A Review of Math Disability MD Literature

By Melissa Murphy,2014-04-08 08:05
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     A Review of Math Disability (MD) Literature

    Submitted to Scott Berenson of the

    California Community Colleges Chancellor‘s Office

    Submitted by College in Focus


     At present, postsecondary institutions face the pressing need to review and, in

    many cases, reform their approach toward the teaching of mathematics. Mathematical

    ability is an increasingly important determinant of success within the academic world and

    beyond it; in a study on quantitative literacy, Rivera-Batiz (1992) asserted that after

    reading ability and general intelligence, mathematical fluency is the single most

    important factor for determining the level of success students achieve in school and their

    income once they complete their education.

    Despite its importance, college studentsparticularly at the community college

    levelare often vastly ill prepared in terms of mathematical competency. A recent article

    in the New York Times reported that ―the nation‘s 1200 community colleges are being

    deluged with hundreds of thousands of students unprepared for college level

    [mathematics] work‖ (Schemo, p. 1). Although the burden of this assessment falls on elementary and secondary educators, its repercussions for the community college system

    are clear. Additionally, our ever increasing understanding of the cognitive processes

    involved in mathematical thought and the many factorspsychological, cultural,

    biological and neuroscientificthat may affect this understanding caution against a static view of mathematical instruction.

    Because of the growing number of students with diagnosed learning disabilities, it

    is essential that any educational reformsif and when they are madespecifically

    include appropriate provisions to address the needs of these students. Woodward &

    Brown (2006) highlighted this need by stating that ―interventions need to be continually

refined to address the increasingly unique characteristics of students in special education‖

    (p. 7).

    Since prevalence statistics depend on the very definition of math disability (MD), the reliability of these statistics is often brought into question. However, extensive and

    frequent studiesamong them those conducted by Badian (1983); Gross-Tsur, Manor, &

    Shalev; Kosc (1974); and Lewis, Hitch, & Walker (1994)estimate prevalence of MD at

    between 4% and 7% in school-age individuals.

    Regardless of the exact figure, many of the interventions intended to help students with MD would be to the benefit of all students, with or without MD. However, this does

    not mean that changes in teaching technique or format intended solely to improve the

    average student‘s understanding of mathematics will be sufficient for those students with

    MD. If these students are to be expected to succeed in mathematics, additional attention

    must be paid to them. Mazzocco & Myers (2005) summarized the relationship in this way:

    ―The RD [reading disability] field has demonstrated how modifications to the language

    arts curriculum benefit readers of all levels. Thus, it is wholly conceivable that other

    interventions will not only benefit many (but not all) children with MD, but also typically

    achieving students‖ (p. 322).

    This review of the pertinent literature concerning MD will cover a variety of issues, including definition and diagnosis, possible causes, intervention techniques, and

    the efficacy of various tested programs.

    Difficulties in effectively addressing the needs of MD students

     Although the need for effective interventions to promote mathematical learning in

    students with MD is clear, a number of factors make this goal particularly difficult to

    achieve. First and foremost, it is nearly impossible to understand the workings of MD due

    to a fundamental lack of understanding of the “normal” functioning of development and

    learning in mathematics. Geary (2005) described the manner in which this lack of

    understanding hinders the study of MD: “Unfortunately, in most mathematical domains,

    such as geometry and algebra, not enough is known about the cognitive systems that

    support the typical learning of the associated competencies to provide a systematic

    framework for the study of MD‖ (Geary, ―Cognitive Theory,‖ p. 306). Mazzocco &

    Myers (2003) pointed out that this deficiency in knowledge may stem from the

    cumulative nature of mathematical development, especially in the elementary years.

     In addition, the first step towards aiding students with MD is identifying them as

    those needing special assistance. Since many students who may qualify as learning

    disabled are often not identified until they reach college (or at all), ensuring that their

    needs are met is a particular challenge (McGlaughlin, Knoop, & Holliday, 2005). This

    problem is furthermore related to the utter lack of consistency in definitions of MD, a

    topic that will be discussed in detail below.

     These difficulties are compounded by the absence of appropriate research

    conducted on MD, particularly when compared to the amount of studies dedicated to

    understanding reading disability (e.g., Rasanen & Ahonen, 1995). Swanson & Jerman

    (2006) described math disability research as in its ―early developmental stages‖

    (Swanson, p. 270). Maccini & Gagnon (2006) noted that there existed no studies

addressing ―empirically validated and recommended instructional practices to assist

    secondary students‖ with MD (Maccini, p. 219).

