Studying the Impact of Video Modeling for Algebra Instruction for Students With Learning Disabilities

Abstract

An established research base exists for using video modeling to teach students with severe disabilities. However, the application of this strategy for teaching academic skills to students with a learning disability is less known, particularly in secondary mathematics. Video modeling provides a resource for supplementary instruction using age-appropriate technology to support student learning. To explore the use of this strategy in algebra, this study assessed video modeling paired with a system of prompting to teach three secondary students with a mathematics learning disability how to graph linear equations. Using a single subject multiple probe design, the researchers found that student performance across multiple measures, including problem-solving accuracy and independence, improved for all three students during treatment phases. These results and their implications for the broader field of mathematics education are discussed.

Keywords

algebra learning disability mathematics video modeling

As of 2016, the most prevalent disability category of students ages 6 to 21 served under the Individuals with Disabilities Education Improvement Act (2004) was specific learning disability (SLD), accounting for 38.6% of students with disabilities (U.S. Department of Education, Office of Special Education and Rehabilitative Services, Office of Special Education Programs, 2018). Within the subject area of mathematics, students with a mathematics learning disability (MLD) commonly exhibit deficits in working memory and long-term memory, and poor organizational skills, all of which serve as significant barriers toward learning grade level curricula (Geary et al., 2012; Scanlon, 2013). To support these problem areas, targeted supplementary instruction beyond what is provided by a single teacher may benefit student outcomes in the classroom. Within this context, video-based interventions (VBI; Mechling, 2005) designed in accordance to an instructional design framework may offer support in mathematics to students who struggle in this area.

Video Modeling for Students With MLD

Video-based interventions entail students watching a video recording delivering instruction through auditory directions and visual examples to learn and then complete a given skill (Cihak et al., 2010). Instructional videos provide teachers the opportunity to enhance learning with supplemental teaching that students can access via mobile technologies such as computers or tablets (Cihak & Bowlin, 2009). The flexibility of video affords students the opportunity to re-watch multiple demonstrations of an exemplar and allows teachers the ability to reuse video recordings across several classrooms and grade levels while differentiating and scaffolding lessons for diverse learners (Mechling, 2005). As an indication of its flexibility in design and use, many formats of VBI exist for teachers to consider, including video prompting, video modeling, video self-modeling, subject point-of-view video modeling, and computer-based video instruction (see Mechling, 2005, for a description of each format). To further explore the benefits of VBI to support students with disabilities in secondary education, researchers studied its use for instruction across a range of disability categories and subject areas.

While the majority of research on VBI in special education has assessed functional skills to students with severe disabilities (see Acar & Diken, 2012; Mason et al., 2012; Yakubova et al., 2015), a growing body of literature has studied its benefits in mathematics for students with MLD. For instance, Bottge and colleagues demonstrated the use of video within anchored instruction for teaching a range of skills, including problem solving (Bottge, 1999; Bottge et al., 2002), pre-algebraic concepts (Bottge et al., 2001), and Geometry skills (Bottge et al., 2003). Elsewhere, Cihak and Bowlin (2009) used a single subject multiple probe design to demonstrate the success of video modeling for teaching three high school students how to solve Geometry problems. Across intervention and maintenance phases, researchers found video modeling effectively taught students how to solve for perimeter of squares, rectangles, triangles, trapezoids, and additional polygons, with treatment session accuracy scores for each student ranging from 70% to 100% and total mean accuracy scores ranging from 88% to 96%. More recently, Satsangi, Hammer, and Bouck (2019) used a single subject multiple baseline design to illustrate the success of video modeling to teach three high school students how to solve area and perimeter word problems. Across intervention and maintenance phases, a functional relationship was established for all three students between video modeling and their problem-solving accuracy, with treatment session accuracy scores for each student ranging from 60% to 100% and total mean scores ranging from 90% to 100%. Shortly thereafter, Satsangi, Hammer, and Hogan (2019) used a single subject alternating treatments design to measure and compare the success of video modeling to face-to-face explicit instruction from an adult for three high school students learning area and perimeter word problems. Across intervention, video modeling was shown to garner positive findings comparable to explicit instruction from a researcher, with mean scores for all three students with both treatments ranging from 92% to 100%. In addition, performance across measures of independence and social validity in both studies returned favorable results for both video modeling and explicit instruction. Collectively, research on differing forms of VBI suggests this strategy offers many benefits for supporting academic instruction for students with MLD. Moreover, the findings of Cihak and Bowlin (2009) and Satsangi, Hammer, and Bouck (2019) and Satsangi, Hammer, and Hogan (2019) suggest video modeling specifically can improve the performance of students with MLD learning secondary mathematics curricula.

Theoretical Framework for Video Modeling

Coupled with positive student performance data, Satsangi, Hammer, and Bouck (2019) and Satsangi, Hammer, and Hogan (2019) demonstrated the value of designing VBI such as video modeling in accordance to evidence-based design principles for multimedia instruction outlined by Mayer (2008). Although many instructional videos exist online for students to use, very few are designed following a theoretical model or established design principles, while others lack pedagogical strategies tailored to students with disabilities (Kennedy et al., 2015). This reality often leads to the adoption of multimedia tools in the classroom that fail to meet the needs of the learners they are intended to support.

