VISUAL-SPATIAL PROCESSING AND MATHEMATICS ACHIEVEMENT:

THE PREDICTIVE ABILITY OF THE VISUAL-SPATIAL MEASURES OF THE

STANFORD-BINET INTELLIGENCE SCALES, FIFTH EDITION AND THE

WECHSLER INTELLIGENCE SCALE FOR CHILDREN- FOURTH EDITION

By

Eldon Clifford

B.S.Ed. Black Hills State University, 1997 M.S. South Dakota State University, 2000

A Dissertation Submitted in Partial Fulfillment of the Requirements for the Degree of

Doctor of Philosophy

Division of Counseling and Psychology in Education School Psychology Program

In the Graduate School The University of South Dakota

December 13, 2008

UMI Number: 3351188

Copyright 2008 by Clifford, Eldon

All rights reserved.

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Copyright by ELDON CLIFFORD

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Members of the Committee appointed to examine the dissertation of Eldon Clifford find it

satisfactory and recommend that it be accepted.

JL ale Pietrzak, Ed.D. Committee Chair

Bruce Proctor, Ph.D. Co-Committee Chair

rbara Yutrzenka, Ph.D.

m

Eldon Clifford (Ph. D., The University of South Dakota, 2008)

Dissertation Directed By Dr. Dale Pietrzak

Visual-Spatial Processing and Mathematics Achievement: The Predictive Ability of the Visual-Spatial Measures of Stanford-Binet Intelligence Scales, Fifth Edition and the Wechsler Intelligence Scale for Children- Fourth Edition

In the law and the literature there has been a disconnect between the definition of a learning disability and how it is operationalized. For the past 30 years, the primary method of learning disability identification has been a severe discrepancy between an individual's cognitive ability level and his/her academic achievement. The recent 2004 IDEA amendments have included language that allows for changes in identification procedures. This language suggests a specific learning disability may be identified by a student's failure to respond to a research based intervention (RTI). However, both identification methods fail to identify a learning disability based on the IDEA 2004 definition, which defines a specific learning disability primarily as a disorder in psychological processing. Research suggests that processing components play a critical role in academic tasks such as reading, writing and mathematics. Furthermore, there has been considerable research that suggests visual-spatial processing is related to mathematics achievement. The two most well known IQ tests, the Stanford-Binet-Fifth Edition (SB5) and the Wechsler Intelligence Scale for Children-Fourth Edition (WISC-IV), were revised in 2003 to align more closely with the most current theory of intelligence, the Cattell-Horn-Carroll theory of cognitive abilities (CHC). Research supports both instruments have subtests that measure visual-spatial processing. The purpose of the current study is to identify which visual-spatial processing measure (SB5 or WISC-IV) is the better predictor of poor mathematics achievement. The participants were 112 6th- 8th grade middle school students. Of the 112 original participants, 109 were included in the study. The comparison of the results of two separate sequential logistic regressions found that both measures could significantly predict mathematics achievement. However, given the relatively small amount of variance accounted for by both the SB5 and WISC-IV visual-spatial processing measures, the results had questionable practical significance.

This abstract of approximately 291 words is approved as to form and content and I approve its publication.

Bu5atesPietrzak, Dissertation Committee Chair

IV

Acknowledgements

I would like to thank the members of my dissertation committee Dr. Dale

Pietrzak, Dr. Bruce Proctor, Dr. Amy Schweinle and Dr. Barbara Yutrzenka for their time

in this endeavor. I would specifically like to thank the committee chair Dr. Pietrzak for

his guidance and stepping in to take on that role when my previous chair left the

university. In addition, I would like to extend my appreciation to Dr. Schweinle for her

statistical expertise and taking the time to read a number of drafts and offer feedback

when she was under no obligation to do so. I would also like to express gratitude to

former University of South Dakota School Psychology professor Dr. Jordan Mulder for

helping me with the conceptualization of my dissertation and his direction and

constructive comments during the proposal stage. Finally, I would like to thank the

School Psychology Department at the University of South Dakota for providing me with

a career that has afforded me much, personally and professionally.

I would like to express my appreciation for my sister Dr. Jessteene Clifford-Kelly.

I am grateful to her for taking the time to read a number of early drafts and providing me

feedback. In addition, I would like to thank her for her encouragement and her

commiserating ear as she similarly went through this sometimes convoluted graduate

education process. I would like to thank my parents Dewayne and Kathy Clifford for

their gentle yet persistent encouragement. Without the strong foundation they built, I

would have not been able to complete this undertaking. I would also like to Ms. Jami

Johnson for her feedback on a number of drafts as well as her encouragement and

support.

Table of Contents

1. Title Page 2. Copy Right Page 3. Signature Page p. iii 4. Abstract _.__ p. vi 5. Acknowledgments _ ..p. v 6. List of Tables and Figures _ ...p. viii 7. Chapter 1/Introduction..__ p. 1

a. Introduction p. 1 b. Significance of the Study. p. 17 c. Statement of the Problem p. 19 d. Definition of Terms _ p. 19 e. Limitations _ .....p. 20 f. Structure of the Proceeding Chapters p. 21

8. Chapter 2/ Literature Review _ p. 22 a. Literature Review p. 22 b. Learning Disabilities..... p. 22

i. Learning Disabilities Defined: Past and Present p. 22 ii. Learning Disabilities Classification and

Identification p. 26 iii. Models of Identification: IQ-Achievement

Discrepancy and Response to Intervention p. 28 iv. Summary p. 31

c. Psychological Processing and Learning Disabilities p. 32 i. Reading p. 32

ii. Writing p. 35 iii. Mathematics... .p. 42 iv. Summary. p. 45

d. Mathematical Disabilities p. 46 i. Mathematical Disabilities: Definition and

Identification p. 47 ii. Specific Mathematical tasks and their

Cognitive Processes p. 49 iii. Subtypes of Mathematical Disabilities p. 61 iv. Summary p. 62

e. Visual Spatial Processing and Mathematics p. 63 i. Visual-Spatial Processing's relationship to

Mathematics p. 64 ii. Visual-Spatial Processing p. 67

iii. Summary. p. 73 f. Modern Intelligence Theory and Assessing Visual-

Spatial Processing _____ p. 73 i. CHC Theory p. 76

vi

ii. The Stanford-Binet Intelligence Test, Fifth Edition p. 82

iii. The Wechsler Intelligence Scale for Children-Fourth Edition _____ _ _p. 87

iv. Summary _p. 92 g. Summary _ __ __p. 93

3. Chapter 3/ Methodology. __p. 96 a. Methodology. _ _ p. 96 b. Participants ____ p. 97 c. Instruments _ p. 100

i. Intelligence Measure _ p. 100 ii. Visual-Spatial Measures ...p. 101

iii. Measure of Mathematics Achievement p. I l l d. Procedures.. .p. 117 e. Data Analysis.. p. 119 f. Summary __ ____ ____ _._p. 122

4. Chapter 4/ Results ...p. 123 a. Preliminary Analysis p. 123 b. Correlation Analysis p. 125 c. Multiple Regression Analysis p. 126 d. Logistic Regression Analysis ___p. 129

i. SB5 Visual-Spatial Processing __...p. 131 ii. WISC-IV Visual Spatial Processing p. 132

e. Comparison of the SB5 and WISC-IV p. 134 f. Summary. _ p. 136

5. Chapter 5/ Discussion __ p. 138 a. Visual-Spatial Processing's Relationship to Mathematics p. 138 b. Predictive Ability of the SB5 and WISC-IV p. 140 c. Comparison of the SB5 and WISC-IV. p. 143 d. Further Implications _ p. 146 e. Limitations. ____ ___ p. 149 f. Future Research p. 150 g. Importance of the Study p. 151

6. Appendices _ p. 152 a. Institutional Review Board Approval p. 152 b. Approval Letters From Participating Schools _ p. 154 c. Demographic Form p. 165

6. References ___ p. 166

vn

List of Tables and Figures

1. Chapter 1 a. Tables:

i. Table 1.1: The 10 Cattell-Horn-Carroll(CHC) Broad Factors of Intelligence and their Abbreviations p. 8

ii. Table 1.2: The 12 CHC Visual Processing (GV) Narrow Cognitive Abilities and their Abbreviations p. 9

iii. Table 1.3: The Visual-Spatial Process Measures of the WISC-IV p. 16

b. Figures: i. Figure 1.1: The Structure of the SB5 _ p. 11

ii. Figure 1.2: The Visual-Spatial Processing Measures of the SB5 p. 14

iii. Figure 1.3: The Structure of the WISC-IV p. 15

2. Chapter 2 a. Tables:

i. Table 2.1: Tasks Used to Measure Visual-Spatial Processing in Current Literature p . 74

ii. Table 2.2: Subtests and Domain Construction of the SB5 Full Scale IQ .p. 82

iii. Table 2.3: Index and Subtests of the WISC-IV that Combine to Form the Full Scale IQ p. 88

b. Figures: i. Figure 2.1: CHC Broad and Narrow Cognitive

Abilities __ _ p. 75 3. Chapter 3

a. Tables: i. Table 3.1: Participants' grade levels p. 97

ii. Table 3.2: Demographics _ p. 98 iii. Table 3.3: Language Spoken at Home _ p. 98 iv. Table 3.4: Level of Parental Education __ p. 98

