Chapter 6: Identification models

Alsamani, Omar A.

The students are the same, and so is the need, yet the decision changed with the model each school relies on. That is why understanding identification models is a practical necessity for every team.

Chapter objectives

Introduction

No single test can detect a learning disability or giftedness; both are judgments built on multiple sources of evidence. A team therefore needs a model that specifies which evidence is gathered, how it is combined, and where the dividing line falls. Choosing a model is a decision with direct consequences for students. As the opening scene shows, the same student may be considered to have a learning disability under one model and not under another, and in giftedness the rule for combining scores changes who is identified as gifted and who is excluded. Understanding the logic and limits of each model is a prerequisite for reading the regulations within which a team works, and for recognizing what those regulations leave to its professional judgment.

We open the chapter by explaining why a decision model is needed (Section 6.1), then present the discrepancy model and the criticisms leveled at it (Section 6.2), followed by response to intervention, the dual-discrepancy criterion and when nonresponse can be determined (Section 6.3). We then take up the patterns of strengths and weaknesses model in its three versions and the debate surrounding it (Section 6.4), the hybrid models with a worked case (Section 6.5), and multiple-criteria models in giftedness, combination rules, universal screening and local norms (Section 6.6). We close by comparing the models and reading the Saudi regulations in their light (Section 6.7).

6.1Why do we need a model?

Some categories have relatively clear criteria: hearing impairment is measured with audiometric equipment, and autism spectrum disorder has detailed criteria in the Diagnostic and Statistical Manual of Mental Disorders, Fifth Edition, Text Revision (DSM-5-TR; American Psychiatric Association, 2022). Two categories in particular, however, need a model that specifies how we reach a decision: learning disabilities, because no single test detects them, and giftedness, because its very definition differs from one system to another. A model answers three questions: What evidence do we gather? How do we combine it into a decision? And where do we set the line?

In this chapter, “learning disabilities” names the educational category that qualifies for services in school systems, and “specific learning disorder” (Specific learning disorder) is used when the discussion concerns the DSM criteria. The two concepts are close, each has its own criteria, and we set them side by side in Section 6.5.

6.2The discrepancy model

For decades, the discrepancy model (Discrepancy model) was the most widely used approach to identifying learning disabilities. Its idea is simple: a student with a learning disability is intellectually capable, but his achievement in a particular area falls well below what his ability would predict. In other words, there is a discrepancy between ability and achievement (Ability-achievement discrepancy). It is usually calculated as the difference between the standard score on an intelligence test and the standard score on an achievement test, and the difference must reach a set threshold, such as one and a half standard deviations, that is, 22.5 points on a scale with a mean of 100 and a standard deviation of 15.

Why has the discrepancy model been criticized?

For these reasons, the U.S. Individuals with Disabilities Education Act (IDEA), as amended in 2004, and its implementing regulations provide that states may not require schools to use a discrepancy, must permit the use of a process based on response to intervention, and may permit other research-based procedures (U.S. Department of Education, 2006, 34 CFR §300.307).

6.3Response to intervention

The response to intervention model (Response to intervention, RTI) turns the question around. Instead of asking “Is there a gap between the student’s ability and achievement?”, it asks “Does the student learn when we provide sound, evidence-based instruction?” If the student does not learn despite good instruction from which peers have learned, that is evidence of a difficulty requiring more than ordinary teaching (Fuchs & Fuchs, 2006). The model is usually implemented in three tiers:

The broader framework that encompasses academic and behavioral domains together is called a multi-tiered system of supports (Multi-tiered system of supports, MTSS). The idea is the same: support that intensifies with need, and decisions based on repeated data. The best-known source of such data is curriculum-based measurement, presented in Chapter 4: brief, equivalent probes administered every week or two, such as the number of words a student reads correctly in one minute, with results graphed to show whether the student is moving toward the goal.

The dual-discrepancy criterion

How do we know that a student “has not responded”? One of the best-known criteria is the dual discrepancy (Dual discrepancy), which Lynn Fuchs proposed as a basis for response decisions (Fuchs, 2003): the student is clearly below peers in the level of performance and also below them in the rate of growth despite intervention. A low-performing student who grows at the same rate as peers, or faster, is responding to intervention and simply needs time. A low-performing student who grows slowly, however, is falling further behind peers and needs more.

