Mathematics interventions for children and adolescents with Down syndrome: a research synthesis.

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Journal of Intellectual Disability Research 767

doi: 10.1111/jir.12188

volume 59 part 8 pp 767 –783 august 2015

Mathematics interventions for children and adolescents with Down syndrome: a research synthesis C. J. Lemons,1 S. R. Powell,2 S. A. King3 & K. A. Davidson1 1 Department of Special Education, Peabody College of Vanderbilt University, Nashville, Tennessee, USA 2 Department of Special Education, The University of Texas at Austin, Austin, Texas, USA 3 Department of Curriculum and Instruction, Tennessee Tech University, Cookeville, Tennessee, USA

Abstract Background Many children and adolescents with Down syndrome fail to achieve proficiency in mathematics. Researchers have suggested that tailoring interventions based on the behavioural phenotype may enhance efficacy. Method The research questions that guided this review were (1) what types of mathematics interventions have been empirically evaluated with children and adolescents with Down syndrome?; (2) do the studies demonstrate sufficient methodological rigor?; (3) is there evidence of efficacy for the evaluated mathematics interventions?; and (4) to what extent have researchers considered aspects of the behavioural phenotype in selecting, designing and/or implementing mathematics interventions for children and adolescents with Down syndrome? Nine studies published between 1989 and 2012 were identified for inclusion. Results Interventions predominantly focused on early mathematics skills and reported positive outcomes. However, no study met criteria for methodological rigor. Further, no authors explicitly considered the behavioural phenotype. Correspondence: Dr Christopher J. Lemons, Peabody College of Vanderbilt University, Special Education, Nashville, Tennessee, USA (e-mail: [email protected]).

Conclusions Additional research using rigorous experimental designs is needed to evaluate the efficacy of mathematics interventions for children and adolescents with Down syndrome. Suggestions for considering the behavioural phenotype in future research are provided. Keywords behavioural phenotype, Down syndrome, mathematics

Introduction Down syndrome (DS) is one of a few genetic syndromes with a relatively well-documented behavioural phenotype – a pattern of behavioural outcomes associated with a specific syndrome (Chapman & Hesketh 2000; Silverman 2007; Fidler et al. 2009). Individuals with syndromes or disorders with documented behavioural phenotypes exhibit a heighted probability or likelihood of displaying phenotypic behaviours relative to individuals who do not have the syndrome (Dykens 1995). Some researchers have suggested that behavioural phenotypes may be useful in designing academic and behavioural interventions (Hodapp & Ricci 2002; Lemons & Fuchs 2010; Reilly 2012). The notion is that it may be possible to use the

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volume 59 part 8 august 2015

Journal of Intellectual Disability Research 768 C. J. Lemons et al. • Considering the behavioural phenotype

phenotype to tailor interventions by targeting deficits, providing additional supports for areas of weakness, or building on areas of relative strength (Fidler 2005; Fidler & Nadel 2007). Oliver & Hagerman (2007) stated that although developing interventions based on basic phenotypic research is ‘perhaps, the greatest challenge[,]. . .there are early signs that this is becoming increasingly possible’ (p. 651). The behavioural phenotype of individuals with DS includes relative strengths in visual processing and social communication and deficits in working memory, language and fine motor skills (Chapman & Hesketh 2000). Several researchers have suggested that adapting early reading instruction based on this pattern of behaviour may increase learning outcomes for children and adolescents with DS (Hodapp & Ricci 2002; Fidler & Nadel 2007; Lemons et al. 2012). Empirical work evaluating such an approach is currently underway (Lemons et al. 2011). The purpose of this review was to extend this line of work into the area of mathematics. Our aim was to provide a better understanding of what is currently known about mathematics interventions for individuals with DS and to consider the extent to which the behavioural phenotype has influenced the design and implementation of such work. To achieve our aims, we conducted a systematic search of empirical research to identify studies that evaluated the efficacy of mathematics interventions for children and adolescents with DS. We decided to focus on mathematics for five reasons. First, mastery of early mathematic skills is critical to the development of more advanced mathematic abilities and is necessary to support post-secondary goals including employment, independence and quality of life (Bynner & Parsons 1997). Second, a majority of individuals with DS fail to achieve adequate mathematics skills (Shepperdson 1994; Rynders et al. 1997). Third, previously published reviews of mathematics intervention research either (1) focused broadly on individuals with intellectual disability (ID; e.g. not focused specifically on DS; Browder et al. 2008), or (2) were non-systematic narrative reviews that did not evaluate study quality or consideration of the behavioural phenotype (e.g. Abdelhameed 2007; Bird & Buckley 2012). Fourth, there is evidence that individuals with DS exhibit differential patterns

of mathematics performance compared with individuals with other genetic syndromes (e.g. Williams syndrome; Paterson et al. 2006; for a review, see Powell, Lemons, King, & Davidson, 2015). Fifth, researchers (Hodapp & Ricci 2002; Fidler et al. 2007) have suggested that tailoring interventions based on the behavioural phenotype may enhance outcomes, thus an exploration of the extent to which researchers are doing this is warranted.

