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Statement of the problem
With passage of section 504 of the Rehabilitation Act of 1973, and the Americans with Disabilities Act of 1990, colleges and universities in the United States and Puerto Rico have been endeavoring to accommodate the increasing population of students with specific learning disabilities (LD). Izzo, Hertzfeld, Reed, & Aaron, (2001), state that many in the higher education community are still struggling with how to support students with disabilities effectively, so that these students can enter and complete their postsecondary programs. Many postsecondary educational settings that admit students with disabilities have not kept pace with the increases in the number of students with disabilities enrolling at their institutions (as cited in Kundu, Dutta, Schiro-Geist, & Crandall, 2003, p. 45). Nevertheless, these laws mandate institutions of higher education to provide equal access to programs and services for students with LD, (National Joint Committee On Learning Disabilities [NJCLD], 1999).
In the decade from 1990-2000 of the students with disabilities, 11 percent reported having a learning disability (U.S. Department of Education, National Center for Education Statistics [NCES], 2003, p. 68). In Puerto Rico 58 percent of students between the ages of six to twenty-one (6-21) have a documented learning disability (Secretaria Asociada de Educación Especial del Departamento de Educación, 2009). In spite of the increasing awareness on behalf of postsecondary institutions, they continue to struggle with limited resources to appropriately educate students with specific learning disabilities. Many view the educational system as a means to alleviate social problems of inequality and provide leadership for a competitive global economy. Education is viewed as a precursor to a successful career, initial stability, and improved social status. Postsecondary education and vocational training are as important for students with disabilities in gaining independence and social respect as for those without disabilities (as cited in Kundu et al., 2003, p. 45). In addition, Postsecondary education is becoming increasingly important in obtaining quality employment for people with disabilities. Students with disabilities still have difficulty obtaining basic accommodations and supports. However, discriminatory attitudes and assumptions about their abilities also negatively influence these individuals in postsecondary education and the workplace (Dorwick, Anderson, Heyer, & Acosta, 2005, p. 41. An area of particular importance for students with LD is career self-efficacy and its impact on higher education and the field of mathematics. According to Cavanagh (2007, p. 21-23), students who complete advanced mathematics courses such as algebra are more likely to succeed in college and obtain better paying jobs.
Limited accessibility and accommodations in mathematics courses for college students, with specific learning disabilities, such as dyslexia (reading disability), and/or dyscalculia (math disability) find these students not only struggling to obtain competency in algebra, and other mathematics courses, but, are also seemingly marginalized to choose majors or career fields that may not have been their first choice. (Burgstahler, 2006, 1994, p. 1) states that individuals with disabilities experience far less career success than their non-disabled peers. Literature reveals three main factors that cause individuals with disabilities to be underrepresented in science, technology, engineering, and mathematics (STEM) fields: 1) preparation of students with disabilities; 2) access to facilities, programs, and equipment; and 3) acceptance by educators, employers, and coworkers.
The United States is increasingly reliant on a technological work force to maintain leadership in a world economy (National Science Board, 2003). As a result, math/science competency is important for professional success in a growing number of occupations (Byars-Winston & Fouad, 1992, p. 425). In Puerto Rico, the need to be part of the technological workforce is evident as indicated in an article written in the Caribbean Business newspaper. Marquez, Ocasio, & Perez-Serrano, 2005, stated that leading regions around the world recognize that regional competitiveness and winning in the marketplace is the result of aligned science, engineering, business, and academic training with both local and global linkages. Science and technology development is global and an essential to value-chain migration, and technology development, transfer and licensing are key underpinnings of global competition. Science and math are the universal language of technology, which will increasingly drive job creation and income growth in Puerto Rico and around the world. Yet, Puerto Rico is producing a smaller share of degrees in science, math and engineering than that of other nations (China 59%, S. Korea, 46%, U.S., 36%, P.R., 24%), ("Graduation Pays: the economic case for high school redesign in Puerto Rico", n.d., p. 1, 4).