    The relative silence of the scientific community is especially noticeable in regard

    to the lack of research conducted specifically on MD in postsecondary students. In their

    review of twenty-three studies, Bryant & Dix (1999) only found two that focused on

    algebra. In point of fact, the majority of studies are concentrated on arithmetic

    computation (Mastropieri, Scruggs, & Shiah, 1991). According to McGlaughlin, Knoop,

    & Holliday (2005), ―empirical evidence for effective interventions for postsecondary

    students is, at best, scarce‖ (McGlaughlin, p. 225).

    As alluded to above, an agreed-upon definition of MD has proven to be elusive

    (Mazzocco & Myers, 2003; Swanson & Jerman, 2006). Mazzocco (2005) indicated that

    not only are the definitions and measurements of MD inconsistent, but the terminology is

    likewise erratic (i.e., mathematics difficulties vs. mathematics disabilities). This variation

    in definitions necessarily complicates the design and implementation of effective


    Another element that presents a challenge is the complex and varied nature of

    mathematical understanding, and therefore of MD. Batchelor, Gray & Dean (1990) have shown that arithmetic performance is affected by a variety of verbal and nonverbal

    neuropsychological factors. It is fair to assume then, as is discussed below, that students

    with MD can have deficits in any one of these specific areas or in a potentially endless

    combination of them. Furthermore, mathematical performance has been linked to

    affective factors, such as math anxiety (Ashcraft & Ridley, 2005), which indicates a need

    for a holistic approach when helping students with MD. The infinite possible

interactions between these areas reveal the need for an approach to intervention that is

    tailor-made for each student.

    Although these factors represent an impressive obstacle in effectively addressing MD, the necessity to do so is clear. Fortunately, the research, though it may be limited,

    does present some important conclusions.

    Defining MD

    ―In the field of MD, work toward establishing a consensus definition is in its early stages‖ (Mazzocco & Myers, p. 219). Indeed, many of the relevant studies point to a need

    for consistent definitions, criteria and testing (e.g., Fuchs, et al., 2005; Geary, 2005). On

    the one hand, there is little debate about the most basic standards, particularly the

    requirement that the student in question be of at least average intelligence. Of course, the

    question then becomes how one defines and quantifies average intelligence. This is

    beyond the scope of this analysis, but should be noted as an example of how difficult

    standardization of MD diagnosis can be. It is clear, however, that students must at least

    be diagnosed as having a learning disability according to whatever established federal,

    state, and institutional guidelines apply (e.g., Title V regulations).

    Various researchers have identified general features of MD and what specific manner of problems tend to be the most difficult for MD students. Nolting (2000)

    asserted that most students with LD will show average abilities in arithmetic, but will be

    unable to learn algebra without assistance. He believes that students therefore often learn

    to compensate for their disability, often going undiagnosed until reaching college, where

    self-taught strategies cease to work. According to Nolting‘s research, trouble with multi-

    step problems and browning errors are the two best methods for predicting MD. Dehaene

    & Cohen (1991, 1995, 1997) researched the neuroscientific base of math disability and believe that inaccurate retrieval of arithmetic facts is related to abnormal functioning of the left basal ganglia, the thalamus, and the left parieto-occipito-temporal areas.

    Sometimes, math disability is defined as a single entity with various deficits. In

    these cases, it is most commonly referred to as dyscalculia or developmental dyscalculia. Kosc (1974) defined it in broad terms, stating that dyscalculia has its basis in a genetic or congenital disorder that affects the specific parts of the brain involved in the development of normal mathematical ability. Recent research (Oliver, et al., 2004) illustrated the genetic basis for mathematic ability. Kosc also divided dyscalculia into two categories: practognostic dyscalculia and ideognostical dyscalculia. According to his differentiation, practognostic dyscalculia involves difficulty with the manipulation of objects, either real or mental, during mathematical work. People with ideognostical dyscalculia, on the other hand, have trouble connecting mathematical concepts to allow for calculation. It should be noted that dyscalculia is often confused with acalculia; the difference between the two being that acalculia is the direct result of brain damage.

    Mahesh Sharma (1986) also chose to divide dyscalculia into two groups:

    quantitative and qualitative. In this model, quantitative dyscalculia involves difficulty with sequential directions and spatial organization, whereas qualitative dyscalculia is characterized by problems with inductive and deductive reasoning, estimation, pattern recognition and/or visualization.

