Teaching Math in Learning Disorder and Behavioral Disorders Classroom - Essay Example

TEACHING MATH IN LEARNING DISORDER AND BEHAVIORAL DISORDERS ROOM 2007 Teaching Math in Learning Disorder and Behavioral Disorders Classroom Introduction The task of improving students' achievement in mathematics was clearly determined as one of the national priorities in the field of education (Goals 2000: Educate America Act). Such attention to this subject is probably due to the traditional perception of mathematics as the most important doorkeeper to a variety of educational and occupational opportunities (Maccini & Gagnon, 2000). This perception remains dominant these days with increasing numbers of educational institutions including additional math assessments students have to pass to graduate. Recently collected statistical data demonstrates that up to 20 percent of American students have some type of learning impairment though the actual figure is likely to be much higher if consider an unknown population of students with learning disorders whom have never been officially undiagnosed (LDA-CA, 2003). Learning disabilities (LD) seriously interfere with students' achievement in mathematics thus putting them at a higher risk of having problems in meeting the obligatory academic standards as compared to the normal student population. Thus, some recent studies report that between 4-7% of the school age population experiences some form of math difficulty as a result of LDs (Fuchs & Compton, 2005). Granted the increasingly strict graduation requirements imposed on high school seniors in mathematics the risk is even greater these days than ever before. The lack of specialized teacher training, coupled with insufficient amounts and poor availability of effective study material and traditional LD-friendly curricula contributes substantially to the already huge educational issues the average US students with a learning disability must face (Miller & Mercer,1997). Various behavioral disorders (BD) such as attention deficit/hyperactivity disorder (ADD/ADHD), conduct disorder (CD) and oppositional defiant disorder (ODD) in students represent another highly important problem in terms of teaching and learning mathematics. Thus, ADD/ADHD is one of the most commonly met behavioral disorders in the U.S.: approximately 7.8% of children and adolescents aged from 4 to 17 are diagnosed with it (Chang, 2005). The base prevalence of ODD is also estimated within the range of 1.7% -almost 10% (Rey, 1993). These behavioral disorders are also commonly associated with serious academic problems, including problems in learning mathematics (Todd et al, 1999). In fact, it will not be an exaggeration to state that BDs are almost always associated with LDs. Thus, one of the latest studies in this field reports that 71% of children with ADHD also have a LD and 26% of children with ADHD have a specific math disability (Mayes & Calhoun, 2006). However, despite the growing recognition that students with some form of LD or BD have unique learning needs, up to now the majority of such students are taught without any reference to their needs, including those in learning mathematics, in the general education classroom. One possible reason for such disappointing situation is lack of literature on teaching math for students with LD and BD: some researchers observe that the literature on teaching math is scarce even when compared with the existing research in the field of teaching other subjects such as language and reading - a situation that is hardly acceptable considering the importance of mathematics in modern world (Steele, 2004). The purpose of this paper is to provide an overview of the most interesting works in the field of teaching math for students with LD. Literature Review There is a solid body of literature exploring definitions, diagnostic criteria, and many other formal aspects of LD with some authors focusing specifically on mathematics (Dockrell & McShane, 1993; Adelman & Taylor, 1993; Lerner, 1993; Butterworth, Cipolotti & Warrington, 1996). Similarly, a serious body of research is dedicated to exploring the relationship between BDs and LDs; many recent works examine the variety of implications of BDs on the process of learning and attempt to explain the role that cognitive impairments (executive function, working memory, inattention play, etc) observed in students with BD play in the relationship between BDs and difficulties in learning math (Swanson & Beebe-Frankenberger, 2004; Fuchs et al., 2006). The term 'learning disability' was first defined in 1967 by the National Advisory Committee on Handicapped Children (NACHC), but it was not until the early eighties that the researchers began to pay serious attention to identifying, documenting and exploring the nature and extent of problems that negatively impacted math performance in students with LD (Fleischner & Garnett, 1980; Fuchs, Bahr & Rieth, 1989; Miller, Strawser & Mercer, 1996). The pioneering work of Arthur Baroody (1983) represented one of the first attempts to investigate and understand the nature of difficulties in math learning using the qualitative methodology. Baroody conducted a case study involving an 11 years old boy, Adam, who had a sever form of math-learning disability (organic brain dysfunction) in order to reveal the unique weaknesses and strength associated with it. The researcher used a series of semistructured interviews (over the period of 14 months) which included problems or assignments followed by flexible questioning. The study results demonstrated that the boy had the basic informal skills and concepts upon which he could build more advanced math skills while the key deficiency was in the realm of his formal math skills: