhanced anchored instruction (Bottge et al., 2010; Bottge et al., 2015), rely on teacher-deliver academic feedback to correct and affirm student responses.

In summary, the results of this synthesis indicate that TMM interventions demonstrate promising effects on the mathematics outcomes of K–12 students with or at risk for MLD. Moreover, findings from our second research questions indicate that a majority of TMM interventions include one or more validated principles of explicit instruction. Taken together, our findings suggest that future research is needed to determine the instructional design features of TMM intervention that optimize the intensity of mathematics instruction needed to meet the instructional needs of students with or at risk for MLD.

Limitations

This synthesis has several limitations. First, there were few available studies on TMM interventions (N = 19), and this may compromise the generalizability of our findings. Relatedly, the definition of MLD used in the identified research varied and thus may constrain our findings. Additionally, while an electronic scan of the literature was conducted, our hand search only included six journals. Consequently, potential studies may have been missed. Half the studies also employed single-case designs, which limited our capacity to use a comparable effect size metric across the different research designs.

Finally, our review included three studies that were published in the early and mid-2000s (i.e., more than 8 years from the end of our search). Therefore, it is plausible that the findings from these particular studies are dated. Recognizing that technology can sometimes advance on a daily basis, we were left with the question about how far back syntheses and meta-analyses of technology-based educational interventions should reach in the literature bases. Our review spanned 16 years (2000–2016). However, to keep pace with the rapid advancement of educational technology, perhaps we should have limited that time frame to 5 years or even 1 year. Future research might consider defining specific time frame parameters for when educational technology should be classified as obsolete.

Implications for Future Research

One implication from this synthesis is a need for additional research with larger samples of students. For a more informed outlook of TMM interventions and their effects on students’ mathematics achievement, the field would benefit from findings across large and diverse student populations. Relatedly, despite calls from expert panels in the field of education (Cook et al., 2014) for researchers to include demographic information of participating students, many of the studies in this synthesis provided limited demographic data, thereby making it difficult to develop nuanced understandings of the treated participants. Therefore, we encourage future studies to thoroughly describe their participating samples.

Additionally, it is encouraging that some of the TMM interventions included more than one principle of explicit instruction. However, few studies tested interventions that fully included the principles of this validated instructional approach, including overt demonstrations, guided and independent student practice opportunities, and specific academic feedback. Such shortfalls may have undermined the full potential of these particular interventions. Given the strong evidentiary basis behind explicit mathematics instruction for students with or at risk for MLD (Gersten et al., 2009), it is recommended that curriculum developers fully incorporate principles of this instructional approach into future technology development efforts.

Further research and development is also needed to address advanced mathematical concepts and skills in TMM interventions. While highly important, over 31% of the identified studies focused on fluency with number combinations or math facts. Encouragingly, we found that four of the studies investigated TMM interventions that targeted three underresearched mathematics concepts and skills (i.e., perimeter and area, linear equations, and quadratic functions). Additionally, recognizing that mathematical proficiency hinges on a deep understanding of a concatenation of concepts, skills, and strategies, future research should design and test TMM interventions that target multiple topics associated with a particular mathematical domain. For example, Fien et al. (2016) designed the NumberShire Level-1 intervention to address the most critical concepts and skills of whole numbers identified in the first grade CCSS-M (2010).

Additionally, 12 of the 19 studies solely relied on researcher-developed outcome measures. In many cases, it appeared that these proximal assessments were closely aligned with or directly tailored to the learning objectives targeted by TMM interventions. As suggested by the What Works Clearinghouse (2014), findings from overaligned outcome measures may inaccurately represent an intervention’s treatment effects. Consequently, future research involving TMM interventions should seek to use a combination of researcher-developed assessments and broader-based measures of mathematics achievement (Gersten, 2016; Ochsendorf, 2016).

Finally, for TMM interventions to be more effective for students with or at risk for MLD, it is important for the field to consider how to integrate TMM interventions within multitiered systems of support (Allsopp et al., 2010). This approach would require researchers and teachers to consider how to best align TMM interventions with mathematics instruction delivered in core (Tier 1 settings). Moreover, it would entail deriving methods for using TMM interventions to intensify the instructional experiences that students receive in Tiers 2 and 3 contexts.