When students of particular groups are absent from advanced mathematics courses, they are not only denied a mathematics education but also the opportunity to experience economic freedom and choice (Miller, 1995, as cited in Stevens, Olivarez, JR., Lan, & Tallent-Runnels, 2004, p. 208). With unemployment rate twice that of their Caucasian counterparts (U.S. Department of Labor, 2003), Hispanic Americans clearly experience disadvantages in the employment arena. Of those Hispanic students who do not enter college with the intent to major in mathematics or related fields, many do not continue past calculus to achieve mathematics-related baccalaureate degrees (Moreno & Muller, 1999, as cited in Stevens et al., 2004, p. 208)
According to (Burgstahler, 2006, 1994) students with disabilities are rarely encouraged to prepare for science, engineering and mathematics fields. Since they do not consider a career in science, engineering, or mathematics an achievable goal, they do not take the courses necessary to prepare for post-secondary studies in these areas. High school and college students with disabilities, counselors, social service agency staff, and special education teachers often lack an understanding of the content and requirements of science, engineering, and mathematics programs in higher education these people also have a limited perspective of the technology and other resources that make it possible for students with disabilities to pursue these fields
(Betz, 1992) affirms that limited completion of math courses can restrict the range of future career opportunities available to an individual. College students need literacy in math/science concepts irrespective of selecting a formal math/science major to increase their later career options and thus, employability in the U. S. labor market (Byars-Winston & Fouad, 1992, p. 426).
Another area of concern in the field of mathematics is gender issues. As non-traditional students progress through the rigors of a postsecondary degree, they must grapple with the challenges of an extensive review of algebraic skills from their past schooling and of their individual mathematics self-efficacy. That, being the specific self-assessed belief in one's own capability of solving mathematical problems and tasks successfully, (Hackett & Betz, 1989 as cited in Goodwin, Ostrom, & Scott, 2009, p. 25). It is in the area of mathematics where we see even more emphasis placed in self-efficacy studies, perhaps because of the valued role that mathematics plays in academia, high- stakes assessments for admissions and scholarships, and the filtering of students in highly technical and specialized careers (as cited in Goodwin et al., 2009, p. 25) . Researchers have suggested that because mathematics skill is required for work in science and engineering, lowered mathematics self-efficacy is a likely contributor to the relatively low number of women in those fields and those deficits in ethnic identity further complicates the problem in the case of minorities (as cited in O'Brian, Pons, & Kopala, 1999, p. 231). "Stereotypes about female inferiority in mathematics are a distinct contrast to the actual scientific data", said Nicole Else-Quest a psychology professor at Villanova University, in Pa. and lead author of a study, which analyzed international research into the subject of gender and mathematics. The results showed that girls would perform at the same level as the boys when they are given the right educational tools and have visible female role models excelling in mathematics (Thilmany, 2010, p. 15). For students with a learning disability the results of these studies suggest that the same is true for them in that, gender specificity is not a determinant of poor mathematics achievement, however, mathematics self- efficacy may be, thus contributing also to limited academic majors and career choices.
Implications for Rehabilitation Counselors
Disability is both a common and a natural fact of life and because all individuals, including people with disabilities, have multiple identities, roles, functions, and environments , clients with disabilities require services of counselors in all specialty areas(Smart & Smart, 2006, p. 76). For rehabilitation counselors working with students transitioning from secondary to post secondary institutions of higher education, the implications are enormous. To appropriately and effectively accommodate a student with a specific learning disability, knowledge of current trends of assistive technology are needed by the rehabilitation counselor. In addition, an understanding of the "content" areas in education that may be challenging to students with a LD, such as mathematics, is as important as knowing that a student with a physical disability has the appropriate accessibility and assistive technology to participate in college studies.
Kurth and Mellard (as cited in Cawthon & Cole, 2010, p. 115) hypothesized that many accommodations offered by universities are ineffective and inappropriate, in part because they assign accommodations based on the student's disability. Rather than understanding, what a specific learning disability will practically need in their classroom environment. Students have felt that they have difficulty assessing academic information, because their professors do not know how to properly accommodate them, or that the accommodation provided by the University was unsubstantial (e.g. a note taker, whose handwriting was illegible) (Cawthon & Cole, 2010, p. 115).
As a field, rehabilitation has produced research contributing to the quality and the breadth of clinical intervention. The disability and rehabilitation community is celebrating a renewed focus on a sociological framework for understanding disability. The new paradigm of disability emphasizes the importance of integrating participatory action research methods and the person-environment conceptualization of disability resulting in how healthcare providers practice and conduct research. It is within this holistic framework, that researchers are encouraged to have knowledge of the dynamic interaction between the person and the environment, to be aware of the importance of consumer participation in the planning, implementation, and evaluation of research activities and interventions strategies, and to recognize the limitations of traditional, more medically oriented, definitions and measures of disability, (Tate & Pledger, 2003, p. 289).
In order for rehabilitation counselors servicing students in institutes of higher education to effectively collaborate with students who have a specific learning disability, more research that is inclusive of evidenced based practices is needed, as well as the rehabilitation counselors obtaining enhanced knowledge of appropriate accessibility and accommodations for the content areas of math, science, and foreign languages . All of which will facilitate students with a learning disability's attainment of their postsecondary educational goals and thus make them more viable candidates for future career- STEM oriented employment.
