mclay2014 (1)

http://informahealthcare.com/pdrISSN: 1751-8423 (print), 1751-8431 (electronic)

Dev Neurorehabil, Early Online: 1–13! 2014 Informa UK Ltd. DOI: 10.3109/17518423.2014.899649

ORIGINAL ARTICLE

Variables affecting the emergence of untaught equivalence relations inchildren with and without autism

Laurie McLay1, John Church2, & Dean Sutherland1

1School of Health Sciences, University of Canterbury, Christchurch, New Zealand and 2School of Psychology, University of Canterbury, Christchurch,

New Zealand

Abstract

Objective: This study examined the formation of equivalence classes among children with ASDand typically developing children. Design: A single-subject AB and BA design was used.Methods: Two of the six equivalence relations were taught. Participants were then tested todetermine whether the remaining four equivalence relations were acquired without teaching.Half of the children were taught naming responses first, then selecting responses. Half weretaught in the reverse order. Results: Five out of 10 participants with ASD demonstrated theemergence of all four untaught relations. The remaining five participants showed variability.Nine of the 10 typically developing children demonstrated emergence of all untaught relations.Variation in teaching conditions had no significant effect on outcomes. Conclusions: Manychildren with ASD are capable of generalising to untaught equivalence relations. The results failto support the claim that acquisition of naming responses is a pre-requisite for the emergenceof untaught equivalence relations.

Keywords

Autism spectrum disorder, derivedresponding, equivalence relations,generalisation, numeracy

History

Received 14 January 2014Revised 24 February 2014Accepted 26 February 2014Published online 28 April 2014

Introduction

The development of equivalence relations is a type of

generalisation that is receiving increasing attention and

analysis. The pioneering research in this area was conducted

by Sidman and colleagues [1–6]. Sidman concluded that the

development of language is underpinned by the acquisition of

many sets of stimulus–response relations. When these sets of

stimulus–response relations demonstrate the three properties

of reflexivity, symmetry, and transitivity, they are said to form

an equivalence class [1, 7].

Reflexivity is demonstrated when a child demonstrates the

ability to perform generalised identity matching. For example,

when a child is presented with an example of stimuli from

the stimulus class A (i.e. quantity of four), they are able to

select a second matching example of A (i.e. quantity of four).

Symmetry refers to the reversibility of certain stimulus–

response relationships, such that if A and B are conditionally

related, then the reverse, that B is conditionally related to A,

is also true. For example, if a child is taught that the quantity

of four (A) is called ‘four’ (B) then the child would

demonstrate symmetry if they respond correctly to both the

question ‘How many is this?’ (i.e. A–B) and the question

‘Give me four’ (B–A). For transitivity to be demonstrated it is

necessary for there to be at least three pairs of symmetrical

equivalence relations. With transitive responding, if a child

learns to respond correctly to a pair of symmetrical responses,

they should then also acquire a third pair of symmetrical

stimulus–response relationships. For example, if a child

acquires the symmetrical relations A1–B1, and A1–C1, then

they should also acquire B1–A1, C1–A1, B1–C1, and C1–B1,

without requiring any additional teaching.

The equivalence class for the number ‘four’ is presented in

Table I. In this example, the teaching of the A1–B1 relation

(hear the word ‘four’ – select the quantity four) and the A1–C1

relation (hear the numeral ‘four’ – select the numeral 4) may

lead to the emergence of the B1–A1 relation (see the quantity

four – say the quantity ‘four’) and C1–A1 relation (see the

numeral 4 – say the numeral ‘four’) as a result of symmetry,

and the C1–B1 relation (see the numeral 4 – select the quantity

four) B1–C1 relation (see the quantity four – select the

numeral 4) as a result of transitivity. In this way, if a child is

taught two conditional relations (e.g. A1–B1 and A1–C1), they

usually acquire four additional relations (B1–A1, C1–A1,

B1–C1, C1–B1) without any further teaching. Given this

sequence, the teaching of just two discriminated responses can

result in the emergence of four additional discriminated

responses without further teaching. When this sequence

occurs, an equivalence class is said to have been formed.

Research conducted by Sidman and colleagues has

provided considerable support for the view that untaught

equivalence relations can emerge following the teaching of

stimulus–response relations for a variety of populations and

a variety of concepts. Sidman’s early findings have since

been replicated on many occasions [8–10]. In the majority

of the studies examined, the emergence of untaught relations

Correspondence: Laurie McLay, School of Health Sciences, Universityof Canterbury, Christchurch, New Zealand. E-mail: [email protected]

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was demonstrated given sufficient exposure to the training

stimuli.

A number of studies have also investigated the acquisition

of equivalence relations in children and adults with an

intellectual disability [11–17]. In the majority of these studies

most participants with an intellectual disability and/or brain

injury demonstrated emergence of untaught equivalence

relations when provided with sufficient practice opportunities

and appropriately sequenced training. The emergence of

untaught relations was not demonstrated in all studies

however. Devany et al. [18] reported the untaught equivalence

relations only emerged in the children who had some

language. In Saunders and McEntee’s study [19], repeated

testing was required before equivalence relations emerged for

some of the participants, and in another study some of the

participants demonstrated emergence for some of the rela-

tions, whilst some did not [8].

While there is a plethora of research into the development

of equivalence relations in typically developing individuals

and those with an intellectual disability, there have been fewer

studies involving children with autism spectrum disorder [20].

The research in this field has primarily included preschool-

to school-aged children and the concepts taught have

included Greek letter names [21], emotions [22], geographical

concepts [23], musical notation [24], noun labels [25],

money skills [26], activity schedules [27] and nonsense

stimuli [28–30]. These studies have examined the effect

of manipulating a variety of variables. Studies including

people with ASD have investigated the role of instruction

in naming [21], the effect of different feedback/consequence

procedures [23], the impact of a one-to-many or many-

to-one training structure [24], and the outcome of teaching

using complex auditory-visual stimuli in which AB-C

relations were taught [25, 28]. Three of these studies have

also included a comparison group of typically developing

children [28–30].

Many of the studies examining the emergence of untaught

equivalence relations in children with ASD have reported

outcomes where all the participants demonstrated the emer-

gence of untaught equivalence relations [23, 25, 27, 28, 30].

Some studies however, have reported variable findings.