4. Chapter 4 a. Tables:

i. Table 4.1: Descriptive Statistics _ p. 125 ii. Table 4.2: Correlation Analysis _____ __p. 126

iii. Table 4.3: R2 Change and Change Statistics p. 129 iv. Table 4.4: Coefficients and Significance Tests

for the Reduced and Full Model __ p. 132 v. Table 4.5: SB5 Model Statistics __ p. 134

vi. Table 4.6: SB5 Model Parameters __ p. 134 vii. Table 4.7: WISC-IV Model Statistics _ _ p. 136

viii. Table 4.8: WISC-IV Model Parameters p. 136

vni

ix. Table 4.9: SB5 & WISC-IV Comparison of Models p. 139 x. Table 4.10: Model Parameters of Both the SB5

and WISC-IV p. 139

ix

CHAPTER I INTRODUCTION

The definition of a specific learning disability (SLD) has changed little from

Samuel Kirk's conceptualization in 1962-1963. Kirk defined a SLD as an

underdeveloped processing disorder in the areas of speech, language, reading, spelling,

writing or mathematics (Hammill, 1990; Kirk & Kirk, 1983). Public Law 94-142,

adopted in 1975, also maintained that a SLD was based on a disorder in psychological

processing. Similarly, the subsequent revisions of the Individuals with Disabilities

Education Act in 1990 and 1997 defined a SLD as a disorder in one or more basic

psychological processes (Jacob & Hartshorne, 2003; Reschly, Hosp & Schmied, 2003).

The current Individuals with Disabilities Education Improvement Act (2004) continued

this trend:

(i) General. Specific learning disability means a disorder in one or more of

the basic psychological processes involved in understanding or in using

language spoken or written, that may manifest itself in the imperfect

ability to listen, think, speak, read, write, spell or to do mathematical

calculations including conditions such as perceptual disabilities, brain

injury, minimal brain dysfunction, dyslexia and developmental aphasia.

(U.S. Department of Education, 2006a, p. 46757)

In a previous review of all 50 state department of education rules, over 80% of

states have adopted this definition of a SLD (Reschly, Hosp & Schmied, 2003). In

addition, 96% of state education departments believe that a SLD is a processing disorder

(Reschly, et al. 2003). Furthermore, a recent unpublished review of how states currently

define a SLD, found that 49 of the 51 states (including the District of Columbia) use the

1

federal definition of a SLD or use the term "processing disorder" in their definition

(Clifford, 2008). However, the main disagreement in special education is not in the

definition, but in the identification of a SLD (Kavale, Holdnack & Mostert 2005).

There is a disparity in the law and the literature between the definition of a

learning disability and how it is operationalized. For the past 30 years, the primary

method of SLD identification has been a severe discrepancy between an individual's

ability level and their achievement (Hallahan & Mercer, 2002; Jacob & Hartshorne,

2003). However, the recent 2004 IDEA amendments have included language that allows

for changes in identification procedures to a procedure based on a student's failure to

respond to an intervention (RTI). In addition, a recent unpublished review of state special

education rules (adopted or in the processes of adoption) found that states are moving

away from using a discrepancy only identification procedure for a SLD (Clifford, 2008).

According to IDEA 2004 the identification of a SLD:

Must not require the use of a severe discrepancy between intellectual

ability and achievement for determining whether a child has a specific

learning disability, as defined in 34 C.F.R. 300.8(c)(10);

Must permit the use of a process based on the child's response to

scientific, research-based intervention; and

May permit the use of other alternative research-based procedures for

determining whether a child has a specific learning disability, as defined in

34 C.F.R. 300.8(c)(10) (U.S. Department of Education, 2006b).

Interestingly, both methods (discrepancy and response to an intervention) of

learning disability identification fail to address the definition, which states a SLD is "a

2

disorder in one or more of the basic psychological processes..." (U.S. Department of

Education, 2006a, p. 46757). If the definition of a SLD is based on the assumption it is a

psychological processing disorder, then it is appropriate that the identification of a SLD

include elements of a psychological processing disorder evaluation (Torgesen, 2002).

Understanding this idea requires a clear conceptualization of what is meant by

psychological processing.

Psychological processes are the cognitive abilities that allow the use of language,

attention, memory, complex problem solving, higher order thinking and perception in

academic and non-academic tasks (Gerring, & Zimbardo, 2002). The literature suggests

there are specific processing components in the three major academic tasks of reading,

writing and mathematics. Research maintains reading requires the psychological

processes of phonological processing, syntactic processing, working memory, semantic

processing, and orthographic processing (Badian, 2001; Gray & McCutchen, 2006;

Holsgrove & Garton, 2006; Hoskyn & Swanson, 2000; Nation & Snowing, 1998; Siegel,

2003). The literature supports that writing involves phonological processing,

orthographic processing, working memory, long-term memory, short-term memory, and

morphological processing (Berninger, Abbot, Thomson, & Raskind, 2001; Hauerwas &

Walker, 2003; Kellogg, 2001b, Swanson & Berninger, 1996). Studies have found

mathematical thinking incorporates working memory, phonological processing, attention,

long-term memory, and the PASS (planning; attention; successive; simultaneous)

cognitive processes (Fuchs et al, 2005; Fuchs et al., 2006; Kroesberger, Van Luit and

Naglieri, 2003; Swanson, 2004; Swanson & Beebe-Frankenberger, 2004; Swanson &

3

Jerman, 2006). Recent literature suggests of the three academic areas, mathematics has

the most need for additional research (Swanson & Jerman, 2006).

Failing to gain proficiency in mathematics while in elementary and middle school

will negatively influence a student's future, both academically and occupationally (Assel,

Landry, Swank, Smith & Steelman, 2003; Griffin, 2003). It is estimated that 4-8% of

public school students have a disability in the area of mathematics (Fleischner, &

Manhemier, 1997; Fuchs et al., 2005; Fuchs & Fuchs, 2003; Geary 2004; Geary & Hoard

2003; Swanson & Jerman, 2006). According to IDEA (2004) students who have a

mathematics disability (MD) have a psychological processing disorder in utilizing written

or spoken language that has resulted in a less than adequate ability to do mathematical

calculations (U.S. Department of Education, 2006a). Recent literature suggests that

understanding the cognitive aspects of mathematical thinking may increase the ability of

professionals to identify and treat students that struggle with mathematics (Fuchs et. al.,

2006). Furthermore, the literature supports there are specific psychological processes in

the areas of mathematical calculation, mathematical fluency, and mathematical word

problems.

Research suggests that attention, working memory, short-term memory, long-term

(semantic) memory, and phonological processing are involved in mathematical

calculation and fluency tasks (Floyd, Evans, McGrew, 2003; Fuchs et al., 2006; Fuchs et

al., 2005: Swanson, 2006; Swanson & Beebe-Frankenberger, 2004). Additionally, studies

have shown that mathematical word problems require the psychological processes of

attention, working memory, short-term memory, and phonological processing (Fuchs et

al., 2005; Swanson, 2006; Swanson & Beebe-Frankenberger, 2004; Swanson, Jerman, &

4

Zheng, 2008). The literature also supports, through understanding the processing

components of mathematical thinking, subtypes of MD can be identified (Cornoldi,

Venneri, Marconato, Molin & Montinari, 2003; Geary, 2004; Jordan 1995). David Geary

has contributed much to this area of research. Swanson & Jerman (2006) stated,

"Although not a quantitative analysis, one of the most comprehensive syntheses of the

cognitive literature on MD was conducted by Geary" (p. 249). Geary (1993; 1996; 2004)

suggests there are three separate subtypes of MD: 1) Procedural; 2) Semantic; 3) Visual-

spatial. Additional literature has also supported a visual-spatial processing deficit as a

subtype of MD (Jordan, 1995; Cornoldi et al., 2003; Swanson & Jerman, 2006).

Several studies suggest visual-spatial processing is indeed related to mathematical

thinking (Ansari et al, 2003; Assel et al., 2003; Busse, Berninger, Smith & Hildebrand,

2001; Cornoldi et al., 2003; Geary, 1993; Geary & Hoard, 2003; Hartje, 1987; Mazzocco,

2005; Reuhkala, 2001). A student who has a visual-processing disorder will have

difficulty conceptualizing mathematical problems that are spatially based (Geary, 2004).

Visual-spatial processing is involved in the mathematical skills of cardinality, estimation,

solving word problems and number alignment (Assel, et al, 2003; Augustyniak, Murphy,

& Phillip, 2005; Jordan, et al, 2003). Other, studies have also shown a relationship

between MD and deficits in visual-spatial processing (Busse et al., 2003; Harnadeck &

Rourke, 1994; McGlaughlin et al., 2005; Reuhkala, 2001). A recent meta-analysis of MD

research has confirmed this relationship (Swanson & Jerman, 2006). Fully understanding

this relationship requires an understanding of visual-spatial processing.