Purpose of the study
The purpose of this study is to explore the correlation between accessibility, accommodations, self-efficacy and career choice for college students with a LD taking mathematics courses.
The subject of mathematics demands from the student both the ability to concentrate and the ability to think and reason abstractly. For students in higher education with a learning disability in mathematics (i.e. dyscalculia), the additional difficulties imposed by inadequate or ineffective accommodations that do not make mathematics courses accessible are issues of serious concern for the student, and the students' ability to enter the global economy. The later depends on a future of well-educated and prepared employees capable of continuing the technological advances within our society today. There are several technical aids for those with dyslexia and there has been a growing understanding of their problems. However, there is no corresponding recognition for individuals with mathematical difficulties (dyscalculia). The consequences can be very damaging. Most importantly, children's self-esteem is at stake and, as a result, this greatly affects the choice of education and occupation as well as the ability to meet everyday planning questions (Malmer 2000, p. 224, 229).
It has been widely noted that mathematics learning disability has not been extensively researched (As cited in Osman, Smerz, Braun, & Plambeck, 2006, p. 84). As a result, the failure of students with LD to appropriately access mathematic courses continues to impede, or marginalize a student's freedom to (a) choose the major they wish to study and (b) to have the self-efficacy of knowing that they will be able to succeed, graduate and find fulfilling career oriented employment.
Ofiesh, (2007) states that many of the accommodations recommended for students with learning disabilities are based on an analysis of the course demands, the student's functional limitations, and a basic understanding of how the accommodations can facilitate the demonstration or acquisition of knowledge. However, little is known about which accommodations are recommended for math, science, and foreign language courses as well as the effectiveness of those accommodations. Cognizant of this fact, it is clear that people with disabilities are under-represented in many challenging careers, including those in science, technology, mathematics, and engineering. Negative stereotyping and attitudes are reported as the most significant factors faced by people with disabilities in these fields. Another factor is that of being "ethnically" a minority with poor or nonexistent early mathematics intervention.
Horowitz, (2008, p. 1, 2) concurs with the later stating that, math difficulties are more pervasive among minority children and among those from low-income families. Many of these children lag behind before they even start school. In addition, between 5 and 10 percent of all children who enter school will be identified as having a math difficulty or disability. Without early and effective instruction and/or appropriate accommodations, many of these children will face math frustration and failure throughout their school careers.
Appropriate accommodations for dyscalculia in higher education are important for several reasons: (a) understanding how dyscalculia affects mathematics learning can help postsecondary disability offices to evaluate and/or utilize appropriate accommodation/ accessibility strategies, (b) research into dyscalculia is limited, but is essential, and the impetus for continued scholarly research, and literature in the field is critical to determining successful evidence-based strategies for appropriate accessibility and accommodations in mathematics in postsecondary institutions, and finally, (c) the primary research that has been available on learning disabilities has been scientifically based studies and interventions. More research is required that is inclusive of "the voices" of those "labeled" with a learning disability. Denhart, 2008, p. 483, posits that the issue of being silenced is apparent in policy and practice where the voice of those labeled with LD has gone missing. Even to the present moment, it continues to be non-labeled researchers, policy makers, and practitioners debating the issues and setting agendas regarding services and accommodations for those who are labeled.
As a result one of the greatest difficulties facing people with disabilities is created when their capacity to be educated and function in the world is evaluated solely by limitations imposed by their disabilities, rather than their broad range of interests and abilities ("Success in math and science", 2006, p. 1). Institutions that provide equal access by the letter of the law, (i.e. primarily to avoid lawsuits) exhibit a philosophy that may not be verbalized on a campus but is felt and observed, and ultimately, limits the success potential of a college and its students. Colleges that embrace the spirit of the law, on the other hand , are likely to invest in an accommodation process that considers the entire context of student life, individual functional needs, trades-offs between the immediate and long-term costs and benefits, and incorporates system wide universal design concepts. In so doing these colleges will reap the rewards of increased enrollments and a more diverse campus with new ways for more students with disabilities to be involved in activities and leadership roles (Kurth & Mellard, 2006, p. 83).
1. Is there a correlation between accessibility, accommodations and student self -efficacy in mathematics/science achievement for students with LD?
2. Is there a correlation between the reasonable accommodations that are allowable for LD students and mathematics/science achievement?
3. Is there a correlation between gender self-efficacy and mathematics?
The research hypothesis and the Nula hypothesis that will be used for this study are as follows:
HÄ± There is a significant correlation between students with a LD self-efficacy towards accommodations and accessibility in mathematics.
