Teaching Math Skills to Individuals with Autism Spectrum Disorder: A Descriptive and Meta-Analysis in Single Case Research Designs *

Headnote

Abstract

The present study aims to evaluate the single-case experimental studies on teaching math skills to individuals with autism spectrum disorders in terms of (a) quality indicators developed by Horner et al. (2005), (b) descriptive analysis of the variables used in these studies, and (c) effect sizes of the interventions to decide whether they are evidence-based. Various databased were searched and the analyses were conducted for 26 studies. Results showed that 10 research studies classified as acceptable in terms of meeting quality indicators developed by Horner et al. (2005). The effect sizes of tese studies were calculated (Tau-U and PND) and results showed that visual presentation instructions and strategy-based instructions are the promising instructions in teaching math skills to individuals with autism. Based on the findings, future research needs and recommendations to the practitioners are discussed.

Keywords: Autism spectrum disorders, math skills, single-case experimental research, meta analysis, evidence-based practice.

The prevalence rate of autism spectrum disorder (ASD), a neurodevelopmental disorder, has shown a tremendous increase for the last two decades (Rice et al., 2012). According to 2014 data, 1 in 59 children has ASD (Baio et al., 2018). Teaching these children in the general education settings has been widely accepted. As a result of these two factors, researchers have started to show their attention for investigating the causes of autism, treatments of autism, and education of children with autism. Including students with ASD into general education settings has motivated professionals to find the effective methods in teaching academic skills as in typically developing children. The need to teach new skills in subject areas such as math, science, and literacy has been continued. Researches have shown that students with ASD have differences and problems while learning academic skills such as literacy and math skills (Minshew, Goldstein, Taylor, & Siegel, 1994; Whitby & Mancil, 2009). Williams, Goldstein, Kojkowski and Minshew (2008) reported that 25% of students with ASD may have problems in learning math skills. On the other hand, although there has been an increase in the number of studies investigating teaching skills to students with ASD, only 12.7% of the students has been related to teaching academic skills to them (Wong et al., 2015). At the same time, studies about teaching math skills is still very few in the literature (Bouck, Satsangi, Doughty, & Courtney, 2014; Knight, McKissick, & Saunders, 2013; Spencer, Evmenova, Boon, & Hayes-Harris, 2014).

Research has shown that basic counting skills (e.g., Jowett, Moore, & Anderson, 2012; Morrison & Rosales-Luiz, 1997), addition-substraction skills (e.g., Rapp et al., 2012; Yıkmış, 2016), matching skills (e.g., McEvoy & Brady, 1988), purchasing skills, calculation a tip, computing the sales tax (e.g., Cihak & Grim, 2008; Collins, Hager, & Galloway, 2011; Kellems et al., 2016), mathematical word problem solving (e.g., Root, Browder, Saunders, & Lo, 2017; Whitby, 2013) and fraction problem solving skills (e.g., Yakubova, Hughes, & Hornberger, 2015), and drawing some geometric shapes (e.g., Barbeau, McLaughlin, & Neyman, 2015) could be taught to individuals with ASD. Video-modelling (e.g., Burton, Anderson, Prater, & Dyches, 2013; Yakubova et al., 2015), number line strategy (e.g., Weng & Bouck, 2014), TouchMath (e.g., Yıkmış, 2016), schema based instructions (e.g, Root et al., 2017), response prompting procedures (i.e., simultaneous prompting, time delay, least to most prompting; e.g., Collins et al., 2011) and systematic teaching procedures delivered via embedded instruction (e.g., Jimenez & Kemmery, 2013) are the instructional procedures that have been used in these studies. A comprehensive evaluation could be possible when the above aferomentioned studies descriptively analyzed and a meta-analysis conducted for the studies which found to be "acceptable" in terms of quality indicators. Hence, teachers, practitioners who work with students with ASD in teaching math skills, and researchers could be advised with more comprehensive information and evidences for the procedures that were used to teach math skills. The present study designed to conduct a systematic analysis of the studies which aimed to teach math skills to students with ASD. Therefore, the present study has threefolds: (a) to conduct a comprehensive systematic analysis (descriptive analysis) of the studies obtained in terms of demographical, procedural, and outcome variables, (b) to evaluate the studies obtained in terms of quality indicators developed by Horner et al. (2005), and (c) to calculate the effect sizes of the studies which the criteria of "acceptability" met.

