Increasing Problem-Solving Ability for Students with Visual Impairments and Intellectual Disabilities

By Nicole Johnson, Ed.D. and Anne Brawand, Ph.D

Dr. Nicole Johnson is a professor in the department of special education, program on visual impairments at Kutztown University.

Dr. Anne Brawand is an associate professor in the department of special education at Kutztown University.

Abstract

Introduction: Despite the national effort to focus on prioritization of mathematical concepts, teachers of students with sensory and cognitive disabilities often do not know how to provide quality instruction to address mathematical skills. Research is limited for this population of students in the area of mathematics. This study is a replication of previous research to determine whether schema-based instruction (SBI) increases problem-solving ability for students with concurrent visual impairments and intellectual disabilities at the secondary level.

Method: A multiple-baseline-across-students design was used to study the effects of SBI on problem-solving skills of three high school students with concurrent visual impairments and intellectual disabilities. During the four-to-five-week intervention sessions, students utilized the find, organize, plan, and solve (FOPS) strategy to solve addition and subtraction word problems.

Results: The three students improved their problem-solving ability using the FOPS. Mastery increased from 13.2 during baseline to an overall level of 72.5%.

Discussion: High school students with visual impairments and intellectual disabilities demonstrated improvement in problem-solving ability after SBI was taught.

Limitations: Limitations of this study include: only three students participated in the study, the duration of the intervention was four to five weeks, and utilizing the FOPS strategy with combined visual impairments and intellectual disabilities within peer-reviewed research has yet to be established. Future studies that address high school students with multiple disabilities are needed to support or contradict this study’s findings. These studies could incorporate other mathematical skills.

Implications for practitioners: When using SBI to teach problem-solving skills, teachers of students with visual impairments and intellectual disabilities can simplify the language they use, use repetitive operation words, and include pictures for those students with low vision.

Keywords

Visual impairments, problem solving, schema-based instruction

 

The Common Core State Standards of Mathematics (CCSSM) (Common Core State Standards of Mathematics, 2012) have prompted educators to focus on prioritization of mathematical concepts. CCSSM addresses the need to build competence in mathematical ability for all students, including those with disabilities. Legally, students with disabilities, including visual impairments, should be included in this national effort. The reauthorization of the No Child Left Behind Act of 2001 (No Child Left Behind, 2002) enforced the inclusion of students with disabilities in standards-aligned systems, and schools are accountable for performance of these students on alternate assessments. Although the law requires instruction in mathematics, often teachers of students with visual impairments and cognitive disabilities do not know how to provide quality instruction to address the standards. Children with multiple impairments may exhibit slower rates of cognitive development (Horn & Kang, 2012), which makes it difficult for them to achieve mastery of grade-level standards in mathematics. Mathematics can be a roadblock for students who are visually impaired. Approximately 75% of students with visual impairments are more than a full grade level behind their peers in mathematics (Gulley et al., 2017). There have been attempts to ensure mathematical content is accessible to students with visual impairments, including applying technology to read mathematical equations (Bouck et al., 2011), describing visual images within mathematical texts and using a talking calculator (Ferrell et al., 2014; Kapperman et al., 2000); however, the educational gap still exists. Mathematical word problem solving may be specifically challenging for students with both visual impairment and cognitive disability because the problems utilize working memory (Swanson & Jerman, 2006), and many basic mathematical concepts take the forms of words that are typically interpreted visually (e.g., “big or bigger;” Jones, 2018).

Mathematics Interventions for Students with Visual Impairments

The amount of research on instruction in mathematics for students with visual impairments is minimal (Ferrell et al., 2014). The research is more limited for students with concurrent visual impairments and intellectual disabilities. Browder and colleagues (2012) found that mathematics performance improved for students with significant disabilities using problem stories, task analysis of problem steps, and graphic organizers. Additional evidence-based interventions that have been effective in the area of mathematics for students with low-incidence disabilities include conceptual models, simultaneous prompting, and hands-on interventions (Browder et al., 2012; Creech-Galloway et al., 2013). Chang and Bin (2019) also found success linked to specialized mathematics instruction for students with visual impairments including one-on-one instruction. 