Conclusion

There is an urgent need to improve students’ mathematics performance, given the persistent low performance of U.S. students in mathematics. However, the call for all students, including students with or at risk for MLD, to develop mathematics proficiency requires the implementation of evidence-based programs and instructional practices. TMM interventions that incorporate features of explicit mathematics instruction can potentially enhance mathematics instruction and increase student mathematics achievement. This synthesis reviewed 19 studies and found promising effects for TMM interventions to improve mathematics outcomes for students with or at risk for MLD. Additionally, it is encouraging that many of TMM interventions reviewed included one or more principles of explicit instruction. Future research is needed, however, to design and test effective TMM interventions.

Study	Sample	Intervention Description	Dependent Variables	Percentage of Nonoverlapping Data
Bryant et al. (2015)	N = 6 fourth-grade students with LD	Alternating treatment	Students received practice on multiplication facts in one of the three conditions: (a) teacher-directed activity, (b) iPad applications (Math Drills and Math Evolve), and (c) combined instruction for 30-min sessions, 5 days per week for 3 weeks	Researcher- developed assessments	100%
Cihak and Bowlin (2009)	N = 3 high school students with LD	Alternating probe	Students received practice on the concept of perimeter via a handheld computer with video clips for 20 sessions	Researcher-developed assessments	100
Gross and Duhon (2013)	N = 3 elementary students at risk for MLD	Nonconcurrent multiple baseline	Students received practice on addition and multiplication facts via computers for 32-min sessions, 4 days per week, for 16 sessions	Researcher-developed assessments	41–100
Nordness, Haverkost, and Voldberding (2011)	N = 3 second-grade students with LD	Multiple baseline	Students received practice on two-digit subtraction facts in 10-min sessions, 3 times a week for 14 weeks	Researcher-developed assessments	75; 80
Ok and Bryant (2015)	N = 4 fifth-grade students with LD	Multiple probe	Students received practice on multiplication facts via iPads in 30-min sessions for 5 days a week for 3 weeks	Researcher-developed assessments	93–100
Satsangi and Bouck (2014)	N = 3 9th- and 11th-grade students with MLD	Alternating treatment	Students received practice on concepts of area and perimeter via VM in 40-min sessions	Researcher-developed assessments	100
Satsangi, Bouck, Taber-Doughty, Bofferding, and Roberts (2016)	N = 3 11th- and 12th-grade students with LD	Alternating treatment	Students received practice on linear equations in three conditions: (a) VM, (b) CM, or no treatment. Each condition lasted 10 sessions	Researcher-developed assessments	100
Seo and Bryant (2012)	N = 4 second- and third-grade students MLD	Multiple probe across subjects	Students received practice on add/sub word problems via Math Explorer in 20- to 30-min sessions, 5 times per week for 18 weeks	Researcher-developed assessments	100
Shin and Bryant (2016)	N = 4 second- and third-grade students with MLD	Multiple baseline with multiple probes	Students received practice on fraction word problems via fun fraction in 20-min sessions, 2 times per week for 13 weeks	Researcher-developed assessments	56–100

