The Effects of the Mathematics Teaching Studies for Students with Intellectual Disabilities: A Meta-Analysis of Single-Subject Researches in Taiwan

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1 Oral Presentation The Effects of the Mathematics Teaching Studies for Students with Intellectual Disabilities: A Meta-Analysis of Single-Subject Researches in Taiwan Yen Chun ChOU (National Changhua University of Education) Chien Hui LIN (National Changhua University of Education) INTRODUCTION This meta-analysis was to check the effectiveness of mathematics instruction for students with intellectual disabilities in Taiwan. Because there were 28 single-subject research design studies were reviewed, an approach of the percentage of nonoverlapping data (PND) was employed to estimate treatment effects. Background Evidence-based Practices in Special Education. For students with intellectual disabilities, mathematics learning could improve their adaptive behavior such as money using skills, time concept, and other number concepts(schalock et al., 2010) to enhance the quality of life. No Child Left Behind Act legislation (2002) stipulates that mathematics is one of the core academic subjects for all children, including children with special needs. Teachers were encouraged to use evidence-based practices in classroom. In January 2003, Council for Exceptional Children's (CEC) Division for Research identified four types of research methodologies to build effectiveness of evidence-based practices in special education: (1) experimental group, (2) correlational, (3) single-subject, and (4) qualitative designs (Odom et al., 2005). Single-subject Research. For the four evidence-based methodologies proposed by CEC, single-subject experimental designs are used most frequently in the field of special education for the students with intellectual disabilities because of a low-incidence population. Special education is a field that emphasizes the individual student as the unit of concern as well as individualized intervention as the treatment for behavior or education, and practical procedures that can be used in typical school, home, and community contexts. Therefore, single-subject research matches well with the needs of special education and plays an important role in the development of evidence-based practices in special education (Horner et al., 2005). Morse and Schuster (1996) reviewed 20 single-subject researches that have focused on teaching grocery shopping behavior to individuals with moderate, severe, or profound intellectual disabilities. The results presented the different features of participant characteristics (ages, disability classifications, and possessed skills prior to the study) and instructional characteristics (skills trained, strategies used, location, instructional methodology, and instructional arrangement). Browder and Grasso's (1999) review 45 experimental researches (82% single-subject design, 18% control group) 562 The 20th Asian Conference on Intellectual Disabilities

2 of money skills instruction. Most of the studies focused on adolescents (36%) or young adults (44%); the levels of disabilities included mild (33%), moderate (44%), and severe (23%) mental retardation; prerequisite skills (70%) were required; skills were taught focused on purchasing strategy (51%); the most common setting was under a combination of classroom and community (74%). Effect Size of Meta-Analysis for Individuals with Intellectual Disabilities. Meta-analysis is an approach to integrate systematically a large body of related research literature. The procedure was first applied to quantitative group-experimental research data (Glass, McGaw, & Smith, 1981). Since that time, literally thousands of meta-analytic studies have been completed, and many of these have been applied to special education (Forness, 2001). In addition to meta-analyses of group-experimental research, this approach has been applied to single-subject research (Scruggs, Mastropieri, & Casto, 1987) and survey research (Scruggs & Mastropieri, 1996). Qualitative meta-analysis research has been previously conducted, mostly in the health sciences (Campbell et al., 2003), and sometimes referred to as " research synthesis " (Scruggs, Mastropieri, & McDuffie, 2007). Scruggs, Mastropieri, and Casto (1987) proposed the use of a percentage of nonoverlapping data (PND) metric to evaluate the effect size of single-participant research. Using this metric, the proportion of treatment data points that exceeds the highest baseline value can be easily calculated. For example, if 9 of 12 treatment data points exceed the highest baseline observation, the PND score is 9/12 (75%). Another advantage of the PND score is that it is immediately meaningful to researchers. That is, if fewer than half of the treatment data points exceed baseline levels, it should be clear that this probably does not represent an unequivocally effective treatment. Recently, to establish evidence-based practices for educators, the PND procedure was frequently used in meta-analysis studies on different instructional fields for the individuals with intellectual disabilities (Wang & Spillane, 2009). Hart and Banda (2010) systematically reviews 13 published single-subject studies to examine the effectiveness (PND) of picture exchange communication system strategy on speech and problem behaviors; Joseph and Konrad (2009) synthesized the PND across 8 studies to identify effective methods for teaching writing to students with intellectual disabilities. Lotan and Gold (2009) review 28 experimental articles to evaluate the therapeutic influence (PND) of multisensory intervention approach for individuals with intellectual disability. The PND procedure was also employed in some literatures of mathematics instruction research. Fowler, Konrad, Walker, Test, and Wood (2007) reviewed 11 studies to exam effects of self-determination interventions on academic performance for students with mental retardation. The results indicated 74% PND for math assignment productivity with self-management intervention. Xin, Grasso, Dipipi-Hoy, and Jitendra (2005) employed meta-analysis approach to examine the effectiveness of purchasing skill instruction for students with intellectual disability. Results indicated a moderately positive effect (median PND = 87%). Study features that were analyzed included participant characteristics (i.e., educational grade, disability level, and preexisting mathematics skills) and instructional features (i.e., instructional strategy, skill adaptation, type of functional skill, error correction procedure, length of instruction, and instructional setting). As the existing empirical studies of mathematics instruction for students with intellectual disabilities in Taiwan have accumulated a considerable amount, so that the motivation of this study was to estimate the overall effectiveness of mathematics instruction researches in Taiwan to explore the possible trends for the research and development in the future. Passing from Freedom to Happiness 563

