The state of learning disabilities: Facts, trends and emerging issues

Cortiella, C., & Horowitz, S. H. (2014). The state of learning disabilities: Facts, trends and emerging issues. New York: National Center for Learning Disabilities.‏

http://superabile.it/repository/ContentManagement/information/P1302547621/The%20State%20of%20Learning%20Disability.pdf

Overview

What We Know About LD

Common Types of Learning Disabilities

Legal Protections for People With LD

 Public Perceptions of LD

NCLD 2012 Survey of Public Perceptions of LD

2013 Research on Parents of Children With Learning and Attention Issues

Emily Hall Tremaine Foundation GfK Roper 2010 Study on Public Attitudes About Children With LD

LD in the Schools

Prevalence and Characteristics of Students With LD .

Academic Performance and School Outcomes

LD Beyond School

Prevalence and Characteristics of Individuals With LD

Postsecondary Education

Employment

Emerging Issues

Response to Intervention

Common Core State Standards and Assessments

Online Learning

Accessible Instructional Materials

Charter Schools

School Vouchers   

Juvenile Justice

 

Flanagan's operationalization of learning disability definition – does it work?

Miciak, J., Fletcher, J. M., Stuebing, K. K., Vaughn, S., & Tolar, T. D. (2014). Patterns of cognitive strengths and weaknesses: Identification rates, agreement, and validity for learning disabilities identification. School Psychology Quarterly, 29(1), 21.‏ http://www.ncbi.nlm.nih.gov/pmc/articles/PMC4111129/

Henry Kissinger is known for his saying: "Israel has no foreign policy, only domestic politics".

This sometimes is the situation in the learning disability field as well.  Many of the professional stances are actually political ones.  Should the identification of a possible neurobiological cause for the low achievement be required as an essential part of the definition? Should there be a requirement to identify deficient cognitive processes or abilities that lie at the base of the child's difficulties in reading, writing or arithmetic?

This issue is in dispute.  The position that demands identification of a cognitive base for the low achievement strengthens psychologists, who are experts at intelligence and cognitive ability assessment.

The aim of the study presented here was to look at the Flanagan model of learning disability definition, which requires linking low achievement with a low cognitive ability (and at another similar model which I will not discuss here).  The model was tested with a group of 139 sixth and seventh grade students that did not respond to intervention.

The group that conducted this research included the renowned Jack Fletcher.

Jack M. Fletcher, Ph.D., is a Professor of Psychology at the University of Houston. For the past 30 years, Dr. Fletcher, a board-certified child neuropsychologist, has worked on issues related to child neuropsychology, including studies of children with spina bifida, traumatic brain injury, and other acquired disorders. In the area of developmental learning and attention disorders, Dr. Fletcher has addressed issues related to definition and classification, neurobiological correlates, and most recently, intervention.  He served on the NICHD National Advisory Council, the Rand Reading Study Group, the National Research Council Committee on Scientific Principles in Education Research, and the President's Commission on Excellence in Special Education. He published 3 books and over 350 papers.  He was President of the International Neuropsychological Society in 2008-2009.

 Fletcher argues, that "there's a big question and a lot of controversy about what cognitive assessments add…I cannot find data that shows that cognitive assessments, strengths and weaknesses in cognitive skills, are related to intervention outcomes.  It's very hard to find… A bigger issue is that there is little evidence that there is additional value added information that you get from an evaluation of cognitive skills if you've carefully evaluated achievement levels".  You can see him make this argument here (minutes07:24-08:10).  This video was shot in 2010, long before this study was published. 

Here is a reminder of the Flanagan definition steps:

The steps depend on each other, in a way that a child who doesn't "pass" the first step cannot move on to the second step.  A child who doesn't "pass" the second step cannot move on to the third step and so on.  The steps are:

1.    Low achievement (a score that is at least one standard deviation below the mean) in reading, writing or arithmetic tests. 

2.    One of the child's cognitive abilities (or more, of the following: fluid ability, visuospatial processing, auditory processing, processing speed, long term storage and retrieval, short term memory or comprehension knowledge) is significantly below average (a score that is at least one standard deviation below the mean).

3.    There is a reasonable or empirical link between the poor achievement and the low ability (for example, poor reading comprehension due to deficient comprehension knowledge).

4.    Most of the child's cognitive abilities are within average limits (within one standard deviation from the mean).

5.    Exclusionary factors (sensory disability, intellectual disability, emotional or social disorders, cultural differences, immigration and insufficient or improper instruction) are not the main reasons for the child’s low achievement.