Visual-spatial processing is defined as "The ability to generate, retain, retrieve

and transform well-structured visual images" (Lohman, 1994, p. 1000). Perhaps, the most

5

comprehensive view of where visual-spatial material is processed may come from the

work of Alan Baddeley (Fisk & Sharp, 2003; Geary, 2004; Pickering & Gathercole,

2004; Reuhkala, 2001; Sholl & Fraone, 2004; Swanson, 2004; Swanson & Beebe-

Frankenberger, 2004). Visual-spatial processing is one aspect of working memory (WM).

WM is the ability to take-in information and mentally manipulate that information while

simultaneously retaining it (Geary, 2004). Baddeley's (1996) theory separates WM into

four parts: 1) Central executive; 2) Episodic buffer; 3) Phonological loop; 4) Visual-

spatial sketchpad. The central executive is viewed as the controller for the remaining

three elements (Baddeley, 1996; Pickering & Gathercole, 2004). The episodic buffer is

responsible for integrating WM and long-term memory (Pickering & Gathercole, 2004).

The phonological loop is the part of WM that holds information of a verbal nature

(Baddeley, 1996). The visual-spatial sketchpad is utilized in such tasks as anticipating

spatial transformations, mental rearrangement of items and visualizing the relationship of

parts to a whole (Sholl & Fraone, 2004). The visual-spatial sketchpad processes visual-

spatial information (Reuhkala, 2001; Pickering & Gathercole, 2004).

The visual-spatial sketchpad is responsible for processing information that is both

visual and spatial in nature (Pickering & Gathercole, 2004). The visual-spatial sketchpad

is of limited duration and serves as a storage and processing center (Baddeley, 1996).

Visual material and spatial material are processed separately; however, when visual and

spatial information is utilized it is done as a gestalt (Baddeley, 1996; Richardson &

Vecchi, 2002; Sholl & Fraone, 2004). Neuropsychologists believe the visual-spatial

material is mainly processed in the right hemisphere of the brain in the parietal cortex

(spatial) and the inferotemproal areas (visual) (Cornoldi, Venneri, Marconato, Molin &

6

Montinari 2003; Geary, 1993; Harnadeck & Rourke, 1994; Morris & Parslow, 2004;

Young & Ratcliff, 1983). Fully comprehending visual-spatial processing also requires an

understanding of how it is assessed.

McGrew (2005) posits tasks that are believed to measure visual-spatial possessing

involve figural or geometric structures that necessitate the visual perception and mental

manipulation of "visual shapes, forms, or images, and/or tasks that require or maintain

spatial orientation with regard to objects that may change or move through space"

(McGrew, 2005 p. 152). To understand how visual-spatial processing is assessed it is

important to conceptualize it in the context of the most current theory of intelligence. The

Cattell-Horn-Carroll theory of intelligence has had a significant impact on the

construction and interpretation of current measures of intelligence (Alfonso, Flanagan, &

Radwan, 2005). The CHC theory of intelligence has a three tiered structure that consists

of a general factor of intelligence or "g", 10 broad factors of intelligence, and

approximately 70 narrow factors of intelligence (Evans, Floyd, McGrew, & Leforgee

2002; McGrew, 2005; Sattler, 2001). The 10 broad factors include: 1) Fluid Intelligence

(Gf); 2) Crystallized Intelligence (Gc); 3) Short-Term Memory (Gsm); 4) Visual

Processing (Gv); 5) Auditory Processing (Ga); 6) Long-term Retrieval (Glr); 7)

Processing Speed (Gs); 8) Reading and Writing (Grw); 9) Quantitative Knowledge (Gq);

10) Decision/Reaction Time (Gt) (see table 1.1) (Evans et al, 2002; Keith, et al. 2006;

Roid, 2003a; Roid, 2003b; McGrew, 2005). The literature overwhelmingly views the

terms Visual-Spatial Processing and Visual Processing (Gv) as the same construct

(Alfanso et al., 2005; DiStefano & Dombrowski, 2006; Evans et al., 2002; Floyd, et al.

7

2003; McGrew, 2005; Osmon, Smerz, Braun, & Plambeck, 2006; Proctor et al., 2005;

Roid, 2003a).

Table 1.1 The 10 Cattell-Horn-Carroll Broad Factors of Intelligence and their Abbreviations

Factor Abbreviation 1. Fluid Intelligence (Gf) 2. Crystallized Intelligence (Gc) 3. Short-Term Memory (Gsm) 4. Visual Processing (Gv) 5. Auditory Processing (Ga) 6. Long-term Retrieval (Glr) 7. Processing Speed (Gs) 8. Reading and Writing (Grw) 9. Quantitative Knowledge (Gq) 10. Decision/Reaction Time (Gf)

The Gv broad category of intelligence incorporates several processing tasks

including the production of visual images, mentally holding and manipulating visual

images and recalling visual images (McGrew, 2005). The Gv broad category of

intelligence includes the narrow cognitive abilities of: 1 ) Visualization (VZ); 2) Spatial

relations (SR); 3) Closure speed (CS); 4) Closure flexibility (CF); 5) Visual memory

(MV); 6) Spatial scanning (SS); 7) Serial perception integration (PI); 8) Length

estimation (LE); 9) Perceptual illusions (IL); 10) Perceptual alterations (PN); 11)

Imagery (IM); 12) Perceptual Speed (PS) (see table 1.2) (Carroll. 1993; Lohman, 1994;

McGrew, 2005; Sattler, 2001). Carroll's (1993) factor analytical work with cognitive

abilities may provide the best understanding of how Gv (i.e. visual-spatial processing) is

assessed.

8

Table 1.2 The 12 CHC Visual Processing (Gv) Narrow Cognitive Abilities and their Abbreviations

Narrow Ability Abbreviation 1. Visualization (VZ) 2. Spatial Relations (SR) 3. Closure Speed (CS) 4. Flexibility of Closure (CF) 5. Visual Memory (MV) 6. Spatial Scanning (SS) 7. Serial Perception Integration (PI) 8. Length Estimation (LE) 9. Perceptual Illusions (IL) 10. Perceptual Alterations (PN) 11. Imagery (IM) 12. Perceptual Speed (PS)

Literature suggests specific tasks measure each of the 12 Gv narrow cognitive

abilities. The first and broadest narrow cognitive ability is Visualization (VZ). Measures

for the VZ factor include assembly type tasks, block counting tasks, block rotation tasks,

paper folding tasks, surface development tasks, and figural rotation tasks (Carroll, 1993;

Lohman, 1994). The Block Design and Object Assembly subtests of the Wechsler

intelligence assessment series and the Form Board and Form Patterns subtests of the

Stanford-Binet series also may measure VZ (Carroll, 1993; G. H. Roid, personal

communication, November, 7 2006; Lohman, 1994; Sattler, 2001; Sattler & Dumont,

2004). Tasks that are thought to measure spatial relations (SR) include irregular card

comparisons, cube comparison tasks and the Block Design subtest of the Wechsler

intelligence assessment series (Carroll, 1993; Lohman, 1994; Sattler, 2001; Sattler &

Dumont, 2004). Tasks that are suggested to measure closing speed (CS) are the Street

9

Gestalt Completion test, tasks that include concealed letters, numbers or figures, and the

Object Assembly task of the Wechsler Intelligence Test series (Carroll, 1993; Sattler,

2001; Sattler & Dumont, 2004). Measures of flexibility of closure (CF) include tests that

have hidden or embedded figures, designs, or patterns (Carroll, 1993). Measures of visual

memory (MV) include a brief exposure to, then recalling in part or whole maps, pictures,

designs or shapes (Carroll, 1993). The Memory for Objects subtest of the Stanford-Binet

Fourth Edition is considered a measure of MV (Sattler, 2001). Measures of spatial

scanning (SS) involve maze tracing or planning and following a route on a two-

dimensional map (Carroll, 1993). The Mazes subtest of the Wechsler series may be a

well-known measure of SS (Sattler, 2001).

There is limited research on measures of the serial perception integration (PI)

factor; however, Carroll (1993) suggests tasks that measure PI involve the rapid

recognition of patterns in ordered and segmented parts (Carroll, 1993). Tasks that are

suggested to measure the narrow ability of length estimation (LE) include length

discrimination, length estimation, and comparison or proximity analysis of lines and

points (Carroll, 1993). Tasks that measure perceptual illusions (IL) may include the

estimation, contrasting, shape identification or direction identification of illusions

(Carroll, 1993). Carroll (1993) suggests that perceptual alterations (PN) measurement

tasks involve mental alternations of stimuli under timed conditions. Measures of imagery

(IM) require the subject to visually manipulate an object and compare it to other similar

non-manipulated objects (Carroll, 1993). Tasks that are believed to measure perceptual

speed (PS) involve the efficiency of recognition and comparison of visual stimuli under

timed conditions (Carroll, 1993). Symbol Search and Cancellation of the Wechsler

10

Intelligence Scale for Children 4 Edition may be measures of PS (Sattler & Dumont,

2004). The most recent revision of the Stanford-Binet Intelligence series is purported to

be aligned more closely with current theory regarding the measure of visual-spatial

processing.

