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Teaching Fraction Problem-Solving to Autists Proposal


Literature Review

Autism Spectrum Disorder (ASD) refers to a condition that affects the development of brain cells in children. Individuals with such disorders are likely to exhibit characteristics of problems of social interaction, repetitive behaviors, as well as challenges in both verbal and nonverbal communication. According to the America Psychiatric Association (2013), such disorders have adverse impacts on the academic outcomes of the affected individuals, as well as their independence. In support of this, Schall, Wehman, and McDonough (2012) noted that ASD affects the overall quality of the affected individuals’ life. On the other hand, Hendricks and Wehman (2009) asserted that the daily life of persons with ASD deteriorates, instigated by the thought of disability.

In spite of the effects on the features of ASD on the daily functioning of individuals, there is a likelihood that affected learners have difficulties in executive functioning such as self-regulation, sequencing, as well as solving-problems. Such a scenario has adverse impacts on the academic outcomes of students with ASD. For this reason, there is a need to improve the academic performance of such learners by the adoption of appropriate learning models. One such approach is the provision of academic as well as functional life skills instruction to the affected students. In the views of Hendricks and Wehman (2009), society expects that learners with ASD should function normally with regard to the conventional societal parameters. Nowadays, there are some instructional approaches that are aimed at the improvement of the learning outcomes of students. Much of the focus as far as learners with ASD are concerned is on the improvement of their behavior skills, communication, and social skills (Petursdottir & Carr, 2011; Banda, Hart, & Liu-Gitz, 2010).

The use of academic skills, as well as knowledge, is the everyday activities play a significant role as far as an individual’s function in society is concerned. According to a survey carried out by Pennington (2010), the majority of the studies in this area emphasize the literacy of learners with ASD as opposed to major other areas such as academic performance and functionality in the society. There are limited studies that focus on the role of instructional strategies on the academic performance of learners with ASD. Particularly, there is scarce research on teaching mathematics to learners with Autism Spectrum Disorders despite the increase in the demand for mathematics knowledge and skills among numerous career choices.

Challenges of mathematics among learners with ASD

According to the National Center for Educational Statistics (2013), the performance of learners with disabilities is low. In support of this, Mayes and Calhoun (2006) pointed out that learners with ASD have challenges with the mathematics subject. On the other hand, a survey carried out by Williams, Goldstein, Kojkowski, and Minshew (2008) indicated that as low as 25% of learners with ASD prefer vocabulary to mathematics. Naturally, the idea of mathematics is challenging to a considerable number of learners. Some of the common challenges in which the majority of learners experience difficulties in mathematics are associated with semantic memory, procedural challenges, and visuospatial challenges. In addition, there are also high chances that some learners would experience difficulties in the linguistic part of mathematics. This is attributable to the fact that such an aspect takes the consideration of various vocabularies that might have varying contextual meaning.

Mathematics subject involves equations and calculations, which differentiate it from traditional texts. As such, to succeed in mathematics, learners are required to be conversant with a number of mathematics rules, including the order of operations. For this reason, learners are required to be in a position of applying the right rule for the right cases, as evident in operations requiring the subtraction of fractions.

Difficulties with fractions

Success in secondary mathematics calls for a strong base in primary as well as the prerequisite skills. According to Pennington (2010), such success is also attributable to a strong foundation in number sense in understanding decimals, fractions, as well as whole numbers. Understanding how to handle operations involving fractions is a foundational skill that can influence a learner’s academic performance in mathematics. This is attributable to the fact that the failure to have the necessary knowledge in fractions is a major contributor to the lack of preparedness among learners for other mathematics classes. In spite of this, fractions are considered to be highly challenging for students considered to have disabilities in mathematics.

Working with fractions requires learners to have a clear understanding of the various quantities such as denominators and numerous, as well as how to relate them. in addition, learners should be conversant with the necessary rules associated with fractions, and understand when to use the specific rules.