As far as technology used to promote students’ skills with math word-problem-solving, Beal and Rosenblum (2018) reported that the use of an iPad application can be effective for students with visual impairments to solve pre-algebraic equations. Research additionally shows that gathering information from graphics to solve problems is a useful strategy (Rosenblum, Cheng, & Beal, 2018). However, the visual nature of graphics has its own challenges for students with visual impairments (Rosenblum & Herzberg, 2015). Although there is limited research on teaching students with visual impairments to understand and solve mathematical word problems, schema instruction has been implemented for other students with low-incidence disabilities (Root & Browder, 2019; Root et al., 2018), autism (Kasap & Ergenekon, 2016), emotional and behavior disorders (Jitendra et al., 2010), and learning disabilities (Jitendra & Star, 2011).

Schema-Based Instruction

Schema instruction was shown to be promising for high school students with intellectual disabilities in solving problems and generalizing skills to real world stimuli (Root et. al, 2018).  Schema-based instruction (SBI) incorporates both representation and cognitive thinking and has been effective with increasing problem-solving ability for students with disabilities across various skills in mathematics (Jitendra et al., 2009; Jitendra et al., 2017; Jitendra et al., 2011). SBI is an explicit procedure that uses diagrams to have students comprehend how to solve word problems (Jitendra & Star, 2012). An advantage of SBI is seeing past the surface likenesses and considering the schema. The way a problem is organized is called its “schemata.” In SBI, the word problem is presented as a story problem first with the answer, which is the completed problem. For example, the following problem illustrates the structure of an addition problem: Today Ming and Sara are building with blocks. Ming counts a stack of six red blocks. She stacks two yellow blocks on top. Ming uses eight blocks in all. Figure 1 shows that six is the first number provided, two is the second number, addition is the operation, and eight is the total. Students are prompted to focus on the structure of the story problem during this initial phase (e.g., placing numbers from the problem into a diagram; Jitendra et al., 2010).

Figure 1. Example of schemata diagram

Picture shows 6 + 2 = 8. The six and two are shown in square boxes while the operation (plus sign) and result (8) are in circles.

Since students with combined intellectual disabilities and visual impairments may have difficulty with working memory, organizing the structure of the problem reduces cognitive load when problem solving (Jitendra & Star, 2012). Although SBI has been a more documented practice for students with intellectual and learning disabilities, to date there has been no research on the use of SBI to solve word problems for students with combined visual impairments and intellectual disabilities.   

The purpose of this study was to replicate and extend the research on the SBI intervention conducted by (Brawand et al., 2020) that demonstrated impact in problem solving for a different sample using an alternate mathematical skill. The rationale for replicating the previous study was to examine the functional relation between SBI and problem-solving ability for a low-incidence population of students. The research question that this study investigated was: Do high school students with visual impairments and intellectual disabilities demonstrate improvement with solving addition and subtraction word problems after SBI is taught?

Method

Participants and Setting

Three students (two females and one male) with severe visual impairments and intellectual disabilities participated in the study. SBI was implemented by a classroom teacher in a specialized school serving students who have visual impairments with additional disabilities in the northeastern region of the United States. The school serves approximately two hundred students who are blind or visually impaired. 

Participants for the study met the following criteria: (a) diagnosed with an intellectual disability and a visual impairment as identified by a school psychologist and in their individualized educational program (IEP); (b) received services from a teacher of the visually impaired; and (c) was a high school student throughout the duration of the study (15-18 years old).

Student A was an 18-year-old Hispanic female diagnosed with an intellectual disability and was functionally blind. She was reading on a kindergarten level in large print and did not reach proficiency on the alternate state assessment but received a satisfactory math grade in the life-skills-support setting. Student B was a 17-year-old Caucasian male diagnosed with an intellectual disability and septo-optic dysplasia. He did not reach proficiency on the alternate state assessment but received a satisfactory math grade in his life-skills-support classroom setting. Student B read at a first-grade level in materials produced at 22-point font and was not able to handwrite. Student C was a 15-year-old African American female diagnosed with an intellectual disability and retinopathy of prematurity. She did not reach proficiency on the alternate state assessment but received a satisfactory math grade in the life-skills-support setting. Student C was reading at a second-grade level in material produced in 20-point font. She was able to write at a kindergarten level as reported by the classroom teacher. Alternate state assessment included reading, mathematics, and science. Participants A and B participated in Level A testing, which is the least complex reading, mathematics, and science-related skills and Participant C participated in Level B, which consists of intermediate skills.