To address this shortcoming, the cognitive theory of multimedia learning (CTML; Mayer, 2008, 2009) and its applied instructional design principles (Mayer, 2008) offer researchers a framework for creating instructional materials that support cognition among diverse learners (DeLeeuw & Mayer, 2008). Operationalized across 12 principles of instructional design, this framework leverages understanding of how individuals utilize auditory and visual inputs to create multimedia for teaching ideas to learners of all ages (DeLeeuw & Mayer, 2008). The CTML framework and design principles possess an established research base informing instruction that appeals to the broadest range of learners; each of the 12 principles is supported by multiple experimental studies assessing its use (Mayer, 2008, 2011). For this reason, it may serve as a framework to design and evaluate video modeling that is tailored for students with MLD using evidence-based practices shown effective for teaching this population. Previous research by Satsangi, Hammer, and Bouck (2019) and Satsangi, Hammer, and Hogan (2019) demonstrated that video modeling created in accordance with the CTML principles with explicit instruction and multiple representations (Gersten et al., 2009) attained positive findings for teaching Geometry to students with D and provides a foundation for further research with this strategy in mathematics education.

Rationale for Study

Research on video modeling in teaching mathematics to students with MLD suggests this strategy may offer substantial benefits for these students. However, despite its growing research base, the application of this strategy for this population across the broad spectrum of mathematics education is still unknown. For instance, while the work of Cihak and Bowlin (2009) and Satsangi, Hammer, and Bouck (2019) and Satsangi, Hammer, and Hogan (2019) demonstrated the success of video modeling to teach concepts taught in early middle school mathematics curricula (e.g., solving for area and perimeter), its use in teaching higher-order concepts such as manipulating and generalizing linear equations is still unknown. In fact, the authors found no research studying video modeling to teach algebra skills to students with MLD. With the significant role algebra plays in K-12 educational programming for students with and without disabilities (National Center for Education Statistics [NCES], 2017), more research is warranted in studying innovative ways to teach this subject area to students who struggle in mathematics and need additional instruction.

This study’s aim was to expand the research base on video modeling and study its use for teaching Algebra 1 skills. Specifically, the authors sought to study video modeling to teach graphing linear equations to high school students with MLD while addressing the following research questions: (a) Is there a functional relation between video modeling paired with a system of prompting and accuracy performance graphing linear equations for secondary students with MLD?; (b) How independent are secondary students with MLD when using video modeling with a system of prompting to graph linear equations?; (c) How many viewings of a video modeling lesson do secondary students with MLD require to graph linear equations?; and (d) How much time do secondary students with MLD need to graph linear equations when using video modeling with a system of prompting?

Method

Participants

Three students were chosen from one self-contained mathematics classroom to participate in this study, with each meeting the following eligibility criteria: (a) identified with MLD per their Individualized Education Program (IEP), (b) enrolled in an Algebra 1 class, (c) received instruction on graphing linear equations in prior classes, (d) scored below 50% on a researcher-created pre-assessment (all three students earned 0% correct on the pre-assessment), and (e) physically able to independently navigate a tablet.

Darren

Darren was a 16-year-old Caucasian male in the 10th grade. He was found eligible for special education services for a SLD and other health impairment (OHI) due to deficits in mathematics, reading, writing, and attention. He was enrolled in a co-taught Algebra 1 course and had a mathematics-reasoning goal written in his IEP. Darren’s full-scale intelligence quotient (IQ) was found to be in the “average” range with a standard score of 95, according to the Wechsler Intelligence Scale for Children, Fourth Edition (WISC-IV). On the Woodcock–Johnson Tests of Achievement, Third Edition (WJ-III), he scored a standard score of 93 in Broad Mathematics, considered to be in the “average” range. Darren scored 338 on the mathematics state standardized assessment in 8th grade (400 was passing).

Lucy

Lucy was a 16-year-old African American female in the 10th grade. She was found eligible for special education services for SLD and OHI due to deficits in mathematics, reading, writing, and attention. At the time of the study, Lucy was enrolled in a co-taught Algebra 1 course and had a mathematics-reasoning goal written in her IEP. Lucy’s full-scale IQ was found to be in the “average” range with a standard score of 91 according to the Woodcock-Johnson III Tests of Cognitive Abilities (WJ-III COG). On the WJ-III, she scored a standard score of 87 in Broad Mathematics, which is considered to be in the “low average” range. Lucy scored 355 on the mathematics state standardized assessment in 8th grade (400 was passing).

Grace

Grace was a 16-year-old Hispanic female in the 10th grade. She was found eligible for special education services for SLD due to deficits in mathematics, reading, and writing. At the time of the study, Grace was enrolled in a co-taught Algebra 1 course and had a mathematics-reasoning goal written in her IEP. Grace’s full-scale IQ was found to be in the “low” range with a standard score of 75 according to the WJ-III COG. On the WJ-III, she earned a standard score of 75 in Broad Mathematics, considered to be in the “low” range. On the eighth grade mathematics state standardized assessment she scored 286 (400 was passing).