In this study, 228 6^th and 7^th grade children received Tier2 intervention.  The intervention took place in groups of 10-15 students, for one period every day for an entire school year (very impressive).  The intervention included reading fluency, vocabulary and reading comprehension.  The intervention teachers received 60 hours of training and supervision throughout the year.  They were also evaluated for their adherence to the intervention program and their teaching quality.

In the spring of the intervention year the children took four tests (I've dropped the test's names for sake of reading clarity):

·         A basic reading test

·         A word reading efficiency test

·         A reading comprehension test

·         A matrix test

A child who received a low score on at least one of the first three tests (measuring reading achievement) was considered as not responding to the intervention.  There were 139 such children.

At this point the authors write that the sample reflects what will emerge in many schools that complete mass screening of all secondary students to identify struggling readers. It includes a large number of economically disadvantaged students (83.46% of the 139 students in this sample) and students from linguistically and culturally diverse backgrounds (13.53% of the 139 students in this sample). The sample of inadequate responders includes a higher percentage of students receiving free and reduced lunch and a larger percentage of students with a history of ESL (all students received English-only core instruction and completed the Tier 2 intervention in English).

The paper doesn't present data on the number of years these ESL children are living in the US.  Immigration is an exclusionary factor for learning disability.  This means that it's possible that a large part of the 13.45% of the ESL children could not have been classified as learning disabled, being in the process of acculturation and English acquisition.  It's also worth noting, that poor socioeconomic background may disrupt cognitive development, especially comprehension knowledge development (but not only this ability). A child from a low SES family may have poor cognitive abilities not because of disabilities but rather from lack of opportunities to develop them. 

Exclusionary factors were not considered in this study.

In the autumn of the year following the intervention the children took the following tests (I omit test names for clarity):

Achievement tests:

·         Word and letter identification

·         Word attack

·         Reading comprehension

·         Spelling

·         Efficiency in single word reading

·         A group assessment of reading comprehension

·         A test for efficiency of silent reading and reading comprehension.

The children also took cognitive tests meant to measure the CHC abilities in order to apply Flanagan's definition.  A sufficient measure of a broad cognitive ability, according to Flanagan, consists of (at least) two tests, each measuring a different narrow ability. 

In this study, Long term storage and retrieval, Fluid ability, Short term memory, Comprehension knowledge and Processing speed were measured with only one test.  Hence these abilities were not sufficiently assessed.  Here are the ways the abilities were measured:

·         Auditory processing: phonological decoding efficiency, phonological awareness index.  It's not clear whether two different narrow auditory abilities were measured.

·         Long term storage and retrieval – naming speed test.

·         Fluid ability – matrix test

·         Short term memory – spatial working memory test.  The test used had no national norms.  The norms were collected from the sample group itself (!)

·         Comprehension knowledge – listening comprehension test.  Listening comprehension is not a very clean measure of comprehension knowledge, since it is affected by other abilities as well (for example, fluid ability, short term memory and processing speed).

·         Processing speed –underlining test.  This test doesn't have national norms as well.  The norms were collected from the sample.

Visuospatial ability was not measured at all.  The authors write that this was the case "because it is not strongly related to LD in reading and because we had a measure of nonverbal reasoning that should be a strength in many with reading LD. For the present study, visual processing skill was assumed to be normal in the calculation of profile normality".

Thus, out of seven cognitive abilities, five were insufficiently measured by one test only.  Two (out of the five) were assessed by tests that did not have adequate norms, and one ability was not assessed at all.

The authors had three hypotheses about the links between cognitive abilities and reading:  students with word decoding difficulties will have low phonological awareness; students with low reading fluency will have low naming speed; students with low reading comprehension will have poor listening comprehension.

It's possible to make more hypotheses about other cognitive abilities' involvement in reading, but the authors did not do this.

To the best of my understanding, the study does not present the cognitive ability scores of students with difficulties in single word decoding, reading fluency or reading comprehension. 

Achievement tests scores:

The authors present the average scores of the whole 139 student group.  The average scores of the group in basic reading and single word decoding efficiency were within normal limits.  Their average score in spelling was also within normal limits, in the low average range.

The group had a poor average score on silent reading efficiency and reading comprehension and on other reading comprehension tests.