When do we say a student has not responded?

“Nonresponse” is a judgment built on a criterion and a threshold set in advance, not on a general impression. Table 6.2 presents the best-known criteria in the literature, with examples of thresholds that have been used in research and practice and the limitations of each. The thresholds here are illustrative and vary from study to study. Some are expressed as percentile ranks, that is, the percentage of peers in the comparison sample (the norm sample or the students in the grade) who scored below the student; a rank of 25 means that the student outperformed 25% of them.

The deeper problem is that these criteria do not identify the same students. When different criteria were applied to the same sample of poor readers, agreement among them on who “had not responded” was generally weak (Barth et al., 2008). The decision thus depends as much on the criterion the team chose as on the student. Added to this is what Ardoin and colleagues found in their review of curriculum-based measurement decision rules: most of these rules rest more on expert opinion than on research, slopes calculated over short periods are unstable, and they shift with variation in the difficulty of passages that are supposed to be equivalent (Ardoin et al., 2013). Three practical conclusions follow: the team should set its criterion and threshold before collecting data, not after; it should collect data over a sufficient period using passages that are truly equivalent; and it should treat the slope as it would any score, that is, as a range of plausible values.

Strengths and limitations of the model

Criticism of the model also comes from the opposite direction. Reynolds and Shaywitz argued that response to intervention has not yet proven its validity as a diagnostic tool, that relying on it alone turns “wait to fail” into “watch the student fail,” that it leaves the question of cause unanswered, and that it may overlook the high-ability student who struggles relative to his own ability rather than relative to his peers (Reynolds & Shaywitz, 2009). This criticism does not cancel the model’s value for early intervention, but it reminds us that nonresponse is one piece of evidence, to be combined with others in a comprehensive evaluation.

6.4Patterns of strengths and weaknesses

The patterns of strengths and weaknesses model (Patterns of strengths and weaknesses, PSW) seeks to restore to diagnosis a question that response to intervention leaves aside: why is the student struggling? It holds that a learning disability is linked to a weakness in a specific cognitive process, such as phonological processing, the ability to perceive, remember and manipulate speech sounds, or working memory, while other abilities remain intact. It therefore looks for a pattern with three corners (Flanagan et al., 2018):

Under this model, a student is classified as having a learning disability in reading, for example, if his general abilities are good, he has a weakness in phonological processing, and his decoding achievement is low, because decoding depends on phonological processing. If, on the other hand, he has a weakness in processing speed and a weakness in reading comprehension, the theoretical link between the two is weaker and the pattern less convincing.

Three versions of the model

The model has three well-known versions that share the logic of the triangle but differ in their theoretical framework and in how “strength” and “weakness” are established. Table 6.4 compares them:

The debate over the model

Proponents argue that the model is consistent with the original concept of learning disability as a disorder in basic psychological processes, and that it offers an explanation of the problem that may guide intervention. Studies that have examined it, however, have found important problems. In a simulation study of the three versions, they were good at ruling out students without a disability, that is, highly specific, but weak at identifying students who actually had one; many of those they identified did not carry the “true” pattern on which the simulation was built, and they identified only small proportions of students (Stuebing et al., 2012). An applied study found that the model’s methods often disagree about who has a disability and who does not, and that their identification rates are low and inconsistent (Miciak et al., 2014). Nor has it yet been shown that tailoring intervention to a cognitive profile improves outcomes more than direct academic intervention. Part of these problems stems from what we saw in the discrepancy model: the pattern rests on differences between scores, and difference scores are less reliable than the scores themselves.

The model’s developers respond that these studies treat it as a mechanical algorithm, whereas, as proposed, it is a framework for organizing evidence within a comprehensive evaluation, one that draws data from multiple sources and methods, including response-to-intervention data, and that is judged through clinical reasoning rather than numerical comparisons alone (Flanagan et al., 2018). They hold that understanding the cognitive weakness helps in choosing accommodations and explaining nonresponse, even if it has not yet been shown to improve the design of the intervention itself. The model therefore remains the subject of genuine scientific debate to this day.