Fractions Interventions for students with ASD

The subject of mathematics cannot be complete without fractions. It is important to learn the concepts required in solving problems involving fractions. For this reason, it has become significant for learners to put a lot of effort in accessing as well as mastering content standards associated with fractions. In spite of this, the learning curriculum in the majority of secondary schools is not adequate and requires to be upgraded. This is attributable to the fact that the majority of the schools lack advanced technology or new models to enhance the learners’ comprehension of fractions. For example, empirical evidence indicates that the majority of special education teachers do not have full knowledge as far as the standards of national mathematics are concerned (Maccini & Gagnon, 2002).

Presently, there are few instructional models to enhance the academic outcomes of learners with ASD. In spite of this, the majority of the available models that teachers can use emphasize on money management, operations, as well as the basic numbers. Nevertheless, empirical evidence shows that there is a high chance of students with ASD learning mathematics content according to the grade-level standards while at the same time bettering their basic skills in mathematics. One of the significant instructional models that can be highly beneficial as far as improving the experience of students with ASD as far as learning fractions in mathematics is concerned is the use of video-based interventions.

The incorporation of video technology in the teaching of learners with the Autism Spectrum Disorders offers a significant background to ensure that students grasp the necessary knowledge and academic content as far as teaching mathematics is concerned. Such an approach not only equalizes learners but also gives them a chance to learn at a pace that is convenient for them. As such, a lot of concerns have been expressed with regard to the role of video technology in improving the academic performance of learners. The video based interventions that are used nowadays include computer-based video instruction, video prompting, point-of-view video modeling, as well as video modeling. One of advantages of adopting video-based interventions o teach mathematics among learners with ASD is that such a technology enhances a teacher’s ability to teach a wide range of skills such as self-help, play, behavior, communication, as well as social skills.

Purpose of Study

This study carries out an extension as far as the application of the point-of-view video modeling in improving the academic skills of high schools learners with Autism Spectrum Disorder is concerned. To achieve this objective the study focusses on content-based academic skills and how video-based approaches can enhance the ability of the learners to solve mathematics problems containing fractions. As such, the study examines the efficiency of video-based problem-solving interventions on learners’ ability to acquire and maintain knowledge on how to handle mixed fractions in a mathematics class.

Research questions

The study has a number of research questions including:

  1. To what extent do video-based problem solving interventions help learners with Autism Spectrum Disorder improve their ability to subtract mixed fractions both at baseline and the intervention phase?
  2. To what extent are learners with ASD able to maintain acquired skills one-week after concluding the intervention phase?

Methods Section

The method used for this study was the single case experimental design. The choice this study design was informed by the need to establish whether or not the video-based intervention was effective in helping learners to improve their performance as far as solving mathematics problems containing fractions was concerned. Therefore, the single case experimental design was very instrumental in ensuring replication of the effects on the intervention on the dependent variable. This was done to examine the possibility of significant link between outcome variable and the intervention. According to Kratochwill et al. (2013), carrying out several attempts provides researchers with the opportunity to obtain precise, accurate, and valid data. For this reason, this study carried out five attempts five different time points before replicating them across five learners.

In line with the study design, it was important to take five baseline measures alongside the making of a point-of-view video modeling clip. Then, the study participants were required to view the clip and solve the mathematics problems up to when all of them met the mastery criterion. After this, maintenance measures that lasted for one week were taken to examine the retention rate of the students regarding the acquired skills. The response accuracy of the participants regarding fraction word problems during the three phases was measured using a permanent recoding approach. After that, the researcher noted the percentage of the correct and incorrect problems for the purpose of making comparative analysis of all the outcomes.

The collected data was synthesized through the visual analysis method. The significance of this method is that it provides effective correlation between dependent and independent variables in any study (Krachwill et al., 2013).


The study used 5 participants. First, the inclusion criteria focused on individuals who had not used video modeling instruction before especially in solving mathematical problems. Secondly, such individuals were required to meet the diagnostic criteria of ASD based on the Diagnostic and Statistical Manual of Mental Disorders-5. Thirdly, the selected individuals should have demonstrated challenges in solving mixed fractions in mathematics according to recommendations from their teacher. Fourthly, the individuals to be selected should have exhibited conceptual understanding as far as the process of solving problems as provided by the teacher is concerned. In addition, the appropriate study participants were required to have no hearing or vision impairments, and were required to be willing to take part in the study.