Hâ‚€1. There is no significant correlation between students with a LD self-efficacy towards accommodations and accessibility in mathematics.
Hâ‚‚. There is a significant correlation between the effectiveness of reasonable accommodations for students with a LD and mathematics achievement.
H â‚€â‚‚. There is no significant correlation between the effectiveness of reasonable accommodations for students with a LD and mathematics achievement.
Hâ‚ƒ. There is a significant correlation between gender self efficacy and mathematics
Hâ‚€â‚ƒ. There is no significant correlation between gender self-efficacy and mathematics
Variables to be studied
The following are a list of terms used within this document.
Accommodations- is the principal by which an organization's employment and for higher education, educational opportunities, must be made accessible to qualified disabled people. Under section 504 and the ADA, organizations are required to make certain adjustments to the known physical and mental limitations of otherwise qualified disabled applicants and employees, unless it can be demonstrated that the accommodation would impose an undue hardship on the operation of the program (504 regulations).
Accessibility- refers to; in the case of the facility, readily usable by a particular individual; in the case of a program or activity, presented or provided in such a way that a particular individual can participate, with or without auxiliary aid(s); in the case of electronic resources, usable by everyone, with or without adaptive computer technology (University of Washington, 2006)
Attitude- is defined as a disposition to respond favorably or unfavorably to an object, person, institution, or event (as cited in Meyers, 2008, p. 9).
Learning Disability- A general term referring to a heterogeneous group of disorders manifested by significant difficulties in the acquisition and use of listening, speaking, reading, writing, reasoning, or mathematical abilities. These disorders are intrinsic to the individual, and assume each is due to central nervous system dysfunction and may occur across the lifespan (NJCLD, 1999).
Dyscalculia- or math disability is a specific learning disability or difficulty involving innate difficulty in learning or comprehending mathematics. It is akin to dyslexia and can include confusion about math symbols. Dyscalculia can also occur as the result of some types of brain injury. ("Dyscalculia", 2010)
Dyslexia- a specific learning disability that is neurological in origin. It is characterized by difficulties with accurate and/or fluent word recognition and by poor spelling and decoding abilities. These difficulties typically result from a deficit in the phonological component of language that is often unexpected in relation to other cognitive abilities and the provision of effective classroom instruction. Secondary, consequences may include problems in reading comprehension and reduced reading experiences that can impede the growth of vocabulary and background knowledge (International Dyslexia Association, 2002).
Paradigm- refers to a group of scientists within the discipline that may come to share similar ideas about the basic assumptions of their field, important questions to be addressed, the kind of explanatory concepts that are preferred, and the methodologies that are appropriate, they are said to share a scientific paradigm (Kuhn, 1962). Paradigms can be distinguished from one
another by their intellectual antecedents, they are pre-theoretical ideas, the subject matter they address, the concepts and language used by their adherents, and the methods they employ (Lachman, and Butterfield, 1979) (as cited in Torgesen, 1986)
Section 504 and ADA- means section 504 of the Rehabilitation act of 1973 and American with Disabilities Act signed into law in 1993 that defines a "Disability" as a physical or mental impairment that substantially limits one or more major life activities including but not limited to walking, talking, hearing, seeing, eating, working, caring for oneself. (Section 504 of the rehabilitation act of 1973 and Americans with Disabilities Act of 1990, OCR, 1987, 1990)
Self-Efficacy- as defined by Bandura (1977) is multidimensional, but can be briefly explained as a person's confidence in his or her ability to perform a specific task.
Although theory has played an integral role in shaping prevailing practices in the learning disability field, broad overviews of paradigms and presentations of theoretical issues have been relatively infrequent and limited in scope (Torgesen 1986, p.399). Two theoretical perspectives that constitute the field of disability are the Medical model perspective and the Social model perspective. Oliver (1998), states that, health research about impairment and disability is dominated by positivist theories. It focuses on searches for cures, means of reducing impairments, or assessments of clinical interventions and uses methods such as controlled trials, random statistical samples, and structured questionnaires. Today people with disabilities are beginning to influence scientific research. This influence poses difficulties for positivist research in questioning its notion of objectivity. Although Positive researchers accept that subjectivity can be studied objectively, they resist involving subjects for fear of bias. In Social Constructionism, the importance of learning from people with disabilities experiences, in order to understand the meaning of disability, is essential to understanding this theoretical approach. Social constructionists view experiences and subjectivity as the most important part of the research process. These two opposing models are the lenses though which learning disability has been viewed. The concept of "disability theory" initiated in the 1980-90's challenges the scientific/medical model of disabilities or Post positivist worldview, by observing learning disabilities through the lenses of social constructivism. Dudley-Marling, 2004, assert that, theory and research has tended toward technical solutions. Underpinning, the technical gaze that dominates learning disability theory and practice, is the assumption that learning disabilities are a pathology that resides in the heads of individual students. LD professionals have generally resisted alternative conceptions of learning that situate learning disability in broader political, social, or cultural contexts of schooling. learning and learning problems, including the identity of having a "Learning Disability", do not reside in people's heads as much as in the complexities of social interactions performed in a place called school that is itself situated in a broader social, political, and cultural context.