Within each of these studies some of the participants

demonstrated the emergence of untaught equivalence rela-

tions, while others did not. There are several possible

explanations for the variability in the outcomes. These

include variation in the instructional conditions used during

teaching [21, 26, 29], whether or not instruction in naming

was provided, and the variability in the characteristics of the

participants.

First, the likelihood that the formation of equivalence

classes in individuals with ASD may depend on the type of

teaching provided receives some support in the research

literature. For example, some of the participants in

Experiment 2 of the O’Connor et al. study [29] required

additional multiple exemplar training and the use of familiar

stimuli before they demonstrated the emergence of symmet-

rical and asymmetrical relations. Furthermore, for some

participants in this study, it was evident that the emergence of

untaught relations improved when the teaching procedures

were individualized to take into account the needs of each

learner. Similarly, Arntzen et al. [24] found that the partici-

pant formed equivalence classes in both the MTO and OTM

conditions for all but one set of stimulus–response relations.

This set of stimulus–response relations was taught using the

MTO procedure and was a part of a four-member equivalence

class. This participant required retraining for some of the

taught relations before they responded successfully during

testing.

Secondly, it appears that instruction in naming may have a

facilitative effect on the emergence of untaught equivalence

relations for some children with autism. This suggestion is

supported by the research of Eikeseth and Smith [21] in which

the emergence of untaught relations appeared to be mediated,

at least in part, by teaching in which participants were

instructed to assign a common name to stimuli. Keintz et al.

[26] made a similar observation in their study where one

participant was unable to respond correctly when the correct

responding required verbal responses.

The research by Wynn and Smith [31] also supports the

possibility that the emergence of derived responses may be

effected by instruction in naming. Wynn and Smith [31]

investigated generalisation (a) from receptive to expressive

vocabulary and (b) from expressive to receptive vocabulary.

This cross-modal generalisation has similar properties to

those of symmetrical responding. The results of this study

indicated that teaching the child to say the word first, led to

a greater likelihood of generalisation to a receptive response

than the reverse. Each of these studies suggests the need for

further research into the effects of instruction in naming on

the emergence of untaught equivalence relations.

Table I. The stimulus–response relations for the number concept ‘four’.

Stimulus Taught response Type of relation

1. Child hears the word ‘four’A

Child selects the quantity 4B

ComprehensionA–B

2. Child sees the quantity 4B

Child says ‘four’A

Oral namingB–A

3. Child hears the word ‘four’A

Child selects the numeral 4C

Aural-written numeral matchingA–C

4. Child sees the numeral 4C

Child says the word ‘four’A

ReadingC–A



Reading comprehensionC–B



Quantity-numeral matchingB–C

2 L. McLay et al. Dev Neurorehabil, Early Online: 1–13

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A third possibility is that inconsistency in the findings to

date is a function of variation in the characteristics of

individuals on the autism spectrum. It is already clear that

some children with ASD require additional generalisation

training in order for response generalisation to occur [32–34]

while others do not. This suggests that children with ASD

vary with respect to the likelihood that they will generalise

skills that they are learning. Additionally, there is some

evidence that children with more advanced language skills

demonstrate the emergence of untaught equivalence relations

more rapidly than those children with less advanced language

skills [30].

In spite of the possibility that it may be the characteristics

of the learners that accounts for variation in equivalence class

formation, very few research studies investigating the forma-

tion of equivalence classes in individuals with autism have

reported on the individual characteristics of the participants.

Some studies have identified the language ability of learners

with ASD using standardized measures [21, 25, 28] and two

studies reported the results of IQ assessments [21, 24]. Few

other studies have reported such measures of participant

characteristics, and as a result, we cannot yet explain why

some children with ASD will demonstrate the formation of

equivalence classes, while some do not.

The research to date leaves several questions unanswered.

From a theoretical perspective, we are still unable to

conclude whether the formation of equivalence classes is a

basic learning process in human language acquisition, as

argued by Sidman and colleagues. While there is some

suggestion that stimulus familiarity and verbal ability may

affect equivalence performance [30], there is also evidence

that contradicts the role of verbal ability [8] and demon-

strates inconsistency across subjects in relation to the role

of naming [21].

In addition, there are examples in the literature where some

individuals with autism have demonstrated the formation of

equivalence classes while others have not. In spite of this

variation, the characteristics of the participants (i.e. their

cognitive functioning level, verbal ability and so on) have not

always been adequately documented, and this makes it

difficult to draw firm conclusions about the role of individual

differences in the emergence of untaught relations in children

with ASD.

Finally, we still do not yet have a clear understanding of

the teaching conditions that affect the emergence of untaught

relations in children with ASD. Further research is needed

into the affects of such variables as the teaching sequence, the

number of practice opportunities provided, the stimuli used,

the rate of reinforcement, and so on. This is particularly

important given the variation among the teaching strategies

and stimuli used in the research to date, and the lack of

replication of many of these procedures.

This investigation aimed to extend prior research by

examining several key questions. First, it included a com-

parison group of language-matched typically developing

children in order to identify more clearly the factors

associated with autism that may be affecting the ability of

children with this diagnosis, to form equivalence classes.

Secondly, this is the first study to investigate the formation of

numerical equivalence relations in children with autism.

Given the functional importance of number skills, it is

important to discover whether the current findings, with

respect to the development of stimulus equivalence generalise

to number concepts. Thirdly, we know little about whether

there are specific teaching conditions that may facilitate the

emergence of untaught equivalence relations. To date, few

studies have examined whether instruction that requires a

verbal response vs. instruction that requires a selection

response affects the likelihood of the emergence of untaught

equivalence relations among children with autism.

The specific research questions investigated in the present

study were (a) Is there variation in the degree of generalisa-

tion amongst children with ASD if prior learning of number

concepts has been controlled? (b) To what extent are there

differences in the likelihood of emergence of untaught

equivalence relations in children with ASD when compared

with typically developing children matched on levels of

language development? (c) Does the teaching of naming

responses first affect the likelihood that untaught equivalence

relations will emerge?

