The Impacts of Mathematics Instructional Strategy on Students with Autism: A Systematic Literature Review

Mathematics is one of the most challenging subjects for many students. A similar problem is faced by special needs students, such as students with Autism Spectrum Disorder (ASD). Various instructional strategies are implemented by specialists to help ASD students understand mathematics in schools. To explore the impacts of an instructional strategy of mathematics on ASD students, the authors conducted a review of literature from 2011 to 2017 using various databases including ProQuest Digital Dissertations and Theses Full Text, Google Scholar, and Science Direct. A total of 39 articles were found. Most of the instructional strategy aimed to assist ASD students in solving mathematics problems. The implications of the study are also discussed in this literature review, which indicates that teachers need to use the appropriate instructional strategy to meet the needs of students with ASD and maximize their mathematics learning outcomes in schools.

encounter in the learning process Vanmeirhaeghe, 2012). Furthermore, one way to improve ASD students' cognitive development is by learning mathematics, which can help to organize the students' brains (Iuculano et al., 2014). Some students diagnosed with ASD have difficulties in mathematics because learning mathematics requires a high level of cognitive ability. Moreover, having a slower understanding compared to their peers, it is difficult for them to learn complex and high-level thinking concepts (Casner, 2016;Hallahan, 2015). Students diagnosed with ASD often struggle to gain a good understanding of mathematical concepts while learning the subject (Burney, 2015). To ensure that they can understand, teachers implement repetitive ASD methods (Hallahan, 2015). However, to date, researches have shown that the teaching and learning of mathematics for students diagnosed with ASD yield a variety of outcomes (Gevarter et al., 2016;Titeca et al., 2014). Carlson et al. (2011) and Wei et al. (2013) showed that the mathematics skills and mathematics test scores of students diagnosed with ASD were lower than those of students with other disabilities.
Concrete evidence-based instruction is commonly used by teachers to overcome the constraints of learning mathematics among students diagnosed with ASD (Green, 2014)-for example, using visual supports such as numbered cards, graphic columns, graphic organizers, numbered lines, highlighted keywords and written models (Casner, 2016). With the use of visual aids, students diagnosed with ASD respond well to mathematics topics such as identification, the use of calculators, number recognition, calculations, algebra, money and geometry skills (Hughes & Yakubova, 2019). Furthermore, students who learn in the kinaesthetic style are those who learn better using physical movements (Ahad & Ahmad, 2019) such as the self and match method or hands-on (Croce, 2015;Vitalo, 2017). The kinaesthetic learning style implemented in mathematical learning means that teachers show the numbers from 0 to 20 using physical interaction (Okkonen et al., 2016). On the other hand, auditory learning styles involve the transfer of information through hearing (Ahad & Ahmad, 2019)-for instance, stories and storybooks (Green, 2014;Jimenez & Kemmery, 2013). Teachers create appropriate questions and ask students verbally, conducting question-and-answer sessions during the teaching and learning process. For example, a teacher asks students to count out loud correct numbers written in a workbook, and the student say the numbers 1, 2, 3 and 4 (Green, 2014).
In implementing appropriate instructional types in the learning process, teachers are always concerned to identify students with ASD students according to their learning style: visual, kinaesthetic or auditory (Meshram & Vaishnav, 2020). Choosing the right learning style, teacher attitude and school administration to manage and implement the programme can positively impact ASD learning outcomes (Mezquita-Hoyos et al., 2018;Ozen & Topal, 2019).