The study participants were provided with instructions in relation to a functional curriculum that was below the grade level. Five learners and a special education teacher formed the functional mathematics class. A separate classroom was used for the research questions.

Study variables

The point-of-video modeling instruction was the independent variable in this study and it was delivered through a problem-solving checklist and iPad. The checklist was made to assist learners whenever deciding what steps to use when solving a given problem.

On the other hand, the accuracy of the learners’ performance regarding their problem-solving ability was the dependent variable for this study. The study calculated the percentage of the equations that were correctly solved and used that to define the learners’ accuracy.


The procedure involved three stages-the baseline, intervention and the maintenance phases.

The baseline phase required all the study participants to go through five sessions and they were in a position to respond to each concern. This phase did not include any intervention or any form of help to the study participants.

The intervention phase comprised of six sessions for every study participants. In addition, the learners were required to achieve at least 80% during this stage. A point-of-view clip was provided to the learners alongside a problem-solving checklist. The learners were required to watch the clip attentively before attempting to solve any problem. In spite of the fact that the instructions required the students to watch the clip twice, but they watched it once. The responses from this phase were marked and the percentage of the correct answers calculated and recorded.

The last phase was the maintenance stage that was implemented one week after the intervention phase. Unlike in the intervention phase, here learners were not allowed to use the checklist or the video clip. The maintenance phase was aimed at establishing where the learners still retained the skills acquired during the intervention session.

Results section

The reliability of the data from the study was assessed through a second trained independent rater. After randomly selecting about 30% of the responses from each of the three phases, the percentage of the correct responses was calculated. It was evident that the interobserver agreement was hundred percent for all the study participants in each of the three phases. The study participants and their teacher were required to respond to informal social questions before the intervention phase.

Baseline Intervention Follow-up
1 0 0 0 0 0 100 80 100 80 80 100 80 100 100 100
2 0 0 0 0 0 100 80 80 100 100 100 100 60 80 80
3 0 0 0 0 0 80 100 100 80 100 100 80 60 100 80
4 0 0 0 0 0 100 80 100 100 100 80 100
5 20 0 0 0 0 100 100 100 100 100
Av 4 0 0 0 0 96.7 100 95 92 96 100 86.7 73.3 90 92

Table 1: Percentage of problems correct by students A-E.

Student av. mean Baseline Intervention Follow-up
A 4 96.7 100
B 0 100 86.7
C 0 95 73.3
D 0 92 90
E 0 96 92

Table 2: Mean percentage of accurate response per student during each phase.

The results of this study showed that the accuracy of the learners regarding the ability to solve mathematics problems involving fractions improved after using the video clip that was provided (See appendix for visual results). In addition, it was evident that each of the students showed significant improvement in their performance during the intervention phase as opposed to the case during the baseline phase. The examination of IRD scores indicated that the learners were more effective as far as solving word problems involving fractions after the intervention phase.

According to the learners’ social validity responses, it was evident that they were positive about the need to have better mathematics skills as well as eager to learn through video-based instructions. After completing all the three phases, the learners reported that they had learnt a lot as far as solving mathematics problem using the instructional clip was concerned. Teacher, on the other hand, showed interest to have the students improve their capability to solve problem problems in mathematics. After the assessment was over, the teacher reported that the video-based approach to solving problems in mathematics was time efficient and easy to use.


The current study was primarily carried out to investigate the possibility of improving the performance of learners with ASD as far as solving problems in mathematics through video-based instruction. According to the results of the study, it was evident that the accuracy of the learners in solving mathematics problems improved following the intervention which included an instructional video clip. As such, the implication of such findings is that it was possible to increase the learners’ accuracy as well as skill maintenance in problem-solving among students with ASD. The video-based intervention is easy to implement, which makes its practicality possible.