6.5Hybrid models

After two decades of debate, many researchers lean toward a hybrid model (Hybrid model) that combines the best of the earlier models and drops what has proven weak. One of its best-known versions is the model proposed by Fletcher and colleagues (Fletcher et al., 2019), which rests on three criteria that must all be met:

Note that this model requires neither an intelligence test to calculate a discrepancy nor an analysis of cognitive processes. It may, however, use an intelligence test for another purpose: to rule out intellectual disability and to gain a fuller understanding of the student (Chapter 8 examines the application of this model to learning disabilities in detail).

The hybrid model is very close to the DSM criteria for specific learning disorder, which makes it a bridge between medical diagnosis and educational eligibility. The DSM requires that the difficulties persist for at least six months despite interventions targeting them (Criterion A), which corresponds to nonresponse. It requires that academic skills be substantially and quantifiably below those expected for the student’s age, as confirmed by standardized achievement measures and a comprehensive clinical assessment (Criterion B), and for this it suggests a threshold of about 1.5 standard deviations below the mean, with leniency down to one standard deviation when other evidence supports it. It requires that the difficulties begin during the school years (Criterion C). And it requires that they not be better explained by intellectual disability, uncorrected visual or auditory acuity, another mental or neurological disorder, psychosocial adversity, limited proficiency in the language of instruction, or inadequate instruction (Criterion D) (American Psychiatric Association, 2022). Note that the DSM compares achievement with what is expected for age; it does not require a discrepancy from intelligence.

A worked case using the hybrid model

Nayef, 9 years 8 months, fourth grade

All three criteria met

Background: Since first grade, Nayef’s teacher had noticed that he sounded out words slowly, guessed words from their first letters, and avoided reading aloud. He understands what is read to him well and takes part in oral discussion. In the universal screening at the start of fourth grade, his reading fluency was at the bottom of his grade, so the school began tiered support with him, with weak decoding as the initial hypothesis.

Step one: tier data. The team set its decision criterion in advance: dual discrepancy, meaning that both his level and his slope fall one standard deviation or more below his grade’s mean after two tiers of support.

Table 6.5: Nayef’s curriculum-based measurement data across the three tiers (words correct per minute; hypothetical figures).
Level	Duration and support provided	Start	End	Weekly slope	Comparison with grade
Tier 1	Regular classroom instruction; screening in week 1 and a confirmatory measurement two weeks later	38	40	—	Grade median 92; Nayef ranked sixth from the bottom among the school’s 100 fourth graders
Tier 2	12 weeks, 4 sessions a week of 30 minutes each, in a group of 4 students, using an explicit decoding program; weekly measurement	40	46	0.5	Grade slope over the same period about 1.0
Tier 3	14 weeks, a daily session of 30–40 minutes, individually or with one other student, using an intensive decoding and fluency program; weekly measurement	46	55	0.64	Grade median at the end of the period 120, SD about 25; grade slope 1.0, SD about 0.3

Figure 6.5: Nayef’s reading fluency across the three tiers (hypothetical data). His slope rose slightly in Tier 3 but remained below his grade’s slope, so the gap widened instead of narrowing.

Reading the data: Nayef’s final level is 55, against 120 for his grade, or about (55 − 120) ÷ 25 ≈ −2.6 standard deviations. His Tier 3 slope is 0.64, against 1.0, or about (0.64 − 1.0) ÷ 0.3 ≈ −1.2 standard deviations. The dual discrepancy is therefore present. Before treating it as evidence about the student, the team checked treatment fidelity: 86% of the planned sessions were delivered, Nayef missed 4% of them, and two observations by the supervisor using the checklist showed 90% adherence to the program’s steps. The intervention was thus delivered largely as planned. And because a slope calculated from 14 weeks remains an imperfect estimate, note that the judgment does not hinge on its exact value: even if his true slope were two-tenths higher, it would still fall below the grade’s slope, and his level would still be far from the grade’s.