DS and mathematics-relevant features of the behavioural phenotype Individuals with DS represent the largest group of individuals for whom ID is genetically caused. The birth rate of DS is approximately 14 out of 10 000 births; however, prevalence rates vary by country (Presson et al. 2013). Challenges with learning mathematics are anticipated because of a general intellectual deficit [i.e. typical standard scores between 30 and 70 (M = 50) on tests of intelligence (Chapman & Hesketh 2000)]. Several researchers have documented patterns of performance in the domains of working memory, language and phonological awareness, fine motor skills, and behaviour and attention that may also influence learning of mathematics (for a review, see Chapman & Hesketh 2000; Fidler 2005). Next, we describe the documented patterns of performance for individuals with DS and highlight how each may impact response to mathematics intervention. Working memory and visual processing Memory deficits are commonly identified in individuals with DS – most notably in verbal working memory and delayed recall (Chapman & Hesketh 2000; Jarrold et al. 2006; Fidler & Nadel 2007). Hodapp & Freeman (2003) reported that individuals with DS show relative strengths when shortterm memory tasks are presented visually instead of verbally. Several studies have demonstrated relative strengths in visuospatial processing (Jarrold et al. 1999; Fidler 2005), although a recent review has suggested that the profile of visuospatial abilities in DS may be uneven (cf. Yang, Conners, & Merrill, 2014). Deficits in working memory are likely to hinder mathematics learning. For example, Fuchs et al.




(2013) demonstrated that, for a sample of typically developing children, working memory measured in grade 1 was a significant predictor of numeration skill at the end of grade 3. The notable deficits in verbal working memory for individuals with DS may be particularly detrimental for mathematics outcomes as Geary et al. (2007) found that verbal working memory partially or fully mediated many mathematics cognition deficits in a sample of children with learning disability. However, the relative strengths in visuospatial processing may support response to mathematics instruction for children with DS. For example, Bull et al. (2008) assessed a sample of 104 preschoolers (M age 4.99 years) and demonstrated that, at the beginning of primary school, visual-spatial short-term memory was a significant predictor of mathematics achievement. Language and phonological awareness Several researchers have demonstrated expressive language to be significantly weaker than receptive language for individuals with DS (Miller 1999; Fidler et al. 2007). Deficits in the development of grammar have been noted (Fidler 2005). Additionally, phonological awareness skills of individuals with DS are delayed compared with typically developing peers who are matched on reading ability, mental age or chronological age (Lemons & Fuchs 2010; Steele et al. 2013). Language deficits, particularly in the area of listening comprehension, receptive vocabulary and grammatical comprehension, are associated with poor outcomes in mathematics (Robinson & Temple 2011; Fuchs et al. 2013). Delays in phonological awareness, however, may be the most concerning risk factor that could inhibit early learning of mathematics skills for children and adolescents with DS. Phonological awareness assessed in preschool and kindergarten is a strong predictor of mathematics outcomes for typically developing children, including numeration and calculation assessed 2 years later (LeFevre et al. 2010) and of mathematics performance in the middle elementary years (Barnes et al. 2014).

motor planning and precise movements of limbs and fingers (Fidler 2005). Dolva et al. (2004) demonstrated that 5-year-old children with DS were most delayed on self-care activities that required fine motor skills. Further, Spanò et al. (1999) assessed 22 individuals with DS between the ages of 4 and 14 years on fine motor functioning and found that all obtained scores below the 5th percentile. All aspects of fine motor skill were severely impaired and there appeared to be no improvement associated with age. Fine motor skills are associated with mathematics ability. For example, Barnes et al. (2011) demonstrated that fine motor skill assessed at 36 months was a unique predictor of large set (i.e. quantities > 4) object-based arithmetic both at 36 and 60 months. Additionally, use of fingers may support early mathematics learning by decreasing the cognitive load of counting and calculating (Barnes et al. 2014). Behaviour and attention Many individuals with DS exhibit low levels of task persistence and high levels of off-task social behaviours and distractibility (Fidler 2006). Wishart (1996) found that many children with DS use both positive and negative behaviours to get out of tasks and often quit working or try to distract the adult with positive social interactions. Weaknesses in cognitive functioning (i.e. deficits in instrumental and strategic thinking) contribute to avoidance of new and challenging activities (Fidler 2006). Numerous studies have demonstrated that attentive behaviour is a robust predictor of mathematical cognition and learning (Fuchs et al. 2005, 2013). For example, in a sample of 394 typically developing children, a teacher rating of attentive behaviour collected at age 6.5 years was a unique predictor of numeration understanding and multi-digit calculations nearly 4 years later (Fuchs et al. 2013). A broader array of central executive skills, including shifting attention, inhibition, goal planning and goal monitoring are also correlated with early mathematics learning (Bull et al. 2008).