Methods

Participants

Two groups of 10 children took part in the present investi-

gations. Ten were children who had been diagnosed with ASD

(the Autism Group). Ten were typically developing children

(the Typically Developing Group). The children in the Autism

Group were recruited in various ways. This included profes-

sional contact with families, contact with schools, and contact

via local charitable and government service providers for

children with autism. The typically developing children in this

study were recruited through family contacts known to the

researcher. The typically developing children were not

recruited until each of the assessments, teaching, and testing

sessions had concluded for the 10 children with autism. This

ensured that the typically developing children were able to be

appropriately matched with the children in the autism group.

Selection into the experiment involved a three step screening

procedure: (1) initial screening, (2) number knowledge

screening, and (3) developmental assessment.

Initial screening

The children in the Autism Group and the Typically

Developing Group were included in the research if they

were using spontaneous mands or labels of at least one word,

were able to identify pictures by pointing to or retrieving the

item, demonstrated an ability and willingness to comply with

simple requests and had parents who were willing to give

informed consent for their child to participate. Children in the

Autism Group were also required to have a formal diagnosis

of Autism Spectrum Disorder as defined by DSM-IV [35].

The majority of the children in the Autism Group were

diagnosed by a developmental paediatrician or registered

clinical psychologist who was employed privately by the

parent/caregiver or appointed within the public education or

health sector. A variety of assessments were undertaken for

each child depending on the age of the child and the clinician

conducting the assessment. Children in the Typically

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Developing Group were required not to have any identified

diagnosis or learning difficulties, and were matched with

children in the Autism Group on their Peabody Picture

Vocabulary Test-IV score [PPVT-IV; 36].

Number knowledge screening

Prior to teaching, each child’s number knowledge was

assessed to ensure that, first, the child was not already

familiar with number concepts beyond 14 and, secondly, to

identify any pre-teaching that would be required. This

assessment was also used to determine the point in the

number sequence 1 to 14 where teaching was to commence.

The screening test sequence is outlined in Table II.

If a child was not able to identify or name and/or

comprehend written numerals and quantities beyond 14 then

they met the criteria for inclusion in the study. Children who

did not demonstrate any numerical understanding were taught

to count with correspondence up to 6, to ensure that they had

the pre-requisite skills necessary. The results of number

knowledge screening tests are presented for each child, in

Table III.

Developmental assessment

Prior to teaching, developmental assessments were adminis-

tered for participants in each group. Assessments included the

PPVT-IV [36], the Adaptive Behaviour Assessment System-II

[ABAS-II; 37] and tests for instruction following. Children in

the Typically Developing Group were included in the study if

they scored within the 3–4-year-old range on the PPVT-IV,

that is, within the range of PPVT-IV scores obtained by the

children in the Autism Group. A summary of each partici-

pant’s chronological age, PPVT-IV age equivalent score and

ABAS-II communication and functional academics/pre-aca-

demics scores are presented in Table III.

Setting and materials

Teaching and testing were undertaken in the individual child’s

home or education setting. Teachers and parents of each of the

20 children in the study were specifically asked to refrain

from teaching any of the number concepts being taught by the

researcher for the duration of the study. This request was

complied with in all cases.

Table III. Chronological ages, PPVT-IV scores, ABAS-II scores, and number screening test results for each of the 10 children in the autism group andthe typically developing group.

Participant C.A. PPVT-IVCOMParent

COMTeacher

FAParent

FATeacher

Screeningtest 1

Screeningtest 2

Screeningtest 3

Screeningtest 4

Screeningtest 5

Screeningtest 6

Screeningtest 7

Child 1 (M) 5:7 4:11 2 2 2 2 20 20 12 12 12 6 6Child 2 (M) 4:5 3:6 1 1 2 1 0 0 0 0 0 0 0Child 3 (M) 5:0 4:8 1 2 4 4 20 20 12 12 0 3 3Child 4 (M) 11:5 2:9 1 1 1 1 10 5 4 4 0 3 3Child 5 (M) 8:5 8:5 1 1 1 1 10 10 10 10 9 4 5Child 6 (M) 6:6 3:8 1 1 1 2 20 15 11 11 11 4 5Child 7 (M) 4:11 2:6 1 1 3 1 3 3 4 4 0 3 3Child 8 (M) 4:6 3:4 1 3 4 2 14 12 12 12 9 4 4Child 9 (F) 6:1 5:5 1 1 2 3 19 12 10 10 5 4 4Child 10 (M) 9:1 5:3 1 1 1 1 6 6 3 5 0 2 2Child 11 (M) 3:3 2:11 5 5 4 4 12 6 0 0 0 0 0Child 12 (F) 3:4 3:8 4 4 4 5 12 3 3 3 0 2 2Child 13 (F) 3:6 3:11 5 4 6 5 18 14 11 11 11 5 5Child 14 (F) 3:5 4:1 5 – 5 – 13 13 3 3 3 3 3Child 15 (M) 3:6 3:10 4 – 4 – 5 5 3 3 3 3 3Child 16 (M) 3:1 4:2 4 5 4 3 14 13 8 8 4 4 4Child 17 (M) 3:5 3:5 4 4 4 4 10 2 0 0 0 2 2Child 18 (F) 3:7 3:7 4 5 4 5 10 10 5 5 4 2 5Child 19 (M) 3:3 4:3 5 – 5 – 10 6 0 3 3 3 3Child 20 (F) 3:2 3:8 5 – 5 – 12 5 0 10 0 0 0

C.A.: Chronological age. PPVT-IV: Age-equivalent score in years and months. ABAS-II COM: communication. FA: functional academics. Parent:Parent ratings. Teacher: Teacher ratings.

1: Extremely Low, 2: Borderline, 3: Below Average, 4: Average, 5: Above Average, 6: Superior.Screening test 1: rote counting, Screening test 2: counting with correspondence, Screening test 3: oral naming of numerals, Screening test 4: numeral

recognition, Screening test 5: numeral comprehension, Screening test 6: quantity naming, Screening test 7: quantity comprehension.

Table II. The screening test sequence for each participant using the example of ‘four’.

Stimulus Response Relation

1. Child sees the numeral 4 Child says the word ‘four’ Numeral reading2. Child hears the word ‘four’ Child selects the numeral 4 Aural written number matching3. Child asked to count Child rote counts (no cubes present) Rote counting4. Child presented with cubes Child counts cubes Counting (one-to-one correspondence)5. Child sees numeral 4 Child gives 4 cubes Number comprehension6. Child sees the quantity card representing 4 Child says the word ‘four’ Quantity naming7. Child hears the word ‘four’ Child selects the quantity card representing 4 Quantity comprehension


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The teaching materials developed for the experiments

included one set of 10� 10 cm flashcards on which the

numerals 1–20 were printed and a second set of 10� 10 cm

flashcards that displayed the quantities from 1 to 20. The

colour, font and the size of the numerals and quantities was

consistent across all teaching materials during each phase.