The Stanford-Binet Intelligence Scales, Fifth Edition (SB5) published in 2003,

was designed to adhere more directly to the modern CHC theory of intelligence. The SB5

was developed around five factor areas. The five factors (and their corresponding CHC

cognitive ability) are Fluid Reasoning (Gf), Knowledge (Gc), Quantitative Reasoning

(Gq), Working Memory (Gsm) and Visual-Spatial Processing (Gv) (see figure 1.1)

(DiStefano & Dombrowski, 2006; Roid, 2003a). Roid (2003a) used confirmatory factor

analysis to confirm the factor structure of the SB5. Research substantiating the five

factors however, has not been conclusive. However, DiStefano's & Dombrowski's

(2006) exploratory factor analyses confirmed the SB5 as an adequate measure of general

intelligence or "g", but did not confirm the five factors. Roid maintains the rigorous

research that he and the test development team conducted fully substantiates the factor

structure of the SB5 (G. Roid, personal communication, November 7, 2006). The SB5

has both verbal and non-verbal measures of visual-spatial processing.

11

Figure 1.1. The Structure of the SB5.

SB5

Full Scale 10

Fluid Reasoning

Nonverbal Domain

Knowledge

Verbal Domain

Quantitative Reasoning

Visual-Spatial Processing

Working Memory

The SB5 defines visual-spatial processing as "... the ability to see relationships

among figural objects, describe or recognize spatial orientation, identify the "whole"

among a diverse set of parts and generally see patterns in visual material" (Roid &

Pomplun, 2005 p. 328). The verbal and nonverbal visual-spatial subtests of the SB5 were

created through a review of previous visual-spatial assessments and consultation with

notable experts in the field of CHC (see table 1.2) (Dick Woodcock, John Horn & John

Carroll; G. Roid personal communication November 7, 2006). The verbal visual-spatial

measure of the SB5 is the Position and Direction subtest. Position and Direction requires

the subject to "identify common objects and pictures using common visual/spatial terms

such as "behind" and "farthest left," explain spatial directions for reaching a pictured

destination or indicate direction and position in relation to a reference point" (Roid,

2003b p. 139). This subtest was derived from previous Stanford-Binet scales (Roid,

2003a). In addition, the subtest is based on Lohman's (1994) conceptualization that

verbal visual-spatial tests that require a subject to create a mental image and answer

12

corresponding questions are representative of real-life usage of visual-spatial processing

(Roid, 2003a). It is unclear however, which narrow cognitive ability Position and

Direction measures. Neither the technical nor the administrative manual directly specifies

the narrow cognitive ability (Roid, 2003a; 2003b). The nonverbal visual-spatial measures

of the SB5 were also designed to align with CHC theory.

The nonverbal visual-spatial processing domain of the SB5 contains two different

measures. At the early levels (1 -2) the measure is the Form Board task. The Form Board

task has been used with previous versions of the Stanford-Binet (Roid, 2003a). The Form

Board task is believed to be a measure of Gv and the narrow cognitive ability of VZ

(Carroll, 1993; Roid, 2003b). In the remaining levels of the nonverbal visual-spatial

processing domain, the Form Patterns task is used. The Form Patterns subtest was

selected by the test developers based on the suggestions by John Carroll, for a hands on

assembly task (G. Roid, personal communication, November 7, 2006). The task requires

subjects to reconstruct visually presented stimuli with geometric shapes. Form Patterns is

a measure of the broad Gv and of the narrow cognitive ability of VZ (G. Roid, personal

communication, November 7, 2006; Roid, 2003a). Currently there is a lack of non-

publisher developed research using the SB5 as a visual-spatial measure. The Wechsler

Intelligence Scale for Children was also recently revised and has tasks that research

suggests measure visual-spatial processing.

13

Figure 1.2. Visual-Spatial Processing Measures of the SB5.

Visual-Spatial Processing

Nonverbal Verbal

Form Board / Form Patterns

Position and Direction

The current revision of the Wechsler Intelligence Scale for Children (WISC-IV)

published in 2003 was undertaken to more accurately align the test with current

intelligence theory, elevate psychometric structure, broaden applicability, and enhance

evaluator usage of the instrument (Sattler & Dumont, 2004). The revision of the test

includes additional subtests to improve the measurement of Fluid Reasoning (Gf),

Working Memory (Gsm), and Processing Speed (Gs) (Wechsler, 2003a; Zhu & Weiss,

2005). The WISC-IV's four Index scores Verbal Compression, Perceptual Reasoning,

Working Memory, and Processing Speed combine to form the Full Scale IQ or measure

of "g" (see figure 1.3). Test developers utilized exploratory and confirmatory factor

analysis research to verify the four factors (Wechsler, 2003 a). However, recent research

on the WISC-IV has disputed the four factors as the most appropriate organization for the

assessment.

Keith et al. (2006) maintains the WISC-IV is better described using five factors of

the CHC Theory. Using factor analysis Keith et al. found a test framework structured on

the CHC factors of Crystallized Intelligence (Gc), Visual Processing (Gv), Fluid

Reasoning (Gf), Short-Term Memory (Gsm) and Processing Speed (Gs) provided the best

14

fit for the test (using the standardization data). Keith et al.'s work suggests that the

WISC-IV is an appropriate measure of visual-spatial processing or Gv.

Figure 1.3. Structure of the WISC-IV

Verbal Comprehension

TnHex

1. Similarities 2. Vocabulary 3. Comprehension 4. Information 5. Word Reasoning

WISC-IV

Full Scale IQ

Perceptual Reasoning

TnHpv

Working Memory

InHe

1. Block Design

2. Picture Concepts

3. Matrix Reasoning

4. Picture Completion

I 1. Digit Span

2. Letter-Number Sequence 3. Arithmetic

Processing Speed TnHpx

I 1. Coding 2. Symbol Search 3. Cancellation

The subtests in bold typeface are the core subtests of the WISC-IV

The subtests of the WISC-IV that purport to measure visual-spatial processing

(Gv) fall under the Perceptual Reasoning Index (see table 1.3). The Block Design subtest

of the WISC-IV may be the most complete measure of visual-spatial processing in the

Perceptual Reasoning Index. Block Design has been consistently utilized with the

Wechsler series. The literature supports Block Design as a measure of the broad cognitive

ability Gv and the narrow abilities of visualization (VZ) and spatial relations (SR)

(Carroll, 1993; Keith et al, 2006; Sattler & Dumont, 2004). In addition, studies often use

Block Design as a primary measure of visual-spatial processing (Carroll, 1993; Cornoldi

et al., 2003; Fuchs et al., 2005; Hegarty & Kozhevnikov, 1999; Lee et al, 2004). Sattler

(2001) cautions however, that children with visual or motor skill difficulties may not do

15

well on the task; suggesting that other abilities may influence students' performance. The

literature supports additional subtests of the WISC-IV as secondary measures of visual-

spatial processing.

For example, there is literature to support that Picture Completion (PCm) is a

measure of Gv. PCm involves visual responsiveness, visual perception, visual

discrimination and visual memory (Sattler & Dumont, 2004; Zhu & Weiss, 2005). In

addition, PCm is suggested to be a measure of the narrow cognitive ability, flexibility of

closure (CF) (Sattler & Dumont, 2004). Research also supports Matrix Reasoning (MR)

as a measure of visual-spatial processing (Keith et al., 2006). Sattler (2001) and Sattler

and Dumont (2004) maintain that because of MR's visual-perceptual and visual-spatial

processing elements it is a good measure of the broad Gv ability and the narrow VZ

cognitive ability. There is some disagreement with Symbol Search (SS) as a measure of

Gv. Keith et al.'s research with the WISC-IV found that SS loaded on the Gv cluster and

the Gs Cluster. Sattler and Dumont (2004) maintain that SS is more strictly a measure of

Processing Speed (Gs).

Table 1.3 Visual-Spatial Processing Measures of the WISC-IV Subtest CHC Cognitive Ability

Broad Narrow Block Design Gv VZ; SR Picture Completion Gv CF Matrix Reasoning Gv VZ Symbol Search* Gv; Gs

* Note: There is some disagreement in the literature regarding whether Symbol Search is a measure of Visual Processing or Processing Speed.

16

Significance of the Study

The current and past definition of a learning disability is grounded in the idea that

a SLD is a disorder in basic psychological processing. The most often used methods of

identifying a SLD involve the ability-achievement discrepancy paradigm and the more

recent response to intervention (RTI) process (Kavale et al., 2005; Reschly et al., 2003).