Fine motor skills

Summary

Individuals with DS demonstrate deficits in several areas of motor functioning, including motor skills,

Overall, several characteristics commonly shared by individuals with DS are predictive of mathematics




outcomes in the broader population of typically developing individuals. Many of these features (e.g. deficits in working memory, phonological awareness, fine motor skill, attention) will likely hinder early learning; however, relative strengths in some aspects of visual processing may serve as a foundation for early mathematics interventions.

Research questions The research questions that guided this review were (1) what types of mathematics interventions have been empirically evaluated with children and adolescents with DS?; (2) do the studies demonstrate sufficient methodological rigor?; (3) is there evidence of efficacy for the evaluated mathematics interventions?; and (4) to what extent have researchers considered aspects of the behavioural phenotype in selecting, designing and/or implementing mathematics interventions for children and adolescents with DS?

Method Inclusion criteria Our primary goal was to identify studies in which the efficacy or effectiveness of a mathematics intervention provided to individuals with DS between the ages of 5 and 21 years was empirically evaluated. We considered any form of instruction provided to enhance mathematics outcomes as an intervention. For the purpose of our review, we considered studies in which the independent variable was an intervention that targeted academic aspects of mathematics (e.g. symbol identification, counting, basic facts, fractions, decimals, measurement, geometry; Stein et al. 2005; National Governors Association Center for Best Practices 2010). We excluded studies that focused only on functional skills (e.g. grocery shopping; Morse & Schuster 2000). In addition, we also applied the following inclusion criteria: 1 Studies were published in an English-language, peer-reviewed journals. 2 Participants were children or adolescents with DS between the ages of 5 and 21 years. We excluded

articles primarily involving young children (e.g. Taubman et al. 2001) or older adults (e.g. Shafer et al. 1986). 3 The study had to report data identifiable and disaggregated data participants with DS. For intervention studies, single-case designs that did not specifically identify which participants were individuals with DS (e.g. Schloss et al. 1997) or group designs that did not disaggregate data for students with DS (e.g. Dihoff et al. 2005) were excluded. 4 Studies included quantitative data directly related to the mathematics skills of students with DS. We excluded narrative case studies (e.g. Germain 2006).

Search procedures We identified relevant articles through a search process consisting of four phases (see Fig. 1). Specifically, we conducted (1) an electronic database search, (2) a review of recent meta-analyses, (3) a hand search of relevant journals and (4) an ancestral search of identified articles. First, we used the PsycINFO, PsycARTICLES and ERIC databases to identify peer-reviewed, English-language articles that included ‘Down syndrome’ or ‘Down’s syndrome’ anywhere in the article, and at least one from each of the two following sets of terms located in the article abstract [set 1 (mathematics focus): ‘addition’, ‘arithmet*’, ‘basic facts’, ‘cardinality’, ‘count*’, ‘decimals’, ‘division’, ‘fractions’, ‘geometry’, ‘math*’, ‘measurement’, ‘money’, ‘multiplication’, ‘number conservation’, ‘number sense’, ‘numerals percent’, ‘place value’, ‘pre-algebra’, ‘problem solving’, ‘ratio’, ‘seriation’, ‘subitizing’, ‘subtraction’, ‘symbol identification’, ‘telling time’ or ‘word problems’; Set 2 (intervention focus): ‘instruct*’, ‘interv*’, ‘learn*’, ‘teach*’ or ‘train*’]. No date parameters were entered to limit the search. This search yielded 299 records. We reviewed 31 full-text articles and identified four studies for inclusion. Second, we reviewed the reference lists of four published reviews of mathematics interventions for individuals with ID (Butler et al. 2001; Kroesbergen & Van Luit 2003; Browder et al. 2008; Hord & Bouck 2012) and two published narrative reviews of mathematic interventions for children and adolescents with DS (Abdelhameed 2007; Bird & Buckley




Figure 1 Study identification procedures.

2012). From our review of 447 references, we chose 123 articles for full-text review. Three of these met inclusion criteria. Third, we conducted a hand search of the tables of contents for articles published between 2011 and 2013 for the following journals: American Journal of Intellectual and Developmental Disabilities, Developmental Neuropsychology, Education and Treatment of Children, Exceptional Children, Intellectual and Developmental Disabilities, International Journal of Special Education, Journal of Intellectual Disability Research, Journal of Special Education, Journal on Developmental Disabilities, Remedial and Special Education, Research and Practice for Persons with Severe Disabilities and Research in Developmental Disabilities. Titles and abstracts were reviewed for 2,510 articles. We reviewed the full-text article for 15 studies and identified two for inclusion. Fourth, we conducted an ancestral search by reviewing the references of articles identified up to

this point of the search. After a review of 304 references, three articles were chosen for full-text review. None met inclusion criteria. Our search process resulted in a total of nine studies published between 1989 and 2012 identified for inclusion. During each step of study identification, two authors independently evaluated records, references and full-text articles to determine whether a study met inclusion criteria. We calculated inter-rater reliability (IRR) for each step in our process by dividing the number of agreements between authors (e.g. article does meet criteria for moving to next phase of coding) by the total number of records, articles or references being reviewed within that step then multiplying by 100. Disagreements were resolved by consensus of a third author before our team progressed to the subsequent step. As indicated in Fig. 1, IRR ranged from 93.5% to 100%.