Study	Sample	Intervention Description	Dependent Variables	Hedges’s g [95% CI]
Fien et al. (2016)	N = 250 first-grade students (n = 125 Tx and n = 125 Ctl). Of the 250 students, 151 scored ≤ 25th percentile on easy CBM-CCSS-M and thus at risk for MLD	Matched in pairs based on pretest scores, students were randomly assigned within classrooms to Tx or Ctl	Students in the Tx condition received the NS1 intervention, which targeted whole number concepts and skills, 4 days per week in 15-min sessions for a total of 48 sessions (12 hr). Ctl students received BAU Tier 2 math instruction supports	easyCBM Math; easyCBM-NCTM^a; Group-Admin MN and QD; NS1 mastery tests (2, 4, and 6 weeks); ProFusion-Revised^b	−0.13 [−0.38, 0.12]^a to 0.30 [0.05, 0.55]^b
Bos (2007)	N = 95 11th-grade students (n = 48 Tx and n = 47 Ctl) from 10 Tx classes and 9 Ctl classes. All students at risk for MLD	No random assignment	In the Tx classes, students received six lessons from Texas Instruments InterActive program delivered across eight 55-min sessions and focused on quadratic functions. Students in Ctl received BAU instruction on quadratic functions	Objective 5—quadratic functions—Texas assessment of knowledge and skills exit level mathematics test	0.65 [0.23, 1.05]
Bottge, Rueda, Grant, Stephens, and Laroque (2010)	N = 54 sixth-, seventh-, eighth-grade students (n = 29 Tx and n = 25 Ctl). Students with MLD	Randomly assigned within classrooms to Tx or Ctrl	Students in the Tx condition received fraction computation practice via computer-based enhanced anchored instruction in 50-min sessions for 24 days. Ctl students received teacher-delivered EAI	Researcher-developed problem-solving^a; fraction Computation.^b ITBS computation and data analysis	0.11 [−0.42, 0.64]^a to 1.05 [0.49, 1.62]^b
Bottge et al. (2015)	N = 134 sixth-, seventh-, eighth-grade students (n = 72 Tx and n = 62 Ctl). Students with MLD	Randomly assigned within schools to Tx or Ctrl	Students in the Tx condition received fraction word problem practice via computer-based enhanced anchored instruction in 45–75 sessions for 66 days. Ctl students received BAU district math curriculum	ITBS computation^a and data analysis. Researcher-developed problem-solving; fraction computation^b	−0.23 [−0.57, 0.11]^a to 0.64 [0.30, 0.99]^b
Burns, Kanive, and DeGrande (2012)	N = 442 third- and fourth-grade students. Third grade (n = 139 Tx, n = 142 Ctl). Fourth grade (n = 77 Tx, n = 84 Ctl). Scored ≤ 25th percentile on Star Math. Students with MLD	No random assignment. Extant data analysis	Students in the Tx condition received A/S/M/D fact fluency practice via CBMFF program in 5- to 15-min sessions, 3 days per week for 8–15 weeks. Ctrl students received CBMFF approximately 1 day per week for < 8 weeks	Star Math third grade^a; Star Math fourth grade^b	0.36 [0.12, 0.59]^a; 0.48 [0.17, 0.80]^b
Fede, Pierce, Matthews, and Wells (2013)	N = 32 fifth-grade students (n = 16 Tx and n = 16 Ctl). Scored ≤ 30th percentile on the process and application subtest of the GMADE	Randomly assigned within classrooms to Tx or Ctrl	Students in the Tx condition received A/S/M/D word problem practice via the GO Solve Word Problems program in 45-min sessions, 2 days per week for 16 weeks	GMADE^a; Massachusetts comprehensive assessment system^b	0.36 [−0.33, 1.03]^a; 0.76 [−0.33, 1.03]^b
Fuchs, Fuchs, Hamlett, and Appleton (2002)	N = 38 fourth-grade (n = 28 Tx, n = 10 Ctl) students with MLD	Randomly assigned within classrooms to one of four conditions; 10 students in each condition	Students randomly assigned to (a) word problem-solving tutoring + computer-assisted practice, (b) computer-assisted practice only, (c) word problem-solving or (d) control. Computer sessions consisted of 24 sessions, 2 times per week for 12 weeks	Story problems^a; transfer story problems; real-world problem-solving^b	0.58 [−0.33, 1.48]^a to 0.88 [−0.07, 1.80]^b
Kanive, Nelson, Burns, and Ysseldyke (2014)	N = 85 fourth- and fifth-grade students (n = 28 Tx, n = 29 Ctl, n = 29 conceptual). Scored ≤ 25th percentile on the measures of academic progress subtest	Two levels of randomization: (1) random assignment to one of three conditions and (2) random assignment to multiplication facts	Students in the Tx condition received multiplication facts practice via computers in two 15-min sessions (30-min total). Students in the conceptual condition received explicit instruction of single-digit multiplication facts	Single-digit multiplication word problem^a; fact fluency CBM^b	0.14 [−0.38, 0.65]^a; 0.59 [0.06, 1.11]^b
Mendiburo and Hasselbring (2014)	N = 67 fifth-grade students (n = 34 Tx and n = 33 Ctl). All students at risk for MLD	Randomly assigned within classrooms to Tx or Ctrl	Students in the Tx condition received practice fraction magnitude via laptops. Ctl students received teacher-facilitated fraction magnitude instruction with concrete manipulatives	Researcher-developed assessments	0.31 [−0.17, 0.78]^a to 1.55 [0.99, 2.08]^b
Stultz (2013)	N = 58 10th-grade students with LD (n = 29 Tx and n = 29 Ctl)	Randomly assigned within classrooms to Tx or Ctrl	Students in the Tx condition received BMCSB instruction, 90 min for 10 sessions. Ctl students received BAU teacher-directed activities	Brigance Comprehensive Inventory of Basic Skills—Revised	−0.15 [−0.65, 0.36]