Materials

Each participant had a booklet with a visual drawing of a four-step strategy provided in the print size used for instruction (large print). All participants were given a checklist with a four-step strategy on it (Jitendra, 2007), and a graphic organizer. Jitendra (2007) refers to this organizer as a schematic diagram. The schematic diagram included three shapes used in a horizontal manner to assist students’ placement of numbers and operation signs from the word problems, resulting in a number sentence. The diagram was provided in large print/bold and tactually. Participants were able to choose which they preferred to utilize and had access to both formats. All three participants chose the enlarged-print formats instead of tactile.

The teacher materials consisted of nine lesson plans (adapted from Jitendra, 2007) lasting 30-35 minutes each. The lesson plans contained addition and subtraction word problems. Addition and subtraction word problem probes were used to measure students’ progress. During the lessons, participants were able to use talking calculators, tactile math manipulatives, and a scribe to write answers. 

Independent Variable

The study consisted of two phases: baseline and intervention. After baseline data were collected and before beginning the intervention phase, students received a one-day workshop on SBI (FOPS). FOPS is a four-step problem-solving strategy developed by Jitendra (2007): Find the problem type, Organize the information, Plan to solve the problem, and Solve the problem. The FOPS checklist referring to the schema, or diagram, was briefly reviewed before each lesson began. Students received explicit instruction on SBI during the intervention phase. Teaching of SBI (FOPS) during the intervention included nine lessons (adapted from Jitendra, 2007).

The nine lessons were organized into three areas of addition, subtraction, and missing addend. An example of an addition word problem is: Today Ming and Sara are building with blocks. Ming counts a stack of six red blocks. She stacks two yellow blocks on top. How may blocks does Ming use in all? A subtraction example is: There are nine dolphins. Some dolphins swim away. There are six dolphins left. How many dolphins swam away? In the missing addend problems, the “total” is usually given last and will be written first in number sentence (e.g., Megan had six crayons. Justin gave her some more crayons. Now Megan has 13 crayons. How many crayons did Justin give to her?). Each of the three kinds (addition, subtraction, and missing addend) of word problems were taught using three levels of difficulty: beginner, instructional, and grade-level (Brawand et al., 2020). Word problems at the beginner level used facts to 10, instructional problems used facts to 15, and grade-level included facts to 20.

Word-Problem Probes

Word-problem probes were used to assess students’ progress solving word problems during the baseline and intervention phases. Each probe included three word problems, with one problem of each kind: addition, subtraction, and missing addend. All three problems on all forms of the probe included basic facts to 20 (“grade level”). There were 19 equivalent forms of the probe used. Two experts certified in mathematics performed content validity of the probes. They examined the 57 word problems to confirm they were of similar degrees of difficulty, used appropriate level numbers, and the probe included one problem for each kind. 

The word-problem-probe rubric had three categories (operation sign, numbers placed on diagram, correct answer), which related to the FOPS steps. It was adapted from (Brawand et al., 2020), with each step weighted by degree of difficulty to determine percent of accuracy. The total amount of points per problem was 8, which meant 24 total possible points could be earned for each probe, and the percent of accuracy was recorded. 

Research Design

A multiple-baseline-across-students design was used to determine whether a functional relation between SBI and problem-solving ability existed (Gast et al.,2014). The start of the intervention was staggered across the students as mandated by the single-subject-research design standards, with students randomly selected for intervention start days (Kratochwill et al., 2013). 

Procedures

The local university institutional review board and school approved this research and informed consent was obtained from students and parents prior to data collection. The study started approximately three months into the school year. Instruction was provided in three small groups of three and only one student from each group was included in the study. Therefore, other students did receive instruction at the same time as the participants; however, their data was not used in the study. All word-problem probes were administered in small groups of three students and sessions were not audio or video recorded.

Baseline.

Data about students’ current level of performance was collected in the baseline phase using the word-problem probe. During each baseline session, students received the probe.

SBI Training.