Torgesen (1986), claims that most research and theory in the field of LD derives from three broad paradigms. These are the neuropsychological paradigm, information-processing paradigm, and the applied behavior analysis paradigm. The neuropsychological paradigm, attempts to understand intellectual behavior in terms of specific brain systems that support it. The information processing approach tends to focus on how information is represented and manipulated in the mind. Theories within this paradigm offer hypotheses about the sequences of psychological processing operations (coding, transforming, comparing, storing, retrieving, and sorting) that underlie observable performance. The applied behavior analysis paradigm explains behavior in terms of its functional relationships to observable events in the environment. Loeser (2002) in her book review "Disability/Post modernity: Embodying Disability Theory", asserts that in this modern era, the medical model has proclaimed disability as a resultant of 'abnormal' functioning of the body of an individual. The social model that attempts to de-center the biological body as constitutive of 'disability' by arguing disability is a social construction challenges the medical model.
Creswell (2009) asserts that social constructivists hold assumptions that individuals seek understanding of the world in which they live and work. Individuals develop subjective meanings of their experiences, meanings directed toward certain objects or things.
Another recent theory the Minority model of disability (also called the "social model") posits also that disability is a social construction, that the problems lie not within the persons with disabilities, but in the environment that fails to accommodate persons with disabilities and the negative attitudes of people without disabilities. Persons with disabilities are seen as a minority group that has been denied civil rights, equal access, and protection. The definition of a minority group includes "identifiability, differential power, differential and pejorative treatment, and group awareness." The minority model takes the problem out of the realm of the person with a disability and places it in the social, political, and economic world. Solutions are universal design, education of those without disabilities, about persons with disabilities, laws ensuring equal access and protection, and better enforcement of such laws. It also maintains that decision making about persons with disabilities should be by persons with disabilities; indeed, the disabilities rights movement has adopted the slogan of South African blacks in the time of apartheid: "nothing about us without us" (As cited in Olkin, 1999, p. 26).
Self - efficacy is a theory that has been widely applied in the behavioral sciences including the rehabilitation literature. Self -efficacy draws on both cognitive and behavioral components and is based on the principle that cognitive processes can mediate behavioral change but that cognitive events are induced and altered most readily by the experience of mastery that develops from effective performance. Central to the construct of self-efficacy is the concept of efficacy expectations, which are defined as an individual's conviction that he/she can successfully execute the behaviors required to produce the desired out-comes (Bandura, 1977, (as cited in O'Sullivan & Strauser, 2009, p. 252).
An individual's self-efficacy influences his or her choice of tasks, level of performance, amount of effort put toward performance, and perseverance. Self-efficacy is typically divided into several different facets, including academic self-efficacy. Academic self-efficacy is the belief that students have in their ability to perform academic tasks (Usher & Pajares, 2006 as cited in Rayburn, 2009, p. 13). It is a measure of the degree to which individuals feel confident in their ability to succeed, understand, and perform at an appropriate level in academics.
Academic self-efficacy can be measured as a global construct or as several distinct domains (e.g., math self-efficacy, science self-efficacy, language arts self-efficacy). For the purpose of this investigation the researcher will measure mathematics self-efficacy to determine its role in accessibility and accommodations in the mathematics achievement of students with learning disabilities. Empirical support has been found for the influence of self-efficacy and outcome expectations on math-/science related pursuits. Specifically, STEM self-efficacy and interests have been found to significantly predict related math/science behavior, such as choice of college major, academic achievement, academic persistence and consideration of math-and science-related careers ( as cited in (Byars-Winston & Fouad, 1992, p. 426).