Step two: standardized achievement and exclusion. With the family’s written consent, a comprehensive evaluation was conducted:

Table 6.6: Results of Nayef’s comprehensive evaluation (hypothetical standard scores with a mean of 100 and SD of 15; 95% confidence intervals).
Source	Result	What it means
Standardized word-reading test (reliability 0.95)	76 (69–83)	About 1.6 standard deviations below the mean, with the entire confidence interval below 85
Standardized reading-comprehension test	84 (77–91)	Higher than word reading, and affected by weak decoding in longer texts
Listening comprehension	101	He understands language when it is read to him, so the problem lies in decoding, not in language
Individual intelligence test, for exclusion rather than to calculate a discrepancy	Full Scale IQ 97 (91–103)	Does not indicate intellectual disability
Vision and hearing screening this year	Both normal	Sensory problems do not explain his difficulty
School record and family interview	Arabic is the home language; regular attendance since first grade; reading difficulty noticed since first grade	Not explained by weakness in the language of instruction or lack of opportunity to learn
Behavior rating scale completed by the teacher and the mother	Within the normal range, with clear avoidance of reading tasks	No emotional disturbance explains the picture; the avoidance is most likely a result of the difficulty, not its cause

Step three: matching the evidence to the criteria.

Table 6.7: Nayef’s evidence against the criteria of the hybrid model, the DSM and the Saudi regulatory text.
Issue	Hybrid model	DSM (DSM-5-TR)	Saudi Regulations
—	✓ Dual discrepancy after two tiers, with acceptable treatment fidelity	✓ Criterion A: 26 weeks, about six months of targeted intervention	✓ Evidence that regular services are “of limited effectiveness” documented with data
Achievement	✓ 76 in word reading	✓ Criterion B: 76, below the 1.5 SD cutoff (78)	? A “clear discrepancy” between ability (97) and achievement (76), and the text does not specify its size (see The lesson)
Start	—	✓ Criterion C: since first grade	—
Exclusion	✓	✓ Criterion D	✓ No mental or sensory impairment and no behavioral disorder

Nonresponse ✓Documented dual discrepancy

Achievement ✓76 (69–83)

Exclusion ✓No other explanation

Decision: Nayef is identified as a student with a learning disability in reading, specifically in decoding and fluency, and he meets the criteria for specific learning disorder with impairment in reading. Continued intensive individual intervention is recommended within an individualized education program, with measurable goals in decoding and fluency, along with accommodations in other subjects, such as reading questions aloud to him and allowing extra time, so that his achievement in science, for example, does not measure his reading instead of his understanding. His slope should be monitored every two weeks and the plan reviewed after one term.

The lesson

Had the team relied on the simple difference with a cutoff of 1.5 standard deviations, Nayef would not have been identified, because the difference between his intelligence (97) and his reading (76) is 21 points, below 22.5. Under regression, however, his expected achievement is about 98, and his reading falls about 22 points below it, exceeding the cutoff of 18. The judgment about the same student changed with the formula, even though his need did not. This is precisely what the hybrid model avoids: it bases the decision on what no one disputes, namely clearly low achievement, documented nonresponse, and the exclusion of other explanations.

What evidence could change the decision? If a retest of word reading with another standardized instrument came out close to average, or if his slope accelerated clearly, approaching his grade’s slope, when measured with passages of established equivalence, the team would need to revisit the identification. And if a weakness in listening comprehension or in hearing emerged on re-examination, another explanation for his difficulty would have to be considered.

6.6Multiple-criteria models in giftedness

In most systems it is no longer acceptable to identify a gifted student by a single intelligence score. In contemporary theories, giftedness encompasses intellectual ability, creativity, motivation and achievement in a particular domain, and it interacts with the environment and with opportunity (Gagné, 2009; Renzulli, 1978). Identifying gifted students therefore draws on multiple sources of evidence: an ability test, an achievement test, a teacher rating scale, a portfolio and perhaps a creativity test.

Gathering multiple sources of evidence, however, raises a question that is often overlooked: how do we combine them into a decision? An important study showed that the method of combination, known as the combination rule (Combination rule), by itself changes how many students are identified as gifted, and which students they are, even when the instruments and scores are identical (McBee et al., 2014). There are three main rules:

The three rules in numbers

Let us apply the rules to seven hypothetical students, each with two standard scores, one on an ability test and one on an achievement test, with a cutoff of 120 on each. Under the “and” rule both scores must reach 120; under the “or” rule one is enough; under the averaging rule their mean must reach 120.