After baseline data were collected, students received a one-day workshop about SBI. This workshop explained how to locate problem information to record onto the schema diagram. The FOPS strategy was modeled with completed problems, and the teacher showed how to follow the checklist of FOPS during problem solving. On the SBI workshop day, no data were collected. 

Intervention.

Data were collected each day before each intervention phase lesson using the word-problem probe. Students were taught SBI using explicit instruction for solving word problems with incomplete information, and each lesson lasted 30-35 minutes, two to three times a week, for four to five weeks. First, students were taught and practiced recording information from the word problem into a diagram, which was the three shapes referred to in the materials section for the strategy. The students labeled the missing number needed to calculate an answer using a question mark and then translated the information from the diagram into a number sentence, as indicated in FOPS.

Procedural Reliability

Data were calculated for procedural reliability by dividing the number of steps observed by the total number of steps planned, and this was measured across all phases. Two educators certified in general or special education observed the classroom teacher using a checklist with FOPS steps, and noted which steps were implemented. Procedural reliability data were collected in 30% of the sessions per phase and was 100%. 

Interobserver Agreement (IOA) for Scoring of the Probe

The primary scorer was the classroom teacher. The secondary scorer, who was certified in general and special education, was trained to a criterion of 90% using sample probes. The secondary scorer checked scoring according to cell-by-cell agreements on the probes for 30% of the probes for each student in each phase. The IOA scores resulted in 95-100% agreement across all sessions and phases. 

Social Validity

An interview with the classroom teacher was conducted after the intervention to measure social validity. The goal of the interview was to determine the teacher’s overall satisfaction regarding improvement in students’ ability to problem solve in mathematics. The classroom teacher felt it was beneficial to the students in her class and expressed that she would recommend the use of SBI to other teachers. The teacher noted that even if the students did not fully understand how to complete the problem that they knew that they had to “do something” with the numbers. This was a marked improvement prior to intervention. The teacher also stated that she did not note any negative side effects and the students did not mind completing the work asked of them during the intervention. She would recommend simplifying the problems, making the wording easier and repetitive, and using enlarged or tactile graphics for those with low vision who need help understanding the word problem. In addition, the teacher reported that she was utilizing interventions and students were continuing to make progress three weeks after the study ended.

Results

Percent of non-overlapping data (PND) was calculated for all students. Six components of visual analysis (level, trend, variability, immediacy, overlap, and consistency) were also used to analyze the average ability of each student (Kratochwill et al., 2013). Scruggs et al., (1986) recommended that a PND higher than 90% suggests high effectiveness, 70-90% indicates fair effectiveness, 50-70% represents questionable effectiveness, and a PND of less than 50% represents that the intervention was ineffective. 

All three students improved their level of solving word problems from a mean of 13.2% (SD= 4.33) to a mean of 72.5% (SD= 21.7) across all phases. PND for all three students combined was 96%, indicating high effectiveness (Scruggs et al., 1986; see Figure 2). Students regularly performed higher during the intervention phase than in the baseline phase.

Figure 2. Percentage of improvement with SBI process across students

Figure 2 shows three boxes in vertical format labeled as Student A, B, & C. Each box has a line showing baseline on left and a line showing intervention (FOPS strategy) on the right. Student A shows a baseline mean level at 4.8% that increased to 54.6% while using the FOPS Strategy. Student B’s baseline performance showed a mean level of 8.0% and an increase mean level of 64.8% using FOPS and student C figure shows that there was a baseline level of 26.7% that increased to 98.1% during intervention.

Student A

Student A’s baseline mean level was 4.8% (SD= 4.4; see Figure 2). When the SBI was taught in the intervention phase, Student A’s mean increased to 54.6% (SD=31.8) for solving word problems, which demonstrated a 49.8% increase from baseline. Baseline data were stable and demonstrated a flat trend. In the intervention phase, Student A demonstrated variability of data compared to the trend line. There was immediacy of change between baseline and intervention for Student A, and there was slight overlap of one data point. The data in the intervention phase were regularly higher than in the baseline phase. Additionally, the PND for Student A was 89% in the intervention phase. That indicated that SBI was fairly effective for this student (Scruggs et al., 1986). 