Quantities were represented by black dots presented as

random arrays. Only one example was used to represent

each numeral and quantity.

Teaching conditions

This study included two teaching conditions. The first

teaching condition is called the ‘Select’ Condition. This

involved teaching the child the A–B relations (hear the word

‘one’ – select the quantity 1’) and the A–C relations (hear the

word ‘one’ – select the numeral 1), as shown in Table IV. The

second teaching condition, the ‘Name’ Condition, involved

teaching the child the B–A relations (see the quantity ‘1’ – say

the word ‘one’) and the B–C relations (see the numeral 1 –

say the word ‘one’), as shown in Table IV.

Six number quantities were taught. These were divided

into two sets: Set 1 which consisted of the first three

consecutive unknown number concepts and Set 2 which

consisted of the next three consecutive unknown number

concepts for each child.

Experimental treatments

The two teaching conditions were crossed with the two

sets of teaching content. The first experimental treatment

(the ‘Select First’ Treatment) involved teaching Set 1 and

Set 2 in the order ‘Select’ Condition first followed

by ‘Name’ Condition. The second experimental treatment

(the ‘Name First’ Treatment) involved teaching Set 1 and

Set 2 in the order ‘Name’ Condition first followed by

the ‘Select’ Condition. Half of the children in the ASD

Group were randomly assigned to the ‘Select First’

treatment and the remainder to the ‘Name First’ treatment.

The children in the Typically Developing Group were

randomly assigned to the two treatments in the same

fashion. The experimental design is shown in Table V.

Also shown in Table V are the numbers taught to each

child and the experimental treatment experienced by each

child, that is, the order in which the two teaching

conditions were experienced by each child in each of the

two groups of children.

Experimental design

This study used a single case within subject A–B design

replicated across the 10 children in the ‘Select First’ treatment

and the 10 children in the ‘Name First’ treatment.

Table V. Experimental design and teaching content for each participant in each experimental treatment.

‘Select first’ treatment ‘Name first’ treatment

‘Select’ condition ‘Name’ Condition ‘Name’ Condition ‘Select’ conditionASD groupparticipant

Number conceptstaught (Set 1)


ASD GroupParticipant

Number conceptstaught (Set1)


Child 2 1, 2, 3 4, 5, 6 Child 1 13, 14, 15 16, 17, 18Child 3 13, 14, 15 16, 17, 18 Child 5 11, 12, 13 14, 15, 16Child 4 5, 6, 7 8, 9, 10 Child 6 12, 13, 14 15, 16, 17Child 9 11, 12, 13 14, 15, 16 Child 7 5, 6, 7 8, 9, 10Child 10 6, 7, 8 9, 10, 11 Child 8 13, 14, 15 16, 17, 18

TD group participant TD group participantChild 12 4, 5, 6 7, 8, 9 Child 11 1, 2, 3 4, 5, 6Child 13 12, 13, 14 15, 16, 17 Child 14 4, 5, 6 7, 8, 9Child 18 6, 7, 8 9, 10, 11 Child 15 4, 5, 6 7, 8, 9Child 19 4, 5, 6 7, 8, 9 Child 16 5, 6, 7 8, 9, 10Child 20 2, 3, 4 5, 6, 7 Child 17 3, 4, 5 6, 7, 8

TD: Typically developing.

Table IV. The stimulus–response relations that were taught and tested during the ‘Select’ condition and the ‘Name’condition.

Stimulus Taught response Type of relation

1. Child hears the word ‘one’A


ComprehensionA–B


Child says ‘one’A

Oral namingB–A

3. Child hears the word ‘one’A


Aural-written numeral matchingA–C


Child says the word ‘one’A

ReadingC–A



Reading comprehensionC–B



Quantity-numeral matchingB–C

The ‘Select’ condition involved the teaching of comprehension and aural-written numeral matching relations.The ‘Name’ condition involved the teaching of oral naming and reading relations.

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General teaching procedure

The general teaching procedure consisted of the following

sequence of events: (a) reinforcer preference assessment, (b)

the teaching of prerequisite performance skills, (c) the

teaching of prerequisite number skills, (d) the first phase of

teaching using discrete trial teaching procedures, (e) testing

for the emergence of first phase untaught equivalence

relations, (f) teaching for the second phase using discrete

trial teaching procedures and (g) testing for the emergence of

second phase untaught equivalence relations.

Reinforcer preference assessment and reinforcement

procedures

A reinforcer preference assessment was conducted prior to

teaching and involved a two-step process. First, the parents of

each of the children were asked about their child’s preferences

in toys. A selection of these preferred toys was then available

for the child to choose from at the beginning of each session.

Prior to beginning teaching, a direct stimulus preference

assessment was conducted using up to six of the child’s most

preferred items. This process involved the simultaneous

presentation of each item, without replacement [38]. The

child was then asked to select one item to act as the reinforcer

for that session. This process was undertaken in order to

establish items that might function as reinforcers for each

individual child. The items that were used as reinforcers

differed for each child. The most commonly selected items

were preferred toys (e.g. trains).

A token system of reinforcement was implemented with

the children in both experimental groups. Tokens took the

form of laminated stickers designed to be velcroed onto a

laminated board. The children were required to earn from 6 to

12 stickers before being given a break and access to the

reinforcer that they selected for approximately 5 minutes.

Tokens were provided for independently correct responses

and for correct responses on trials involving prompts which

had been faded from the level provided in the preceding trial.

All 20 children required prior teaching in order to

familiarize them with the token system that was used. This

was done using identical picture matching tasks and the

stimuli used were materials that were unrelated to numeracy

(e.g. pictures of animals and pictures of clothing). During this

pre-teaching, the children were provided with a token

and verbal praise for each independently correct response.

When the child had received all of their tokens they were

given their choice of preferred item or activity for approxi-

mately 5 minutes.