Study	Mathematical Concept/Skill	Overt Demonstrations	Practice Opportunities	Academic Feedback
Fien et al. (2016)	Whole numbers concepts	X	X	X
Bos (2007)	Quadratic functions		X	X
Bottge, Rueda, Grant, Stephens, and Laroque (2010)	Fractions—computation	X	X
Bottge et al. (2015)	Fractions—word problems	X	X
Bryant et al. (2015)	Fact fluency (M)		X
Burns, Kanive, and DeGrande (2012)	Fact fluency (A/S/M/D)		X	X
Cihak and Bowlin (2009)	Perimeter	X	X
Fede, Pierce, Matthews, and Wells (2013)	A/S/M/D—word problems	X	X
Fuchs, Fuchs, Hamlett, and Appleton (2002)	Addition—word problems		X	X
Gross and Duhon (2013)	Fact fluency (A/M)		X	X
Kanive, Nelson, Burns, and Ysseldyke (2014)	Fact fluency (M)		X	X
Mendiburo and Hasselbring (2014)	Fraction magnitude		X	X
Nordness, Haverkost, and Voldberding (2011)	Fact fluency (S)		X
Ok and Bryant (2015)	Fact fluency (M)		X	X
Satsangi and Bouck (2014)	Area and perimeter		X
Satsangi, Bouck, Taber-Doughty, Bofferding, and Roberts (2016)	Linear equations		X	X
Seo and Bryant (2012)	A/S—word problems	X	X	X
Shin and Bryant (2016)	Fractions—word problems	X	X	X
Stultz (2013)	Fractions—computation		X

Footnotes

Declaration of Conflicting Interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: The research reported here was supported by the National Science Foundation through Grant 1503161 awarded to Drs. Christian T. Doabler, Ben Clarke, Nancy Nelson, and Hank Fien of the Center on Teaching and Learning at the University of Oregon.

References

Allsopp

McHatton

Farmer

(2010). Technology, mathematics PS/RTI, and students with LD: What do we know, what have we tried, and what can we do to improve outcomes now and in the future? Learning Disability Quarterly, 33, 273–288.

Atkins

D. E.

Bennett

Brown

J. S.

Chopra

Dede

Fishman

… Williams

. (2010). Transforming American education: Learning powered by technology. Retrieved from http://www.ed.gov/sites/default/files/netp2010.pdf

Baker

Gersten

Lee

(2002). A synthesis of empirical research on teaching mathematics to low-achieving students. The Elementary School Journal, 103, 51–73. doi:10.1086/499715

*Bos

(2007). The effect of the Texas instrument interactive instructional environment on the mathematical achievement of eleventh grade low achieving students. Journal of Educational Computing Research, 37, 351–368. doi:10.2190/EC.37.4.b

*Bottge

Rueda

Grant

Stephens

Laroque

(2010). Anchoring problem-solving and computation instruction in context-rich learning environments. Exceptional Children, 76, 417–437.