Both methods fail to diagnosis a SLD based on a disorder in processing (Torgesen, 2002).

It is logical if the definition of a SLD is stated as "a disorder one or more of the basic

psychological processes..." then an evaluation should include an assessment of

psychological processing (U.S. Department of Education, 2006a, p. 46757). There is

research to support that certain processing components play an important role in reading,

writing and mathematics achievement.

In comparison to reading and writing, mathematics achievement has had the least

amount of research in understanding the potential cognitive process involved (Swanson

& Jerman, 2006). Recent literature maintains improved understanding of the cognitive

components involved in mathematics achievement may increase the ability of

professionals to identify and treat disabilities in mathematics (Fuchs, et. al. 2006). There

are believed to be specific psychological processes involved in the basic mathematical

tasks of calculation, fluency and word problems. Of the psychological process involved

in the application and understanding of mathematics, working memory appears to

contribute to all areas of mathematical thinking (Swanson & Beebe-Frankenberger, 2004;

Swanson & Jerman, 2006). A significant sub-process of working memory is visual-

spatial processing (Baddeley, 1996; Pickering & Gathercole, 2004; Swanson & Jerman,

17

2006). Studies have shown that visual-spatial processing is related to mathematics

(Geary, 2004).

The recently revised Stanford-Binet Intelligence Scales, Fifth Edition (SB5) has

been designed to align closely with the most current theory of intelligence, the combined

Cattell-Horn-Carroll (CHC) theory of cognitive abilities (Roid, 2003a). The Visual-

Spatial factor of the SB5 is purported to be a measure of visual-spatial processing or Gv.

The Visual-Spatial factor of the SB5 includes verbal (Position and Direction) and

nonverbal (From Board; Form Patterns) measures of visual-spatial processing. There

currently is limited non-publisher developed research on the visual-spatial measures of

the SB5. In addition, the Wechsler Intelligence Scale for Children (WISC-IV) was also

recently updated to align more closely with the CHC theory of cognitive abilities (Sattler

& Dumont, 2004; Wechsler, 2003). Research has suggested that Bock Design, Picture

Completion, and Matrix Reasoning are measures of visual-spatial processing (Gv) (Keith

et al, 2006; Sattler & Dumont, 2006).

There are five reasons for the current study. First, if a SLD is defined as a disorder

in a basic psychological process it is important to show that processing deficits are related

to a SLD. Second, there is a literature supported need for increased research in

mathematics achievement. Third, there is a limited amount of research on the revised

visual-spatial measures (Position and Direction; Form Board; Form Pattern) of the SB5.

In addition, to date, there has been no research with visual-spatial measures of the SB5

and poor achievement in mathematics. Finally, to date there has been no research

investigating the relationship between the combined visual-spatial processing measures

18

of the WISC-IV (Block Design, Matrix Reasoning, and Picture Completion) and poor

mathematics achievement.

Statement of the Problem

The primary purpose of this study is to investigate the ability of the visual-spatial

measures of the Stanford-Binet-Fifth Edition (SB5) and the Wechsler Intelligence Scale

for Children- Fourth Edition (WISC-IV) to discriminate between students with and

without difficulties in mathematics achievement. It is suggested from a review of

literature, visual-spatial processing, as measured by the SB5 and the WISC-IV, will be

significantly different between students who have a potential disability in mathematics

and those who do not. In addition, the study will identify which visual-spatial measure or

index has the most potential as a discriminator between students who have poor

mathematics achievement and those who do not.

The following research questions will be used as a guide to the current study:

1. Is there a relationship between the psychological process of visual-spatial

processing (as measured by the SB5 and WISC IV) and mathematics

achievement (as measured by the Woodcock-Johnson III Tests of

Achievement-Normative Update (WJ-III-NU)?

2. Can the visual-spatial measures of the WISC-IV and the SB5 predict

mathematics achievement (as measured by the WJ-III-NU)?

3. What visual-spatial measure (SB5; WISC-IV) is the best

predictor of poor mathematics achievement (as measured

by the WJ-III-NU)?

19

Definition of Terms

The following definitions will be useful in understanding the preceding study.

Specific Learning Disability: ".. .Specific learning disability means a disorder in one or

more of the basic psychological processes involved in understanding or in using language

spoken or written, that may manifest itself in the imperfect ability to listen, think, speak,

read, write, spell or to do mathematical calculations including conditions such as

perceptual disabilities, brain injury, minimal brain dysfunction, dyslexia and

developmental aphasia" (U. S. Department of Education, p. 46757, 2006a).

Working Memory: The cognitive process that allows one to keep information at the

forefront of one's thoughts while mentally manipulating that information (Geary, 1996).

Visual-Spatial Processing: "The ability to generate, retain, retrieve and transform well-

structured visual images" (Lohman, 1994, p. 1000).

Limitations

One limitation of the current study may be some concerns regarding

generalizability. Using only middle schools students in grades 6A-Sth from specific

geographic locations in the West and Midwest may limit the application of the findings to

specific age groups and geographic locations. This limitation may prohibit the application

of the study's findings to students that are not in grades 6^-%^ and not from similar

geographic areas; making it difficult to generalize the study to students that are in

different age groups (younger or older) and/or come from larger or smaller communities.

Another factor that may cause some concerns regarding generalizability is, only students

from which parental or legal guardian consent is obtained will participate in the study

limiting the subject pool. This potentially limits the participants in the study to

20

individuals that are motivated enough to obtain parent consent. That in turn may exclude

those students that lack motivation to participate or may not be willing to participate do

to an aversion toward testing. An additional limitation may be that the measures of the

SB5 and the WISC-IV used in the study, purporting to measure visual-spatial processing,

may not accurately measure this construct. Due to the complexities of how the brain

analyzes and applies information, additional cognitive mechanisms may interfere with a

pure measure of relationship between visual-spatial processing and mathematical

achievement, confounding the results of the current study.

The Structure of the Proceeding Chapters

The literature review in Chapter 2 will provide a structural understanding of the

elements of the current study. It will identify the current literature regarding: 1) How

learning disabilities are defined operationally; 2) An understanding of mathematical

disabilities; 3) A conceptualization of visual-spatial processing and mathematics; 4) How

visual-spatial processing is assessed. Chapter 3 will provide the methodology for the

current study. The third chapter will address: 1) The participants used in the study; 2)

Instruments that were utilized; 3) The procedural aspects of the study; 4) How the data

were analyzed. Chapter 4 will present the results of the data analyses. Finally, Chapter 5

provides a summarization of the findings of the current study and a discussion of the

implications for this research.

21

CHAPTER II LITERATURE REVIEW

Learning Disabilities

The assessment, identification and remediation of learning disabilities are a

significant focus of special education programs in today's public schools. According to

the most recent data from the United States Office of Special Education (2004) there are

over 2.8 million students identified as having a specific learning disability in the United

States. That number translates into approximately 47% of all students being served

through special educations services have a learning disability (Heward, 2006). There are

disagreements with both the definition and identification of a learning disability. This

first section will address the definition and identification of learning disabilities.

Learning Disabilities Defined: Past and Present

Defining a learning disability is complicated. In one article alone, the author

identified 11 separate definitions for a learning disability (Hammill, 1990). The

conceptualization of the term learning disability, in the United States, is credited to the

work of Samuel Kirk in 1962-1963 (Hallahan & Mercer, 2001; Hammill, 1990; Hammill,

Leigh, McNutt & Larsen, 1981; Heward, 2006; Kirk & Kirk, 1983; Reschly, Hosp, &

Schmied, 2003). In Kirk's original definition, he defines a learning disability as an

underdeveloped process disorder in the academic and non-academic areas of speech,

language, reading, spelling, writing or mathematics (Hammill, 1990: Kirk & Kirk, 1983).

The process disorder may originate from either a brain dysfunction, behavioral

dysfunction or emotional dysfunction (Hammill, 1990; Kirk & Kirk, 1983). Kirk's

definition excluded individuals with mental retardation, any type of sensory deficit, and

individuals whose abilities were negatively impacted by culture or instruction (Hammill,

22

1990; Kirk & Kirk, 1983). Kirk's learning disability definition is the framework for the

current definition.

The current learning disability definition used by special education professionals

has its roots in Kirk's original definition. One main reason is Samuel Kirk was the head

of the National Advisory Committee on Handicapped Children (NACHC) that formulated

and presented the original definition to congress and the U. S. Office of Education in

1969 (Hallahan & Mercer, 2001; Hammill, 1990; Kirk & Kirk, 1983; Reschly, Hosp, &

Schmied, 2003). The NACHC definition also identified a learning disability as a process

disorder. More specifically it stated a child with a specific learning disability has a

".. .disorder in one or more of the basic psychological processes involved in

understanding or using spoken language. These may be manifested in a disorder of

listening, thinking, talking, reading, writing, spelling or arithmetic" (NACHC, 1968, p.