Teaching method

The teaching method used in the present experiment was

discrete trial teaching [39]. Discrete trial teaching consists of

three parts. The first is the presentation of the discriminative

stimulus such as a question or a card plus a question. The

second is the behaviour or response which follows (e.g. the

child correctly identifies the item, fails to identify the item or

does not respond at all). If the child made an error, he or she

was provided with a prompt where the teacher repeated the

question and then modelled the correct response. During the

Select Condition teaching a hand-over-hand prompting

procedure was used. During the Name Condition teaching a

verbal model of the correct response was provided as a

prompt. Following unprompted correct responses, the child

was given a token and praise (e.g. ‘well done, that was it’).

Prompted responses were scored as incorrect.

Teaching of prerequisite skills

Before commencing teaching two children were taught pre-

requisite performance skills. Child 8 and Child 10 required

teaching in order to help them to understand how to respond

to the instruction ‘Point to___’. The screening assessments

described above identified various pre-requisite numeracy

skills which needed to be acquired. The discriminated

responses that were taught during pre-teaching sessions

varied for each child and were dependent upon the results

of the screening test. No comprehension skills were taught

regardless of the child’s level of skill in this area as this was

tested for during tests for the emergence of untaught

equivalence relations.

Whether children were taught pre-requisite skills as an

identification task or naming task was dependent upon

whether they were first taught according to the ‘Select’

Condition or the ‘Name’ Condition. If children were first

taught under the ‘Select’ Condition, then they were taught

pre-requisite skills as a receptive identification task. If the

child was first taught under the ‘Name’ Condition, then they

were taught the pre-requisite skills as an expressive naming

task. When individual children demonstrated that they were

able to identify or name numerals to an equal level (e.g. they

could both label the number five and identify number five)

and were also able to count six numbers beyond those

numbers which were to be taught in each of the teaching

conditions, then teaching commenced.

Teaching the targeted equivalence relations

In the ‘Select’ Condition, when relations A–B and A–C were

mastered for all three target numerals and quantities the

emergence of the untaught pairs B–A, C–A, B–C, and C–B

were tested. In the ‘Name’ Condition, when relations B–A

and C–A were mastered for all three target numerals and

quantities the emergence of the untaught A–B, A–C, B–C,

and C–B relations were tested. During teaching, taught

numerals/quantities were presented within a field of three.

Two of the numerals/quantities were the teaching targets and

one of the numerals/quantities was a mastered numeral/

quantity.

Teaching and testing schedule

The teaching and testing was scheduled so that each session

except the first began with a test for acquisition of one set of

taught stimulus–response relations. The child was then tested

for acquisition of the second set of taught stimulus–response

relations. Following these tests, teaching commenced for

stimulus–response relations not yet acquired. Tests for the

emergence of untaught stimulus–response relations were

conducted at the end of each session but only if the child

demonstrated that they had mastered all taught stimulus–

response relations. Four sets of tests were conducted. One set

for each of the four untaught stimulus–response relations.


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Testing procedures

Tests for taught relations

Three test trials were conducted per taught relation for each

of the two taught relations. If the participant responded with

3 out of 3 correct responses for one of the taught relations

then that test was repeated at the beginning of the next

session. A taught relation was considered to be mastered if the

child responded with 100% accuracy across the three test

trials for that relation across two consecutive days. If a child

responded incorrectly during a test then teaching for that

relation continued. Teaching and testing for the taught

stimulus–response relations only stopped when each of the

two taught relations for all three quantities were mastered.

Tests for untaught relations

At the point at which the learner demonstrated mastery of

both of the taught stimulus–response relations for all three

of the numerals and quantities in the teaching set, testing

for the emergence of the untaught relations commenced.

This involved three tests for symmetry and three tests for

transitivity. Where the child had been taught three ‘Select’

relations, they were tested for the emergence of the three

‘Name’ relations as the test for symmetry. Children who had

been taught the three ‘name’ relations were tested for the

emergence of the three ‘Select’ relations as the test for

symmetry. In both conditions, tests for numeral comprehen-

sion and quantity to numeral matching comprised the tests for

transitivity.

Tests for emergence were always undertaken on two

separate days. The first test was conducted on the day in

which the child demonstrated mastery of the three pairs of

taught relations. The second test was conducted either one or

two days later. Three testing trials were conducted per relation

for each of the four sets of untaught stimulus–response

relations. If the child responded incorrectly on one of the

trials and then proceeded to respond correctly on another trial

then on these occasions, four successive testing trials were

conducted.

A child was deemed to have demonstrated emergence of an

untaught relation if they responded with 100% accuracy

across the three test trials for that relation or, where four test

trials had been conducted, if three out of the four responses

were correct. If untaught relations did not emerge for some or

all of the relations then the testing procedure was repeated the

next day or as soon as possible thereafter. If untaught relations

did not emerge following the two tests then testing ceased

for the four untaught relations.

Results

Individual results

A summary of the results showing the teaching condition, the

chronological age, the total trials to criterion across the

‘Select’ Condition plus ‘Name’ Condition, the percentage of

derived relations that emerged in the ‘Select’ Condition and

the ‘Name’ Condition, and the total percentage of derived

relations is presented for each participant in Table VI.

As can be seen in Table VI, five of the 10 children in the

Autism Group were able to demonstrate the emergence of

both symmetry and transitivity under both teaching conditions

and were therefore able to demonstrate the ability to form 6-

member equivalence classes. For the remaining five children

with ASD, the emergence of untaught equivalence relations

was variable. Two children with ASD (Child 10 and Child 5)

demonstrated symmetry but not transitivity in both the

‘Select’ and ‘Name’ teaching conditions. Two children in

the Autism Group did not demonstrate emergence of any of

the untaught relations in the ‘Select’ teaching condition.

However, one of these students (Child 2) demonstrated

Table VI. Chronological ages, teaching condition, total trials to criterion and the results of testing for derived relations for each child in the autismgroup and the typically developing group.

