etadd_47(3) - Division on Autism and Developmental Disabilities

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ing skills about mathematics and deeper conceptual understanding of mathematical ideas to empower students with knowledge that is transferable to various situations rather than knowledge of procedures specific to certain mathematical situations (van Garderen, 2007; Woodward & Montague, 2002). Mathematical reasoning and conceptual understanding can help students achieve higher levels in mathematics and face increased expectations for academic performance in K-12 education (IDEA, 2004; NCLB, 2002; NCTM, 2000; Woodward, 2004). While some might question the need for more rigorous focused mathematics education for students with MID, it is imperative for multiple reasons: (a) these students are capable of being successful with these pedagogical approaches if given a chance (Baroody, 1996; Jimenez, Browder, & Courtade, 2008; Erez & Peled, 2001; Neef et al., 2003), (b) a decreased focus on procedures or rote recall is consistent with research suggesting students with MID struggle with working memory (Schuchardt et al., 2010), and (c) helping these students to be successful on high-stakes assessments (NCLB, 2002; Woodward, 2004). First, although limited in quantity, the little research on more conceptual instruction for students with intellectual disability demonstrated success. Neef et al. taught students with MID how to use basic algebraic procedures (e.g., solving for the unknown) while solving word problems. Related, in a study by Jimenez et al., students with IQs below 50 were successful with solving for an unknown in an algebraic equation (e.g., 3 a 5). These findings, when considered along with those of Baroody (1996) and Erez and Peled (2001), suggest students with MID possess a number of skills related to higher order mathematical understanding and the field may need to raise its expectations for what these students can– and should be expected–to do. Second, students with MID struggle with working memory (Schuchardt et al., 2010). Rather than focus on instructional approaches steeped in storage and recall, practitioners can focus on conceptual understanding and use technology to circumvent student struggles (NCTM, 2000; Woodward & Montague, 2002). Students with MID experience success using calculators (Bouck et al., 2009; Horton, Lovitt, & White, 1992). Calculators can be used as a cognitive prosthesis (Edyburn, 2006) and teachers can then potentially devote more instructional time to developing a thorough and deep understanding of mathematical ideas and connections between those ideas–instruction consistent with recommendations by NCTM (2000) and even special education researchers (Woodward & Montague). Last, higher level mathematical ability and understanding is needed by students with MID if they are expected to take general largescale assessment (Bouck, 2007). Given that students with MID across all grade levels typically take the same assessment as their peers without disabilities (Bouck; Yell & Drasgow, 2005; Ysseldyke et al., 2004), instruction in mathematics for this population needs to focused on the areas that can promote student success. If these students are expected to take the general large-scale assessment, they should be given general education academic instruction to increase the opportunity for success (Bouck, 2007). While assessment should not drive instructional practice (Faulkner & Cook, 2006; Shepard, 2010), students with MID have to be given a fighting chance to be successful by covering the content. Hence, research should focus on how to help students with MID be successful in mathematics classes if the field of education continues the practice of high stakes testing. Implications for Practice The results of this review of the literature suggest practices exist that assist students with MID in ascertaining basic facts as well as conceptual understanding of mathematical ideas, although more research is needed on the latter. Multiple studies in the review suggest teachers can rely on flashcards as an educational tool for teaching mathematical facts to students with MID (Dihoff et al., 2005; Hayter et al., 2007; Rao & Mallow, 2009; Sante et al., 2001). However, teachers need to make careful decisions about how much time is devoted to memorization of facts as compared to critical thinking about mathematical ideas and the connections between these ideas (NCTM, 2000; van Garderen, 2007; Woodward & Montague, 2002). 396 / Education and Training in Autism and Developmental Disabilities-September 2012
Neef and colleagues (2003) demonstrated some of the benefits of diagramming information in word problems. Diagramming and other forms of visual representation may also be included in instruction to give students with MID opportunities for access to more challenging mathematics (van Garderen, 2006). By teaching students with MID methods for storing information on paper while working through challenging, multistep problems, teachers give these students an important tool for overcoming deficits in working memory which may have previously contributed to the struggles of some students with MID in mathematics (Allen et al., 2006; Baddeley, 2003; Barrouillet, Bernardin, Portrat, Vergauwe, & Camos, 2007; Schuchardt et al., 2010). Instructional principles applied by Neef and colleagues may be also applicable to various situations in which students with MID are likely to need help with storing and organizing information and using metacognition to complete proper analysis of the mathematical problem and the steps taken to solve it. Teachers can apply these principles to multiple mathematical situations as well as in other content areas when students with MID feel overwhelmed with the amount and complexity of information they need to store, organize, and process. Limitations and Future Directions A challenge exists when studying students with MID due to variation in ways of defining and