Setting

This study took place in a public high school within a Mid-Atlantic city in the United States. Of the approximately 2,000 members of the student body, 44% were Hispanic, 22% African American, 20% Caucasian, 9% Asian, and 5% were two or more ethnicities. Data collection sessions took place in a 10 ft × 10 ft conference room. One researcher sat adjacent to a student for all data collection sessions; each session lasted approximately 15 min in length.

Independent and Dependent Variables

The independent variable in this study was an instructional video teaching how to graph linear equations paired with a system of prompting. The video was created in accordance to the applied instructional design principles of Mayer (2008) and met all 12 standards for developing multimedia materials. A system of least prompts was used as part of the intervention; prompts featured verbal direction, physical gesturing with verbal direction, and physical modeling with verbal direction (Doyle et al., 1988). Prompting was included as part of the intervention to assess how long students take to autonomously use video instruction to learn algebraic curricula.

The dependent variables in this study included: (a) the percentage of correctly graphed linear equations per session, (b) the percentage of steps within each problem completed independently per session, (c) the average number and percentage of each type of prompt needed to complete each problem per session, (d) the number of times a student viewed the video while completing each session, and (e) the time needed to complete each session. A researcher-created recording system and permanent product recording procedures were used to assess student performance across each dependent variable. The total number of problems solved correctly out of five determined percent accuracy in each session. The total number of steps within each problem completed without a prompt across five problems determined percent independence. Time for each session was measured using a digital watch. Two adult researchers collected data on all dependent variables for all three students. All members of the research team were current or previously licensed special education teachers.

Materials

Pre-assessment

To identify eligible participants for this study, students were provided a pre-assessment to assess their ability to graph linear equations. The pre-assessment entailed five equations presented in a variation of the following form: y = mx + b (i.e., values were rearranged in varying order on both sides of the equal sign). Students were tasked with arranging each equation into the correct form (y = mx + b), identifying the y-intercept and slope, and then graphing each equation by marking at least two points on a coordinate plan and drawing a line connecting each. Students were ineligible to participate if they scored above 50% on the pre-assessment.

Video modeling

As the independent variable in this study, one instructional video was created by researchers using a 9.7-in. Apple® iPad Pro with a compatible connecting keyboard, stylus, and the ShowMe® app (www.showme.com). The app features an interactive whiteboard format that allows users to create, save, and access videos. The video taught students how to graph linear equations—a skill aligned to the standards for Algebra 1 as defined by the Common Core State Standards Initiative (CCSSI, 2010; CCSS.Math.Content.8.F.A.3) and the Virginia Mathematics Standards of Learning. The video featured expository second-person point-of-view instruction through voice-over narration and incorporated the following three evidence-based practices for students with MLD as identified by the What Works Clearinghouse and the National Center for Education Evaluation and Regional Assistance (Woodward et al., 2012) and a meta-analysis of instructional components of mathematics instruction by Gersten et al. (2009): (a) explicit instruction (Archer & Hughes, 2011), (b) multiple representations (van Garderen et al., 2012), and (c) a metacognitive strategy (i.e., a self-monitoring checklist; Shimabukuro et al., 2000). The targeted skill within the video was taught in a stepwise sequence.

The video began by introducing students to the skill that would be taught within the lesson and explaining the definition of the following vocabulary terms: equations, variables, constants, slope, y-intercept, coordinate plane, points, and lines. Next the equation y = mx + b was depicted on screen as the narrator explained its significance for graphing equations and noted the slope (m) and y-intercept (b) notations. An example equation was then shown on screen in black text (i.e., y = 2x + 4) followed by a red colored line underlining the slope and y-intercept values represented in the equation. Beneath the equation, the slope and y-intercept values were recorded (i.e., slope = 2/1 and y-intercept = 4). Next, the same example equation was presented on screen but with its values placed in a different order (i.e., y – 4 = 2x). The narrator then demonstrated on screen how to isolate the y variable on one side of the equal sign by completing one or more inverse operations in order to represent the equation in the y = mx + b form. Next, a coordinate plane was depicted on the right side of the screen with the same equation (y = 2x + 4) to its left with the slope and y-intercept values recorded beneath. The narrator then plotted the y-intercept on the coordinate plane using a blue dot. From this point, the slope value in a fraction form was used to plot a second point on the graph with a green colored dot. Finally, both points were connected with a red intersecting line. Next, a second example problem was presented on screen (i.e., y = x + 2). The narrator walked through each of the steps outlined above to graph this second equation (refer to Figure 1). Afterwards, a self-monitoring checklist was illustrated and reviewed onscreen to remind students to verify whether they completed each step correctly. The checklist encompassed each problem-solving step listed sequentially and directed students to record their work on their handout beneath the problem listed. In total, the video was 7 min in length and was narrated by one adult female.

Figure 1.

Screenshot of the video modeling lesson.