The Definition of a Learning Disability, and Dyscalculia
The Federal government defines a specific learning disability as a disorder in one or more of the basic psychological processes involved in understanding or in using language, spoken or written, which may manifest itself in an imperfect ability to listen, think, read, write, spell, or to do mathematical calculations. The terms include such conditions as perceptual handicaps, brain injury, minimal brain dysfunction, dyslexia, and developmental aphasia. The term does not include children who have problems that are primarily a result of visual, hearing, or motor disabilities, or mental retardation, emotional disturbance, or of environmental, cultural, or economic disadvantage (National Advisory Committee on Handicapped Children, 1967) (Public law 94-142 as amended by Public Law 101-76[Individuals with Disabilities Act-IDEA], 1973)
Although many positive outcomes have come because of this law (PL-94-142) according to the National Joint Committee on Learning Disabilities (NJLD,1990) there has been some mis-interpretation of the federal definition, such as regarding all learning-disabled people as one homogeneous group, so that a "standard" approach to assessment and educational management is given. This has affected the appropriate delivery of accommodation services. The NJCLD is a member organization that includes the American Speech-Language-Hearing Association (ASHA); The Association of Handicapped Student Services Programs in Post Secondary Education; Counsel for Learning Disabilities; Division for Children with Communication Disorders; Division for Learning Disabilities; International Reading Association; Learning Disabilities Association of America; National Association of School Psychologists; and Orton Dyslexia Society. The NJCLD (1990) defines learning disabilities as "a general term referring to a heterogeneous group of disorders manifested by significant difficulties in the acquisition and use of listening, speaking, reading, writing, reasoning, or mathematical abilities. These disorders are intrinsic to the individual presumed to be due to central nervous system dysfunction, and may occur across the life span. Problems in self -regulatory behaviors, social perception, and social interaction may exist with learning disabilities but do not by themselves constitute a learning disability. Although learning disability may occur concomitantly with other handicapping conditions (i.e. sensory impairment, mental retardation, serious emotional disturbance), or with extrinsic influences (such as cultural differences, insufficient or inappropriate instruction), they are not the result of those conditions or influences". For this research investigation, the NJCLD (1990) definition for learning disabilities will be used.
More students with learning disabilities are entering postsecondary institutions than ever before (U.S. Department of Education, 2000). For those students with varying degrees of learning disabilities which include, dyscalculia, the need for appropriate accommodations can help to make the university learning experience a fruitful and successful one. However, the challenges that ineffective accommodations can present, the academic and social demands associated with higher education and the need for a strong sense of self-determination, self-efficacy and persistence are some of the issues that student's with a LD will have to face as they navigate their way to obtaining a college degree.
Many freshmen with learning disabilities are unaware of the differences that exist between higher education and high school. Students transitioning to postsecondary education may encounter confusion as a result of role transformation, independent decision-making, and assumption of responsibility for one's actions (Kundu, Dutta, Schiro-Geist, & Crandall, 2003, p. 46). Many students entering postsecondary education institutions have a limited understanding of their specific learning disabilities that prevent them from accurately explaining their academic needs to faculty and disability services personal (Wegner, 2008, p. 2, 3). Thus, because of the students inability to adequately describe his/her disabilities, accommodations are often ill conceived and inappropriately applied.
Dyslexia and Dyscalculia
There is currently no widely accepted definition of dyscalculia. In attempting to define dyscalculia, much of the focus has been on the discrepancy between intelligence and mathematical ability. The Diagnostic and Statistical Manual of Mental Disorder IV (DSM lV, American Psychiatric Association, 2000, section 315.1) defines mathematics disorder in terms of test scores: measured by a standardized test that is given individually, the person's mathematical ability is substantially less than would be expected from the person's, age, intelligence, and education. This deficiency materially impedes academic achievement or daily living. The National Center for Learning Disabilities (2006) defines dyscalculia as a term referring to a wide range of life-long learning disabilities involving math. There is no single form of math disability and difficulties vary from person to person and effect people differently in school and throughout life. Because most institutions of higher education provide dyslexia support, which is traditionally language, rather than mathematics support, in order to discuss the issues of dyscalculia and the need for appropriate accommodations and accessibility, one must first look at the issues concerning dyslexia, and its relationship to dyscalculia.
According to Trott (2003), students with dyslexia are characterized by a "marked inefficiency in their working or short-term memory." This means that they may have problems retaining the meaning of text when reading at speed or fail to recall learning facts. Their written work may be disjointed. Dyslexics also may have inadequate phonological processing skills, which can affect reading, spelling and comprehension. Dyslexics may have difficulties with motor skills or coordination and particular difficulty listening and taking notes simultaneously. Dyslexics can also have visual perceptual problems. This can also affect reading, especially when dealing with large amounts of text. In addition, dyslexia can affect the learning of mathematics in several ways:
They may have poor arithmetical skills and find that mathematical procedures and sequence of operations are difficult
They may have difficulty recalling the theorems and formula they need
In multi-step problems students frequently lose their way or omit sections and fail to hold all the relevant aspects of the problem in mind, and combine them to achieve a final solution
They may have problems in sequencing complex instructions and past/future events
Some students will experience difficulties reading the words that specify the mathematical problems, especially if the problem is embedded in large amounts of text
Dyslexics may be slow at reading, mis-read frequently or not understand what has been read.