Adam had difficulties learning part/whole relationships and base ten notions. In order to help the subject deal with these difficulties Baroody employed games and interactive exercises. As a result, the boy demonstrated significant improvements in base ten concept skills basic place value. Baroody assumed that the improvements were largely due to involvement of the affective factors during the experimental corrective course: thus the subject demonstrated willingness to assert himself, improved his confidence in his abilities, and was less defensive than in traditional learning. The most evident strength of Baroody's study is that he studied the phenomenon of interest in its natural setting using one of the most informative qualitative techniques - interviewing. Therefore, the researcher obtained a very rich contextual data which allowed him to make valid conclusions about the nature of learning difficulties experienced by the subject; effectiveness of the corrective strategy tested by Baroody convincingly demonstrated that the conclusions drawn from the data were correct. At the same time, the case study involved only one subject which significantly limited its generalizability: further research was needed to show that Baroody's conclusions and recommendations would remain valid in other contexts involving other students with different types of LDs. Later studies revealed other aspects of the difficulties experienced by LD-students acquiring and retaining basic math skill. A good attempt to summarize these aspects belongs to Miller & Mercer (1997). Overall, Miller & Mercer (1997) report that math performance among LD is limits below their non-learning disabled peers: the describe research studies that document LD high school seniors as having reaching a seventh-grade level "mathematics plateau", with approximately 1 year of mathematical progress for every 2 years throughout their education while earlier statistical data demonstrates even lower levels of achievement among the average LD high school student, with mean scores that rival fourth and fifth grade students. They identified the most common learning obstacles in LD students mentioned in the most credible research and divided them into the following categories: information-processing, cognitive and meta-cognitive, and language. According to the Information-Processing Theory, the process of information acquisition involves mechanisms which require attention, sensation, perception, memory and response, but students with LD often have difficulties one or several areas of memory and encoding, and these problems produce deficiencies in attention, processing auditory and/or visual information. Besides, Miller and Mercer are among the first to emphasize that students with dyscalculia - a form of dyslexia which impairs comprehension of math concepts and symbols - are often ignored by the researchers. Miller and Mercer have not carried out an empirical research to justify at least some of their assumption: this limits credibility of their study since they had to rely on the results reported by other researchers, and even the most experienced scholars sometimes make mistakes or demonstrate some biases. However, the author's choice of only credible peer-reviewed sources does seem to compensate for this potential limitation. Furthermore, despite the lack of empirical data, the work of Miller and Mercer is not without substantial practical value. Accurate and comprehensive summary of the available data allowed the authors to issue a series of highly effective recommendations for improving mathematics education in LD students: 1. Developing a refining rather than reforming stance in teaching including: a) the use of validated approaches that create success among students; b) teacher -learner verification strategy; c) consideration of diversity of learners. 2. Accommodating learner characteristics and needs. Use formal/informal assessments to diagnose students' characteristics and needs. The emphasis with student with disabilities should be to prepare students to function independently in the life after school. Individual attention is critical because students do not learn the same mathematics within the same time span due to different intellectual and cognitive abilities. 3. Use instructional practices with research support: a) Demonstration, modeling and feedback; b) providing reinforcement; c) using concrete to abstract teaching sequence; d) setting goals; e) combining demonstration with permanent model; f) using verbalization in problem-solving; g) teaching strategies for problem-solving; h) using peers, computers and videodiscs. These recommendations identified the most crucial directions in development of special needs math education for the next decade and helped properly structure the abundant literature covering the problem of LD students in math classrooms. The relationship between increasingly diverse student population and teaching math for LD students has been one of the most topical issues over the last two decades. Student population attending American schools become increasingly diverse each year. Estimates indicate that by the 21st century more than 30 percent of the overall student population in the US will be from diverse cultural and linguistic backgrounds (predominantly African American, Asian, and Hispanic) (Smith & Luckasson, 1995). The tendency will produce another serious challenge in terms of addressing special needs of LD students in math classrooms. An interesting work by Scott & Raborn (1996) analyzes the set of unique difficulties facing culturally and linguistically diverse (CLD) students with LD in mastering math skills. In its essence, mathematics represents a language system in itself, but