Coding procedures First, we created a summary table to describe the key features (e.g. design, duration, targeted skills) of included studies. For each article, one author independently completed the summary table and a second author reviewed the table for accuracy. Second, we evaluated the methodological rigor of studies using two rubrics adapted from Jitendra et al. (2011). The rubrics allowed us assess whether studies met quality standards for rigorous single case (see Supporting Information Table S1; Horner et al. 2005) or group and quasi-experimental (see Supporting Information Table S2; Gersten et al. 2005) designs. Third, we calculated two statistics to supplement interpretation of findings. For group experimental and quasi-experimental designs, we calculated an effect size to evaluate the magnitude of the treatment effect. We calculated Hedge’s g by dividing the difference between treatment and control means by the pooled standard deviation corrected for small sample size (Institute of Education Sciences 2011). For studies that did not allow for a treatmentcontrol contrast, we used the same formula to estimate the magnitude of treatment-comparison contrast. Additionally, an adjustment was applied to account for the correlation of scores when an effect size for within-group pre-to-post-test change was estimated (Borenstein 2009). Caution should be applied in interpreting effects from the nonexperimental studies because the experimental design does not allow for a clear differentiation of what portion of the effect is attributable to treatment (Shadish et al. 2002). For the single-case design studies, we calculated percentage of non-overlapping data (PND) by dividing the number of intervention data points that are outside the range of baseline data points by the total number of data points in the intervention phase and multiplying this by 100 (Gast & Spriggs 2014). Greater percentages for PND reflect less overlap of performance between treatment and baseline phases. This calculation is one of many quantitative methods that can be used to supplement visual analysis in single-case design studies. However, readers should use caution when comparing this statistic to effect sizes estimated from group studies as there is no agreed upon statistic that

accounts for the replication logic of single-case design (see Wolery et al. 2010). Fourth, we developed a rubric to examine whether authors’ reported considering the behaviour phenotype in the selection, design and/or implementation of their mathematics interventions. Our rubric included seven domains (i.e. working memory, visual processing, language, phonological awareness, fine motor skills, behaviour, attention). Each domain was scored on the following threepoint rating scale: (1) There was no evidence in the manuscript that the domain had been considered; (2) there was implicit evidence in the manuscript that the domain had been considered (e.g. authors described a characteristic associated with DS, but did not detail how this characteristic was considered in selecting, designing and/or implementing the mathematics intervention); and (3) there was explicit evidence in the manuscript that the domain had been considered (e.g. the authors stated that a characteristic was considered in selecting, designing and/or implementing the mathematics intervention and/or they detailed how it was considered). Study authors were trained in coding procedures and several practice articles were coded until sufficient IRR was demonstrated (i.e. >90%). Thereafter, two authors independently coded each study. Any disagreements in coding were resolved through a review of the studies, discussion and consensus of a third author. For our evaluation rubrics (i.e. quality indicators, consideration of the behavioural phenotype), we calculated IRR using a point-bypoint method in which the total number of agreements was divided by total number of coded items then multiplied by 100. Use of the rubrics for coding methodological rigor resulted in an average IRR of 91.7% (SD = 11.7, range = 70–100%). We obtained an average IRR of 94.6% (SD = 10.6, range = 71–100) for coding consideration of the behavioural phenotype.

Results Description of included studies and evaluated mathematics interventions Nine studies met inclusionary criteria (see Table 1). Studies were published by researchers from eight




Table 1 Key features of included studies

Citation

Design

n

Mean age* (SD)

Session duration, frequency, and study duration

Abdelhameed (2009) (Egypt)

One-group post-test-only

12

10.2 (1.1)

Browder et al. (2012) (USA)

SCD (A-B)

2

10.0 (1.0)

Gaunt et al. (2012) (Australia)

Pretest-post-test comparison group (non-randomised, non-matched)

12

Irwin (1991) (New Zealand)

SCD (multiple probe across participants/settings) Pretest-post-test control group (randomised) and comparison group (non-randomised, matched) Pretest-post-test comparison group (non-randomised, matched) Pretest-post-test comparison group (non-randomised, matched) One-group post-test-only

9

12.3 (0.6)

30

6.4 (0.6)

25–30 min; frequency not reported; 6–18 sessions (M = 10.25; SD = 4.11). 30 min; 4× week (plus embedded instruction); 6 months. Group A: 70 min instruction plus 50 min game session; 1× week; 9 weeks. Groups B and C: 50 min game session; 1× week. 9 weeks. Session duration not reported; 1× day; 5 days. 1 h; 1× week; 6 months.

Klein & Arieli (1997) (Israel)

Lister et al. (1989) (UK) Lister et al. (1992) (UK) Martinez & Pellegrini (2010) (Italy) Ortega-Tudela & Gómez-Ariza (2006) (Spain)

Pretest-post-test control group (randomised)

19.5 (-)

16

15.2 (-)

15–30 min; 1 session.