Assessments

Researchers created 20 unique assessments for this study to assess student performance. All questions were designed in accordance to the Virginia Mathematics Standards of Learning and curriculum-based problems provided in the Holt McDougal Larson© 2011 Algebra 1 textbook. Each assessment was identical in format and possessed five equations on one side of an 8.5 in. × 11 in. sheet of paper, with no equation repeated twice. Each equation possessed a “y,” “mx,” and “b” value presented in a randomized order within one of 12 variations of an equation (e.g., y = mx + b, mx = y + b, b = mx + y). No two consecutive assessments possessed identical variations of equations. All “m” and “b” values were represented by whole numbers ranging from –9 through 9 (excluding 0). To graph equations, students were provided a separate 8.5 in. × 11 in. sheet of paper illustrating multiple coordinate plane graphs. Students graphed each equation within each assessment on a separate graph. Students were provided a four-function calculator for each assessment.

Experimental Design

In accordance to the single case design standards of Kratochwill et al. (2014) and the single case quality indicators for methodological rigor by Horner et al. (2005), this study used a single subject multiple probe design (Gast & Ledford, 2014) across three students with MLD to examine the functional relation between video modeling instruction and student performance graphing linear equations. A multiple probe design provides a staggered offering of the independent variable to each participant in a systematic and successive order. Following evidence of a stable baseline, the first participant is introduced to the independent variable as the remaining participants continue baseline sessions. Then, following three successive sessions of stable performance in the intervention phase by the first participant, the second participant is introduced to the independent variable, while the remaining participant(s) remain in baseline; this repeats until all participants are introduced to the independent variable and to demonstrate stable intervention performance (Gast & Ledford, 2014). At least five sessions of baseline and intervention data were collected with each student participant in this study. Sessions within both of these phases continued until the level of each student’s data were deemed stable.

Procedures

Baseline

For baseline, students were assessed on their ability to graph equations while receiving no instruction or prompting from a researcher. Researchers collected data on accuracy performance and duration using a researcher-created data collection sheet. Stable performance was required from each student across a minimum of five sessions before beginning intervention.

Intervention

Following baseline, each student was trained and then required to demonstrate mastery on accessing and viewing a video on a tablet; this included using the play, pause, fast-forward, and rewind features in the video independently. Following this training, students partook in intervention. For each session, students were given a tablet with one video modeling lesson presented on the screen, an assessment sheet that contained five linear equations, and a second sheet illustrating blank coordinate plane graphs. Students were required to watch the video once in its entirety teaching them how to graph linear equations. Next, students completed the same steps demonstrated in the video with the five problems on their assessment sheet. Students identified the y-intercept and slope values of each equation in the blank area beneath each problem. If needed, they solved the equation for the y variable in order to arrange it in the y = mx + b form as taught within the lesson. Then, students graphed the y-intercept and a second point using the slope on a blank coordinate plane graph, sketching a line through both points. As students completed each problem, they were permitted to re-watch the video or any portion of the video. For each session, researchers collected data on all dependent variables using a researcher-created data collection sheet. Following a system of least prompts (Doyle et al., 1988), if a student required assistance on any step of a problem, a researcher would first offer them a prompt (verbal direction) instructing them to re-watch relevant portions of the video or to review the self-monitoring checklist at the end of the video. If the student struggled navigating the video or reviewing the checklist, physical gesturing with verbal direction was provided. If the student continued to struggle after re-watching the video one time, a researcher provided them the highest-level prompt (physical modeling with verbal direction). In these instances, a researcher replayed relevant portions of the video once and explained each step while marking it incorrect. Stable intervention performance (as it relates to the level of the data) was required from each student for a minimum of five sessions.

Extended intervention

After a 4-week break following intervention, students completed five additional sessions graphing linear equations using video modeling with a system of prompting. This phase was conducted to measure whether students retained the ability to use a video modeling lesson to support them solving problems. Sessions were conducted in an identical manner to the intervention phase with the same dependent variables assessed.

Social Validity Interviews

Social validity interviews were conducted one-on-one with all three students by one member of the research team prior to and following the study. Researchers asked students open-ended questions and transcribed their responses using paper and pencil. Questions assessed students’ views of mathematics, technology use for learning, past experiences watching videos to learn skills, and their perceptions of the treatment condition after completing the study.

Treatment Integrity and Inter-observer Agreement

Treatment integrity and inter-observer agreement (IOA) data were collected for 40% of sessions in all phases of the study. The two researchers responsible for all data collection were trained simultaneously across one 60-min session on implementing the intervention and delivering the system of prompting to students as well as data collection procedures for all dependent variables measured. In addition, a checklist was used to ensure students were provided an assessment sheet, writing utensil, four-function calculator, and the video modeling lesson. Treatment integrity data regarding the checklist were 100% for all three students. IOA data were collected on percent accuracy, percent independence, and prompting provided to each student. IOA was calculated by dividing the number of agreements by the number of agreements plus disagreements and multiplying by 100 to report a percentage. Cumulative IOA scores for each student in intervention and extended intervention sessions were as follows: Darren’s IOA was 96% for accuracy (range = 80%–100%), 98.7% for independence (range = 76.7%–100%), and 81.8% for prompting (range = 78.9%–100%); Lucy’s IOA was 100% for accuracy, 97.5% for independence (range = 86.7%–100%), and 87.5% for prompting (range = 66.7%–100%); and Grace’s IOA was 100% for accuracy, independence, and prompting.