Cognitive ability scores:

The group's average score on phonological awareness (auditory processing), rapid naming (long term storage and retrieval) and listening comprehension (comprehension knowledge) were within average limits   - in the low average range.  The group's average scores on matrices test (fluid ability), visual working memory (short term memory), and underlining test (processing speed) were average.

Only 24 students out of the 139 non-responders, 17%, were classified as leaning disabled according to CHC theory (Flanagan's model).

The authors see this number as low, and as attesting that the Flanagan model is not efficient for the identification of children with learning disabilities.

However:

A.   We have no way of knowing what should be the "real" percentage of learning disabled children in the 139 non-responder group.  It's possible that not all children that did not respond to intervention are learning disabled.  Some of them may have not responded because of different exclusionary factors not assessed in this study (for instance, emotional difficulties).  The group's difficulties were in reading comprehension and not in reading decoding.  Because of the high percentage of children from low SES background and ESL students, it's possible that learning disability was not the main reason for many of these students' low achievement.   It's possible that many of these students have reading comprehension difficulties resulting from cultural and linguistic differences.  And so it may be not surprising that the CHC method identified only 24 of them as learning disabled. I wonder how many of the 139 students had a g score lower than one (meaning, had many poor broad abilities).  I think this data is not presented.

B.   As written above, there were shortcomings in the implementation of the Flanagan learning disability definition steps in this study:  the use of only one test to measure each cognitive ability; using tests without norms; and not assessing visuospatial processing.  Because of these shortcomings, I'm not sure that a conclusion about the method's efficiency can be drawn.   Fletcher and his colleagues write that due to time considerations, they were not able to use more than one test for each ability.  But they also write that "the addition of extra indicators for each CHC factor would be unlikely to affect the results of the present study" (I didn't understand why).  As for the measured that lacked norms, the authors write that "the effect of this limitation is unlikely to change the conclusions of the study. First, the two measures were utilized only for the purpose of establishing a “normal” cognitive profile within the XBA [Flanagan] method. The effect of a restricted norming sample would likely result in inflated scores and thus a higher frequency of normal profiles. Utilizing population norms may have decreased the number of normal cognitive profiles and decreased the number of students identified as learning disabled. Second, weak correlations between the two measures and all reading measures suggest that the restriction of range displayed by the reading-impaired sample may have been minimal".  But, it's better to make sure that profiles are normal with tests that have good norms…  Furthermore, some children's disability resides in short term memory or processing speed or visuospatial ability (and the rest of their abilities are average).  If there were good measures of short term memory and processing speed, and if visuospatial ability were measured, it's possible that more children could have been found learning disabled.

Children with developmental dyscalculia have more difficulty with subtraction than addition. Why? And what is unique in their brain activity?

Rosenberg‐Lee, M., Ashkenazi, S., Chen, T., Young, C. B., Geary, D. C., & Menon, V. (2015). Brain hyper‐connectivity and operation‐specific deficits during arithmetic problem solving in children with developmental dyscalculia.Developmental science, 18(3), 351-372.‏http://www.ncbi.nlm.nih.gov/pmc/articles/PMC4320038/

 In this research done with 7-9 year old children, the authors compared addition and subtraction abilities of children with developmental dyscalculia (DD) and typically developing children (TD).

Children diagnosed as DD scored at or below the 25^th percentile on the Numerical Operations subtest of the Wechsler Individual Achievement Test – Second Edition; WIAT-II.  Children diagnosed as TD scored at or above the 75^th percentile on this test.  Children in both groups had a FSIQ of 80 or above, and scored at or above the 25^th percentile  on  the Word Reading subtest of the WIAT-II.  Sixteen  DD and 20 TA children participated in the study.

The fMRI experiment consisted of addition and subtraction problems which were either simple or complex.   Each calculation trial lasted five seconds.  In the Complex addition task, participants were presented with an equation involving two addends and asked to indicate, via a button box, whether the answer shown was correct or incorrect (e.g. ‘3 + 4 = 8’). The first operand ranged from 2 to 9, the second from 2 to 5 The Simple addition task was identical except that one of the operands was always ‘1’ (e.g. ‘3 + 1 = 4’). In the Complex subtraction task, the first operand ranged from 3 to 14 and the second operand from 2 to 5. In the Simple subtraction task, the first operand ranged from 2 to 14 and the second operand was always ‘1’.

Here I'll focus on a few findings that are of interest for me, and not on all findings of this study.