34 as cited in Hammill, 1990, p. 75). That definition with minimal changes was adopted

into law in 1975 as part of Public Law 94-142.

The 1975 definition also identified a specific learning disability as a

psychological processing disorder. More specifically it states, "The term "specific

learning disability" means 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, speak, read, write, spell or to do mathematical

calculations" (U. S. Office of Education, 1977, p 65083 as cited in Hammill, 1990, p. 77).

Analyzing the current federal definition adopted by the U.S. Department of Special

Education reveals the definition of a specific learning disability (SLD) has remained

23

constant from the original definition in 1977. The Individuals with Disabilities

Improvement Act (2004) states a SLD is:

(i) General. Specific learning disability means a disorder in one or more of

the basic psychological processes involved in understanding or in using

language spoken or written, that may manifest itself in the imperfect

ability to listen, think, speak, read, write, spell or to do mathematical

calculations including conditions such as perceptual disabilities, brain

injury, minimal brain dysfunction, dyslexia and developmental aphasia,

(ii) Disorders not included. Specific learning disability does not include

learning problems that are primarily the result of visual, hearing, or motor

disabilities, of mental retardation, of emotional disturbance, or of

environmental, cultural or economic disadvantage (U.S. Department of

Education, 2006a, p. 46757).

Some have questioned the adequacy of the current definition (Reschly, Hosp, &

Schmied, 2003). The National Joint Committee on Learning Disabilities (NJCLD)

contends that there are limitations with the federal definition. The NJCLD believes the

federal definition: 1) Fails to include adults; 2) The use of the term "basic psychological

processes" is ambiguous; 3) Spelling as a disability category is redundant and can be

included under a written expression disability; 4) Terms such as dyslexia, minimal brain

dysfunction, perceptual impairments and developmental aphasia are outdated; 5) The

exclusionary clause in the second section is confusing by failing to clearly explain why

these areas are not included (NJCLD, 1991). Others have also suggested the federal

definition maybe inadequate. Kavale, Holdnack and Mostert (2005) suggest one of the

24

main problems with the category of SLD in special education is the definition not the

identification. They contend the federal definition lacks specificity and is fraught with

vagueness (Kavale, et al, 2005). Regardless of any dissatisfaction with the current

definition, little has changed regarding the federal definition of a SLD since its

acceptance in 1977. Analyzing the regulations used by state education departments

reveals wide spread adoption of the current federal definition of SLD.

The majority of state education departments have adopted the federal definition of

a SLD. Reschly, et al. (2003) investigated state education agencies (SEA) in all 50 states

and identified that over 80% of states have used the federal definition. Only nine states

diverted substantially from the federal definition (AL, CO, FL, MA, NV, VT, WV, NC,

WI) (Reschly, et al., 2003). In further analysis of Reschly, et al.'s study, the data reveals

of the 50 states, 48 states conceptualize a SLD as a possessing disorder. The only two

states that do not utilize a processing disorder as a main component of their state

definition of a SLD are West Virginia and Illinois (Reschly, et al, 2003). In addition, a

recent unpublished review of how states currently define a SLD, found that 49 of the 51

states use the federal definition of a SLD or use the term "processing disorder" in their

definition (Clifford, 2008).

To conclude this section, the definition of the term SLD was first conceptualized

in the early 1960's. The current definition of a SLD in the reauthorization of IDEA

(2004) has changed little from the original definition in 1977 as part of P. L. 94-142. The

idea that a processing disorder is a foundational element of a SLD has been held constant

throughout the revisions of the definition and the law. The majority of states utilize the

federal definition of a SLD. Finally, all but two of the SEAs explicitly state that a specific

25

learning disability is defined by a processing disorder. Where the majority of

disagreement occurs among SEAs and professionals in the field of learning disabilities is

how to best identify an individual with a SLD.

Learning Disability Classification and Identification

The current methods of identifying a SLD can be traced back to the U.S. Office

Education in 1976. The U.S. Office of Education stated that a SLD was identified by a

"severe" discrepancy between an individual's intellectual ability and academic

achievement (Hammill, 1990; Reschly, et al, 2003). Specifically, it operationalized a

severe discrepancy when achievement was at or below 50% of what could normally be

expected given the child's age and education (Hammill, 1990). The discrepancy criteria

of 50%, offered in 1976 received significant criticism by education professionals and

laypersons, and was not included in the final regulations adopted as P. L. 94-142 in 1977

(Hammill, 1990; Reschly, et al., 2003). In 1977 without further guidance, the majority of

states adopted the practice of classifying a SLD as a discrepancy between ability and

achievement (Reschly, et al., 2003). That practice has been consistently employed by

state departments of education over the past 30 years.

With the initial 1975 implementation of P. L. 94-142 and the subsequent

reauthorizations of the Individuals with Disabilities Education Act in 1990 and 1997 the

language continued to included identifying a SLD through a sever discrepancy between

ability and achievement (Hallahan & Mercer, 2002; Jacob & Hartshorne, 2003). The

regulations indicate the multidisciplinary team determines if an individual has a

significant discrepancy between their level of achievement and level of ability (U.S.

Department of Education, 2006a). The discrepancy can be in a single area or in any

26

combination of the areas of oral and written expression, listening and reading

comprehension, mathematics calculation and reasoning, and in basic reading skills (U.S.

Department of Education, 2006a). No precise criteria have been offered to quantify what

was meant by significant. Current regulations have offered SEAs more options. Recently

within the Individuals with Disabilities Improvement Act of 2004, there has been a shift

in the identification procedures involved with specific learning disabilities. No longer is

there an implied requirement to use only a severe ability-achievement discrepancy for

identification and classification purposes. The new regulations indicate that states may

use as an evaluation procedure based on whether or not the student responds to a

researched based intervention. In identifying a SLD SEAs:

Must not require the use of a severe discrepancy between intellectual

ability and achievement for determining whether a child has a specific

learning disability, as defined in 34 C.F.R. 300.8(c)(10);

Must permit the use of a process based on the child's response to

scientific, research-based intervention; and

May permit the use of other alternative research-based procedures for

determining whether a child has a specific learning disability, as defined in

34 C.F.R. 300.8(c)(10) (U.S. Department of Education, 2006b).

Some are in support of this change. Stanovich (2005) contends that the use of the

achievement-discrepancy paradigm for learning disability identification in some ways is

equitable to malpractice, and flies in the face of substantial research noting its

inadequacy. Others believe there are unknown questions and limitations with the use of

response to intervention that need to be explored before wholesale adoption (Kavale, et

27

al., 2005). To understand the complicated nature of SLD diagnosis it is relevant to

discuss both methods of identification.

Models of Identification: IQ-achievement Discrepancy and Response to Intervention

The three most commonly used discrepancy models are the grade level

discrepancy model, standard score/ standard deviation model, and the regression model

(Mercer, Jordan, Allsopp & Mercer, 1996; Proctor & Prevatt, 2003; Reschly, et al.,

2003). The grade level discrepancy model is the least frequently used and is often called

the deviation from grade level model (Mercer, et al., 1996; Proctor & Prevatt, 2003). In

this model, a SLD is identified by a difference between the child's actual grade level and

the child's achievement level (Mercer, et al, 1996; Proctor & Prevatt, 2003). The

difference is indicated by a grade equivalence score on an academic achievement test

(Mercer, et al., 1996; Proctor & Prevatt, 2003). In the model, the child is often required to

have a minimal IQ (often 80 or 85) to receive a diagnosis of SLD (Proctor & Prevatt,

2003). In addition, the difference required for SLD identification can vary from 1-2 grade

levels (Proctor & Prevatt, 2003). Concerns regarding this method include the potential for

over identification of slow learners, under identification of students with higher IQ sores

and the inaccuracy of grade level placements (Mercer, et al., 1996; Proctor & Prevatt,

2003).

The standard score/ standard deviation model, also called the simple discrepancy

model, is a frequently used model by state departments of education (Reschly, et al.

2003). This method identifies a SLD by a discrepancy between an intelligence

assessment score and an achievement test score. State criteria can vary for identifying a

severe discrepancy. Some states use standard deviation (SD) differences of between 1.0-

28

2.0 to indicate a severe discrepancy (Reschly, et al. 2003). Other states may use standard

score units with magnitude variations of between 15-20 standard score points (Reschly, et

al. 2003). The use of varying standard scores and SD levels produces inconsistencies in

SLD identification among state departments of education. Some contend that problems

with using this model lie in three areas: 1) Difference scores are unreliable; 2) The model

fails to identify poor readers; 3) The model does not account for regression to the mean

(Proctor & Prevatt, 2003).

The third model is the regression model. The regression model is also frequently

used by state departments of education (Mercer, et al. 1996; Reschly, et al. 2003). The

regression model improves on the simple discrepancy model by controlling for the

correlation between cognitive and achievement tests (Proctor & Prevatt, 2003). The

regression model for determining SLD is founded on two critical items: 1) The

discrepancy between the individuals' achievement score and the mean achievement score

of individuals with similar ability levels; 2) A discrepancy between the individual's level

of achievement and ability level (Proctor & Prevatt, 2003). Some suggest that issues with

this model center on a lack of consistency in implementation, and laypersons difficulty in

understanding the model (Mercer, et al. 1996; Proctor & Prevatt, 2003).