34

11.4 (-)

20–30 min; 1 session.

15

13.9 (0.7)

120–180 min; 2× week; 6 months.

18

6.5 (-)

Average 35 min; frequency not reported; 21 weeks (15 sessions).

* Age in years. DS, Down syndrome; SCD, single-case design.

countries between 1989 and 2012 and included 148 participants with DS. Of the nine studies, two used a group experimental design with random assignment to treatment or control, two employed a single-case experimental design, and five implemented a quasi-experimental design (e.g. one-group post-test-only, pretest-post-test group comparison without random assignment). Interventions were delivered in sessions that ranged between 15 and 180 minutes. Two studies (Lister et al. 1989, 1992) delivered only one intervention session; the range of duration in the other studies ranged from 1 week to 6 months. Targeted mathematics skills are included in Table 2. Six studies focused on beginning mathematic skills including counting, number identification, or addition or subtraction of objects, dots and numbers from 1 to 10 (Irwin 1991; Klein & Arieli 1997; Ortega-Tudela & Gómez-Ariza 2006; Abdelhameed 2009; Browder et al. 2012; Gaunt et al. 2012). Two studies focused on

teaching children and adolescents with DS the property of conservation applied to objects, liquid, numbers or length (Lister et al. 1989, 1992). Only one study focused on advanced mathematics in the form of algebra equations, fractions and percentages, and problem solving (Martinez & Pellegrini 2010). A description of each intervention is provided in Table 2. All interventions included aspects of direct instruction, modelling and guided practice. For example, Gaunt et al. (2012) incorporated explicit teaching strategies, repeated practice, and modelling and guided practice with concrete materials and games. Most researchers reported included scaffolding, fading of instructor support and praise in the delivery of the intervention. For example, Browder et al. (2012) supported learning with graphic organizers and consistent response materials and instructors were trained to provide systematic prompting with feedback. Ortega-Tudela & Gómez-Ariza (2006) were the


Targeted mathematics skills

Counting (1–5, 1–10).

Counting (1–5, 1–10, 1–15), number identification, symbol use, calendar skills.

Counting (1–20, 1–100, by 10s), place value (1, 2 and 3 digit numbers).

Addition by counting-on. Components skills: oral rote counting from a number greater than 1, giving the cardinal value of a set, and giving the count word that follows the cardinal number of a set.

Citation

Abdelhameed (2009)

Browder et al. (2012)

Gaunt et al. (2012)

Irwin (1991)

Direct instruction, modelling and guided practice following precision teaching techniques.

Teacher modelled counting, student practised various games with teacher support. Students were taught to count to either 5 or 10. After child did this correctly 10 times within a session, the student received 5 more sessions of instruction. Small group, story-based lesson with system of least prompts and time delay. Graphic organisers used as support. Additional embedded instruction (paraprofessional scaffolded instruction in general education setting). Strategies included explicit teaching, repeated practice, and use of concrete materials. Game sessions for practice.

Intervention description

Table 2 Description of targeted math skills, interventions and outcomes

All students demonstrated learning of the counting-on strategy during intervention. 7 of 8 who received intervention maintained performance after intervention and generalised skill to counting of disordered blocks. Average accuracy improved from between 38% and 59% during baseline to >90% during final intervention and follow-up sessions.

Average performance on tasks on the Booker Profiles of Mathematics improved by: group A = 0.60 points (14%), group B = 0.31 (7%) and group C = 0.36 (7%).

Both students with DS improved in directly taught skills based on an intervention-aligned measure.

Students learned to count aloud to 5 or 10 in between 1 and 13 sessions (total sessions received minus 5).

Summary of outcomes

Hedge’s g for group A within-group pre-to- post-test change on Booker Profiles of Mathematics = 0.93 (adjusted for within-group comparison). Unable to calculate for groups B and C. Average PND for use of counting-on strategy: intervention: 97.5%; follow-up: 95.8%.

Average PND: 84.0%.

–

ES or PND

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C. J. Lemons et al. • Considering the behavioural phenotype


Conservation of objects, liquid, and plasticine.

Conservation of number and length.

Fractions and percentages, algebraic equations, problem-solving with equations, problem-solving with equations in physics.

Counting objects (1–10) and matching count to numerals.

Lister et al. (1989)


Martinez & Pellegrini (2010)

Ortega-Tudela & Gómez-Ariza (2006)

Computer-assisted teaching: Students played a game on the computer where they counted (1–10) fish and balloons and associated this count with a numeral. Students were provided with feedback. Pencil and paper teaching: students completed the same activities, but using printed tasks with teacher feedback.

Instructors presented topic of the day, presented examples and gave students exercises to be solved. Assistance was given as needed.

Teacher modelling and hands-on activities.

Teacher modelling and hands-on activities.

Mediational Intervention in Math included parent training in mediation and direct mathematical training of students.