*Bottge

Toland

Gassaway

Butler

Choo

Griffen

(2015). Impact of enhanced anchored instruction in inclusive math classrooms. Exceptional Children, 81, 158–175. doi:10.1177/0014402914551742

Bouck

Flanagan

(2009). Assistive technology and mathematics: What is there and where can we go in special education. Journal of Special Education Technology, 24, 17–30. doi:10.1177/016264340902400202

Bryant

B. R.

Bryant

D. P.

Kethley

Kim

S. A.

Pool

You-Jin

(2008). Preventing mathematics difficulties in the primary grades: The critical features of instruction in textbooks as part of the equation. Learning Disability Quarterly, 31, 21–35.

*Bryant

B. R.

Kang

Kim

Lang

Bryant

Pfannestiel

(2015). Performance of fourth-grade students with learning disabilities on multiplication facts comparing teacher-mediated and technology-mediated interventions: A preliminary investigation. Journal of Behavioral Education, 24, 255–272. doi:10.1007/s10864-015-9218-z

10.

*Burns

Kanive

DeGrande

(2012). Effect of a computer-delivered math fact intervention as a supplemental intervention for math in third and fourth grades. Remedial and Special Education, 33, 184–191.

11.

*Cihak

Bowlin

(2009). Using video modeling via handheld computers to improve geometry skills for high school students with learning disabilities. Journal of Special Education Technology, 24, 17–29.

12.

Common Core State Standards Initiative. (2010). Common core state standards for mathematics. Retrieved from http://www.corestandards.org/assets/CCSSI_Math%20Standards.pdf

13.

Cook

Buysse

Klingner

Landrum

McWilliam

Tankersley

Test

(2014). Council for exceptional children: Standards for evidence-based practices in special education. Teaching Exceptional Children, 46, 206–212. doi:10.1177/0040059914531389

14.

Cozad

Riccomini

(2016). Effects of digital-based math fluency interventions on learners with math difficulties: A review of the literature. The Journal of Special Education Apprenticeship, 5, 1–19.

15.

Doabler

C. T.

Fien

Nelson Walker

N. J.

Baker

S. K.

(2012). Evaluating three elementary mathematics programs for presence of eight research-based instructional design principles. Learning Disability Quarterly, 35, 200–211.

16.

Dynarski

Agodini

Heaviside

Novak

Carey

Campuzano

… Sussex

. (2007). Effectiveness of reading and mathematics software products: Findings from the first student cohort (Report to Congress No. NCEE 2007–4005). Washington, DC: U.S. Department of Education, Institute of Education Sciences.

17.

*Fede

Pierce

Matthews

Wells

(2013). The effects of computer-assisted schema-based instruction intervention on word problem solving skills of low performing fifth grade students. Journal of Special Education Technology, 28, 9–21.

18.

Fien

Doabler

C. T.

Nelson

Kosty

Clarke

Baker

(2016). An examination of the promise of the NumberShire Level 1 gaming intervention for improving student mathematics outcomes. Journal of Research on Educational Effectiveness, 9, 635–661. doi: 10.1080/19345747.2015.1119229

19.

Fitzgerald

Koury

Mitchem

(2008). Research on computer-mediated instruction for students with high incidence disabilities. Journal of Educational Computing Research, 38, 201–233. doi:10.2190/EC.38.2.e

20.

*Fuchs

Fuchs

Hamlett

Appleton

. (2002). Explicitly teaching for transfer: Effects on third-grade students’ mathematical problem solving. Learning Disabilities Research & Practice, 17, 90–106.

21.

Gersten

R. M.

(2016). What we are learning about mathematics interventions and conducting research on mathematics interventions. Journal of Research on Educational Effectiveness, 9, 684–688. doi:10.1080/19345747.2016.1212631

22.

Gersten

R. M.

Chard

Jayanthi

Baker

Morphy

Flojo

(2009). Mathematics instruction for students with learning disabilities: A meta-analysis of instructional components. Review of Educational Research, 79, 1202–1242.

23.

*Gross

Duhon

(2013). Evaluation of computer-assisted instruction for math accuracy intervention. Journal of Applied School Psychology, 29, 246–261.

24.

Hedges

L. V.

(1981). Distribution theory for Glass’s estimator of effect size and related estimators. Journal of Educational Statistics, 6, 107–128. doi:10.3102/10769986006002107

25.