Even though there are numerous studies that have been carried out in the past on learners with disabilities, there is still less focus on the studies on mathematics interventions especially for learners with Autism Spectrum Disorders (Yakubova, Hughes, & Hornberger, 2015). With the current rate of technology use in the education system, it is no doubt that there is a need for the implementation of individualized instruction to enhance the performance of learners with ASD. According to the responses from the study participants, it was evident that the learners and their teacher applauded the use of the video-based intervention citing its ease to use and efficiency.

Suggestively, the study findings indicated that the adoption of the pint-of-view video modelling to teach students with ASD can have positive impacts on the performance and accuracy of the learners in solving problems in mathematics. This is attributable to the fact that such interventions provide teachers with an appropriate platform to offer the necessary support to the students through an approach that can enhance their memorability as well as help them retain acquired skills. In addition, contrary to the provision of one-size fits all instruction to the learners then examining their performance, the video-based model gives instructors the opportunity to offered individualized support to learners.

Limitations and directions for future research

There is a need for future research as far as the subject of the performance of students with ASD in solving problems in mathematics is concerned. This study used a small sample size of five study participants. However, to enhance the accuracy and precision of results, future studies should consider using a large sample size. in addition, a large sample size would be effective in generalizing the findings.

Given the scarcity of literature about this subject, future research is important for the purpose of providing more insights on more approaches that can be adopted to improving the conceptual as well as procedural mathematics among learners with Autism Spectrum Disorders. Nevertheless, it is important for institutions to adopt video interventions to improve the specific learning needs of learners with ASD. For this reason, future research should focus on addressing the extent of the video intervention in influencing the conceptual understanding of learners with ASD.


Appendix A: Baseline


Appendix B: Intervention


Appendix C: Follow-up



American Psychiatric Association. (2013). Diagnostic and statistical manual of mental disorders: DSM-5 (5th ed.). Washington, DC: Author.

Banda, D. R., Hart, S. L., & Liu-Gitz, L. (2010). Impact of training peers and children with autism on social skills during center time activities in inclusive classrooms. Research in Autism Spectrum Disorders, 4(2), 619–625.

Hendricks, D. R., & Wehman, P. (2009). Transition from school to adulthood for youth with autism spectrum disorders: Review and recommendations. Focus on Autism and Other Developmental Disabilities, 24(3), 77–88.

Kratochwill, T., Hitchcock, J., Horner, R., Levin, J., Odom, S., Rindskopf, D., & Shadish, W. (2013). Single-case intervention research design standards. Remedial & Special Education, 34(3), 26–38.

Maccini, P., & Gagnon, J. C. (2002). Perceptions and application of NCTM standards by special and general education teachers. Exceptional Children, 32(1), 1–22.

Mayes, S. D., & Calhoun, S. L. (2006). Frequency of reading, math, and writing disabilities in children with clinical disorders. Learning and Individual Differences, 16(1), 145–157.

National Center for Educational Statistics. (2013). The nation’s report card: Mathematics 2013. Washington DC: U.S. Department of Education.

Pennington, R. C. (2010). Computer-assisted instruction for teaching academic skills to students with autism spectrum disorders: A review of literature. Focus on Autism and Other Developmental Disabilities, 25(1), 239–248.

Petursdottir, A., & Carr, J. E. (2011). A review of recommendations for sequencing receptive and expressive language instruction. Journal of Applied Behavior Analysis, 44(2), 859–876.

Schall, C., Wehman, P., & McDonough, J. (2012). Transition from school to work for students with ASD: Understanding the process and achieving better outcomes. Pediatric Clinics of North America, 29(2), 189–202.

Williams, D. L., Goldstein, G., Kojkowski, N., & Minshew, N. J. (2008). Do individuals with high-functioning autism have the IQ profile associated with nonverbal learning disability? Research in Autism Spectrum Disorders, 2(3), 353–361.

Yakubova, G., Hughes, E., & Hornberger, E. (2015).Video-based intervention in teaching fraction problem-solving to students with autism spectrum disorder. Journal of Autism Development Disorders, 45(9), 2865–2875.

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