Methodology and Results
This section discusses the steps used in the literature review to answer a given research question. In accordance with Khan et al. (2003), five stages were applied to conduct the literature review, namely 1) developing the research question; 2) identifying articles; 3) evaluating articles' appropriateness; 4) summarizing articles; and 5) interpreting articles' findings.
Step I: Developing the Research Question Developing the research question is an important step, as it forms the basis for initiating the study (Squires et al., 2013). Also, this help find and define the terms or keywords that fit the scope of the study by using databases, narrowing and refining the questions and reducing errors (Parfrey & Ravani, 2008;Squires et al., 2013). The research question for this literature review is: What were the methods of teaching mathematics to students diagnosed with ASD between the years 2011 and 2017?
Step II: Identifying Articles This section discusses two steps to identify related articles. The first step was to identify the right keywords in the search process using the database. The keywords used were "Mathematics Instruction for Autism Students"; "Mathematics AND Autism"; "Mathematics AND Disorder"; "Mathematics AND Disability"; and "Mathematics AND Students with ASD". The databases used in this literature review are a) ProQuest Digital Dissertations and Theses Full Text, b) Google Scholar and c) ScienceDirect. The search was limited to articles published between 2011 and 2017. The second step was to search for the articles, which resulted in 49,800 articles (ProQuest: n = 37,900; Google Scholar: n = 11,186; ScienceDirect: n = 714). It was found that not all of the articles met the topics required in this study. Therefore, the second round of the search was conducted, which resulted in a total of 52 articles. The final step was to review the articles in depth.
It was found that only 39 articles met the criteria. All articles were theses, dissertations and journal articles. The eligibility criteria that constituted inclusion in this review were: (a) published on a valid database; b) involved students at the preschool, primary and secondary levels; c) involved students diagnosed with ASD; d) experimental research design; e) reporting teaching and learning applied by teachers in teaching mathematics; and f) published in English.
Step III: Evaluating Articles Inclusion and exclusion criteria were set and established to evaluate the suitability of the articles for this literature review. Both requirements were intended to act as feedbacks to achieve the objectives of the review. In addition, the aim of setting the criteria was to optimize the external and internal validity of the studies. The most critical aspect in evaluating individual article always refers to "what methods are used by the teachers in teaching mathematics to students diagnosed with ASD." This literature review is based on a recent study by Hord and Bouck (2012, who asked what kind of academic instruction in mathematics was used to teach students diagnosed with mild intellectual disability (MID) in the last 11 years. The conclusions drawn from the findings of Hord and Bouck (2012) suggested that a majority of teachers were concerned with the planning of mathematics teaching interventions to improve computational procedures, knowledge of mathematical facts, and mathematical problem-solving. Some of the interventions implemented by teachers were 1) using flashcards, 2) using traditional algorithms, and 3) using technology. In addition, Desoete et al. (2013) and Praet et al. (2013) suggested that teachers' knowledge plays a significant role in determining the method of intervention or type of instruction in the teaching and learning of mathematics to address the needs of students with disabilities.
Step IV: Summarizing Articles The researcher summarized the related articles to answer the research question (Oxman et al., 2002). As stated in step II, the articles used in this study underwent several screening steps based on the determined criteria until only 39 articles remained. A total of 13 articles were excluded because they did not meet the criteria of this study. The articles were all relevant to the topic to be discussed in this literature review, mathematical instruction for autistic students. Galvan and Galvan (2017) encouraged the development of a table that would assist researchers in compiling, summarizing and concluding articles that are in line with the literature review. Table 1 below details the articles used in this literature review. Step V: Interpreting Findings A total of 39 articles were included based on the inclusion and exclusion criteria. The next step was to perform the coding process based on the information obtained from the study. The purpose of the coding process is to examine the mathematics instructions used during the seven-year period under study. Codes were given according to the characteristics of the study-e.g. author, number of participants, study area, instructional strategy, study design, teaching duration. A summary of the research findings is given in Appendix A. Data in Appendix A present the specific instructional strategies implemented by teachers during the teaching and learning of mathematics. The application of instructional strategies was based on students with different ASD learning styles, which are categorized as visual (V), kinaesthetic (K), auditory (A) or a combination of VKA. The analysis showed that teachers more often implement visual teaching styles than kinaesthetic, auditory or VKA styles. Twenty-two empirical studies apply visual teaching styles, such as ( Oie , 2016;Rasmussen & Bisanz, 2011;Rockwell, 2012;Rockwell et al., 2011;Root et al., , 2018Shamir & Baruch, 2012;Titeca et al., 2014;Toll et al., 2011).
The remaining 11 studies integrated either A, K or a combination of several teaching styles. Only five empirical studies in Appendix A implemented instructional strategies based on kinaesthetic learning: for example, (a) self and match, (b) hand technique and manipulation, (c) mathematical cognition, (d) mathematics recovery programme and (e) functional magnetic resonance imaging (Croce, 2015;Geary et al., 2012;Iuculano et al., 2014;Tzanakaki et al., 2014;Vitalo, 2017). Another three studies used instructional strategies based on auditory learning styles such as (a) mathematics instruction based on stories with systematic instruction; (b) metacognitive monitoring (one-on-one); and (c) storybooks (Brosnan et al., 2016;Green, 2014;Jimenez & Kemmery, 2013). The final three studies utilizing a combination of several instructional strategies, namely (a) clinical and cognitive criteria, (b) mathematical problemsolving, and (c) the multi-component approach (Alter, 2011;Oswald et al., 2016;Titeca et al., 2015).