ChildExperimental

Treatment Group Chronological ageTotal trialsto criterion

Derived relations‘Name’ Condition

Derived relations‘Select’ Condition

Total derivedrelations

2 ‘Select’ Autism 4.5 306 0% 100% 50%3 ‘Select’ Autism 5.0 175 100% 100% 100%4 ‘Select’ Autism 11.5 332 0% 50% 25%9 ‘Select’ Autism 6.1 202 100% 100% 100%

10 ‘Select’ Autism 9.1 365 50% 50% 50%12 ‘Select’ TD 3.4 259 100% 100% 100%13 ‘Select’ TD 3.6 132 100% 100% 100%18 ‘Select’ TD 3.7 214 100% 100% 100%19 ‘Select’ TD 3.3 186 100% 100% 100%20 ‘Select’ TD 3.2 160 100% 100% 100%1 ‘Name’ Autism 5.7 133 100% 100% 100%5 ‘Name’ Autism 8.5 236 50% 50% 50%6 ‘Name’ Autism 6.6 193 100% 100% 100%7 ‘Name’ Autism 4.11 212 100% 100% 100%8 ‘Name’ Autism 4.6 287 25% 50% 37.5%

11 ‘Name’ TD 3.3 195 50% 50% 50%14 ‘Name’ TD 3.5 167 100% 100% 100%15 ‘Name’ TD 3.6 190 100% 100% 100%16 ‘Name’ TD 3.1 173 100% 100% 100%17 ‘Name’ TD 3.5 194 100% 100% 100%

0%¼No untaught equivalence relations emerged. 25%¼One pair of symmetrical relations emerged. 50%¼Two pairs of symmetrical relationsemerged. 100%¼All possible symmetrical and transitive relations emerged. Total derived relations¼ average percentage of symmetrical andtransitive relations that emerged in each teaching condition.

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symmetry and transitivity in the ‘Name’ teaching condition

and the other child (Child 4) demonstrated symmetry but not

transitivity the ‘Name’ teaching condition. The final child

(Child 8) only demonstrated symmetrical responding for one

of the taught stimulus–response relations (C–A) in the

‘Select’ teaching condition but not for the other taught

stimulus–response relation (B–A) in this set. This child

demonstrated the emergence of both of the symmetrical

relations for each of the taught stimulus–response relations

following the ‘Name’ teaching condition. They did not

demonstrate transitive responding in either teaching

condition.

Nine out of 10 of the children in the Typically Developing

Group were able to demonstrate the emergence of six-member

equivalence classes. Child 11 demonstrated the emergence of

symmetrical relations following teaching in both the ‘Select’

teaching condition and the ‘Name’ teaching condition how-

ever, he did not demonstrate transitive responding under

either teaching condition.

Group results

In an initial exploration of between group effects and the

possibility that the emergence or non-emergence of untaught

relations might be related to one or more of the entry

characteristics or training characteristics of the subjects,

Pearson product moment correlations and intercorrelations

were calculated for selected pretest, acquisition and posttest

variables.

The outcome variable in this initial group analysis was the

number of untaught relations which emerged during the

experiment. The score for derived relations was a score from

zero to four. One point was awarded for symmetry and one

point for transitivity following instruction in the ‘Select’

condition, plus one point for symmetry and one point for

transitivity following instruction in the ‘Name’ condition. It

was possible for children to score zero if symmetrical or

transitive relations did not emerge.

The experimental treatments (‘Select First’ or ‘Name

First’) were entered into the analysis as a binary variable.

Also the total number of trials to criterion (across both

treatments) was calculated and entered into the analysis for

each child. The training variables used in the analysis were (a)

the trials to criterion across the ‘Select’ teaching condition,

(b) the trials to criterion across the ‘Name’ teaching condition

and (c) the total trials to criterion.

The following student characteristics were included in the

analysis: group membership (whether Autism or Typically

Developing Group), PPVT-IV age equivalent scores, ABAS-II

functional academics scores, ABAS-II communication scores,

highest number reached for rote counting during the number

screening test and highest number reached for one-to-one

counting during the number screening test. The results of the

correlational analysis for the two groups combined are

presented in Table VII.

Group membership

As shown in Table VII, there was a significant correlation

between group membership (Autism or Typically Developing)

and the total number of derived relations (r¼ 0.451, p50.05). Tab

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A total of 28.5 untaught stimulus–response relations emerged

for children in the Autism Group compared to 38 for children

in the Typically Developing Group.

Experimental treatment

There was no relationship between experimental treatment

and the total number of untaught equivalence relations which

emerged.

Teaching conditions

The number of occasions in which untaught equivalence

relations emerged during the ‘Select’ Condition and the

‘Name’ Condition was 31.5 and 35.0, respectively. There was

no significant difference between the number of emerged

relations following the ‘Select’ teaching condition compared

to the ‘Name’ teaching condition in the present sample of 20

children (�2¼ 1.19, p40.20). As there was no correlation

between the experimental treatments (or the teaching condi-

tions) and the emergence of untaught equivalence relations,

no further analysis of treatment effects was undertaken.

Entering characteristics

The functional academics scores that were used for each child

in the correlation analysis were the norm-referenced scaled

scores on the ABAS-II. As can be seen from Table VII,

a statistically significant relationship was found between

functional academics scores on the ABAS-II and total

derived relations (r¼ 0.550, p50.05). Other student charac-

teristics measured in this study were not correlated with

performance on tests for the emergence of untaught equiva-

lence relations.

Trials to criterion

The number of trials to criterion was significantly correlated

with the emergence of untaught equivalence relations. As can

be seen in Table VII, the number of trials required to reach

mastery in the ‘Select’ Condition was strongly correlated with

the emergence of symmetry and transitivity (r¼ 0.602,

p50.01), as was the number of trials to criterion in the

‘Name’ Condition (r¼ 0.674, p50.01). These correlations

indicate that those children who acquired the taught

discriminated responses more rapidly, were more likely to


regardless of experimental condition.

An unpaired t-test was conducted in order to identify

whether there was a significant difference between the

number of trials required to meet mastery criterion in the

‘Select’ Condition and the ‘Name’ Condition across all 20

children. Results of this analysis revealed that there was a

significant difference (t¼ 2.35, p¼ 0.024) between the trials

to criterion in the ‘Select’ Condition (M¼ 93.5, SD¼ 36.1),

and the trials to criterion in the ‘Name’ Condition (M¼ 122.1,

SD¼ 40.7). This result suggests that, while teaching condi-

tions did not have a significant effect on the emergence of

untaught equivalence relations, it did have an effect on the

rate of acquisition with children acquired taught skills more

rapidly under the ‘Select’ Condition, than under the ‘Name’

Condition.