Method

Search Procedures

The search procedure included the studies published in peer review journals in English between January 1980 and February 2017 aiming to teach math skills to individuals with ASD. The search was started at 1980 since autism took place as a different category in DSM-III in 1980. We located studies via ERIC, Academic Search Complete, MEDLINE, PsycINFO, PsycARTICLE, ScienceDrirect, Education Source, MathSciNet, and Scopus using the keywords in three main categories. Those categories were keywords about math skills, instruction, and target population. Keywords for the math skills included math(ematics), arithmetic, algebra, graphing, geometry, addition, subtraction, multiplication, division, number concepts, number sense, numeracy skills, counting, subitizing, measurement, quantity comparison, matching, telling time, purchasing, using calculator, word problems, fraction facts, problem solving, data analysis, probability; for the instruction included intervention, instruction, train(ing), teach(ing); and for the target population included autism, Asperger Syndrome, Autism Spectrum Disorder, PDD-NOS, high functioning autism. Forty-six studies obtained through these search procedures. Then, the researchers conducted a search of the table of contents, titles, and abstract of all volumes of the following journals published between January 2013 and January 2017: Journal of Autism and Developmental Disorders, Education and Training in Autism and Developmental Disabilities, Research in Autism Spectrum Disorders, Focus on Autism and Other Developmental Disabilities, and Remedial and Special Education. These journals were selected based on the experiences of the researchers and familiarity with autism and math teaching. Only one study (i.e., Bae, Chiang, & Hickson, 2015) located via this search. Last, the researchers also reviewed the reference lists of the systematic analyses and meta analyses studies conducted about teaching math skills to individuals with ASD. Two studies (Ault, Wolery, Gast, Doyle, & Eizenstat, 1988; Polychronis, McDonnell, Johnson, Riesen, & Jameson, 2004) located via this search. As a result, the researchers located a total of 49 studies to be reviewed. Figure 1 displayed the search procedures followed in the study.

Inclusion and Exclusion Criteria

We included the studies in the review that met the following criteria: (a) published in English in internationally disseminated peer-reviewed journals from 1980 to 2017, (b) having at least one participant or all participants diagnosed with ASD or others (i.e., autism, Asperger Syndrome, PDD-NOS, high functioning autism), (c) aiming to teach math skill(s), and (d) designed with single case experimental research. Exclusion criteria in the study were as follows: (a) designed with other research methods (e.g., group experimental research) beyond single case experimental research, (b) review studies about teaching math to individuals with ASD, (c) designed to examine the effects of math instruction in different populations (e.g., intellectual disabilities), and (d) comparative studies aiming to reveal the differential effects of different strategies on teaching math to individuals with ASD. We excluded three review studies (Barnett & Cleary, 2015; Gevarter et al., 2016; King, Lemons, & Davidson, 2016), three studies with group experimental research (Bae et al., 2015; Hua, Morgan, Kaldenberg, & Goo, 2012; Huang, Lai, & Rivera, 2010), and a case study (Tan & Alant, 2016) out of 49 identified studies. Six studies were excluded since they were comparative research studies (Ault et al., 1988; Bouck et al., 2014; Cihak & Foust, 2008; Fletcher, Boon, & Cihak, 2010; Leaf, Sheldon, & Sherman, 2010; Polychronis et al., 2004) comparing the effectiveness of different interventions in teaching math skills. We also excluded 5 more studies (Banda & Kubina, 2009; Cihak, Wright, & Ayres, 2010; Legge, DeBar, & Alber-Morgan, 2010; Neely, Rispoli, Camargo, Davis, & Boles, 2013; Schatz, Peterson, & Bellini, 2016) since they were designed to examine variables such as involvement to math activities and decrease delay interval while responding to the questions. Moreover, two graduate theses/dissertations (Rockwell, 2012; Whitby, 2009) and three research reports (Berry, 2009; Burney, 2015; Eichel, Montgomery, & Young, 2007) were also excluded. As a result, 23 out of 49 studies included for further analyses.

Data Analysis

A comprehensive descriptive analysis had been conducted followed by the analysis of design quality of the studies to identify the studies that met the criteria of "acceptability". The rubric of "Quality Indicators of Single-Case Experimental Research Studies" was used to evaluate the design quality. The studies that met "acceptability" criteria retained for effect size analysis. We used both percentage of nonoverlapping data (PND; Scruggs, Mastropieri, & Casto, 1987) and Tau-G (Parker, Vannest, Davis, & Saube, 2011) to calculate the effect sizes of the study. Moreover, we also looked at the consistency between these two calculations.