labeling intellectual disability, and thus researchers face dilemmas when determining criteria for participant inclusion (Sandieson, 1998). In this study, the criteria was based on IQ scores which can be problematic due to variation of student performance that often occurs within the 50–75 IQ range (Cawley & Parmar, 1995; Fletcher, Blair, Scott, & Bolger, 2004). However, the researchers chose IQ for determination of inclusion of participants due to the ambiguity of the MID label especially when considering studies done outside the United States where a student can be labeled as having MID due to having an IQ of up to 85 in countries (e.g., the Netherlands). While it is necessary to be specific about participant characteristics when reporting findings, the drawback of excluding studies done in foreign countries, as well as following strict guidelines for participant IQs, is the exclusion of some important studies in mathematics for students with disabilities completed recently by researchers in other nations (e.g., Chung & Tam, 2005; Kroesbergen & Van Luit, 2003; Kroesbergen & Van Luit, 2005). Therefore, some important studies to the field may have been excluded due to the strict, yet necessary, inclusion criteria set by the researchers in this study. Aside from difficulties with defining and labeling students with MID, the lack of information on characteristics of students with MID also presents a challenge. To better study students with MID, it may be necessary to more thoroughly investigate the characteristics of students with MID by specifically studying this population (as in Schuchardt et al., 2010) rather than aggregating data with other populations which is a common problem and has made it difficult to determine the characteristics and outcomes for students with MID (Polloway et al., 2010). Also, due to the lack of research on mathematics and students with MID, it may be important for researchers to examine the performance of these students using qualitative research designs to gain insight into the specifics of how students with MID understand and reason about mathematics. After a foundation of research regarding mathematical reasoning as well as the characteristics (e.g., memory and processing abilities) of students with MID has been established, interventions may be more effectively developed. Eventually, considering that teachers are expected to use evidence-based practices to guide their instruction, researchers need to provide a more thorough research base regarding effective interventions for students with MID so teachers can have a better foundation upon which to build their instructional practices. References * Indicates articles used in this review of the literature Allen, R. J., Baddeley, A. D., & Hitch, G. J. (2006). Is the binding of visual features in working memory resource-demanding? Journal of Experimental Psychology, 135, 298–313. Algozzine, B., O’Shea, D. J., Crews, W. B., & Stoddard, K. (1987). Analysis of mathematics compe- Mathematics and Students with MID / 397
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Education and Training in Autism an
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ities. Scholars have argued that do
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discussions were held with 12 addit
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TABLE 1 A Sample of Community Funds
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et al., 2007). At the school, stude
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students opportunities to work and
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Browder, D. M., & Cooper-Duffy, K.
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of words, and in the short term wer
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TABLE 3 Word Lists List No. Trainin
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TABLE 6 Pairwise Comparisons on Pos
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Word Identification or Word Attack
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erate to severe disabilities. Excep
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ess in a variety of subjects includ
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TABLE 1 Target Vocabulary Words by
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Figure 1. Example of PowerPoint Sli
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TABLE 3 Mean Percentage of Correct
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Figure 4. Jake’s percentages corr
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man-Martin et al. (2005) by demonst
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used in the study that did not foll
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with the removal of the interventio
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Method Participants Four male child
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TABLE 2 Play Scale - Developmental
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elated utterances, which were used
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Figure 1. Ian’s Progress in Play
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Figure 3. Ryan’s Progress in Play
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Figure 5. Social Validity: Average
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(2000). A comparison of video model
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Method Participants Four high schoo
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TABLE 1 Task Analyses for all Tasks
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Figure 1. Holly multiple baseline g
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Figure 3. Norman multiple baseline
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tion, some aspects of the target be
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table.” During the session, the t
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