An unpaired t-test was also conducted for the purpose of

investigating whether there was a significant difference

between the number of teaching trials required for children

in the Autism Group and children in the Typically Developing

Group to reach mastery criterion. The results of this analysis

demonstrated that there was a significant difference (t¼ 2.19,

p¼ 0.042) between total trials to criterion required by the

Autism Group children (M¼ 244.1, SD¼ 75.0) and the total

trials to criterion required by the Typically Developing Group

children (M¼ 187.0, SD¼ 34.0). This finding indicates that

the children in the Autism Group required a significantly

greater number of teaching trials in order to meet mastery

criterion than the children in the Typically Developing Group.

While most entering characteristics were not associated

with performance on tests for the emergence of untaught

equivalence relations, they were correlated with trials to

criterion. As shown in Table VII, there were significant

correlations between trials to criterion and functional aca-

demics scores on the ABAS-II, communication scores on the

ABAS-II, rote counting at entry and counting with one-to-one

correspondence at entry.

The correlations between trials to criterion and functional

academics, counting with one-to-one correspondence and rote

counting suggest that these pre-test measures predicted rate of

acquisition but not the likelihood of emergence of untaught

equivalence relations, with the exception of the functional

academics scores.

Discussion

Emergence of untaught equivalence relations

Only five of the 10 children in the Autism Group were able to

demonstrate both symmetry and transitivity during tests for

the emergence of untaught equivalence relations. For the

remaining five children with ASD, the emergence of untaught

equivalence relations was variable. These results indicate that

with the type and level of training provided in the present

study, some children with ASD are able to demonstrate the

emergence of untaught equivalence relations and are capable

therefore of forming six-member equivalence classes while

others are unable to do so or are only able to demonstrate

generalisation to symmetrical, but not transitive responding.

Few research studies have examined the emergence of

untaught equivalence relations in children with ASD. The

present finding that some children with ASD were able to

demonstrate the emergence of all of the untaught equivalence

relations is consistent with the findings of other researchers

who also found that untaught relations emerged for some

or all of the participants with ASD who were included in their

investigations [23, 25, 27, 28, 30].

The emergence of untaught equivalence relations inlanguage matched typically developing children

When compared to the children in the Autism Group, it is

apparent that those in the Typically Developing Group

showed a greater likelihood of demonstrating the emergence

of untaught equivalence relations even although they had been

matched on language development and were much younger.

They also required significantly fewer training trials in order

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the master the taught discriminated responses than was the

case with the children in the Autism Group.

Three other experiments have compared the emergence of

untaught equivalence relations in people with ASD with that

of typically developing children [28–30]. Within each of these

studies all of the typically developing children demonstrated

the formation of equivalence classes. By contrast, there was

variability in the ability of those with autism to demonstrate

the emergence of untaught equivalence relations. It was

evident in the study by O’Connor et al. [30] that there was

little difference in the performance of typically developing

children and children with ASD when the children with ASD

had high levels of verbal competence. However, for those

children with less advanced language, additional instruction

was required for equivalence class formation to occur. Similar

variability was found in the study by O’Connor et al. [29].

In this study, variable performances were able to be

remediated through multiple exemplar training and explicit

teaching of correct and incorrect responses.

The present study differed from earlier research in that it

attempted to match the typically developing children and

children with autism in terms of language ability. This meant

that it was possible to conclude that the difference in

performance between the children with autism and the

typically developing children is unlikely to be the result of

language ability but may in fact be a characteristic that is

uniquely associated with the way in which children with

autism acquire and generalise new skills.

Effects of instruction in naming

The current study found no advantage for the ‘Naming First’

treatment as far as the emergence of untaught equivalence

relations is concerned. This result differs from that reported

by Eikeseth and Smith [21] and Wynn and Smith [31]. There

are several possible reasons for this. First, there were a

number of procedural differences between the three experi-

ments. In the Wynn and Smith [31] study, participants were

provided with multiple practice opportunities in order to teach

only one set of relational concepts, however in the current

study a greater number of stimulus–response relations were

taught and tested. Secondly, the nature of the teaching content

was vastly different. In the Eikeseth and Smith [21] study

participants were taught Greek letters and the written names

corresponding with these letters, and in the Wynn and Smith

[31] study stimuli consisted of opposite word pairs (e.g. hot/

cold). Finally, in the Eikeseth and Smith [21] study, teaching

participants to name stimuli was introduced as a remedial

treatment for the students who had failed to demonstrate the

emergence of untaught relations. This is procedurally quite

different to the present study in which participants were

taught and tested according to the specified teaching condi-

tion, without being provided with any additional remedial

instruction. It is quite possible that these methodological

differences account for the variability between the results of

the current study and those of Eikeseth and Smith [21] and

Wynn and Smith [31] . In the present experiments children

took significantly longer to acquire taught skills (and hence,

for the taught relations to emerge) when taught using the

‘Name’ teaching condition than when using the ‘Select’

teaching condition. This finding aligns with what we know

about language development which shows that children

acquire receptive understanding prior to mastering expressive

use of individual words [40].

Variables affecting the emergence of untaughtequivalence relations

There was significant variation amongst the children with

ASD in terms of the likelihood that these children would

demonstrate the emergence of untaught equivalence relations.

This variability was related to four variables. These were

Autism status, scores on the functional academics domain of

the ABAS-II, age, and rate of acquisition.

The current investigation found that five out of the 10

children with ASD demonstrated the emergence of both

symmetry and transitivity and were therefore able to form

6-member equivalence classes. For the remaining five

children the emergence of symmetrical and transitive rela-

tions was highly variable. The differences among children

with ASD are difficult to explain and highlight the need for

further experimental research in this area.

In the present investigation children who scored more

highly on the measure of functional academics were more

likely to demonstrate the emergence of untaught relations.

The Adaptive Behaviour Assessment System measures adap-

tive functioning in 10 different domains, one of which is

Functional pre-academics (children 0–5 years of age) or

Functional Academics (5–21 years of age). The ABAS-II has

not been used in previous research so this is a new finding.

Its implications are unclear and need to be explored further.

Possibly the correlation between functional academics scores

and the emergence of untaught equivalence relations simply

reflects differences in the rate of developmental or prior

experience with this kind of learning task for the children

included in the present study

In the present study, children who required fewer teaching

trials to reach mastery of the taught stimulus–response

relations were significantly more likely to demonstrate

the emergence of untaught equivalence relations. In fact,

rate of acquisition was found to be the best predictor of

the emergence of untaught equivalence relations in the

present study.