Student B

Student B’s baseline performance showed a mean level of 8.0% (SD= 0), which increased to a mean level of 64.8% (SD= 27.7) when SBI was taught in the intervention phase. Baseline data were stable with a flat trend line. The data in the intervention showed a downward trend with low variability. There was immediacy of change between the baseline and intervention phase for Student B, with a quick change from 100% to 33.3%. Student B’s performance in the intervention was regularly higher than in the baseline phase. The PND for Student B was 100% in the intervention, which showed SBI was highly effective for this student (Scruggs et al., 1986).

Student C

Student C had a baseline level mean of 26.7% (SD= 8.6). When SBI was taught in the intervention phase, the mean level increased to 98.1% (SD= 5.6). The data in the baseline phase were stable and demonstrated a flat trend after the fourth data point. The data in the intervention demonstrated a flat trend and low variability as compared to the trend line. There was immediacy of change between the baseline and intervention phase for Student C with no overlap. Student C’s performance in the intervention was regularly higher than in the baseline phase. The PND for Student C was 100% in the intervention, indicating that SBI was also highly effective for this student (Scruggs et al., 1986).

Discussion

This study enhanced external validity by replicating and extending previous findings (Brawand, et. al., 2020) by including students with visual impairments and intellectual disabilities receiving SBI instruction. Results indicated that high school students with visual impairments and intellectual disabilities demonstrated improvement in their ability to solve addition and subtraction word problems after the FOPS strategy was taught. Overall, social validity data collected from the classroom teacher demonstrated positive views on the use of the schema-based instruction for teaching addition and subtraction problem-solving skills to participants. 

Several limitations of this study are acknowledged. Only three students participated in the study. The heterogeneity of the group may limit how the findings of this study can be applied to other children if they differ significantly from the participants and setting of this research. However, in other studies involving the same number of students or less, SBI was also found to have positive results. For example, functional relation between modified SBI and mathematical word-problem solving was found in a study implemented by Root and Browder (2019), including three students with autism and intellectual disability in a multiple-baseline-across-participants design. In a case study with only two students with EBD, results suggested the participants can successfully learn problem-solving skills when instruction is designed to promote understanding (Jitendra et al., 2010). Finally, Kasap & Ergenekpn (2016) demonstrated that the schema approach was effective in teaching problem solving to three individuals with ASD.

Another limitation of the study is the duration only lasting four to five weeks. A longer period of time may have strengthened external validity since the current study included nine lessons lasting 30-35 minutes, two to three times a week, for four to five weeks. In comparison, some SBI research studies involving high-incidence disabilities at the secondary level averaged a duration of 12 lessons, lasting approximately 45 minutes each, for about four days per week, across three weeks (Jitendra et al., 2009; Jitendra & Star, 2012). If there were similar studies to validate the current studies results it could be generalized across other settings. The effectiveness of FOPS strategy has been established. However, utilizing SBI with combined visual impairments and intellectual disabilities within peer-reviewed literature has yet to be established. Future studies that address high school students with multiple disabilities are needed to support or contradict this study’s findings and could incorporate other mathematical skills. Elementary students with multiple disabilities may also benefit from instruction using the FOPS strategy. Comparative research studies can be done in the future as well to analyze the effect of additional interventions. Future studies should also be conducted to determine the effectiveness of utilizing SBI with manipulatives and tactile graphics only instead of enlarged print and pictures. All three participants in this study chose large print so this aspect could not be determined. Future research is needed on the effectiveness of SBI with non-print readers. 

Implications for Practitioners and Families

When teachers of students with visual impairments use SBI to teach the solving of word problems, they can simplify the language, use repetitive operation words, and include large pictures or tactile graphics to help students understand the word problem. Teachers can also use rubrics to analyze problem-solving errors and determine the need for more practice or re-teaching. As far as instructional planning, it is also recommended to use probes over time, to personalize word problems to student interests, and to give students the opportunity to generalize across different instructors. Finally, students with visual impairments would also benefit from adapted materials created by the classroom teacher in order to reinforce the accuracy of solving addition and subtraction problems. Families can easily be trained on the FOPS strategy in order for instructional strategies to be utilized in both home and school settings for best outcomes.

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