Reliability Analyses

We conducted reliability analyses in three phases. First, we conducted reliability analyses for both demographical variables and methodological and outcome variables of the studies reviewed. The mean consistencies between the coders for demographical variables and methodological and outcome variables were 96.3% (range = 85.7% to 100% and 99% (range = 93.7% - 100%) respectively. The researchers discussed the variables that consistency was not obtained and reached 100% consistency. Then a reliability analysis was conducted for the coding of the studies in terms of design quality and 93.1% (range = 85.7% - 100%) consistency was found. The researchers discussed each criterion that consistency was not obtained and reached 100% consistency. The last reliability analysis was conducted for calculating the consistency between the researchers for using UnGraph5 and calculations of PND and Tau-^. For these calculations we included 331 data points and obtained 95.3% consistency for the use of UnGraph5 and 100% consistency for PND and Tau-^ calculations.

Results

Findings for Descriptive Analysis

We provided the findings for the descriptive analysis of the studies (n = 26) in two main groups: (a) findings for demographical variables and (b) findings for methodological and outcome variables. Table 1 and Table 2 present these data.

(a) Findings for demographical variables. Demographical variables were analyzed and in three groups: (a) participants' characteristics (number of participants, diagnosis of participants, IQ scores, instruments used for diagnosis, gender, and age), (b) intervention settings, and (c) instructional arrangements. Table 1 presents the data.

(b) Findings for methodological and outcome variables. Methodological and outcome variables were analyzed and in eight groups: (a) target skills/behaviors (b) intervention (prompt type, reinforcement/reinforcement schedule, interventionist), (c) kind of single case experimental design, (d) dependent variable reliability, (e) treatment fidelity, (f) generalization, (g) maintenance, and (i) social validity. Table 2 presents the data.

Findings for Quality Indicators

We used "Quality Indicators of Single-Case Experimental Research Studies" (Horner et al., 2005) for analyzing the design quality of the single-case studies (n = 26) which met inclusion criteria. Table 3 summarizes the quality indicators for single-case studies according to Horner et al. (2005). No study met all the quality indicators. However, 5 studies (e.g., Akmanoğlu & Batu, 2004; Waters & Boon, 2011) were found to meet all the indicators except one. Horner et al. (2005) stated that for a study named as "acceptable", they need to meet specific indicators (see, items with asterisk in Table 1). When the acceptability of these 26 studies were evaluated if they met these items, it is seen that 10 studies (e.g., Burton et al., 2013; Yıkmış, 2016) could be evaluated as acceptable. We also looked at the studies whether publication year made a difference in terms of design quality of the studies published before and after Horner et al.'s (2005) study published. Seven studies published before 2005 and 19 studies published after 2005. Only one study (Akmanoğlu & Batu, 2004) published before 2005 and 9 studies (e.g., Cihak & Grim, 2008; Yıkmış, 2016) published after 2005 met acceptability criteria in terms of design quality. In sum, 10 out of 26 studies found to be "acceptable". These studies retained for further analyses in the study.

Findings for Meta-Analysis

The studies which met the "acceptability" criteria of Horner et al.'s (2005) rubric were retained for effect size analyses in the study. Percentage of nonoverlapping data (PND) and Tau-^ analyses were conducted between baseline-intervention sessions. Anaylses showed that seven studies (e.g., Cihak & Grim, 2008; Root et al., 2017) classified as "very effective" with at least 90% and two studies (e.g., Jimenez and Kememry, 2013; Yıkmış, 2016) classified as "effective" with 88,69% and 70% in PND analysis. Last, one study (Akmanoğlu & Batu, 2004) was found be "questionable" since effect size between baseline-intervention condition was 66.77%. Tau-^ analyses showed that seven studies (e.g., Burton et al., 2013) were also found as "very effective" with at least 93% effect size. Two studies (Jimenez & Kemmery, 2013; Yıkmış, 2016) classified as "effective" with 88.23% and %88 respectively. A study (Akmanoğlu & Batu, 2004) was found to be "low effective" with effect size below 65%. A high positive correlation (rs = 1, p < .01) was also found in Spearman rho analysis in the study.

Discussions

A descriptive analysis and meta-analysis of the studies on teaching math skills to individuals with ASD were carried out in the study with studies which met "acceptability" criteria of single-case experimental studies suggested by Horner et al. (2005). Twenty-six studies were first taken into descriptive analysis in terms of demographical, procedural, and outcome variables. Then these studies were taken into analyses to find out the studies which meet "acceptability" criteria according to single -case experimental research quality indicators suggested by Horner et al. (2005). Last, meta-analysis of the studies meeting "acceptability" criteria were conducted in the study.