Students were able to complete assignments with a range of apx. 35–93% accuracy. Authors report variation within subjects regarding performance across the various exercises. Increases on multiple measures for students in the computer-assisted teaching condition [correspondence, stable order (10), cardinality, stable order (20), quantity].

Trained students did better on post-test measure of recognition of conservation.

Treatment (group 1) outperformed control (group 2) and caught up to comparison (group 3) on key math number ID and computation. Increase in overall mean for trained students at post-test on assessment of conservation.

Hedge’s g for treatment vs. control on interventionist-designed post-test for correspondence (1.10), stable order (10) (1.91), cardinality (1.67), stable order (20) (1.43), quantity (4.60).

Hedge’s g for treatment vs. comparison on interventionist-designed post-test of conservation = 2.22. Hedge’s g for treatment vs. comparison gain on interventionist-designed measures of conservation of number (0.71) and conservation of length (0.69). –

Hedge’s g for treatment vs. control gain on Key Math = 2.21.

Journal of Intellectual Disability Research

DS, Down syndrome; ES, effect size; PND, percentage of non-overlapping data; SCD, single-case design.

Counting and addition/subtraction of objects, dots and numbers 1–10.

Klein & Arieli (1997)

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Indicator Participant and setting Participant description Participant selection Setting description Dependent variable (DV) Description of DV Measurement procedure Measurement validity and description Measurement frequency Measurement reliability Independent variable (IV) Description of IV Manipulation of IV Fidelity of implementation Baseline Measurement of DV Description of baseline condition Experimental control/internal validity Experimental effect Internal validity Results External validity Replication of effects Social validity Social importance of DV Magnitude of change in DV Implementation of IV is practical and cost-effective Nature of implementation of IV Average

Browder et al. (2012)

Irwin (1991)

3 2 2

3 2 1

2 3 3 3 3

3 3 3 3 1

3 2 3

3 3 1

3 1

3 1

1 1 1

3 3 3

1

3

3 3 2 3 2.3

2 2 1 2 2.3

Table 3 Essential quality indicator ratings for single-case design studies

Based on quality indicators proposed by Horner et al. (2005). Adapted from Jitendra et al. (2011). 1 = indicator not met; 2 = indicator partially met; 3 = indicator met. DV, dependent variable; IV, independent variable.

only authors to explore the efficacy of computerassisted teaching to improvie counting compared with traditional pencil and paper activities.

Methodological rigor Studies were evaluated according to indicators of research quality following the procedures used by Jitendra et al. (2011). We evaluated single-case design studies on seven indicators of quality including: participants and setting, dependent variable, independent variable, baseline, experimental control/internal validity, external validity and social validity (Supporting Information Table S1; see Horner et al. 2005). Indicators for group experimen-

tal and quasi-experimental designs were used to evaluate studies across four major areas: description of participants, description and implementation of intervention and comparison conditions (if applicable), outcome measures and data analysis (Supporting Information Table S2; see Gersten et al. 2005). For each study, we used the appropriate rubric and assigned a rating (1 = not met, 2 = partially met, 3 = met) for each of the included indicators of quality. As suggested by Jitendra et al. (2011), we established the criterion for adequate quality of receiving no ratings less than 2 on any indicator. Ratings for the two single-case design studies are in Table 3; ratings for group and quasiexperimental studies are in Table 4.


1 – 1

3 1 –

2 1 – 1 1.4

3 1 –

1 1 – 1 1.3

Gaunt et al. (2012)

1 – 1

Abdelhameed (2009)

1 1.4

3

1

2

1

2 1

1 1 1

Klein & Arieli (1997)

1 1.7

3

3

1

1

3 1

1 2 1


1 1.5

3

2

1

1

2 1

1 2 1


1 1.9

3

3

1

–

3 1

1 – 2


1 1.7

3

1

1

2

3 1

2 2 1

Ortega-Tudela & Gómez-Ariza (2006)

Journal of Intellectual Disability Research

Based on quality indicators proposed by Gersten et al. (2005). Adapted from Jitendra et al. (2011). 1 = indicator not met; 2 = indicator partially met; 3 = indicator met; – = not applicable.

Participants Information on participants’ disability Equivalence of groups across conditions Information in intervention agents Description and implementation of intervention and comparison conditions Description of intervention Description and measurement of procedural fidelity Description of intervention in comparison groups Outcome measures Multiple measures or measures of generalised performance Appropriateness of time of data collection Data analysis Linked to research questions; appropriate for unit of Effect sizes Average

Indicator

Table 4 Essential quality indicator ratings for group experimental and quasi-experimental design studies

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No study met the standard for adequate research quality. Regarding the single-case design studies, Browder et al. (2012) were unable to exhibit experimental control or to replicate effects because of the use of an A-B design. Irwin (1991) did not report fidelity of implementation data or provide evidence of measurement reliability. All group experimental and quasi-experimental design studies lacked sufficient description of procedural fidelity. Other common areas where the quality indicators were not met included information on participants’ disability, description of interventionists, use of multiple measures including a measure of generalised performance and evidence documenting the appropriateness of time of data collection.