Data Analysis

Data were assessed using visual analysis and an effect size measure. Visual analysis entailed assessing the level, trend, variability, overlap, immediacy of effects, and consistency of data patterns between phases for each student’s graphed data (Gast & Ledford, 2014). The level of data was determined stable when 80% of the data fell within a 25% range of the median in a specific phase. Trends in the data were identified via the split middle method technique within and across phases (Gast & Ledford, 2014). In addition, the effect size Tau-U (Parker et al., 2011) was conducted to assess the effect of the treatment on student accuracy performance. Tau-U is a non-parametric statistical measure of effect size found by combining the non-overlap data between two phases with the trend within the intervention phase. An online calculator was used to compute Tau-U effect sizes (http://www.singlecaseresearch.org). The effect size scale for Tau-U results is as follows: 0.93 to 1 is considered a large effect, 0.66 to 0.92 a medium effect, and 0 to 0.65 a small effect (Parker et al., 2011). A combined weighted average Tau-U score and individual student scores were calculated.

Results

Each of the three students demonstrated increased performance during both treatment phases compared with their baseline data. Intervention and extended intervention performance for all three across the dependent variable of percent accuracy ranged between 20% and 100% and between 83.3% and 100% for percent independence (refer to Table 1). The combined weighted Tau-U score for all three students was 1.0, 95% confidence interval (95% CI = [0.5848, 1.0]), indicating the treatment was highly effective for all three (Parker et al., 2011).

Table 1.

Participant Data Averages.

Student	Phase	Percent accuracy	Percent independence	Prompts	Duration (min)	Video viewings
Darren	Baseline	0	—	—	2.4	—
	Intervention	74	94.8	4.7	8.9	1.3
	Extended intervention	88	98	1.8	5.2	1
Lucy	Baseline	0	—	—	3.8	—
	Intervention	68	92	6.6	12.8	1.2
	Extended intervention	88	97.4	2	7.4	1
Grace	Baseline	0	—	—	4	—
	Intervention	88	98	1.8	10.4	1.8
	Extended intervention	96	99.3	0.6	9.8	1.4

Darren

Darren did not answer any questions correctly during baseline sessions. The level and trend stability of his data were stable, and the trend direction was zero-celerating. He averaged 2.4 min to complete each session (range = 2–4). During intervention, Darren’s accuracy performance improved above his baseline data, demonstrating an immediate change in level between conditions (Gast & Ledford, 2014; refer to Figure 2). Using video modeling, Darren earned an average accuracy of 74% (range = 20%–100%) across seven sessions of intervention. His average percent independence per session was 94.8% (range = 83.3%–100%; refer to Figure 3), and he averaged 4.7 prompts per session (range = 0–15), of which 100% were physical modeling with verbal direction. Three out of the seven sessions (42.9%) and 27 out of 35 problems (77.1%) solved were completed without a prompt. His average time to finish each session was 8.9 min (range = 3–23), while he watched each video an average of 1.3 times per session (range = 1–2). Darren’s intervention data were determined stable with 80% of his data falling within 25% of the median level (Gast & Ledford, 2014). The trend direction of his data was accelerating, while trend stability was deemed stable based on the level stability envelope and the trend line (Gast & Ledford, 2014). The effect size Tau-U was 1.0 (90% CI = [0.421, 1.0]), suggesting a highly effective intervention (Parker et al., 2011). For the extended intervention phase, Darren had an average accuracy of 88% (range = 80%–100%) over five sessions. His percent independence average per session was 98% (range = 96.7%–100%), and he needed an average of 1.8 prompts per session (range = 0–3), 100% of which were physical modeling with verbal direction. Two out of the five sessions (40%) and 22 out of 25 problems (88%) were solved without a prompt. His average time to complete each session was 5.2 min (range = 4–8), and he watched each video one time per session. The level and trend stability of his extended intervention data were stable, and the trend direction was accelerating and variable.

Figure 2.

Percentage of correctly graphed linear equations.

Figure 3.

Percentage of steps completed independently per session.

Lucy

Lucy did not answer any questions correctly on six consecutive baseline sessions. The level and trend stability of her data were stable, and the trend direction was zero-celerating. She averaged 3.8 min to complete each assessment (range = 3–5). Once provided the treatment condition in intervention, Lucy’s performance increased above her baseline scores, demonstrating a change in level between conditions (Gast & Ledford, 2014). Lucy earned an average accuracy of 68% (range = 60%–80%) across five consecutive sessions, an average percent independence of 92% (range = 83.3%–100%), and an average of 6.6 prompts (range = 0–12), of which 9.1% were verbal direction and 90.9% were physical modeling with verbal direction. One out of the five sessions (20%) and 16 out of 25 problems (64%) solved were completed without a prompt. Her average time per session was 12.8 min (range = 6–24), and she watched each video an average of 1.2 times per session (range = 1–2). The level stability of her intervention data was deemed unstable as 60% of her data fell between 25% of the median point (Gast & Ledford, 2014). The trend direction of her data for this phase was accelerating, demonstrating a positive change in performance. Lucy’s Tau-U score was 1.0 (90% CI = [0.399, 1.0]), signifying the treatment was highly effective (Parker et al., 2011). Within the extended intervention phase, Lucy earned an average accuracy of 88% (range = 80%–100%), while her percent independence average was 97.4% (range = 96.7%–100%), and she required an average of two prompts per session (range = 0–3), 10% of which were verbal and 90% were physical modeling with verbal direction. One out of the five sessions (20%) and 21 out of 25 problems (84%) solved were completed without a prompt. Her average time per assessment was 7.4 min (range = 6–10), and she watched each video once per session. Level and trend stability of her extended intervention data were stable, and the trend direction was zero-celerating.