Frequent problems occur in associating the word with its symbol or function, for example, relating "integration" to its symbol, and knowing what procedure to carry out
There may be visual perception difficulties and reversals.
Work is often poorly presented and positioned on the page. Students can make transcription errors when transferring between mediums, for example question paper to computer or calculator, and frequently lose their place.
Copying errors can occur from line to line, for example x+3 becomes x -3. In addition, even though copying errors are common in many students, the problem appears to arise more frequently amongst dyslexic students.
They may have an inadequate documentation of their methods. Slow information processing means that students may have few notes. Overload occurs more frequently, and the student is forced to stop.
In many postsecondary institutions, mathematics support through student service centers that offer tutoring in various subjects is available. However, it is usually the case that there is no specialist expertise for dealing with students who have dyscalculia (Trott, 2003, p. 17).
Historically, mathematics instruction for students with learning disabilities and at-risk learners has not received the same level of consideration and scrutiny from the research community, policy makers, service providers and school administrators as the field of reading.
A recent review of the literature found that the ratio of studies on reading disabilities to mathematics disabilities and difficulties was 5:1 for the years 1996-2005 (as cited in Jayanthi, Gersten, & Baker, 2008). Nevertheless, the passage of time, the continued increase of technological and scientific advances, and the awareness of the need for more phenomenological input, are some of the primary ingredients' necessary for a field of mathematics disability research that can eventually be the source from which the opportunities for adequate and specific accommodations and accessibility can be produced.
The history of accessibility and accommodations in postsecondary institutions
In 1964, the Civil Rights Act was passed, and with the passage of this act which prohibited discrimination based on race, color, religion or national origin, also included were federally funded schools and colleges. This initiated the expansion (over the years) to include people with disabilities. Colleges and universities in these early days focused primarily on people with physical disabilities.
In 1973, the passage of section 504 of the Rehabilitation Act, a civil rights statute, solidified the civil rights act of 1963 that had included federally funded schools. It stated: "no handicapped person in the United States can be excluded from participation, benefits, or subject to discrimination under any program receiving Federal financial aid or assistance" (public Law 93-112, 87. 394 (29 USC 794), as amended. The passage of this section recognized "learning disabilities" as a federal category. Learning disability organizations where formed and educational programs where established. Section 504 provided protection for the rights of individuals who wanted to attain post secondary education who did not have the opportunity prior to the passage of this right. Madaus (as cited in Mayer, 2008) states that since section 504 prohibited discrimination in post secondary programs and services, it ensured that the potential of these students was no longer restricted, and resulted in a reframing of perspective on the use of laws to provide, rather than restrict, access. Disability could no longer be a reason for exclusion from the post secondary environment if the student proved that they were capable of performing the necessary work.
In 1990 the American with Disabilities Act (ADA) was passed this act made it illegal to discriminate against people in employment, public accommodations, transportation, and telecommunications regardless of age, gender, religion, ethnicity, sexual orientation, ability or disability. Since all universities and colleges receiving federal funding had to comply with the 1973 section 504, what the Americans with disabilities act helped to do was to allow access across the campus experience to people with disabilities.
Section 504 of the 1973 Rehabilitation act and the ADA are not designed to provide academic remediation to students with disabilities; instead, the intent of both is to ensure that the institution does not discriminate against an individual's right to education and protection of architectural and informational access. The emphasis is solely on the permission of support and accommodations so that the student has greater access to the information presented in classes as well as alternative ways to demonstrate his or her knowledge or skills (Ofiesh, 2007).
The purpose therefore of accommodations in postsecondary settings is to allow students with learning disabilities to have the same opportunity to college course exams, fair access to instruction, and to increase retention.
This investigation will be a non-experimental, correlational, descriptive, quantitative study. Ellis & Levy, 2009, position that the primary focus of the correlational type of research is to determine the presence and degree of a relationship between two factors (p.237). Quantitative data will be analyzed to determine if a relationship exists between variables.
The target populations for this study will be full time undergraduate students with a documented learning disability at a private university in the southern region of Puerto Rico.
The demographic characteristics of the students with LD will include full time undergraduate students (freshman, sophomore, juniors, and seniors) Gender, GPA, number of accommodations.
Instrument or procedures for collecting data information
Students will complete seven (7) surveys, to assess the relationship between math/science self- efficacy, math/ science outcome, math/science interests, math/science coping self-efficacy, math/science intentions-goals, career barriers inventory-modified and, math/science accessibility /accommodations. The survey will take approximately 25 minutes to complete.