Possible causes of variability in the emergence of untaught

equivalence relations

There are two main possible explanations for why some

children in the Autism Group demonstrated the emergence of

untaught relations and some did not. The first is that the

difference is due to the differences in rate of development.

The second is that it is due to differences in prior teaching

history.

Rate of development

There is strong indirect evidence in this study that, for the

children in the Autism Group, the emergence of untaught

equivalence relations is related to rate of development.

Because the two groups were matched on PPVT-IV scores

there was no correlation between PPVT-IV scores and the

number of derived relations demonstrated. However, there


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was a significant and strong negative correlation between age

and number of derived relations. In other words, when

matched on receptive vocabulary scores, the older children

in the ASD group were the children who required the greatest

number of teaching trials to reach the mastery criterion and

they were the least likely to demonstrate emergence of

untaught equivalence relations. They also tended to have

the lowest functional academics scores on the ABAS-II.

In the present study it was the children with higher levels

of pre-requisite skills (as measured by rote counting and

counting with one-to-one correspondence), higher functional

academics scores and higher communication scores who

required fewer trials to reach criterion. This provides further

indirect evidence for a link between rate of development and

the emergence of untaught equivalence relations.

This observation suggests that it may be the rate of

development of the child and not autism per se, which is

the major determinant of whether or not equivalence

relations will emerge during teaching. A similar conclusion

was reached by O’Connor et al. [30] who argued that

children with higher levels of language skills can be expected

to acquire equivalence relations more rapidly regardless of

whether or not they have a diagnosis of ASD.

Prior teaching history

A second possible explanation for the failure to demonstrate

the emergence of untaught relations by half of the children in

the Autism Group may possibly be found in the prior teaching

history of these children. Because many of the children in the

Autism Group had experienced long periods of discrete trial

teaching, there is a possibility that they had received little

in the way of generalisation training.

Previous research suggests that additional teaching is

required for some children with autism if they are to learn to

generalize across and within response types. One of the key

components of training to generalize is that of providing

reinforcement for response variability, that is, reinforcing the

child for demonstrating some variation in desired responses.

Due to the highly structured nature of much of the prior

teaching of the children with ASD, it is possible that they may

not have experienced much in the way of reinforcement for

varying their response topography. The need to reinforce

variation in response topographies has been demonstrated

in several research studies [41, 42]. Cooper, Heron and

Heward [43] recommend that instructors should ensure

contact with reinforcement in the presence of stimuli

to which generalised responding is desired in order to

ensure that students will respond correctly within the

generalisation setting.

It is also possible for children with ASD to become

dependent on the prompts used during teaching. This effect

has been observed in prior investigations [32, 34]. In the

present study, all teaching trials began with a verbal

discriminative stimulus (e.g. ‘What number is this?’) and if

the correct response was not given the child was then

prompted (e.g. the teacher modelled the correct response, ‘It’s

number three’). During testing these prompts were all

abruptly removed. Both Betz, Higbee and Pollard [32] and

Williams, Carnerero and Perez-Gonzalez [34] found that

children who had been taught to respond to questions (e.g.

‘What is she doing?’) needed additional training in order to

learn to generalize responses when the verbal discriminative

stimuli were faded.

It is not possible to determine whether aspects of the prior

learning history of the children with ASD may have limited

the likelihood of the emergence of untaught relations.

However, it is possible that a combination of reinforcement

history and a history of prompt dependence may have

restricted generalisation to untaught equivalence relations

for some children in the Autism Group.

Implications for the teaching of children with ASD

When compared with typically developing children, children

with ASD take a significantly longer period of time to acquire

new discriminated responses. In addition, children with ASD

tend to have greater difficulty in generalizing across responses

and stimuli and often require additional teaching in order to

learn to do so [32, 34]. If teaching two stimulus–response

relations leads to the emergence of four additional stimulus–

response relations without having to directly teach these

discriminated responses, then we can greatly improve the

efficiency with which new skills are taught to children who

require remedial instruction. Further investigation into the

range of applications of stimulus equivalence is also import-

ant here, as Rehfeldt [44] points out in her review of the

literature.

The evidence that some children with ASD did not


also has very important implications. The first is that some

children with ASD will be able to demonstrate stimulus

equivalence and they will be able to be taught using an

efficient teaching procedure. Others however, will not and

these children will need to be systematically taught all

discriminated responses for each concept. The second is that it

may be necessary to conduct an assessment in order to

determine whether a particular child is able to be taught using

an efficient teaching method or whether the direct teaching of

each discriminated response is required. To date, no such

assessment exists and therefore more research is required in

order to assist practitioners to distinguish between children

who will require instruction in only two stimulus–response

relations and those who will require instruction in all six

stimulus–response relations. The third is that, if particular

children fail to demonstrate the emergence of untaught

equivalence relations then it may be valuable to explore and

implement strategies that facilitate the development of this

kind of generalised responding. The finding that the emer-

gence of symmetrical and transitive responding may be

related to learning history and/or the teaching method utilised

suggests that we should ensure that the appropriate method is

implemented when teaching discriminated responses.

The results of the current study have implications for the

teaching of language and communication skills. There are a

number of research studies which have applied the principles

of Relational Frame Theory to successfully teach derived

language responses such as intraverbals [45], mands [46–51]

and tacts [52]. The principles of Relational Frame Theory

have also been applied to the teaching of second languages,

DOI: 10.3109/17518423.2014.899649 11

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including Spanish vocabulary using observational learning

[53]. This research has highlighted the potential utility of a

training protocol that facilitates derived responding in a one-

to-one capacity, and also within the classroom. As children

with ASD often have delayed language development a method

that increases the rate at which children acquire new language

concepts, in a way that also enhances the comprehension and

meaning behind new language, could greatly improve

outcomes for children with ASD.

Finally, further research clarifying the variables which are

likely to facilitate the emergence of untaught discriminated

responses is required if we are to provide educators with a

knowledge of the teaching strategies and teaching conditions

that are likely to be most effective in developing language in

children with developmental disabilities.

Declaration of interest

The authors report no conflicts of interest. The authors alone

are responsible for the content and writing of this paper.

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