·         DD children solved addition tasks with the same level of accuracy as TD children, but were slower.  DD children were significantly deficient with the subtraction tasks, in comparison with the TD children. Children with DD failed to respond in the allotted time in a large proportion of trials during the subtraction task. However, for trials in which they made a response, accuracy in the DD participants was relatively high at 75.4%, suggesting that DD participants were actively engaged in the task but were unable to solve many of the problems with the same fluency as their TD peers.

·         Timed trials exacerbate the difficulties children with DD have when solving subtraction problems consistent with their difficulties on timed number fact and story problems. The latter are typically due to use of slower and more effortful counting strategies to solve the problems, as contrasted with direct retrieval of the answer in children without mathematical difficulties. This pattern may be exacerbated with subtraction because, unlike addition, subtraction problems are not commutative (e.g. 4 − 3 ≠ 3 − 4), which makes memorization of answers more difficult and thus results in less fluent problem solving for all students.

·         Children with DD engage multiple fronto-parietal circuits differently from TD children. Children with DD may require greater engagement of these circuits, even while achieving only weaker levels of performance. Alternatively, greater engagement of these circuits may result in the activation of problem-irrelevant information that in turn disrupts problem solving. The latter view is consistent with behavioral studies that show the intrusion of problem-irrelevant information into working memory when children with DD attempt to retrieve arithmetic answers from long-term memory. 

·         Hyper-connectivity, rather than gross under-activation, is the primary neural source of problem solving difficulties in children with DD.  DD children showed hyper-activation on both addition and subtraction problems in multiple frontal, parietal and visual areas. Children with DD showed especially high levels of hyper-activation in parietal cortex for both correctly and incorrectly solved subtraction problems.

·         There is a network of brain regions that show aberrant responses during arithmetic problem solving.  Arithmetic deficits in DD are unlikely to be localized to a single brain region.  Rather, both localized processing deficits in multiple brain areas as well as the coordination between multiple brain circuits are impaired in DD. These conclusions are consistent with the proposal that most neurodevelopmental disorders and learning disabilities arise from diffuse disruptions and aberrant connectivity between regions rather than focal lesions.

Procedural learning - what is it and what does it have to do with dyslexia?

Procedural learning is the acquisition of a series of processes for the performance of a certain task.  The ability to learn sequences of actions helps us learn how to ride a bike, produce and perceive phoneme sequences, tie shoelaces, drive, play music and perform any activity with a serial aspect.  All these skills are acquired through lots of practice. 

The interesting thing about procedural learning and memory is that they can happen out of awareness.  That means that we learn to perceive regularities and sequences in the stimuli surrounding us, even when we are not aware of it and certainly don't pay attention and effort to it.

In this study done by Yafit  Gabay  , Rachel Schiff  and Eli Vakil of Bar Ilan university in Israel, procedural learning was examined with adults with dyslexia.

Dissociation between the procedural learning of letter names and motor sequences in developmental dyslexia.  Yafit  Gabay  , Rachel Schiff  , Eli Vakil.  Neuropsychologia 50 (2012) 2435–2441

The researchers used a procedure called serial search task.  University students with and without dyslexia saw four letters presented on a computer screen, and heard the name of one of the letters.  Upon hearing the letter name, they pressed one of four possible keys – the one that was in a corresponding position to the visual representation of the letter that was named. This was repeated again and again.  The order of letters presented on the screen changed each trial, and so did the letter that was named.   For half of the participants, the order of key presses created a specific recurrent motor sequence.  For the other half, the order of the letters named created a specific pattern.  The participants were not aware of the existence of a motor sequence or a letter sequence.

Both student groups, with and without dyslexia, implicitly learned the motor sequence.

How did the researchers know this?

During performance, the participant's reaction times for the motor sequence became shorter. This was one of the signs that they were learning the sequence even though they were not aware of it.  But when the specific motor sequence was changed to a random motor sequence, the participant's reaction times became longer.  When the motor sequence was reinstated, the reaction times became shorter again.

But students with dyslexia could not learn the letter name sequence!  Their reaction time for the letter name sequence did not become shorter, while the reaction time of students without  dyslexia did.  When the letter sequence was altered to a random sequence, the reaction time of the students without dyslexia became longer, while the reaction time of the students with dyslexia did not change.