Descriptive analysis of the studies showed that the majority of the participants had IQ score below 80. Moreover, it is seen that even though any score for intellectual functioning of the participants were available for some participants, they were labeled as having intellectual disabilities (e.g., Jimenez & Kemmery, 2013; Akmanoğlu & Batu, 2004). This finding indicates that there is a consistent correlation between demographics of the participants of ASD in the reviewed studies and their academic profiles (Chiang & Lin, 2007; Troyb et al., 2014). Among the reviewed studies it is seen that the majority of the studies were carried out either in special education classrooms or individual/therapy rooms with one on one instructional arrangement, and some studies were carried out at home settings again in one on one instructional arrangement. Very few studies were conducted at general education classrooms with one on one instructional arrangement.

It is seen that basic math skills and functional math skills were aimed to teach in the reviewed studies. Many studies were focused on teaching basic academic skills addition-subtraction-multiplication and division to individuals with ASD. Purchasing skill is the most frequently targeted skill among studies focusing on teaching functional math skills. However, it is observed that teaching basic math skills has gained attention from the researchers in the recent years. This tendency could be explained by the use of inclusion policy and the right to access to general education curriculum for the students with ASD.

The majority of the reviewed studies were conducted with primary school age students aiming to teach basic math skills (e.g., addition, multiplication), then with high school age students aiming to teach functional math skills (e.g., purchasing skill). Rather complex academic math skills such as fractions and functional skills such as comparing the prices of the production were aimed at teaching young adults with ASD between the ages of 18 and 21. Few studies aiming to teach basic academic and functional math skills were conducted with middle school age students. Also, few studies were obtained aiming to teach basic math skills such as counting, drawing geometrical shapes to preschool age students with ASD.

The researchers used six different intervention procedures/packages to teach academic or functional math skills. These are (a) visual presentation (e.g., video modelling/prompting, schema based interventions, TouchMath), (b) strategy-based interventions (e.g., counting strategy, meta-cognitive strategies, self-management based interventions), (c) instructional arrangements (e.g., contingent reinforcement, using preferred items, precurrent behaviors, peer based interventions), (d) instructional packages (e.g., blended interventions, systematic instructions with embedded intervention), (e) errorless teaching procedures (e.g., constant time delay procedure, simultaneous prompting procedure), and (f) consequence based strategies (e.g., differential reinforcement, response repetition). Barnett and Cleary (2015) and King et al. (2016). grouped the procedures into two in their reviews as (a) visual presentations and (b) cognitive based interventions and (a) response-prompting procedures and (b) consequence-based procedures, respectively. Gevarter et al. (2016) grouped them into three in their review as (a) visual presentations, (b) strategy-based interventions, and (c) curriculum-based interventions. The present study enhances the findings of the previous review studies by adding new groups that were used to teach math skills to individuals with ASD.

It is seen that when using "Quality Indicators of Single-Case Experimental Research Studies" (Horner et al., 2005) rubric, the researchers adopted different approaches (e.g., Chard, Ketterlin-Geller, Baker, Doabler, & Apichatabutra, 2009; Mayton, Wheeler, Menendez, & Zang, 2010; Rogers & Graham, 2008). Some used all indicators (n = 21), and some added more criteria. We evaluated the studies by using all the indicators in our study.

It is understood that no studies met the quality indicator of having at least five data points during baseline as suggested by Horner et al. (2005). Therefore, we adopted this quality indicator as having at least three data points during baseline phase. Horner et al. (2005) suggested having five data points has a strong control in case of having a therapeutic trend and/or variability during baseline phase in a study. However, as an effect size analysis method Ta-^ controls such undesirable positive trend during baseline phase.

The present study revealed that only few studies (n = 10) could meet the "acceptability" criteria suggested by Horner et al. (2005). Thus, it could be said that the studies designed to teach math skills to individuals with ASD are not as experimentally strong as they should have been.

Video-modeling, video-prompting, counting strategies, schema-based interventions and Solve It! strategy were classified as "very effective" intervention and systematic interventions with embedded intervention were classified as "effective" intervention according to PND effect size estimation. The simultaneous prompting procedure was found to be as "questionable" intervention in teaching math skills. Although PND analysis has been criticized by the researchers, a high positive correlation between PND and Tau-^ analyses obtained in the present study. This finding may justify that (a) there is no undesirable therapeutic trend in the studies reviewed and (b) as stated by Lee, Wehmeyer, and Shogren (2015), when utilized correctly PND analysis would provide reliable outcomes.