3 Purpose of Study 1. To examine the effectiveness of mathematics instruction researches for students with intellectual disabilities in Taiwan. 2. To examine the effectiveness of different students demographic dimension, such as disability level, educational grade, and gender. 3. To examine the effectiveness of different instructional design dimension, such as strategies, curriculum, and time spending. 564 The 20th Asian Conference on Intellectual Disabilities

4 METHOD Literature Selection Procedures In this meta-analysis, there were only 28 empirical studies be included from over 120 articles during the preliminary searching stage. The literature selection procedures included the following two-step process. 1. Search of electronic database. Authors first conducted broad computerized searches of the literature on mathematics instruction for students with intellectual disability using the following databases: Chinese Electronic Periodicals Service(CEPS) database (1991 to 2011) and National Digital Library of Theses and Dissertation in Taiwan database (1956 to 2010) using full and truncated versions of the following terms: disabilities, intellectual disability, mental retardation, effectiveness, instruction, teaching, and mathematics instruction. 2. Check of selection criteria. The first author read the study abstracts to determine whether the articles met the criteria for inclusion. To judge the appropriateness of each article, there were five criteria to be checked: (a) studies had to include an intervention to teach mathematics, (b) the participants of the studies were identified as students with intellectual disability (IQ 75 and below), (c) single-subject research design studies were included in the methodologies. (d) studies had to provide baseline and treatment data that allowed for the computation of effect sizes(pnd), (e) only empirical studies, such as thesis or peer reviewed journal articles, were included in this review. Effectiveness feature s that were analyzed included two dimensions: student characteristics (i.e., disability level, educational grade, and gender) and instructional design features (i.e., strategy, curriculum, and time spending). Figure 1. Framework of the Study Passing from Freedom to Happiness 565

5 Analysis of Mathematics Instruction Effectiveness Because all studies in this review used a single-subject research design, a percentage of nonoverlapping data (PND) procedure was employed to estimate the effectiveness (Scruggs & Mastropieri, 2001). Computation of Effectiveness. First, the most extreme (highest for targeting high performance and lowest for targeting low performance) data point in the baseline phase was noted. Second, all points in the intervention phase that exceeded that point were counted and divided by the total number of points in the intervention phase (Scruggs, et al., 1987). This number was converted to a percentage and reported as the PND (figure 2). Figure 2. Formulation of PND Interpretations of Effectiveness. The interpretative framework for PND (figure 3) articulated by Scruggs and Mastropieri (1998) are as follows: (a) above 90% is a large effect, (b) 70% to 90% is a moderate effect, (c) 50% to 70% is a low effect, and (d) below 50% is not effective. Figure 3. The Interpretative Framework for PND 566 The 20th Asian Conference on Intellectual Disabilities

6 RESULTS The Effect Size of Total Mathematics Teaching Researches Table 1 presents the effect size of 28 studies related to the mathematics instruction for the students with intellectual disability in Taiwan from 2001 to 2010, with a PND range of 67% to 100%. In this table, there were 20 studies revealed a large effectiveness (PND above 90%); 7 studies suggested a moderate effectiveness (PND = 90% to 70%); and only one study indicated low effectiveness (PND = 70% to 50%). On the average, the median PND was 93%, revealed a large effectiveness of mathematics instruction for students with intellectual disability in Taiwan. Table 1 Overview of All Studies Effects (PND) Passing from Freedom to Happiness 567

7 Effects Size of Students with Different Disability Level Regarding the four disability levels (table 2), those students with mild disabilities were the majority of the participants (79% studies). The worse the disability level was, the fewer participants involved. The effectiveness of all the four disability levels is large: mild disability (PND = 93%), moderate disability (PND = 95%), severe disability (PND = 94%), and profound disability (PND = 100%). Table 2 Summary of Effects (PND) on Different Disability Level 568 The 20th Asian Conference on Intellectual Disabilities

8 Effects Size of Different Students Educational Grade The results presents in table 3 indicate the concern of mathematics instruction studies for student with intellectual disability in Taiwan focused on elementary education stage (79% studies). All the six grades in this stage revealed a large effectiveness. The studies of secondary education, only 6 studies (21%), are clearly less than elementary education. Both the effectiveness of the 7th grade (PND = 94%) and the 9th grade (PND = 97%) were large, whereas the 8th grade (PND = 87%) had a moderate effectiveness. So far, none of studies extended the educational stage to the senior high school or university. Table 3 Summary of Effects (PND) on Different Educational Grades Passing from Freedom to Happiness 569