*Kanive

Nelson

Burns

Ysseldyke

(2014). Comparison of the effects of computer-based practice and conceptual understanding interventions on mathematics fact retention and generalization. The Journal of Educational Research, 107, 83–89. doi:10.1080/00220671.2012.759405

26.

Kena

Musu-Gillette

Robinson

Wang

Rathbun

Zhang

… Dunlop Velez

. (2015). The condition of education 2015 (NCES 2015-144). Washington, DC: U.S. Department of Education, National Center for Education Statistics. Retrieved January 15, 2016, from http://nces.ed.gov/pubsearch

27.

(2010). A meta-analysis of the effects of computer technology in school students’ mathematics learning. Educational Psychology Review, 22, 215–243.

28.

Maccini

Gagnon

J. C.

Hughes

C. A.

(2002). Technology-based practices for secondary students with learning disabilities. Learning Disability Quarterly, 25, 247–261. doi:10.2307/1511356

29.

*Mendiburo

Hasselbring

(2014). Technology’s impact on fraction learning: An experimental comparison of virtual and physical manipulatives. Journal of Computers in Mathematics and Science Teaching, 33, 209–231.

30.

National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Retrieved from http://standards.nctm.org

31.

Nelson

Fien

Doabler

C. T.

Clarke

(2016). Using education technology to differentiate and intensify instruction to support student learning outcomes. TEACHING Exceptional Children, 48, 293–300. doi: 10.1177/0040059916650639

32.

*Nordness

Haverkost

Volberding

(2011). An examination of hand-held computer-assisted instruction on subtraction skills for second grade students with learning and behavioral disabilities. Journal of Special Education Technology, 26, 15–24.

33.

Ochsendorf

(2016). Advancing understanding of mathematics development and intervention: Findings from NCSER funded efficacy studies. Journal of Research on Educational Effectiveness, 9, 570–576. doi:10.1080/19345747.2016.1222144

34.

*Ok

Bryant

. (2015). Effects of a strategic intervention with iPad practice on the multiplication fact performance of fifth-grade students with learning disabilities. Learning Disabilities Quarterly, 1–13. doi:10.1177/0731948715598285

35.

*Satsangi

Bouck

(2014). Using virtual manipulative instruction to teach the concepts of area and perimeter to secondary students with learning disabilities. Learning Disability Quarterly, 1–13. doi:10.1177/0731948714550101

36.

*Satsangi

Bouck

Taber-Doughty

Bofferding

Roberts

(2016). Comparing the effectiveness of virtual and concrete manipulatives to teach algebra to secondary students with learning disabilities. Learning Disability Quarterly, 39, 240–253. doi:10.1177/0731948716649754

37.

*Seo

Bryant

(2012). Multimedia CAI program for students with mathematics difficulties. Remedial and Special Education, 33, 217–225.

38.

*Shin

Bryant

. (2016). Improving the fraction word problem solving of students with mathematics learning disabilities: Interactive computer application. Remedial and Special Education. doi:10.1177/0741932516669052

39.

Sood

Jitendra

A. K.

(2013). An exploratory study of a number sense program to develop kindergarten students’ number proficiency. Journal of Learning Disabilities, 46, 328–346. doi:10.1177/0022219411422380

40.

*Stultz

(2013). The effectiveness of computer-assisted instruction for teaching mathematics to students with specific learning disability. The Journal of Special Education Apprenticeship, 7, 1–13.

41.

Weng

Maeda

Bouck

(2014). Effectiveness of cognitive skills-based computer assisted instruction for students with disabilities: A synthesis. Remedial and Special Education, 35, 167–180.

42.

What Works Clearinghouse. (2014). What works clearinghouse: Procedures and standards handbook. Washington, DC: National Center for Education Evaluation and Regional Assistance, Institute of Education Sciences, U.S. Department of Education.

43.

Woodward

Rieth

(1997). A historical review of technology research in special education. Review of Educational Research, 67, 503–536.