Grace

Grace did not solve any questions correctly on five sessions of baseline. The level and trend stability of her data were stable, and the trend direction was zero-celerating. She took an average of 4 min to complete each assessment (range = 2–7). Afterwards, her intervention performance increased above her baseline data, demonstrating a change in level between phases. She earned an average accuracy of 88% (range = 80%–100%) across five sessions, an average percent independence of 98% (range = 96.7%–100%), and an average of 1.8 prompts (range = 0–3), of which 100% were physical modeling with verbal direction. Two out of five sessions (40%) and 22 out of 25 problems (88%) solved were completed without a prompt. Her average time per session was 10.4 min (range = 7–16), and she watched each video an average of 1.8 times per session (range = 1–3). The level stability of Grace’s intervention data was stable, trend direction was accelerating, and the trend stability was stable based on the level stability envelope and trend line (Gast & Ledford, 2014). The Tau-U score for her data was 1.0 (90.0% CI = [0.370, 1.0]), suggesting the intervention was highly effective (Parker et al., 2011). Within the extended intervention phase, she earned an average accuracy of 96% (range = 80%–100%), an average percent independence of 99.3% (range = 96.7%–100%), and an average of 0.6 prompts (range 0–3), 100% of which were physical modeling with verbal direction. Four out of five sessions (80%) and 24 out of 25 problems (96%) solved were completed without a prompt. Her average time per session was 9.8 min (range = 4–18), and she watched each video an average of 1.4 times (range = 1–3). The level and trend stability of her extended intervention data was stable, while the trend direction was accelerating, indicating a positive change in performance.

Social Validity Responses

All three students expressed video modeling helped them solve and graph equations for varying reasonings. Lucy and Grace stated they liked the videos because they did not understand how to solve problems initially, but they could watch the video repeatedly until they were able to grasp the steps. Darren stated that he liked the video modeling because, “It was better than watching a teacher stand at the board . . . and I could go back to the video for help instead of bothering the teacher.” All three students expressed a desire to use more videos in their classes to rewind instruction at their own discretion.

Discussion

This study contributes to the growing body of research assessing VBI for mathematics instruction with students with MLD. Prior work in the field from Bottge and colleagues (2001, 2002, 2003) studied video within anchored instruction for teaching problem solving whereas Cihak and Bowlin (2009) and Satsangi, Hammer, and Bouck (2019) and Satsangi, Hammer, and Hogan (2019) demonstrated successful use of video modeling for teaching Geometry to this population. Our findings extend the research base on video modeling for students with MLD to include Algebra. Within at least five sessions in intervention, all three students in this study demonstrated a functional relation between video modeling with a system of prompting and accuracy performance graphing equations.

Assessing data from the treatment phases, key observations are worth noting. For instance, of the three students, Darren possessed the highest full-scale IQ and Broad Mathematics scores on the WJ-III COG. Yet, his initial accuracy performance was lower, and his improvement was more gradual compared with Lucy and Grace. Conversely, Grace possessed lower scores on these same two measures compared with Darren and Lucy yet demonstrated mastery faster and earned higher overall average accuracy and independence scores throughout intervention. Finally, Lucy was the only student not to meet and sustain 100% accuracy during intervention, with her scores ranging between 60% and 80% for this phase. Nevertheless, Lucy, Darren, and Grace all exhibited improved performance from intervention to extended intervention on all measures, including increased accuracy and independence, fewer prompts, shorter duration of sessions, and needing fewer viewings of the video to complete sessions.

The gradual improvement for all three students in this study from intervention to extended intervention sessions suggests students may need greater practice solving problems to master skills using video modeling. In addition, individual student performance noted in this study may be explained by the design of the treatment. The authors theorize creating video modeling lessons in accordance to the CTML framework and design principles (Mayer, 2008, 2009) provided lower performing students such as Grace with instruction that did not overwhelm their cognitive processes as they learned the multiple steps needed to manipulate equations, identify values, and then graph each equation based on these values. Moreover, prominent features within the video may have aided students in learning specific procedural and conceptual tasks. For instance, the multiple visual representations of concepts (Krawec, 2014; van Garderen et al., 2012) illustrated in the video may have aided students in making connections between the values in an equation and their representation on a coordinate plane. To teach slope, this concept was first conveyed as a fraction in symbolic notation form, and then using multicolored points and lines on a graph. Likewise, metacognitive strategies, such as the self-monitoring checklist (Shimabukuro et al., 2000) in the video, may have aided students in recalling the sequential steps needed to graph each line. For students, such as Darren, learning to utilize the checklist at the end to verify his work may have contributed to his gradual improvement throughout the study.