The math and science self-efficacy, outcome expectancies, interests, and goal intentions constructs were measured with the math/science subject-matter scales developed previously by Smith and Fouad (1999) and reported in Ferry et al. (2000) and Fouad, Smith, and Zao (2002).
All items for all four of the Smith and Fouad scales were rated on a 6-point, Likert-type scale ranging from 1(very strongly disagree) to 6 (very strongly agree). The Career barriers inventory-modified is a version of Swanson and Tokar's (1991b) original Career Barriers Inventory (CBI; 112 items), (as cited in Byars-Winston & Fouad, 1992, p. 433). The math/science accessibility /accommodation scale assesses whether students agree or disagree on accessibility /accommodations in the area of mathematics and science. It will be rated on a 6-point, Likert-type scale ranging from 1(very strongly disagree) to 6 (very strongly agree).
The Math/Science Self-Efficacy Scale
Developed by Smith and Fouad (1999), assesses how confident participants are that, with proper training, they could complete various tasks in math/science domains that college students are likely to encounter. Smith and Fouad, and their colleagues reported internal consistency reliabilities for scores on this scale at either .84 or .85 in their research (as cited in Smith & Fouad, 1999, p. 432). The Validity coefficient was .90 (as cited in Ferry, Fouad, & Smith, 2000, p. 353)
The Math/Science Outcome expectancies Scale
Includes 9 items assessing the extent to which participants agreed with statements about outcomes expected from and perceived utility of math/science behavior. Internal consistency reliability for this scale with the present sample was .78, whereas a coefficient alpha of .81 was reported in the Smith and Fouad studies (as cited in Smith & Fouad, 1999, p. 432).
The Math/Science interest scale
Includes 17 items designed to assess participants level of interest in various math-and/or science-related activities. The internal consistency reliability for the Interest scale reported in previous studies by Fouad and Smith were either .93 or .94. The internal consistency reliability for this subscale was .81. Total scores were obtained summing the responses, ranging from 9 to 54 and dividing by the number of items. Higher values indicated higher outcome expectancies (Ferry et al., 2000, p. 353)
The Math/Science coping efficacy scale
Is an 18-item measure, developed by Lent et. al., (2000), that assesses barrier-coping efficacy. The Cronbach's alpha coefficient was used for this scale and was .94 in the current sample, identical to the alpha coefficient reported by Lent et. al. (as cited in Smith & Fouad, 1999, p. 433).
The Intentions-Goals Scale
Is a 6-item scale where participants indicate the extent to which they intended to engage in various math- and/or science-related activities in the future. Internal consistency reliability was .84. Total scores on this scale ranging from 7 to 42, were also obtained by summing and dividing by the number or items with higher scores indicating higher goals with respect to math and science (Ferry et al., 2000, p. 353).
The Careers Barrier inventory-Modified,
A 28 item version of Swanson and Tokar's (1991b) original Career Barriers Inventory (CBI; 112 items), as cited in (Byars-Winston & Fouad, 1992, p. 433) measures students perceptions regarding anticipated barriers that may interfere with their job choices or career progress. In Byars-Winston and Fouad's study ((Byars-Winston & Fouad, 1992, p. 433), only the first of the two responses -likelihood of encountering a given barrier---was used in the analyses. The negative correlation between barrier perceptions and coping efficacy provided an index of construct validity. An internal consistency reliability of .93 was achieved.
The Accessibility /Accommodation scale
This scale assesses the student's perceptions regarding math / science accessibility and math/science accommodations.
The following documentation will be prepared prior to the study
The purpose of the investigation
Confidentiality form/Protection of the rights of the population being studied
Instrument validation form
Reliability of the instruments of investigation
Solicitation and authorization from the institutional review board(IRB)
Solicitation for authorization from the campus Office of Service to Persons with Disabilities (OSPI) for distribution of the study surveys.
Procedures for data collection.
A cover letter explaining the study, including the confidentiality, anonymity of the student, and consent form will be distributed with the survey instrument to students with a documented learning disability as they come to OSPI to solicit accommodations for the beginning of the spring 2011 semester. An incentive for a drawing of a $25 dollar gift card will also be included in the package for all surveys completed and returned.
Descriptive statistics and intercorrelations will be computed for the research measures and will be summarized.
Some of the limitations that may be considered in this study, concerns the size of the study population and the sample characteristics. The sample is relatively small and from only one university. This will influence the generalizability of the findings. The survey can be affected by unrepresentative samples or poor survey questions.