Consequently, it is seen that various math skills such as purchasing skills, time-telling skills, counting skills, addition and subtraction skills, problem solving skills, and drawing geometrical shapes could be taught in various settings. The majority of these studies were conducted in one on one instructional arrangement. Group instructional arrangement was used in a very limited number of studies. However, when widespread of inclusion is taken into consideration, conducting research investigating the effective procedure in teaching math skills to individuals with ASD during group instructional arrangement including both students with and without ASD would contribute the literature and enhance current findings. Moreover, it is also seen that the instructors in the reviewed studies were either the researchers of the studies or the special education teachers. The use of general education teachers or peers to teach their students with ASD is very few. Therefore, the researchers could be advised to design studies investigating the effects of peer delivered and/or general education teacher delivered interventions to teach math skills to students with ASD in general education settings in the future. Last, to the knowledge of the authors of this study, no studies designed to investigate the parent/family member delivered interventions in teaching math skills. However, there is a great deal of studies showing that the parents or family members could be effective teaching agent and teach many different skills to their children with ASD (e.g., Batu, 2008; Batu, Bozkurt, & Öncül, 2014; Cavkaytar, 1999; Coolican, Smith, & Bryson, 2010; Özcan & Cavkaytar, 2009; Seung, Ashwell, Elder, & Valcante, 2006; Tekin-İftar, 2008). Therefore, future researchers can be suggested to design studies examining the effectiveness of parent delivered instruction in teaching math skills to the children with ASD.

Although visual presentation and strategy-based interventions found to be as "promising" intervention, the research needs for these two interventions are evident. Therefore, researchers can be recommended to ask themselves questions to answer under what conditions, with what math skills, and which types of participants these procedures would be effective. It is highly noticeable that the research examining the effects of response prompting procedures in teaching math skills to individuals with ASD scarce. The simultaneous prompting procedure investigated by Akmanoglu and Batu (2004) was found to be "questionable" for teaching math skill to children with ASD. However, Tekin-Iftar, Olcay-Gul, and Collins (2018) documented that in a comprehensive review and meta-analysis study that the simultaneous prompting procedure is an evidence-based procedure in teaching various skills and tasks. Therefore, the researchers can be suggested to design new studies on response-prompting procedure including the simultaneous prompting procedure in teaching math skills to individuals with ASD. An increase in the number of these studies would provide impetus for the researchers to conduct systematic review and meta-analysis studies to find out evidences about response-prompting procedures.

We used Hornet et al.'s (2005) rubric to identify which intervention has evidences for teaching math skills to individuals with ASD. The researchers can be advised to work with other populations (e.g., intellectual disabilities) in the future meta-analysis studies. In addition, other rubrics for identifying evidences are available (Kratochwill et al., 2013; Reichow, Volkmar, & Cicchetti, 2008; What Works Clearinghouse [WWC], 2014) in the literature and the researchers can be suggested to conduct new meta-analysis studies and analyze the consistency of outcomes when using different rubrics in in a study conducted for identifying the evidences for math teaching to individuals with ASD. Another recommendation could be raised in terms of including studies designed by other research designs (e.g., group experimental research, correlational research) into meta-analysis in the future research.

Like other research studies the present study has some limitations too. First, this study includes only single-case experimental research studies published in internationally disseminated peer-review journals. The studies published in other languages, with other research designs, published in peer reviewed journals with peer review, and graduate studies (i.e., thesis and dissertations) are not included in this study. In addition to that, the findings of this study are limited with the studies which met "acceptability" criteria when quality indicators suggested by Horner et al.'s (2005) taken into consideration and with two only effect size analyses.

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Recommended Citation

Aydın, O., & Tekin-İftar, E. (2020). Teaching math skills to individuals with autism spectrum disorder: A descriptive and meta analysis in single case research designs. Ankara University Faculty of Educational Sciences Journal of Special Education, 21(2), 383-426. doi: 10.21565/ozelegitimdergisi.521232

*The study was produced by the master thesis of the first author, that was completed at Anadolu University Educational Sciences Institute, Special Education Department. It was supported by Scientific Research Projects of Anadolu University (Project Number: 1609E619)

*·Corresponding Author: Res. Assist., E-mail: [email protected], https://orcid.org/0000-0002-9695-2414

*··Prof., E-mail: [email protected], https://orcid.org/0000-0001-5512-616X