Study	Sample		Intervention Description	Dependent Variables	Percentage of Nonoverlapping Data
Study	Participants	Design	Intervention Description	Dependent Variables	Percentage of Nonoverlapping Data
Bryant et al. (2015)	N = 6 fourth-grade students with LD	Alternating treatment	Students received practice on multiplication facts in one of the three conditions: (a) teacher-directed activity, (b) iPad applications (Math Drills and Math Evolve), and (c) combined instruction for 30-min sessions, 5 days per week for 3 weeks	Researcher- developed assessments	100%
Cihak and Bowlin (2009)	N = 3 high school students with LD	Alternating probe	Students received practice on the concept of perimeter via a handheld computer with video clips for 20 sessions	Researcher-developed assessments	100
Gross and Duhon (2013)	N = 3 elementary students at risk for MLD	Nonconcurrent multiple baseline	Students received practice on addition and multiplication facts via computers for 32-min sessions, 4 days per week, for 16 sessions	Researcher-developed assessments	41–100
Nordness, Haverkost, and Voldberding (2011)	N = 3 second-grade students with LD	Multiple baseline	Students received practice on two-digit subtraction facts in 10-min sessions, 3 times a week for 14 weeks	Researcher-developed assessments	75; 80
Ok and Bryant (2015)	N = 4 fifth-grade students with LD	Multiple probe	Students received practice on multiplication facts via iPads in 30-min sessions for 5 days a week for 3 weeks	Researcher-developed assessments	93–100
Satsangi and Bouck (2014)	N = 3 9th- and 11th-grade students with MLD	Alternating treatment	Students received practice on concepts of area and perimeter via VM in 40-min sessions	Researcher-developed assessments	100
Satsangi, Bouck, Taber-Doughty, Bofferding, and Roberts (2016)	N = 3 11th- and 12th-grade students with LD	Alternating treatment	Students received practice on linear equations in three conditions: (a) VM, (b) CM, or no treatment. Each condition lasted 10 sessions	Researcher-developed assessments	100
Seo and Bryant (2012)	N = 4 second- and third-grade students MLD	Multiple probe across subjects	Students received practice on add/sub word problems via Math Explorer in 20- to 30-min sessions, 5 times per week for 18 weeks	Researcher-developed assessments	100
Shin and Bryant (2016)	N = 4 second- and third-grade students with MLD	Multiple baseline with multiple probes	Students received practice on fraction word problems via fun fraction in 20-min sessions, 2 times per week for 13 weeks	Researcher-developed assessments	56–100