The most recent method of SLD identification, endorsed by federal legislation, is

centered on a student's failure to respond to a research based intervention. The failure to

respond method is often described in the literature as response to intervention (RTI). In

the reauthorization of IDEA, RTI is not specifically mentioned nor are any procedural

guidelines given (National Research Center on Learning Disabilities [NRCLD], 2005).

The lack of specific methodological requirements in the law leaves the process open to

29

interpretation by individual states. RTI bases the identification of a SLD on the failure of

a student to respond to rigorous implementation of empirically backed interventions

(Kavale, et al. 2005). Some experts in the field have defined RTI as an observable change

in academic performance or behavior precipitated by an intervention (Gresham, 2002).

The first step in identifying a SLD by RTI is to provide and implement well-researched

and proven instructional techniques in the classroom (Kavale et al, 2005; NRCLD,

2005). Second, each individual student's performance is monitored for changes (Kavale

et al, 2005; NRCLD, 2005). Third, students that fail to respond to research validated

instructional techniques receive additional intensive instruction (Kavale, et al., 2005;

NRCLD, 2005). Fourth, progress or lack of progress is again monitored (Kavale, et al,

2005; NRCLD, 2005). If a student does not adequately progress with intensive

instructional interventions, the student is identified with a SLD and qualifies for special

education services (Kavale, et al., 2005; NRCLD, 2005). Often in the RTI model,

students' progress is monitored by using curriculum-based measurements and graphing of

certain academic benchmarks (Gresham, 2002). There is some concern in the literature

regarding the use of this SLD identification model.

Some contend that RTI models focus heavily on reading disabilities and fail to

address other areas of academic weakness (Kavale, et al, 2005). In addition, an aspect

associated with RTI models is the need for validated screening of academic difficulties;

however, there is a lack of constancy regarding what type of screening method should be

used (Semrud-Clikeman, 2005). Another criticism of RTI is that previous research has

mainly been conducted with younger students (K-2) and there is a dearth of evidence of

appropriateness with older students (Semrud-Clikeman, 2005). Other areas of concern

30

regarding RTI include: 1) Identifying the best intervention for each individual student; 2)

Deciding how long and to what degree an intervention should be implemented; 3)

Uncertainty over who is responsible for implementing the intervention, monitoring the

intervention, and the rigor of implementation; 4) The associated costs of providing

intensive interventions to students (Gresham, 2002).

Summary

There are a substantial number of students in public schools identified as having a

learning disability. The definition of a SLD has changed little from its first acceptance in

1977 as part of P. L. 94-142 to the present IDEA improvement act of 2004. The

identification of a student with a SLD has in the past, primarily consisted of a

discrepancy between an individual's ability and their achievement level. Recently federal

regulations are allowing a student's failure to respond to a researched based intervention

as a classification method of SLD. It is apparent there is a disconnect between the current

definition of a SLD and how it is identified. The definition of SLD adopted by both the

federal government and the majority of states is centered on the concept that learning

disabilities are at their roots a processing disorder; however, processing disorders in the

identification of a SLD are often not considered. Of the previously noted 49 states that

define a SLD as processing disorder, only one utilizes processing in their classification

criteria (Clifford, 2008). If the definition of a SLD is based on the idea it is a processing

disorder, then it is prudent that SLD identification should include elements of a

processing disorder evaluation (Torgesen, 2002). If the classification of SLD does not

include the evaluation of processing components then the definition of a SLD may need

to be modified. Completely understanding the definition of a SLD requires understanding

31

what is meant by psychological processes. The next section will address the processing

components most often involved in academic abilities.

Psychological Processing and Learning Disabilities

Psychological processes are those processes that involve the effective use

of higher cognitive abilities such as the use of language, attention, utilization of memory,

thinking abstractly, solving problems, and perceptually based skills (Gerring, &

Zimbardo, 2002). Because the federal definition and the majority of state definitions of a

SLD emphasize a SLD as a processing disorder it is relevant to identify which

psychological process are involved in learning disabilities. The most common academic

learning disability diagnoses found in schools (excluding speech disorders) are learning

disabilities in reading, written language and mathematics (Heward, 2006). This next

section will address each learning disability area (reading, written language and

mathematics) identifying the most common psychological processes involved.

Reading

Reading difficulties are the most frequently diagnosed learning disability (Joseph,

2002). Some estimate almost 90% of students identified as learning disabled have a

reading disability (Heward, 2006). Others suggest that as many as 15% of all students

have reading difficulties (McCormick, 2003). The research suggests there are five main

cognitive processes involved in reading: 1) Phonological processing; 2) Syntactic

processing; 3) Working memory; 4) Semantic processing; 5) Orthographic processing

(Siegel, 2002).

Phonological processing is often considered the most important processing area in

reading development (Gray and McCutchen, 2006; Hoskyn & Swanson, 2000: Siegel,

32

2003). Phonological processing involves the association of sounds with single or

combined letters (Siegel, 2003). Specifically, it is the understanding of the relationship

between graphemes and phonemes in language (Siegel, 2003). Support for the

importance of phonological processing's role in reading comes for the work of Gray and

McCutchen (2006). Gray and McCutchen found a strong correlation between

phonological awareness (a significant component of phonological processing) and

reading tasks such as word reading and sentence comprehension. Gray and McCutchen

compared scores on the Test of Phonological Awareness Skills to timed word reading and

sentence comprehension tasks with students in kindergarten, first grade and second grade.

Gray's and McCutchen's results suggest children whose scores were high in phonological

awareness were more than twice as likely to score above the mean on word reading tasks

compared to those who scored low in phonological awareness (Gray and McCutchen,

2006). The results of the study suggest that aspects of phonological processing such as

phonological awareness may be important for early reading skills. Syntactic processing

also appears to be involved with reading skills.

The second significant processing component of reading is syntactic processing

(Siegel, 2003). Syntactic processing is the understanding of basic sentence structure or

the grammatical structure used in language (McCormick, 2003; Siegel, 2003). Support

for syntactic processing as a process of reading comes from the work of Holsgrove and

Garton (2006). The study involved assessing the reading comprehension of middle school

students. Holsgrove and Garton used measures of working memory, phonological

processing and syntactic processing. To measure syntactic processing Holsgrove and

Garton employed the aural moving-window technique that required students to analyze

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syntactically ambiguous printed sentences. The authors found that syntactic processing

was a significant predictor of reading comprehension among the 13-year-old students.

Additionally, Holsgrove and Garton with regression analysis determined that syntactic

processing was a significant discriminator of students with and without reading

difficulties (Holsgrove & Garton, 2006). Working memory may also play a role in

student's ability to read.

In reading, working memory involves the ability to decode words while

simultaneously retaining what has been read (McCormick, 2003; Siegel, 2003). Swanson,

Howard and Saez (2006) found, with students varying in age from 7-to-17 years-of-age,

that working memory was a significant discriminator between students with and without

reading disabilities. Swanson, et al. (2006) used working memory measures such as digit

and sentence span tasks, a semantic association task, a listening span task and the

backward digit span of the Wechsler Intelligence Scale for Children-Ill to assess the

working memory of the subjects. Matching subjects for IQ and written math calculation

Swanson et al. found that students identified as reading disabled performed poorer on

working memory tasks when compared to non-reading disabled students. Swanson et

al.'s results suggest that working memory may be a contributing cognitive process in

reading ability. The literature suggests semantic processing may also be related to

students reading ability.

Semantic processing, understanding the meaning of sentences, is an important

cognitive process in reading (McCormick, 2003; Siegel, 2003). Evidence for this comes

from a study conducted by Nation and Snowling (1998). Nation's and Snowling's study

involved a comparison of average readers and students identified as having significant

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difficulty with comprehension. Nation and Snowling matched students for decoding and

nonverbal ability. The authors used measures of both expressive and receptive language

to assess semantic processing differences between the two groups. Nation and Snowling

found that semantic processing significantly discriminated between readers with

comprehension difficulties and average readers. The results of the study suggest that

semantic processing may be an important component in children's ability to comprehend

written material. Some research also supports orthographic processing's relationship to

students' reading ability.

The final research identified significant cognitive process in reading is

orthographic processing. Orthographic processing is the knowledge or awareness of word

structure, specifically the knowledge of letters and spelling patterns (McCormick, 2003;

Siegel, 2003). Badian (2001) suggests a link between orthographic processing and

reading. Badian conducted a longitudinal study that followed the same group of children

from preschool to seventh grade. Badian used letter identification tasks as orthographic

processing measures. Badian found, among students with average to above average

intelligence, that orthographic processing skills at kindergarten were a significant

predictor of poor reading skills of those children in 7th grade. The results of the Badian

study suggest that deficits in orthographic processing may lead to poor reading ability in

later years. The next section will look at the cognitive processes involved in writing.