this system differs substantially from the common language due to its conceptual density and absence of contextual meaning: unknown mathematical symbols can not be understood by reading the familiar context in which they are used. Consequently, students must comprehend the meaning of each mathematical symbol they face in the context of a 'mathematical sentence'. This is the most essential difficulty waiting for CLD students with LD for whom English is a second language: they are likely to struggle with the new language system and the correct meaning of the mathematical symbols. Besides, Scott & Raborn assume that CLD student often face an additional challenge associated with the different methods/ways of learning mathematic in their home environment. Therefore, adequate attention and special instructional design are even more crucial for CLD student with LD than for their American counterparts whom master the mathematical language in their native linguistic environment. The work of Scott and Raborn (1996) bears much resemblance to Miller and Mercer's (1997) article in terms of design: instead of collecting the empirical data relevant to their topic they conduct a solid literature review to make their conclusions and issue recommendations. However, Scott and Raborn seem to demonstrate more critical attitude toward the results reported by the past studies in the field. Instead of simply summarizing the existing findings drawn from the classic works of Bley and Thornton (1989), Dawe (1983), Cummins (1989), Secada (1992) and others the authors carefully analyze and contextualize the data to suggest their own assumptions. Such critical attitude allows the authors to come up with a series of concrete recommendations and effective instructional practices about how to facilitate learning math skills for CLD students with LD. In one of the classic works, Bley and Thornton (1989) manage to cover almost every aspect of teaching math for students with LDs. Although the authors focus specifically on the elementary school, many concepts described and comprehensively explained in the book can be successfully applied to improving students' achievements in math in secondary and high school. These include problem solving approaches and techniques that can be used by students to compensate, fully or at least partially, with their LDs. The book covers virtually every problematic area in teaching math skills to students with LD: number and place value, the four basic operations, money and time, problem solving, ratio, proportions, fractions, percents, and computer use. However, the primary intent of the authors is not only describe the nature and incidence of difficulties to be faced by LD student population, but also to provide the most effective approaches and techniques to help such students compensate for their learning disabilities and to deal effectively with mathematics in academic and everyday situations. Specially designed alternative instructional activities supported by detailed diagrams represented the last word in the field of LD education at the time the book was published. While the importance of instructional design is stressed in virtually every study in the field of LD students' education, the use of technology to facilitate learning is probably the most promising alternative these days. Although the research and development of technology-supported math instruction can be traced back to the mid 1980s (Hasselbring, Lott & Zydney, 2005) potential of this new option is still too far from being fully realized. Hasselbring and Goin (2005) were among the first to design a comprehensive advanced technology-based intervention strategy called Fluency and Automaticity through Systematic Teaching with Technology (FASTT). The FASTT approach is based on the use of specific cognitive mechanism: the key to making the retrieval of basic math facts fluent is to first establish a mental link between the facts and their answers which must be stored in long term memory. FASTT provides 7 features to develop these relationships: 1. Identification of fluent and non-fluent facts; 2. Restricted presentation of non-fluent information; 3. Student generation of problem/answer pairs; 4. Use of 'challenge times'; 5. Spaced-presentation of non-fluent information; 6. The appropriate use of drill-and-practice; 7. Computer monitoring of student performance. The authors carried out a very serious validation of the basic principles upon with FASTT Math model rests: the validation procedure took several years of intensive research and involved more than 400 students with various forms of LD. Overall, the findings reported by Hasselbring and Goin are very positive: when used daily, for about 10 minutes, most students with math difficulty can develop fluency in a single operation after approximately 100 sessions. Consistency is identified as one of the most important contributors to the positive outcomes after comparison drawn between regular and non-regular users. The first controlled study of the FASTT model involving 3 groups of students were matched for age, sex, and race. Two of the groups consisted of students with math difficulty and the remaining group consisted of students without math difficulty. In the experiment, one of the math difficulty groups (Math-Disabled Experimental) received an average of 54 ten-minute sessions on the FASTT software for addition; the other two groups (Non Math-Disabled and Math-Disabled Contrast) received only traditional fluency instruction from their teachers. As the result, the students with LD gained approximately 24 new fluent facts after receiving the instructions via FASTT model; the group of LD students whom received instructions in the traditional way demonstrated