Implications for Practice

Pairing video modeling with a system of prompting as done in this study has implications for how this strategy can be used in secondary classrooms, particularly general education inclusionary settings. Prompting was included as part of the intervention to assess how long students take to independently use video modeling to learn how to graph equations. While percent independence averages for all three students in our study ranged from 97.4% to 99.3% during extended intervention sessions, students still periodically required prompting. This indicates video modeling cannot be seen as a fully autonomous form of self-learning for secondary students with MLD. Instead its application must be measured, and its use accompanied with continuous adult supervision. Thus, teachers are encouraged to view video modeling as a complimentary resource to their current classroom practices. For instance, teachers can use video modeling lessons for station work within their classes by providing a brief video highlighting key concepts in a scaffold-like manner to each group (e.g., students working at Station 1 review a video and practice solving one-step equations while students at Station 2 can skip ahead and learn to solve two-step equations). Teachers can also use video modeling across multiple stakeholders. For instance, parents of students with disabilities can support their child completing homework afterschool using videos created by their teachers. Teachers can also embed accommodations, such as subtitles for English language learners, to aid students and their parents when studying for exams or practicing problems at home. In doing so, students and their parents are provided flexible supplementary instruction in a targeted manner to support learning.

Limitations and Future Directions

While this study provides valuable findings that contribute to the research base on Algebra instruction for students with MLD, there are limitations worth considering. First, equations did not require students to combine like terms while arranging each into the y = mx + b form. Second, while a multiple probe design does not require a maintenance phase as part of its construct (Gast & Ledford, 2014), the lack of such a measure combined with the periodic need for prompting from students during extended intervention means researchers cannot say whether video modeling will ultimately lead to complete independent problem solving for students.

Moving forward, greater research on video modeling is needed to better understand its use for students with MLD across all mathematics curriculum standards. Different conceptual skills in Algebra and Geometry vary in the cognitive demands they place on students, and thus may or may not lend themselves to being taught via video. Moreover, comparative research designs, such as group comparisons and single subject alternating treatments designs, are needed to assess how teaching students through video modeling compared with instruction provided face-to-face by a teacher. Findings from such work may indicate whether video modeling can help teach mathematics skills to students who require supplementary classroom support or, in some instances, even replace the need for adults to be continuously present to teach these skills.

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) received no financial support for the research, authorship, and/or publication of this article.

References

Acar

Diken

I. H.

(2012). Reviewing instructional studies conducted using video modeling to children with autism. Educational Sciences: Theory and Practice, 12, 2731–2735.

Archer

A. L.

Hughes

C. A.

(2011). Explicit instruction: Effective and efficient teaching. Guilford Press.

Bottge

(1999). Effects of contextualized math instruction on problem solving of average and below-average achieving students. The Journal of Special Education, 33(2), 81–92. https://doi.org/10.1177/002246699903300202

Bottge

B. A.

Heinrichs

Chan

Mehta

Z. D.

Watson

(2003). Effects of video-based and applied problems on the procedural math skills of average- and low-achieving adolescents. Journal of Special Education Technology, 18(2), 5–22. https://doi.org/10.1177/016264340301800201

Bottge

B. A.

Heinrichs

Chan

Serlin

R. C.

(2001). Anchoring adolescents’ understanding of math concepts in rich problem solving environments. Remedial and Special Education, 22(5), 299–314. https://doi.org/10.1177/074193250102200505

Bottge

B. A.

Heinrichs

Mehta

Z. D.

Hung

Y. H.

(2002). Weighing the benefits of anchored math instruction for students with disabilities in general education classes. The Journal of Special Education, 35(4), 186–200. https://doi.org/10.1177/002246690203500401

Cihak

D. F.

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(4), 17–29. https://doi.org/10.1177/016264340902400402

Cihak

D. F.

Fahrenkrog

Ayres

K. M.

Smith

(2010). The use of video modeling via a video iPod and a system of least prompts to improve transitional behaviors for students with autism spectrum disorders in the general education classroom. Journal of Positive Behavior Interventions, 12, 103–115. https://doi.org/10.1177/1098300709332346

Common Core State Standards Initiative. (2010). Common core state standards for mathematics. National Governors Association Center for Best Practices and the Council of Chief State School Officers. http://www.corestandards.org/the-standards

10.

DeLeeuw

K. E.

Mayer

R. E.

(2008). A comparison of three measures of cognitive load: Evidence for separable measures of intrinsic, extraneous, and germane load. Journal of Educational Psychology, 100, 223–234. https://doi.org/10.1037/0022-0663.100.1.223

11.

Doyle

P. M.

Wolery

Ault

M. J.

Gast

D. L.

(1988). System of least prompts: A literature review of procedural parameters. Journal of the Association for Persons with Severe Handicaps, 13, 28–40. https://doi.org/10.1177/154079698801300104

12.

Gast

D. L.

Ledford

J. R.

(2014). Single case research methodology: Applications in special education and behavioral sciences. Routledge.

13.

Geary

D. C.

Hoard

M. K.

Nugent

Bailey

D. H.

(2012). Mathematical cognition deficits in children with learning disabilities and persistent low achievement: A five-year prospective study. Journal of Educational Psychology, 104, 206–223. https://doi.org/10.1037/a0025398

14.