Writing

Prevalence rates of writing disabilities are difficult to estimate due to differences

in qualitative and quantitative distinctions (Hooper, Swartz, Wakely, de Kruif, &

Montgomery, 2002). As a measure of the number of students that struggle with writing,

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14 % of all 4 graders, 15% of all 8 graders, and 26% of the 12 graders students who

took the National Assessment of Educational Progress in 2002 were below basic skill

levels in writing (National Center for Educational Statistics, 2002). The literature

regarding the cognitive processes involved in writing is less clear in comparison to

reading. The research suggests that there are six psychological processes involved in

writing: 1) Phonological processing; 2) Orthographic processing; 3) Working memory; 4)

Long-term memory; 5) Short term memory; 6) Morphological processing. The section

will look at the cognitive processes of writing in two ways. First, it will discuss the

processes in the holistic act of writing. Second, it will discuss spelling as a sub-skill

within writing.

Writing Processes

One of the more well know cognitive processing models of writing was developed

by Flower and Hayes in 1980 and latter expanded by Hayes (2000). The Hayes model

identifies the cognitive processes of writing as text interpretation, reflection and text

production (Hayes, 2000). Within those areas, Hayes states that working memory

(specifically phonological memory) is related to text interpretation because it

incorporates reading, listening and graphical scanning. Hayes theorizes that within

working memory the visual/spatial sketchpad is related to reflection skills. Hayes posits

that visual-spatial processing is involved when the individual utilizes internal

representations to prepare for the production of text. Hayes also believes text production

is related to long-term memory. Text production requires an individual to use previous

knowledge to construct text in a meaningful and coherent manner (Hayes, 2000). One

apparent criticism of Hayes model is, at best, it is a general model of cognitive process

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and lacks specificity. In addition, Hayes offers little empirical research to support his

theory. In order to identify the specific processes involved one must look beyond his

model.

Research suggests that phonological processing is involved in writing (Berninger,

Abbot, Thomson, & Raskind, 2001; Johnson, 1993; McGrew & Knopik, 1993). McGrew

and Knopik (1993) found phonological processing to have a significant relationship to

writing achievement. McGrew and Knopik studied the cognitive clusters of the

Woodcock-Johnson Tests of Cognitive Ability-Revised (WJC-R) in comparison to

individual's Basic Writings Skills and Written Expression clusters scores on the

Woodcock-Johnson Psycho-Educational Battery-Revised (WJ-R). McGrew and Knopik,

using the WJ-R standardization sample, found that phonological processes (Auditory

Processing) were significantly related to basic writing skills and written expression skills.

Berninger et al. (2001) offers a more comprehensive study of the processing components

of writing.

Berninger, et al. (2001) found phonological processing to be a significant

predictor of writing skills. Berninger et al. discovered phonological measures contributed

unique variance to written composition abilities of students in first through sixth grades.

Berninger et al. used structural equation modeling to compare the relationship between

phonological processing tasks such as phonemic deletion, segmentation, and nonword

memory and writing tasks including handwriting and written composition. Berninger et

al. found that phonological processing contributed unique variance to writing

composition beyond what could be accounted for by intellectual ability. In addition,

Berninger et al. found that orthographic processing appears to be important in written

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composition tasks and handwriting. Berninger et al. compared letter cluster coding, an

orthographic measure that required no memory usage and an orthographic measure that

tapped long-term memory to students' story composition skills and handwriting. The

results suggested that a combined orthographic processing factor was a significant

contributor to story composition and handwriting ability. The role of working memory

and long-term memory in writing is less clear.

Some support for the role of working memory in writing comes from the work of

Kellogg (1994; 2001a), Hopper et al. (2002), and Swanson and Berninger (1996).

Kellogg (1994) maintains that in writing working memory is involved in temporarily

holding and manipulating ideas that are constructed into sentences. Kellogg (2001a)

supports this view through the study of text generation and response time analysis.

Kellogg's (2001a), study involved college students and writing ability. The study

compared the construction of narrative texts (in both longhand and word processing) in

combination with an interference task (a computer-generated tone that required students

to say their thoughts regarding their work at varying 10-15 second intervals). Kellogg

(2001a) suggests students' response times were an indication of working memory

capacity. Kellogg (2001a) contends because students' response times across the tasks of

planning, translating and reviewing were all consistent it provided evidence for the

utilization of working memory across all three areas. A caveat is warranted with this

study. First, Kellogg offered little researched support for the idea that response time and

reflection were an indication of working memory capacity. Second, Kellogg failed to use

any empirically validated measures of working memory in his study.

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A study by Hooper et al. (2002) also offers inconclusive results regarding the role

of working memory in writing. Hopper et al.'s study involved the assessment of working

memory as a component of a larger assessment of central executive tasks, including

measures of inhibition, and attention. Hooper et al. compared a working memory task that

employed sentence construction from visually displayed pictures (while performing an

interference task) and student scores on a written narrative task. Hopper et al. maintains

the study's results suggested that working memory plays an important role in the

differentiation between good and poor writers of narrative material. As with Kellogg's

study, caution should be used in the interpretation of this study's results. First, Hopper et

al 's measure of working memory capacity involved an interference task and not an

empirically validated measure of working memory. Second, Hopper et al 's results, failed

to separate out the working memory assessment, leaving it as an element of a larger

domain that consisted of other nonworking memory related measures. Swanson's and

Berninger's (1996) study of fourth graders may offer a more concise explanation of

working memory's role in writing.

Swanson and Berninger (1996) used both verbal and visual-spatial working

memory measures to explore working memory in writing. The authors employed working

memory tasks that included sentence spans, rhyming, semantics (categorization and

association), phrase sequencing and story recall in conjunction with visual matrices,

mapping tasks and direction tasks (Swanson & Berninger, 1996). The authors compared

both verbal and visual-spatial measures to writing tasks that included expository and

narrative composition, handwriting and spelling. Swanson and Berninger, controlling for

the effects of age, found that overall there was a significant relationship between working

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memory tasks and writing skills, particularly as it related to the executive system. An

important component of the Swanson and Berninger study is the authors found that short-

term memory contributed significantly to spelling and handwriting, but not text

construction. The results suggest a separation of roles of working memory and short-term

memory in writing. Long-term memory processing may also be involved in writing

ability.

Some suggest that long-term memory may play an important role in the

generation of text (Hayes, 2000; Kellogg, 1994; Kellogg 2001b). Limited support for the

role of long-term memory comes from a study conducted by Kellogg (2001b). Kellogg

conducted two experiments with college-aged students. In the first experiment, Kellogg

used domain knowledge as an indicator of long-term memory. Kellogg analyzed narrative

and persuasive text production in comparison to verbal ability (as measured by verbal

domain scores on a standardized test) and quality of production. Kellogg's results suggest

verbal ability did not affect text recall; rather text recall was affected by domain

knowledge. In the experiment, Kellogg used an interference task to measure response

time in combination with individual differences in verbal ability and domain knowledge.

The results of the study suggest that short-term memory (as measured by response time)

and verbal ability (as measured by verbal score on the standardized test) were not as

important as domain knowledge regarding text quality (Kellogg, 2001).

Caution should be used in unqualified acceptance of Kellogg's results. First, long-

term memory as Kellogg conceptualizes is difficult to quantify. Second, Kellogg offers

little evidence regarding response time as a true measure of short-term memory.

Kellogg's study contributes confusion to psychological processing and writing. A better

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understanding of the psychological processes involved in writing may come from an

analysis of processes involved in spelling.

Spelling Processes

Spelling is a key component of writing. As a subcomponent of writing, it appears

that phonological processing, orthographic processing, morphological processing, short-

term memory and working memory may play a role in spelling skills (Berninger &

Amtmann 2003). Cornwall (1992) studied phonological awareness and spelling skills in

elementary students. Controlling for age, IQ, SES, and behavior problems Cornwall,

identified that phonological awareness (measured by decoding, blending and phonemic

deletion) was a significant predictor of spelling ability. Hauerwas and Walker (2003)

investigated the phonological, orthographic and morphological processing in 11-13 year-

old students with and without spelling deficits. The authors divided the students into two

groups (spelling deficit and non-spelling deficit) based on their scores on the spelling

subtest of the Wide Rage Achievement Test 3 and one group as an age-matched control.

The authors compared measures on phonemic deletion tasks, non-word cloze

tasks, non-word-choice tasks and inflection spelling tasks among the three groups.

Hauerwas and Walker (2003) found that orthographical and phonological awareness were

significant predictors of the spelling of base words, while morphological awareness was a

significant predictor of students' ability to spell inflected verbs. The results suggest

phonological, orthographic and morphological processing may play a role in the spelling

ability of students. Support for the role of short-term and working memory in spelling

comes from the previously mentioned Swanson and Berninger (1996) study. Swanson

and Berninger used th