zero gain; and finally, the group of students without LD showed only an 8 new facts gain after receiving the traditional instruction. Furthermore, the experiment also demonstrated impressive maintainability of the gains: after almost 4 months of summer vacation, the participants regressed by only 4 facts. Based upon such solid body of evidence the authors conclude that the FASTT Math model has an exceptionally positive effect on developing mathematical fluency in both students with and without LD though it is especially effective for the former group. There is absolutely no doubt to put this conclusion in question: such flawless and credible studies are rare even in the scholarly community. Use of multiple controlled studies, large numbers of participants with various forms of LD matched by at least three criteria, and quantitative methodology ensure full replicability of the results. Conclusion Evidently, students with LD - regardless of its form and definition - commonly have serious difficulties acquiring even the most basic math skills. These difficulties involve a range of complex cognitive and information-processing mechanisms which have not been fully understood yet. However, lack of comprehensive knowledge on this issue does not prevent the educators from designing increasingly effective intervention strategies in order to facilitate learning math for LD students. These strategies include specific instruction techniques, visual means, games, music and other. The variety of disciplines involved in creation of the intervention strategies and techniques is impressive ranging from traditional theories of learning to neurobiology and the most advanced technology. Yet, such multidisciplinary approach is likely to be the most important contributor to the recent advances in the field of teaching LD students for math skills. References The Goals 2000: Educate America Act (Public Law 103-227) Adelman, H.S., & Taylor, L. (1993). Learning problems and learning disabilities: Moving forward. Pacific Grove, CA: Brooks/Cole. Baroody, A. J. (1983). The Case of Adam: A Specific Evaluation of a Math Learning Disability. Paper presented at the Annual Meeting of the American Educational Research Association. Montreal, Canada, April 11-14. Bley, N. S., & Thornton, C. A. (1989). Teaching mathematics to the learning disabled. Austin, TX: PRO-ED. Butterworth, B., Cipolotti, L. & Warrington, E.K. (1996). Short-term memory impairments and arithmetical ability. Quarterly Journal of Experimental Psychology 49A, 251-262. Chang, K. (2005). Attention-Deficit/Hyperactivity Disorder. EMedicine. Retrieved June 27, 2007 from http://www.emedicine.com/med/topic3103.htm Cummins, J. (1984). Bilingualism and special education. Clevedon, England: Multilingual Matters. Dawe, L. (1983). Bilingualism and mathematical reasoning in English as a second language. Educational Studies in Mathematics 14, 325-353. Dockrell, J., & McShane, J. (1993). Children's learning difficulties: A cognitive approach. Cambridge, MA: Blackwell. Fuchs, L. S., Bahr, C. M., & Rieth, H. J. (1989). Effects of goal structures and performance contingencies on math performance of adolescents with learning disabilities. Journal of Learning Disabilities 22, 554-560. Fleischner, J., & Garnett, K. (1980). Arithmetic learning disabilities: A literature review (Research Review Series Volume 4). New York: Teachers College, Columbia University Research Institute for the Study of Learning Disabilities Hasselbring, T. S., & Goin, L. I. (2005). Research Foundation & Evidence of Effectiveness for FASTT Math. Tom Snyder Productions White Paper [available online at http://www.tomsnyder.com/reports/FM_White_Paper.pdf] Hasselbring, T. S., Lott, A. L., Zydney, J. M. (2005). Technology-supported math instruction for students with disabilities: Two decades of research and development. Paper presented at the Center for Implementing Technology in Education Summer Institute, Bedford, NH. Lerner, J. (1993). Learning disabilities: Theories, diagnosis, and teaching strategies (6th ed.). Boston, MA: Houghton Mifflin. Maccini, P., & Gagnon, J. C. (2000). Best practices for teaching mathematics to secondary students with special needs. Focus on Exceptional Children, 32, 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, 145-157. Miller, S. P. & Mercer, C. D. (1997). Educational Aspects of Mathematics Disabilities. Journal of Learning Disabilities 2(1), 47-56. Miller, S. P., Strawser S., & Mercer C. D. (1996). Promoting strategic math performance among students with learning disabilities. LD Forum 21(2), 34-40. Rey, J. M. (1993). Oppositional Defiant Disorder. American Journal of Psychiatry 150, 1769-1778) Todd, A. W., Horner, R. H., Sugai, G., & Sprague, J. R. (1999). Effective behavior support: Strengthening school-wide systems through a team-based approach. Effective School Practices 17(4), 23-37. Scott, P. B., & Raborn, D. T. (1996). Realizing the gifts of diversity among students with learning disabilities. LD Forum 21(2), 10-18. Secada, W. G. (1992). Race, ethnicity, social class, language, and achievement in mathematics. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning. New York: MacMillan Publishing Co, 623-660. Smith, D. D., & Luckasson, R. (1995). Special education: Teaching in an age of challenge. Boston: Allyn & Bacon Steele, M. M. (2004). A review of literature on mathematics instruction for elementary students with learning disabilities. Focus on Learning Problems in Mathematics 26(2), 62-67. Swanson, H. L., & Beebe-Frankenberger, M. (2004). The relationship between working memory and mathematical problem solving in children at risk and not at risk for serious math difficulties. Journal of Educational Psychology 96, 471-491. Read More