Study	Sample		Intervention Description	Dependent Variables	Hedges’s g [95% CI]
Study	Participants	Assignment	Intervention Description	Dependent Variables	Hedges’s g [95% CI]
Fien et al. (2016)	N = 250 first-grade students (n = 125 Tx and n = 125 Ctl). Of the 250 students, 151 scored ≤ 25th percentile on easy CBM-CCSS-M and thus at risk for MLD	Matched in pairs based on pretest scores, students were randomly assigned within classrooms to Tx or Ctl	Students in the Tx condition received the NS1 intervention, which targeted whole number concepts and skills, 4 days per week in 15-min sessions for a total of 48 sessions (12 hr). Ctl students received BAU Tier 2 math instruction supports	easyCBM Math; easyCBM-NCTM^a; Group-Admin MN and QD; NS1 mastery tests (2, 4, and 6 weeks); ProFusion-Revised^b	−0.13 [−0.38, 0.12]^a to 0.30 [0.05, 0.55]^b
Bos (2007)	N = 95 11th-grade students (n = 48 Tx and n = 47 Ctl) from 10 Tx classes and 9 Ctl classes. All students at risk for MLD	No random assignment	In the Tx classes, students received six lessons from Texas Instruments InterActive program delivered across eight 55-min sessions and focused on quadratic functions. Students in Ctl received BAU instruction on quadratic functions	Objective 5—quadratic functions—Texas assessment of knowledge and skills exit level mathematics test	0.65 [0.23, 1.05]
Bottge, Rueda, Grant, Stephens, and Laroque (2010)	N = 54 sixth-, seventh-, eighth-grade students (n = 29 Tx and n = 25 Ctl). Students with MLD	Randomly assigned within classrooms to Tx or Ctrl	Students in the Tx condition received fraction computation practice via computer-based enhanced anchored instruction in 50-min sessions for 24 days. Ctl students received teacher-delivered EAI	Researcher-developed problem-solving^a; fraction Computation.^b ITBS computation and data analysis	0.11 [−0.42, 0.64]^a to 1.05 [0.49, 1.62]^b
Bottge et al. (2015)	N = 134 sixth-, seventh-, eighth-grade students (n = 72 Tx and n = 62 Ctl). Students with MLD	Randomly assigned within schools to Tx or Ctrl	Students in the Tx condition received fraction word problem practice via computer-based enhanced anchored instruction in 45–75 sessions for 66 days. Ctl students received BAU district math curriculum	ITBS computation^a and data analysis. Researcher-developed problem-solving; fraction computation^b	−0.23 [−0.57, 0.11]^a to 0.64 [0.30, 0.99]^b
Burns, Kanive, and DeGrande (2012)	N = 442 third- and fourth-grade students. Third grade (n = 139 Tx, n = 142 Ctl). Fourth grade (n = 77 Tx, n = 84 Ctl). Scored ≤ 25th percentile on Star Math. Students with MLD	No random assignment. Extant data analysis	Students in the Tx condition received A/S/M/D fact fluency practice via CBMFF program in 5- to 15-min sessions, 3 days per week for 8–15 weeks. Ctrl students received CBMFF approximately 1 day per week for < 8 weeks	Star Math third grade^a; Star Math fourth grade^b	0.36 [0.12, 0.59]^a; 0.48 [0.17, 0.80]^b
Fede, Pierce, Matthews, and Wells (2013)	N = 32 fifth-grade students (n = 16 Tx and n = 16 Ctl). Scored ≤ 30th percentile on the process and application subtest of the GMADE	Randomly assigned within classrooms to Tx or Ctrl	Students in the Tx condition received A/S/M/D word problem practice via the GO Solve Word Problems program in 45-min sessions, 2 days per week for 16 weeks	GMADE^a; Massachusetts comprehensive assessment system^b	0.36 [−0.33, 1.03]^a; 0.76 [−0.33, 1.03]^b
Fuchs, Fuchs, Hamlett, and Appleton (2002)	N = 38 fourth-grade (n = 28 Tx, n = 10 Ctl) students with MLD	Randomly assigned within classrooms to one of four conditions; 10 students in each condition	Students randomly assigned to (a) word problem-solving tutoring + computer-assisted practice, (b) computer-assisted practice only, (c) word problem-solving or (d) control. Computer sessions consisted of 24 sessions, 2 times per week for 12 weeks	Story problems^a; transfer story problems; real-world problem-solving^b	0.58 [−0.33, 1.48]^a to 0.88 [−0.07, 1.80]^b
Kanive, Nelson, Burns, and Ysseldyke (2014)	N = 85 fourth- and fifth-grade students (n = 28 Tx, n = 29 Ctl, n = 29 conceptual). Scored ≤ 25th percentile on the measures of academic progress subtest	Two levels of randomization: (1) random assignment to one of three conditions and (2) random assignment to multiplication facts	Students in the Tx condition received multiplication facts practice via computers in two 15-min sessions (30-min total). Students in the conceptual condition received explicit instruction of single-digit multiplication facts	Single-digit multiplication word problem^a; fact fluency CBM^b	0.14 [−0.38, 0.65]^a; 0.59 [0.06, 1.11]^b
Mendiburo and Hasselbring (2014)	N = 67 fifth-grade students (n = 34 Tx and n = 33 Ctl). All students at risk for MLD	Randomly assigned within classrooms to Tx or Ctrl	Students in the Tx condition received practice fraction magnitude via laptops. Ctl students received teacher-facilitated fraction magnitude instruction with concrete manipulatives	Researcher-developed assessments	0.31 [−0.17, 0.78]^a to 1.55 [0.99, 2.08]^b
Stultz (2013)	N = 58 10th-grade students with LD (n = 29 Tx and n = 29 Ctl)	Randomly assigned within classrooms to Tx or Ctrl	Students in the Tx condition received BMCSB instruction, 90 min for 10 sessions. Ctl students received BAU teacher-directed activities	Brigance Comprehensive Inventory of Basic Skills—Revised	−0.15 [−0.65, 0.36]