    Various elements of college mathematical curriculum prove to be difficult for

    students with dyscalculia, including timed tests (Landerl, Bevan, & Butterworth, 2004) and higher-level reasoning (Sullivan, 2005). Nolting (2000) also suggested that some

    students‘ math disability may only be related to a particular mathematical domain, specifically referring to dysalgebria and dysgeometria.

    It is clear that even when mathematical disability is defined as a single entity, a

    variety of subgroups become necessary to further qualify the problems that an individual student has. For this reason, the majority of researchers choose to define MD as a composite disability and highlight various cognitive areas where problems have been identified in students with mathematics difficulty or disability. These areas differ depending on the model, but they often overlap or are interconnected. Judging by the complex nature of mathematical thought, it is a distinct possibility that all of these elements are involved.

    In their recent study on college students with MD, McGlaughlin, Knoop, &

    Holliday (2005) concluded that the most significant contributors to these students‘ difficulties were working memory, mathematical fluency, reading comprehension, and visual/spatial/nonverbal weaknesses. Other researchers specifically mention some of these elements and others are related or affected by areas included in different models.

    One of the most commonly referenced models is that of Geary (1993), which

    divides MD into three categories: semantic retrieval, executive-procedural and visuospatial MD. In this model, semantic memory MD is characterized by difficulty in retrieving mathematical facts and variation in response time. People with procedural MD have more conceptual difficulty, involving problems with strategizing, execution, and the acquisition of mathematical concepts. Finally, visuospatial MD, the least understood of the three (Mazzocco & Myers, 2003), is identified by sign confusion (x vs. +), improper

numerical alignment, or any other difficulty visually processing numerical information

    incorrectly and then presenting in similarly.

    Cirino, Morris & Morris (2007) recently tested the efficacy of using Geary‘s three

    categories to predict MD among 337 college students. They found that ―overall predictive

    power for [calculation and mathematical reasoning] was high,‖ but also alluded to the possibility that other cognitive factors may be involved (Cirino, p. 103). They concluded

    that these factors had the same ability to predict MD in college students as they did in

    children, which is significant, considering that the majority of studies on MD focus on

    younger children and not adults.

    Nolting (2000), in his work with college students with MD, proposed another model that is supported by other research (McGrew & Hessler, 1995; Batchelor, Gray, &

    Dean, 1990; McGrew, 1994; Meyers, 1987; etc.). In this model, students‘ specific

    cognitive deficits, in combination with their content problem (e.g., algebra), are used to

    further categorize their specific difficulties. For example, ―a student may have

    dyscalculia with a visual processing speed deficit‖ (Nolting, p. 27). In his model, the

    cognitive clusters tested on The Woodcock Johnson Psycho-Educational Battery

    Revised: Test of Cognitive Ability (WJTCA-R) (Woodcock & Johnson, 1989) were used

    to differentiate specific areas where a student with MD may have problems. These

    clusters are: processing speed, auditory processing, visual processing, short-term memory,

    long-term retrieval (working memory), comprehension-knowledge (long-term memory),

    and fluid reasoning. Fluid reasoning was found to have the highest correlation to

    mathematical performance, but it remains unknown how students can improve in this

    area (Hessler, 1993; McGrew, 1995). This points again to the need for further research in the understanding of MD and successful interventions.

    One area that has received particular attention in the literature is memory,

    specifically short-term memory. Nolting (2000) divided memory into eight stages (sensory input, sensory register, short-term memory, working memory, long-term memory, abstract reasoning and memory output) and asserts that MD can affect any one of them. In their comparison study between children with and without MD, Swanson & Jerman (2006) observed significant differences in performance between the two groups when testing verbal working memory, visual-spatial working memory, and long-term memory. They found that verbal working memory was the main cognitive factor differentiating MD students and their non-MD peers. In their study on the arithmetic word problem solving of children, Passolunghi, et al. (1999) found that MD children had deficits in working memory, but not short-term memory. Geary & Hoard (2002) also underlined the importance of working memory, proposing that it may be the central deficit of MD.

    Nolting (2000) stated that working memory is especially important in math since

    mathematical problem solving often involves multiple steps and keeping track of different information throughout the full process. Also, if students have difficulty memorizing arithmetic facts (such as the multiplication table), they will have to dedicate more working memory to computation, leaving less available for more complex problem solving. This is particularly evident in higher-level math, but can be seen even in children with MD learning to count (Carr & Hettinger, 2002).

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