The scores are the same, yet the number identified ranges from one student to six. Three observations in the table deserve attention. First, Student E has an ability score of 140 and an achievement score of 95, a pattern that may point to twice-exceptionality or to limited opportunities to learn; this student is identified only under the “or” rule, because the averaging rule lets the weakness consume the strength. Second, Students C and D are very close: the difference between 121 and 118 is too small to be trusted, since the standard error of a test with a reliability of 0.95 is about 3.4 points. Even so, one of them is identified under two rules and the other under none. Third, each rule errs in its own way. The “or” rule gives measurement error on every criterion a chance to lift a student above the cutoff, increasing false identifications, while the “and” rule gives it a chance to push a student below the cutoff on any criterion, increasing false exclusions (McBee et al., 2014). Choosing a rule, technical as it may appear, is therefore a decision about which of the two errors a program is willing to accept, and it should follow from the program's definition of giftedness and the services it provides.

Universal screening and local norms

One of the greatest sources of inequity in gifted identification is reliance on nomination alone instead of universal screening (Universal screening), which is applied to all students. A student whom the teacher does not nominate, because the student is quiet, speaks a different home language, or has a difficulty that masks ability, never enters the assessment at all. A study in a large U.S. school district found that adding universal screening of all second graders markedly increased the representation of students from low-income and minority families in gifted programs (Card & Giuliano, 2016).

Likewise, comparing a student with national norms can exclude an entire school's students in a less advantaged setting, despite their clear superiority over their peers there. Researchers therefore propose using local norms (Local norms), which identify the highest-performing students in each school relative to their schoolmates, because these are the students who need services beyond what their classroom offers (Peters et al., 2019). (Chapter 12 addresses this in detail.)

6.7Comparing the models and reading the Saudi regulations

Conclusion

We conclude in this chapter that every identification model accepts some kind of error in exchange for what it offers. The discrepancy model is simple, but it delays help and fluctuates with measurement error. Response to intervention offers help early and rules out poor instruction as an explanation, but it does not explain why a student fails to respond. Patterns of strengths and weaknesses are high in specificity and low in sensitivity, and hybrid models combine nonresponse, low achievement, and exclusion. In giftedness, the combination rule determines who is identified and who is left out. It follows that a team should recognize the kind of error accepted by the model it works with, should not let the label “slow learner” become a verdict that closes the question of what the student needs, and should not allow response to intervention to become a reason for delaying assessment.

Some questions remain unsettled by research, such as the value of patterns of strengths and weaknesses for guiding intervention and the weak agreement among nonresponse criteria. Also open in the Saudi context is the fact that, for learning disabilities, the regulations prescribe discrepancy, exclusion, and the ineffectiveness of regular instruction without a numerical cutoff, leaving the cutoff to the team's discretion, and that, for giftedness, they use different combination rules, the most consequential being the cognitive abilities requirement of 120 for gifted classes.

6.8Summary, key terms, and activities

Chapter summary

Glossary of terms

Review questions

Case for application: Lujain, age 13, Grade 7

The story: Lujain moved with her family from another region in the middle of sixth grade; this is her third school since fourth grade. Her teacher says she “understands the explanation but falls apart in arithmetic.” She counts on her fingers to add small numbers and takes a long time on multiplication problems. Her grades in other subjects are average. The school placed her in Tier 2 support in mathematics and then, at her family's request, referred her to the assessment team.

Table 6.11: Evidence available on Lujain at referral (hypothetical data).
Source	Result
Tier 2 in mathematics	10 weeks, three sessions a week; 55% of planned sessions were delivered because of scheduling conflicts; no session was observed with a checklist
Curriculum-based measurement in computation (correct digits in two minutes)	From 18 to 22, a slope of 0.4 per week; class slope about 0.8
Standardized test of arithmetic operations	81 (75–87)
Standardized test of mathematical reasoning	88 (81–95)
Individual intelligence test	Full Scale IQ 92 (86–98)
Vision and hearing screening	Last recorded screening in first grade
School record	Absent about 20% of school days last semester because of the move; no data from the two previous schools

Tasks: (a) Apply the three criteria of the hybrid model to the evidence, and for each criterion state whether it is met, not met, or unresolved, with your reasoning. (b) Match the evidence against the DSM criteria for specific learning disorder, especially Criteria A and D. (c) Does the evidence meet the conditions of the Saudi regulations? (d) What is your decision now? What three pieces of evidence would you request before the final decision, and how would you gather them without delaying Lujain's access to support?