Evidence of efficacy In considering the potential efficacy of evaluated interventions, the fact that no study met an accepted standard for methodological rigor should be kept in mind. This said, authors of the studies did report findings that could be useful in the design of future studies. A summary of outcomes and related statistics (i.e. effect size or PND) is provided in Table 2. Six studies targeting beginning mathematic skills (e.g. counting, number identification) reported evidence of student learning. Abdelhameed (2009) reported that students with DS were able to learn to count to five or ten after 1 to 13 sessions. Gaunt et al. (2012) reported a 14% improvement on an early mathematics profile assessment for adolescents receiving intervention compared with a 7% improvement for comparison students (Hedge’s g = 0.93). In the two single-case design studies, authors used visual analysis to examine student outcomes. Graphed data provided by Browder et al. (2012) and Irwin (1991) demonstrated improvements in directly taught mathematics skills (PND range = 84.0–97.5%). Klein & Arieli (1997) found a statistically significant effect (Hedge’s g = 2.21) on the KeyMath assessment (Connolly et al. 1986). The average combined score from the number identification and computation subtests was higher for children participating in the mathematics intervention compared with that of the non-treated control group children. Children with DS receiving a computer-based counting intervention provided by Ortega-Tudela & Gómez-Ariza

(2006) performed statistically higher than control students receiving a teacher-facilitated intervention on measures of correspondence, stable order, cardinality and quantity (Hedge’s g range = 1.10–4.60). Researchers who targeted mathematics skills other than early mathematics also reported positive findings. Lister et al. (1989, 1992) provided brief intervention sessions to increase understanding of conservation. Participants in the treatment conditions outperformed comparison students on posttreatment researcher-designed measures of conservation (Hedge’s g range = 0.69–2.22). Martinez & Pellegrini (2010) reported that many participants with DS were able to complete assignments involving algebraic equations and problems solving. Performance ranged from 35% to 93% accuracy with variation across the different types of exercises.

Evidence of the behavioural phenotype Studies involving only children or adolescents with DS were reviewed to evaluate whether there was evidence that researchers considered aspects of the behavioural phenotype of DS in the design or implementation of their mathematics intervention (see Table 5). No author directly stated that the behavioural phenotype was accounted for in the study. However, authors of four studies explicitly described considering one or more characteristics associated with the behavioural phenotype in the selection, development and/or implementation of their intervention. Gaunt et al. (2012) reported they considered expressive and receptive language skills during intervention design. Klein & Arieli (1997) stated their intervention was designed to support the ‘visual simultaneous mode’ (p. 299). Lister et al. (1989) indicated they had considered the learning processes of individuals with DS, specifically ‘physical and sensory, concentration and stamina, and impaired language. . .(and) the complex interaction of these and other factors likely to affect functioning’ (p. 59). Ortega-Tudela & Gómez-Ariza (2006) specifically selected to deliver intervention via computer to support visual processing, retention problems and motivation. Several authors provided implicit evidence that they had considered a component of the behavioural phenotype (Irwin 1991; Klein & Arieli 1997; Abdelhameed 2009; Martinez



Journal of Intellectual Disability Research 779

1 = no evidence; 2 = implicit evidence; 3 = explicit evidence; – = not applicable because of independent variable being administered to a sample that included individuals with and without DS.

1.6 1.6 1.6 1.0 1.0 1.6 1.6 1.4 3 3 1 1 1 3 3 2.1 2 2 1 1 1 1 1 1.3 2 1 2 1 1 2 1 1.4 Working memory Visual processing Language Phonological awareness Fine motor skills Behaviour Attention Average

– – – – – – – –

1 1 3 1 1 1 1 1.3

2 1 1 1 1 1 1 1.1

1 3 1 1 1 3 2 1.7

1 1 3 1 1 1 3 1.6

1 1 1 1 1 1 1 1.0

Ortega-Tudela & Gómez-Ariza (2006) Lister et al. (1989) Klein & Arieli (1997) Irwin (1991) Gaunt et al. (2012) Browder et al. (2012) Abdelhameed (2009) Behavioural phenotype characteristics

Table 5 Consideration of behavioural phenotype in selection, development and/or implementation of independent variable



Average


& Pellegrini 2010). Authors received credit for implicit evidence when they described features of the behavioural phenotype (e.g. working memory or language deficits) in a portion of their manuscript, but did not explicitly detail that the features was considered in the implementation of the study. Thus, although no research team specifically indicated they had considered the behavioural phenotype when they selected, developed and/or implemented their intervention, several did consider aspects of the phenotype in their study.

