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The Effects of an Early Numeracy Intervention Package for Students with Moderate to Severe Developmental Disabilities and Significant Behavior Challenges

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Title: The Effects of an Early Numeracy Intervention Package for Students with Moderate to Severe Developmental Disabilities and Significant Behavior Challenges
Language: English
Authors: Melissa E. Hudson (ORCID 0000-0002-7673-4719), Taylor L. Krueger, Tosha L. Owens
Source: Education and Training in Autism and Developmental Disabilities. 2025 60(4):361-379.
Availability: Division on Autism and Developmental Disabilities, Council for Exceptional Children. DDD, P.O. Box 3512, Fayetteville, AR 72702. Tel: 479-575-3326; Fax: 479-575-6676; Web site: http://www.daddcec.com/
Peer Reviewed: Y
Page Count: 19
Publication Date: 2025
Document Type: Journal Articles
Reports - Research
Education Level: Elementary Education
Descriptors: Numeracy, Mathematics Skills, Intervention, Program Effectiveness, Elementary School Students, Students with Disabilities, Developmental Disabilities, Severe Disabilities, Behavior Problems, Teacher Attitudes, Student Needs, Severe Intellectual Disability, Moderate Intellectual Disability, Autism Spectrum Disorders, Self Contained Classrooms
DOI: 10.1177/21541647251399489
ISSN: 2154-1647
Abstract: This study examined the effects of an early numeracy intervention package on the acquisition of foundational math skills in three elementary students with moderate to severe developmental disabilities and significant behavior challenges. The intervention package included the "Early Numeracy Curriculum" and systematic instructional strategies. A multiple probe across participants design was used to evaluate changes in correct independent responses on a curriculum-aligned assessment. All participants demonstrated improved performance during intervention, although gains were gradual and overlapped with baseline trends for some students. The teacher rated the intervention as feasible and effective and reported that it aligned with students' IEP goals. Findings support the use of structured early numeracy intervention packages that incorporate systematic instruction for students with complex learning and behavior needs.
Abstractor: As Provided
Entry Date: 2026
Accession Number: EJ1496461
Database: ERIC
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  Value: <anid>AN0189916318;[b6wv]01dec.25;2025Dec11.04:19;v2.2.500</anid> <title id="AN0189916318-1">The Effects of an Early Numeracy Intervention Package for Students with Moderate to Severe Developmental Disabilities and Significant Behavior Challenges </title> <p>This study examined the effects of an early numeracy intervention package on the acquisition of foundational math skills in three elementary students with moderate to severe developmental disabilities and significant behavior challenges. The intervention package included the Early Numeracy Curriculum and systematic instructional strategies. A multiple probe across participants design was used to evaluate changes in correct independent responses on a curriculum-aligned assessment. All participants demonstrated improved performance during intervention, although gains were gradual and overlapped with baseline trends for some students. The teacher rated the intervention as feasible and effective and reported that it aligned with students' IEP goals. Findings support the use of structured early numeracy intervention packages that incorporate systematic instruction for students with complex learning and behavior needs.</p> <p>Keywords: moderate/severe; intellectual; disability/ies; mathematics; instructional strategies; developmental; academic; quantitative; research</p> <p>Students with autism and moderate to severe developmental disabilities (MSDD) often experience persistent challenges with early academic skills, particularly in mathematics ([<reflink idref="bib22" id="ref1">22</reflink>]; [<reflink idref="bib26" id="ref2">26</reflink>]). For this manuscript, MSDD refers to students with autism and co-occurring intellectual, adaptive, and/or communication impairments that significantly impact learning and require individualized, intensive instruction. Early numeracy skills, including number recognition, counting, and one-on-one correspondence, are foundational for later mathematical understanding and daily living ([<reflink idref="bib23" id="ref3">23</reflink>]). While effective interventions for teaching these skills have been identified ([<reflink idref="bib5" id="ref4">5</reflink>]; [<reflink idref="bib7" id="ref5">7</reflink>]; [<reflink idref="bib26" id="ref6">26</reflink>]), few studies have explored how these interventions can be implemented successfully for students who also display interfering behaviors that limit their engagement or participation in instruction.</p> <p>Students with MSDD and significant behavior challenges represent a particularly underserved population in the mathematics intervention literature ([<reflink idref="bib3" id="ref7">3</reflink>]). Significant behavior challenges refer to disruptive, aggressive, or noncompliant behaviors that interfere with learning and instruction, and require individualized, evidence-based interventions ([<reflink idref="bib25" id="ref8">25</reflink>]). Understanding how behavior supports can be integrated into academic instruction is essential to ensure equitable access to meaningful learning opportunities for this group.