What does that mean?  The authors interpret the results as showing that people with dyslexia have difficulties learning procedures with linguistic components.  This argument was supported in this study by a learning task that is outside awareness (implicit learning).  This finding is joined by findings from explicit learning tasks: children with specific language disability have a severe difficulty to repeat nonwords.  The difficulty mounts  as the number of syllables in a word rises.  Repeating nonwords is a task that requires serial processing with a linguistic component.  Learning to pronounce a new word is a procedural learning task. 

Difficulty with serial learning impacts the ability to acquire grammar.  This argument is also supported by an interesting procedural learning task:  artificial grammar learning.  In this task, a person memorizes sets of letter sequences that appear random, but are formed by a complicated set of rules (an "artificial grammar").  After the memorizing phase, the person is presented with new sets of letter sequences.  Some of the sequences are built by the "grammar" rules and some are not.  The person is asked to sort the new "words" into "grammatical" words and "nongrammatical" words.  Although people are usually unable to describe the sorting rule, and often say they are only guessing, they do succeed in sorting above chance level.  That means they have implicitly learned the "grammar".  It appears that children with dyslexia are not able to perform this sorting task.

Identifying the psychological/cognitive ability underlying achievement difficulties - important or redundant?

During the summer I ran into this article:  Psychiatrists split on whether to ditch DSM by Antony Funnell,  which  deals with the debate in the psychiatric community concerning the DSM5.  This article enlightens an aspect related to an issue that was discussed here – the relations between cognitive abilities and reading, writing and math achievement.  Funnell writes, that psychiatrists around the world, led by the US NATIONAL INSTITUTE OF MENTAL HEALTH are in open revolt against the DSM5, demanding that psychiatry be based on science and not on conjecture.  Traditional psychiatry, these psychiatrists say, relies too much on diagnosis based on symptoms  and  clinical observations .  Treating people coping with psychiatric conditions by the symptoms they present is not reasonable, just as it's not reasonable for a physician to prescribe the same medicine for everybody who feels chest pain, regardless of the pain's reasons: heartburn, a   muscle spasm or cardiac arrest. 

Here we reach the differences between SLD (specific learning disability) definition according to CHC theory, as developed by Flanagan, and SLD (specific learning disorder) definition according to the DSM5.  The essential elements of both definitions are presented here, along with the main differences between them.

As written in the presentation, Flanagan's definition requires linking the symptoms (the difficulties the child has in achievement) to the psychological/cognitive disabilities that lie at their base (empirically or reasonably).  The developers of the DSM5 definition, represented here by Rosemary Tannock, write in the DSM5 text, that specific learning disorder is "a neurodevelopmental disorder with a biological origin that is the basis for abnormalities at a cognitive level that are associated with the behavioral signs of the disorder".  But they argue that the relations between deficits in psychological/cognitive processing and reading are not proven enough (they are probabilistic and not deterministic).  That is, it's not possible to use a specific cognitive profile to confirm or reject the diagnosis of  a reading learning disability disorder, and the psychological processes underlying math and written expression difficulties are not clear.

The proponents of the CHC/Flanagan definition would agree with the claim, that learning disability cannot be diagnosed only on the basis of the child's cognitive profile.  Even if the cognitive profile shows difficulties, as long as they don't affect the child's daily functioning in the achievement domains (reading, writing, math), the child cannot be diagnosed as learning disabled according to this definition.

If the cognitive profile is not enough to diagnose learning disabilities, why is it needed at all?

It's evident, that treating and addressing the symptoms only (that is, remediating reading, writing or math directly)  - only partially   alleviates the problems in learning disabled children.  If we could prove in a   convincing way, that treating the cognitive disability improves the child's achievement in reading, writing or math, we would be able to say that identifying the cognitive/psychological difficulty underlying  the lowered performance in the achievement domains, will help us   plan an intervention that will assist the child more than treating the symptoms only. 

Our goal should be, in my view, to strengthen that evidence base (of the relations between treating/strengthening cognitive abilities and improvement in the achievement domain) so that we'll be able to reach an evidence based diagnostic practice.  Otherwise, the diagnosis of learning disability will remain an empty and a general lable,  that is not conducive to efficient treatment for the specific   child being diagnosed.

Learning disabilities definition steps

In order to define a child as "learning disabled", the following five main step/conditions have to be met.  These five steps are an application of CHC theory to the field of learning disabilities. 

To note: CHC is a theory about the structure of cognitive abilities and not about learning disabilities, but it can be applied to learning disability definition.  (You can find out more about CHC theory and cognitive abilities in the presentation series "intelligence and cognitive abilities" found at the right column of this blog.  This series also gives information about which tests measure which abilities).