Discussion
The majority of the researchers designed learning methods for students diagnosed with ASD based on the data from formative and summative assessments to identify the needs of the students in the teaching and learning process before a learning plan was created (Forbringer & Fuchs, 2014;Hagaman et al., 2013). Students who succeed in studying mathematics possess two types of knowledge: (a) conceptual understanding and (b) procedural skills (Rittle-Johnson, 2017). Conceptual understanding is a student's ability to understand the principles of mathematics or the relationship underlying the targeted concepts (Rittle-Johnson & Schneider, 2015). However, conceptual understanding is one of the most challenging aspects for students diagnosed with ASD to achieve, because they have impaired functional skills (Happe et al., 2006), making it difficult to grasp the multidimensional relationships that require knowledge of many mathematics concepts (Rittle-Johnson & Schneider, 2015). For example, when teaching fractions to students diagnosed with ASD, teachers must be able to relate previous knowledge of the whole number and use concrete models to scaffold knowledge construction.
Meanwhile, procedural skills denote the ability of students to identify which procedure needs to be used to find the right answer (Rittle-Johnson & Schneider, 2015). The most challenging problem for students diagnosed with ASD is the difficulty they face when translating mathematical forms into mathematical concepts and applying them to solve mathematical problems . By emphasizing high conceptual and procedural understanding, students diagnosed with ASD will be able to use the knowledge they have to solve mathematical problems ( ). In addition, this strategy emphasizes computational skills (addition and subtraction) and problem-solving (Forbringer & Fuchs, 2014;Rockwell, 2012). The modified schema strategy focuses on three aspects of instruction: 1) the technique of solving problems in writing and pairing them with pictures; b) every image being colour-coded or coded with the main criteria from the type of problem (concrete scheme); and c) clearly and systematically emphasizing each step of the question so that the students can understand in more depth the concept of the knowledge and the procedural skills . This strategy has assisted ASD students in computational problems, solving mathematical problems, and improving their cognitive abilities (Rockwell et al., 2011;Spooner et al., 2017). Meanwhile, the second method is computer-based (iPad-based video modelling, physical objects and 3-D virtual objects). This method is based on conceptual approaches (symbolic numbers, flashcards, CRAs, and real-life problems).

Conclusion
Instructional strategies implemented by teachers are one way to improve the quality of teaching in schools, especially for students with ASD. Many studies have called for a change in the way teachers teach mathematics as a subject in schools and have encouraged comparisons with instructional strategies used globally. Effective mathematics-based methods have a positive impact on ASD students' skills in solving mathematical problems. Therefore, teachers should use instructional strategies to meet the needs of students to maximize their learning outcomes in schools.

Recommendation
Based on the findings, it is recommended that other researchers further identify teachers applying instructional strategies based on (a) the type of learning style, (b) age, (c) gender, and (d) family background of each study, and (d) analyse the interaction between these variables.

Limitations
There are several limitations to this study. The article search process was based on particular keywords, so the researcher only obtained a few articles. Moreover, the researcher set appropriate article criteria for analysis in this study so that the citation information obtained was more limited. The databases used in this study were ProQuest Digital Dissertations and Theses Full Text, Google Scholar and ScienceDirect. The most cited database is Google Scholar. Future studies need to find and use more diverse databases with a longer duration.