</p> <p>In 2013, Browder and colleagues conducted a pilot study in both special education and general education settings with seven students with MSDD in Grades 3, 4, and 5 to investigate a conceptual model for teaching early numeracy skills to these students. This study was guided by a conceptual framework for delivering effective early numeracy instruction to students with MSDD and included five key instructional components: (a) planning instruction based on student needs and goals, (b) using systematic instruction strategies, (c) incorporating evidence-based practices, (d) monitoring student performance, and (e) adapting instruction to promote generalization and engagement. These components reflect recommended practices for supporting students with MSDD and aligned with approaches used in prior research on early numeracy interventions ([<reflink idref="bib5" id="ref9">5</reflink>]).</p> <p>The conceptual model described by [<reflink idref="bib4" id="ref10">4</reflink>] informed the development of the <emph>Early Numeracy Curriculum</emph> ([<reflink idref="bib11" id="ref11">11</reflink>]), a commercially available, research-based instructional program designed to teach foundational math skills to students with MSDD. Grounded in systematic instruction and repeated practice, the curriculum targets 12 essential early numeracy skills across multiple domains (e.g., counting, sets, and measurement). Since its development, the curriculum has been the focus of multiple applied studies aimed at evaluating its impact on student learning. This growing body of research has sought to understand the curriculum's effectiveness across various student populations and instructional contexts.</p> <p>Particularly relevant to the current study are five investigations that evaluated the effects of the <emph>Early Numeracy Curriculum</emph> ([<reflink idref="bib11" id="ref12">11</reflink>]) on early numeracy skill acquisition with students with MSDD ([<reflink idref="bib8" id="ref13">8</reflink>]; [<reflink idref="bib9" id="ref14">9</reflink>]; [<reflink idref="bib10" id="ref15">10</reflink>]; [<reflink idref="bib12" id="ref16">12</reflink>]; [<reflink idref="bib13" id="ref17">13</reflink>]). These studies offer important insights into how the curriculum has been implemented across varied contexts, participants, and instructional conditions. For example, in their 2013 study, Jimenez and Kemmery examined the impact of an early numeracy intervention on five elementary students with MSDD across three self-contained special education classrooms. All were verbal except for the student who chose not to speak and she used a communication board during the study. The intervention used the lessons from Units One and Two from the <emph>Early Numeracy Curriculum</emph>, systematic prompting and feedback, task analytic instruction, and real-life contexts provided by the curriculum's theme-based math stories. Each lesson began with the teacher reading a math story aloud followed by activities to teach 12 early numeracy skills. To assess the effectiveness of the intervention, the researchers employed a single-case multiple probe across classrooms design, collecting data on students' independent correct responses on the Unit One and Unit Two assessments. Researchers found a functional relation between the intervention and gains in students' early numeracy skills, suggesting the <emph>Early Numeracy Curriculum</emph> can promote early numeracy skills for this population.</p> <p>In their 2015 study, Jimenez and Staples explored the impact of systematic early numeracy instruction on the acquisition of grade-aligned Common Core math skills ([<reflink idref="bib17" id="ref18">17</reflink>]) for fourth and fifth-grade students aged 10–11 years with MSDD, including a student with a co-occurring hearing impairment. Students were taught lessons from Unit One of the <emph>Early Numeracy Curriculum</emph> ([<reflink idref="bib11" id="ref19">11</reflink>]). The researchers used a multiple probe across students design to evaluate the effects of the intervention and collected data on the number of task-analyzed steps of selected grade-aligned math standards (e.g., Geometry ‒ graph points on a plane to solve real-world and math problems) completed independently. Researchers found a functional relation between the early numeracy instruction and the students' independent correct responses on grade-aligned math tasks, suggesting the intervention enhanced math skill acquisition for these students.