Discussion The aims of this review were to examine the types of mathematics interventions that researchers have evaluated for improving mathematics outcomes in children and adolescents with DS and to consider the methodological rigor, potential efficacy and consideration of the behavioural phenotype in this work. Our systematic review identified nine relevant articles. Interventions predominately focused on counting or early mathematic skills (e.g. one-to-one correspondence, number identification) and researchers reported favourable outcomes for students who received mathematics intervention (Hedge’s g range = 0.69–4.60; PND range = 84%– 97.5%). Despite this, the poor quality of the studies warrants strong caution in interpreting these outcomes. Although no research team reported considering the behavioural phenotype in the selection, design and/or implementation of their intervention, several authors did provide explicit or implicit evidence that they had considered one or more characteristics associated with the phenotype in their work. Our findings are similar in several ways to results of previously published reviews that included a broader range of individuals with ID. Browder et al. (2008) and Hord & Bouck (2012) found that interventions targeting students with mild and severe ID, respectively, were predominantly focused on beginning mathematics skills including numeration, basic facts, computational procedures and measurement (i.e. money skills). Additionally, previous reviews (Butler et al. 2001; Kroesbergen & Van Luit 2003; Browder et al. 2008; Hord & Bouck 2012) also reported overall favourable outcomes for children




and adolescents with ID. Unfortunately, Browder et al. (2008) also noted a concern regarding the lack of rigorous studies in their review. The authors identified 19 of 54 studies (35%) as having adequate quality. Additionally, because of the limited number of high-quality studies, we were unable to compare the efficacy of various approaches to teaching mathematics to individuals with DS or to evaluate the importance of tailoring interventions based on the behavioural phenotype. Our findings are also in line with the two previously published narrative reviews focused on individuals with DS (Abdelhameed 2007; Bird & Buckley 2012). Both came to the conclusions that intervention work has predominantly focused on early mathematics skills, that interventions appear to be at least modestly effective for many individuals with DS and that additional research is needed. The unique contribution of the present review is that we extended the literature base by conducting a systematic review, evaluating study quality and examining whether authors considered behavioural phenotype characteristics in the design and implementation of their intervention studies. Notwithstanding these contributions, the number and quality of available studies limit our conclusions on the efficacy of mathematics interventions for children and adolescents with DS. Our review has primarily demonstrated that the research base in this area is inadequate. Our findings may have been different had we broadened the parameters of our search to include a larger age range of participants (e.g. preschool children or adults) or had we relaxed our inclusion criteria to allow for review of nonpeer-reviewed manuscripts (e.g. unpublished reports, dissertations). Despite these limitations, we believe the literature base identified in the present review is interesting in at least two ways. First, it is surprising, so few empirical studies have been conducted to evaluate the efficacy of mathematics interventions for a syndrome that is the most common genetic cause of ID. Second, and perhaps of greater interest, of the eight included studies that did limit participation to individuals with DS, none clearly explicated a rationale for focusing on this subgroup of learners with ID. Perhaps, as Hodapp & Ricci (2002) discussed, the limited amount of research conducted

with individuals with DS reflects a viewpoint that aetiology is unimportant. According to this philosophy, special education should be more concerned with individualising interventions to meet the unique needs of each learner rather than focusing on group characteristics. Hodapp and Ricci, however, argued that considering aetiology might be useful in determining how to intervene with specific groups of children and adolescents with genetic syndromes. We share their opinion that aetiology – specifically when a documented behavioural phenotype has been established – may have an important role to play in increasing our understanding of typical and atypical development. It is unclear if authors of the reviewed papers share this viewpoint, although it is unclear why individuals without DS would be excluded if authors did not believe that specific features of DS might influence treatment outcomes.

Directions for future research Our review has indicated a clear need for increased quantity and quality of mathematics intervention research for children and adolescents with DS. We believe one potential line of research may be to follow the suggestion made by Hodapp & Fidler (1999) to focus on the behavioural phenotype and possible interactions with treatment outcomes. Such an approach could lead to improvements in the interventions we provide, and it may increase our understanding of cognitive correlates of learning challenges in the general population (Mazzocco et al. 2007). While the approach may hold promise, it has yet to be tested empirically. Experimental studies are needed to determine whether interventions adapted based on the behavioural phenotype lead to greater gains in learning when compared with non-adapted interventions. Additionally, although there is general consensus on many characteristics of the behavioural phenotype (Chapman & Hesketh 2000; Fidler 2005), our understanding could be improved in several ways. An appropriate measurement model has not been thoroughly defined and we need a better understanding of the sensitivity and specificity of the behavioural phenotype. Further, few studies have examined relationships between phenotypic characteristics and outcomes in mathematics or reading.




Finally, we have very limited information regarding how features of the phenotype change with development and how these features interact with the environment. Large-scale longitudinal studies that document developmental trajectories across a broad set of phenotypic characteristics and academic outcomes would increase our understanding of the long-term importance of early intervention, potential academic achievement levels and of factors that are associated with increased post-secondary independence, employment and quality of life.

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Accepted 17 December 2014

Supporting Information Additional Supporting Information may be found in the online version of this article at the publisher’s web-site: Table S1 Quality indicators of single-case design research articles. Table S2 Quality indicators for group and quasiexperimental studies.


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