Learning activities

For any activity that uses real student data: it is conducted with the consent of the family and the school administration, without any data that identify the student, and under professional supervision; no decision is based on its results, and they are communicated only through official channels. All the activities can be carried out with hypothetical data.

Student	Intelligence	Reading	Simple difference	Judgment	Expected	Below expected	Judgment
First (Figure 6.1)	105	78	27	✓	103	25	✓
High IQ	130	105	25	✓	118	13	✗
Slightly low IQ	85	68	17	✗	91	23	✓

Criterion	What it measures	Example thresholds used	Limitations
Normative final status	The student’s level on a standardized test after intervention ends	Remaining below roughly the 25th percentile (standard score 90) after intervention	Ignores the amount of progress; a student who started very low and made substantial gains may be judged a nonresponder
Benchmark	Whether the student reaches a level set for the grade and term	The number of words correct per minute set for the end of the term in that grade	Relies on norms that may not exist in Arabic, and is affected by the difficulty of the passage chosen for measurement
Slope	Weekly rate of growth during intervention	A slope below the 25th percentile of peer slopes, or below the slope needed to reach the goal on time	A slope calculated from only a few weeks is unreliable and is affected by variation in passage difficulty (Ardoin et al., 2013)
Dual discrepancy	Level and slope together	Both level and slope fall one standard deviation or more below the peer mean	Inherits the unreliability of the slope and is affected by the level of the reference class; the same student may be judged a responder in a weak class and a nonresponder in a strong one

Strengths	Limitations
Provides help early, without waiting for failure or a diagnosis	Requires high-quality instruction, evidence-based interventions and careful monitoring, which are unevenly available across schools
Rules out poor instruction as an explanation for the problem before the student is diagnosed	If used on its own, it may delay the evaluation of a student who needs a comprehensive evaluation immediately, such as one suspected of having an intellectual disability
Yields direct instructional data that are useful for planning	Does not explain why the student failed to respond, nor distinguish among the causes of nonresponse
Reduces misdiagnosis of students who simply need better instruction	May miss twice-exceptional learners, that is, gifted students with a learning disability, because their performance may not fall below that of their peers
Rests on repeated data rather than a single measurement	Nonresponse criteria often disagree with one another, and the reliability of slopes over short periods is limited

Format	Developers	Theoretical framework	How the pattern is established
Dual discrepancy/consistency (DD/C)	Flanagan and colleagues (Flanagan et al., 2018)	Cattell-Horn-Carroll theory of abilities and cross-battery assessment	A weakness in a cognitive ability and an academic weakness, both below average, with general ability “average or above” estimated from the intact abilities, and a theoretical consistency between the two weaknesses
Concordance-discordance (C-DM)	Hale and Fiorello (Hale & Fiorello, 2004)	School neuropsychology, with no commitment to a particular battery	Significance tests of differences based on the standard error of the difference: a significant discordance between the cognitive strength and each of the two weaknesses, and concordance between the cognitive weakness and the academic weakness, that is, a nonsignificant difference between them
Discrepancy/consistency (D/CM)	Naglieri (Naglieri, 1999)	PASS theory of four processes: planning, attention, simultaneous processing and successive processing	A significant discrepancy between the highest and lowest processes, with the weak process below average; consistency between the weak process and the weak achievement; and a discrepancy between the strong process and the weak achievement

Student	Ability	Achievement	Mean	“And” rule	“Or” rule	Averaging rule
A	128	126	127	✓	✓	✓
B	135	108	121.5	✗	✓	✓
C	121	119	120	✗	✓	✓
D	118	117	117.5	✗	✗	✗
E	140	95	117.5	✗	✓	✗
F	110	131	120.5	✗	✓	✓
G	119	122	120.5	✗	✓	✓
Number identified	—	—	—	1	6	5

Identification models