9 Effects Size of Different Gender Three studies (Lin & Niew, 2001; Lin, 2005; Chen, 2008) did not present the gender of participants were excluded from table 4. The results highlight the difference between boys and girls. The number of boys (43) is about 1.5 times to the number of girls (28). Boys revealed a large effectiveness (PND = 92%), whereas girls suggested a moderate effectiveness (PND = 88%). Table 4 Summary of Effects (PND) on Different Gender 570 The 20th Asian Conference on Intellectual Disabilities

10 Effects Size of Different Strategies for Mathematics Teaching Table 5 provides effectiveness of different strategies. The strategies that indicated large effectiveness included computer-assisted instruction (PND = 95%), cooperative learning (PND = 98%) and cognitive strategies (PND = 92%). The strategies that revealed moderate effectiveness were communication training (PND = 90%) and functional curriculum (PND = 90%). For the other strategies, with only one study was included, a variety of effectiveness was found: graphic representational strategy (PND = 87%), touch math instruction (PND = 100%), universal design (PND = 73%), and temperament-responsive teaching (PND = 100%). Table 5 Summary of Instructional Strategies Effects (PND) Passing from Freedom to Happiness 571

11 Effects Size of Different Mathematics Curriculum The results reflected in table 6 indicated that the majority of mathematics curriculums are addition & subtraction (36% studies) and shopping skills (25% studies). The curriculums that indicated large effectiveness were addition & subtraction (PND = 92%), shopping skills (PND = 97%) and multiplication & division (PND = 97%). The curriculums that suggested moderate effectiveness were measurement (PND = 83%) and numbers & quantities (PND = 86%). The other three curriculums with only one empirical study respectively, revealed large effectiveness: time (PND = 100%), geometric instruction (PND = 100%), and statistics & charts (PND = 95%). Table 6 Summary of Mathematical Curriculum Effects (PND) 572 The 20th Asian Conference on Intellectual Disabilities

12 Effects Size of Different Time Spending for Mathematics Teaching As show in the table 7, there are three time periods design (below 1000 minutes, 1000~2000 minutes and 2000~3000 minutes), the time periods spent for the studies of mathematics instruction in Taiwan were usually below 1000 minutes (71% studies). The effectiveness of all three time periods are large: below 1000 minutes (PND = 93%), 1000 to 2000 minutes (PND = 96%) and 2000 to 3000 minutes (PND = 100%). Table 7 Summary of Different Time Spending Effects (PND) Passing from Freedom to Happiness 573

13 DISCUSSION Conclusions In sum, the studies related to mathematics instruction for students with intellectual disability in Taiwan presents a large effectiveness (PND = 93%). On the dimension of student characteristics, participants with mild, moderate, and severe disability present large effectiveness; whereas the effectiveness of profound disability can t be sure due to the deficiency of literature (only one study). Speaking of educational grade, all grades of elementary and secondary education indicated large effectiveness except 8th grade. As for the gender, boys present large effectiveness, but girls reveal moderate effectiveness. On the part of instructional design, about half of the strategies indicate large effectiveness (computer-assisted instruction, cooperative learning, and cognitive strategy), other strategies reveal moderate effectiveness (communication training, functional curriculum). However, over half of the curriculums present large effectiveness (addition & subtraction, shopping skills, and multiplication & division), and other two curriculums reveal moderate effectiveness. Finally, all the three instructional time spending periods (below 1000 minutes, from 1000 to 2000 minutes, and over 2000 minutes) indicate large effectiveness. Limitation and recommends Selection criteria for the literatures included. In this study, two parts of literature sources were theses and journal articles. However, Council for Exceptional Children in 2005 proposed the following standard to allow confidence in the effects of evidence based single-subject research (Horner, et al., 2005): (a) a minimum of five single-subject studies that have been published in peer-reviewed journals, (b) the studies are conducted by at least three different researchers across at least three different geographical locations, and (c) the five or more studies include a total of at least 20 participants. Above criteria would be taken into account in the following researches if a comparison is made with international literatures. Methodologies of the literatures reviewed. All the literature reviewed in this meta-analysis employed single-subject research design, but there are others meta-analysis approaches for different methodologies. In the continuant research, other methodologies, such as experimental design, correlational research, questionnaires investigation, or qualitative studies, should be tried to include in the literatures reviewed. Effectiveness of maintenance and generalization. In this meta-analysis study of single-subject research design, the results just presented the effect size between baseline stage and intervention stage, what about the effect size of maintenance stage and generalization stage? There were examples provided by other meta-analysis reports (Scruggs & Mastropieri, 2001; Xin, et al., 2005). Literature selection procedural. A hand search procedural should be involved to find the full text of the latest theses or journal articles that were not available to be downloaded from the database. More over, both the ancestry search and descendant search procedurals are useful strategies in some electronic database engine (Scruggs, et al., 2007). 574 The 20th Asian Conference on Intellectual Disabilities

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