Gersten

Chard

D. J.

Jayanthi

Baker

S. K.

Morphy

Flojo

(2009). Mathematics instruction for students with learning disabilities: A meta-analysis of instructional components. Review of Educational Research, 79, 1202–1242. https://doi.org/10.3102/0034654309334431

15.

Horner

R. H.

Carr

E. G.

Halle

McGee

Odom

Wolery

(2005). The use of single-subject research to identify evidence-based practice in special education. Exceptional Children, 71, 165–179. https://doi.org/10.1177/001440290507100203

16.

Individuals With Disabilities Education Act, 20 U.S.C. § 1400 (2004).

17.

Kennedy

M. J.

Deshler

D. D.

Lloyd

J. W.

(2015). Effects of multimedia vocabulary instruction on adolescents with learning disabilities. Journal of Learning Disabilities, 48, 22–38. https://doi.org/10.1177/0022219413487406

18.

Kratochwill

Levin

Horner

Swoboda

(2014). Visual analysis of single-case intervention research: Conceptual and methodological issues. In Kratochwill

T. R.

Levin

J. R.

(Ed.), Single-case intervention research: Methodological and statistical advances (pp. 91–126). American Psychological Association. https://doi.org/10.1037/14376-001

19.

Krawec

(2014). Problem representation and mathematical problem solving of students of varying math ability. Journal of Learning Disabilities, 47, 103–115. https://doi.org/10.1177/0022219412436976

20.

Mason

R. A.

Ganz

J. B.

Parker

R. I.

Burke

M. D.

Camargo

S. P.

(2012). Moderating factors of video-modeling with other as model: A meta-analysis of single-case studies. Research in Developmental Disabilities, 33, 1076–1086. https://doi.org/10.1016/j.ridd.2012.01.016

21.

Mayer

R. E.

(2008). Applying the science of learning: Evidence-based principles for the design of multimedia instruction. American Psychologist, 63(8), 760–769. https://doi.org/10.1037/0003-066x.63.8.760

22.

Mayer

R. E.

(2009). Multimedia learning (2nd ed.). Cambridge University Press.

23.

Mayer

R. E.

(2011). Applying the science of learning. Pearson.

24.

Mechling

(2005). The effect of instructor-created video programs to teach students with disabilities: A literature review. Journal of Special Education Technology, 20, 25–36. https://doi.org/10.1177/016264340502000203

25.

National Center for Education Statistics. (2017). Graphs of results of the 2017 National Assessment of Educational Progress (NAEP). The nation’s report card. https://www.nationsreportcard.gov/math_2017/nation/achievement?grade=4

26.

Parker

R. I.

Vannest

K. J.

Davis

J. L.

Sauber

S. B.

(2011). Combining nonoverlap and trend for single-case research: Tau-U. Behavior Therapy, 42, 284–299. https://doi.org/10.1016/j.beth.2010.08.006

27.

Satsangi

Hammer

Bouck

E. C.

(2019). Using video modeling to teach geometry word problems: A strategy for students with learning disabilities. Remedial and Special Education. Advance online publication. https://doi.org/10.1177/0741932518824974

28.

Satsangi

Hammer

Hogan

C. D.

(2019). Video modeling and explicit instruction: A comparison of strategies for teaching mathematics to students with learning disabilities. Learning Disabilities Research & Practice, 34, 35–46. https://doi.org/10.1111/ldrp.12189

29.

Scanlon

(2013). Specific learning disability and its newest definition: Which is comprehensive? And which is insufficient? Journal of Learning Disabilities, 46, 26–33. https://doi.org/10.1177/0022219412464342

30.

Shimabukuro

S. M.

Prater

M. A.

Jenkins

Edelen-Smith

(2000). The effects of self-monitoring of academic performance on students with learning disabilities and ADD/ADHD. Education and Treatment of Children, 22(4), 397–414.

31.

U.S. Department of Education, Office of Special Education and Rehabilitative Services, Office of Special Education Programs. (2018). 40th annual report to congress on the implementation of the individuals with disabilities education act. https://www2.ed.gov/about/reports/annual/osep/2018/parts-b-c/40th-arc-for-idea.pdf

32.

van Garderen

Scheuermann

Jackson

. (2012). Examining how students with diverse abilities use diagrams to solve mathematics word problems. Learning Disability Quarterly, 36(3), 145–160. https://doi.org/10.1177/0731948712438558

33.

Woodward

Beckmann

Driscoll

Franke

Herzig

Jitendra

Koedinger

K. R.

Ogbuehi

(2012). Improving mathematical problem solving in grades 4 through 8: A practice guide (NCEE 2012-4055). National Center for Education Evaluation and Regional Assistance, Institute of Education Sciences, U.S. Department of Education. http://ies.ed.gov/ncee/wwc/publications_reviews.aspx#pubsearch/

34.

Yakubova

Hughes

E. M.

Hornberger

(2015). Video based intervention in teaching fraction problem-solving to students with autism spectrum disorder. Journal of Autism and Developmental Disorders, 45, 2865–2875. https://doi.org/10.1007/s10803-015-2449-y