These five steps are my abbreviation of the process detailed in this article (and many others) of which I already recommended here before:

INTEGRATION OF RESPONSE TO INTERVENTION AND NORM-REFERENCED TESTS IN LEARNING DISABILITY IDENTIFICATION:

LEARNING FROM THE TOWER OF BABEL. 

DAWN P. FLANAGAN , SAMUEL O. ORTIZ, VINCENT C. ALFONSO and

AGNIESZKA M. DYNDA.  Psychology in the Schools, Vol. 43(7), 2006

This is a free article.  The definition steps are somewhere in the middle of it. 

These five steps are serial and dependent on each other.  If a child does not "pass" step 1, he doesn't have learning disability and there's no need to check if he passes step 2.  If he passes step 1 but doesn't pass step 2, clearly he doesn't have learning disability and there's no need to continue to step 3 and so on.

Step 1:  reading decoding and/or reading comprehension and/or basic writing and/or expressing complex ideas through writing and/or math are significantly lower than expected for the child's age and grade (the child's results in tests that measure reading/writing/math are lower than average for his age and grade by at least one standard deviation).

Note that we are not talking here about the child's grades in various school subjects.  We are talking about the basic skills of reading/writing/math as measured by specific tests for reading/writing/math.

Nor are we talking about measures like phonological processing, rapid naming etc.  We are talking only about measures of reading/writing/math themselves, like reading speed, word decoding precision etc.

Step 2:  One (or more) cognitive ability (fluid ability, short term memory, processing speed, visual processing, auditory processing, long term storage and retrieval, crystallized knowledge) is significantly lower than expected for the child's age and grade (the child's results in tests that measure a specific ability or this ability's index score are lower than average for his age and grade by at least one standard deviation).

Step 3:  There is an empirical or a logical link between the findings in step1 and the findings in step 2.  We want to see whether the low cognitive ability/abilities found in step 2 can explain the child's reading/writing/math difficulties.

For example, if the child has poor word decoding, and poor auditory processing (especially phonological processing), we can assume that the decoding difficulties are due to the phonological disabilities. 

This step assumes that the child's functioning in reading/writing/math is a symptom of disabilities found in one or more cognitive abilities.  The disabilities are not in reading/writhing/math.  The disabilities are in the cognitive abilities and they are expressed in reading/writing/math.

Step 4:  most of the child's cognitive abilities (fluid ability, short term memory, processing speed, visual processing, auditory processing, long term storage and retrieval, crystallized knowledge) are within normal limits.

This step emphasizes that learning disability is a specific phenomenon and not a global, wide-scale one.   A child who functions poorly at most abilities is not learning disabled according to this definition.  It's certainly possible that this child will have learning disabilities as well, but it's reasonable to assume, that they will not be the main reasons for his poor functioning in reading/writing/math.  The main reason for these difficulties would be low ability.

Step 5:  exclusionary factors are not better explanations of the child's poor performance in reading/writing/math.  If the child's parents are going through divorce and the child is preoccupied with this and can't concentrate in class, or if the child has significant other emotional problems that impair his functioning, or if the child has just immigrated or had poor teachers or switched schools too often etc.  - these factors might explain the poor performance in reading/writing/math better than a learning disability. In this case we won't define the child as having learning disability.

As in the previous step, it's possible that a child whose main reason for poor functioning is exclusionary factors, also has learning disabilities.  But because learning disability is not the main reason for his difficulties, we won't define him as learning disabled.  It's possible that in the future, after the family situation stabilizes or after the child get therapy and so on, we'll assess him again and see if the main problem then would be learning disability. 

Only if the child "passes" all five steps, he can be defined as learning disabled and the source of his disability can be identified (this is the low cognitive ability/abilities that we found in step 2).

This is a "narrow" definition.  Working in light of this definition will reduce the number of children identified as learning disabled.  I can add from my own and my colleagues' experience, that using these steps makes the picture clear and helps pinpoint the reasons for the child's difficulties and plan an intervention targeted at the source of the problem.

The definition can be summarized in one sentence:

Below average aptitude – achievement consistency within otherwise normal ability profile.

Aptitude is measured by cognitive abilities, achievement is measured by reading/writing/math tests.  Below average aptitude – achievement consistency:  the child's low functioning level in a specific cognitive ability fits his low performance pattern in reading/writing/math.