</p> <p>In their 2020 study, Jimenez and Besaw examined the effects of integrating virtual manipulatives with the <emph>Early Numeracy Curriculum</emph> ([<reflink idref="bib11" id="ref20">11</reflink>]) to enhance early numeracy skills for two elementary students with MSDD, aged eight and nine years. A third student began the study but was withdrawn early during the intervention phase due to a marked escalation in challenging behaviors across educational and community settings (e.g., biting, kicking, and scratching). The students were selected based on their need for intensive support in mathematics and their ability to use tablet devices. This study's intervention included portions of the <emph>Early Numeracy Curriculum's</emph> Unit One lessons (i.e., theme-based manipulatives, graphic organizers, and story-based lessons) and virtual manipulatives created by the authors. The virtual manipulatives—digital objects representing concrete mathematical concepts—were presented using a tablet-based application as part of the <emph>Early Numeracy Curriculum's</emph> story-based instructional package. Five trials of each skill were embedded into each lesson, providing students five opportunities to demonstrate an independent correct response. The researchers used a single-case multiple probe across participants design to assess the effects of the intervention and collected data on the students' independent correct responses when completing three early numeracy skills (i.e., set making, non-standard measurement, and patterning) during baseline, intervention, and maintenance phases. The researchers also compared the effectiveness of virtual manipulatives to traditional concrete manipulatives by presenting both forms during baseline data collection. Researchers determined a functional relation existed between the use of virtual manipulatives within the <emph>Early Numeracy Curriculum</emph> and improvements in the targeted early numeracy skills among the participants.</p> <p>In their 2022 study, Jimenez and Barron investigated the effects of specially designed instruction (SDI) on early numeracy skills for elementary students aged 6, 8, and 10 years with MSDD and varying levels of intellectual disability (mild to moderate ID) within inclusive classroom settings. The intervention used Unit One of the <emph>Early Numeracy Curriculum</emph> ([<reflink idref="bib11" id="ref21">11</reflink>]) and the lessons incorporated story-based instruction, graphic organizers, and theme-based manipulatives to teach these skills. The special education teacher taught the <emph>Early Numeracy Curriculum</emph> in pull-out sessions once per week, either one-on-one or in small groups. Additionally, early numeracy skills were embedded into inclusive math lessons in the general education setting three times per week, allowing students to practice these skills within their regular classroom activities. The system of least prompts (SLP) and error correction were used to support student learning. The intervention's effects were assessed using a single-case multiple probe across students design. The independent variable was the number of independent correct responses for 11 of the 12 early numeracy skills taught during the weekly math lessons and the generalization of these skills within inclusive math lessons. Rote counting was not assessed because not all the participants were verbal. Researchers determined embedded systematic early numeracy instruction within inclusive classrooms was effective and feasible to support SDI for these students.</p> <p>In their 2016 study, Hudson et al. investigated the effects of systematic instruction combined with individualized adaptations on the acquisition of early numeracy skills for three elementary students aged seven to 10 years with MSDD. All three students had co-occurring intellectual and orthopedic impairments, and one student was also blind with extensive medical and sensory needs. Each required individualized supports across communication, mobility, and learning domains and all engaged in academic instruction and demonstrated learning through single-switch voice output devices. The intervention included lessons from Unit One of the <emph>Early Numeracy Curriculum</emph> ([<reflink idref="bib11" id="ref22">11</reflink>]) and the teacher-delivered lessons included math story read-alouds, manipulatives, and graphic organizers, all tailored to support the students' learning and communication requirements (e.g., the calendar was made tactile, bowls were added to the setmaker graphic organizer). Researchers used a single-case multiple probe across participants design to assess the intervention's effects, collecting baseline and instructional probes on the Unit One assessment to establish initial performance and monitor progress. Researchers identified a functional relation between the intervention and improved early numeracy performance across all participants, indicating the intervention effectively supported skill acquisition for these students.</p> <p>While several aspects of these studies are similar (e.g., teaching lessons from Unit One of the curriculum with elementary students), they offer limited insight into the effectiveness of the <emph>Early Numeracy Curriculum</emph> ([<reflink idref="bib11" id="ref23">11</reflink>]) for students with co-occurring significant behavior challenges. These behaviors, such as difficulty with self-regulation, following directions, or engaging appropriately with peers and adults, often require individualized supports and strategies to ensure access to instruction and promote academic success ([<reflink idref="bib6" id="ref24">6</reflink>]). Notably, only one study ([<reflink idref="bib10" id="ref25">10</reflink>]) mentioned a participant with behavior needs, and that student was withdrawn early in the intervention due to escalating behaviors across settings.</p> <p>This lack of representation is especially concerning given the prevalence of significant behavior challenges among students with MSDD and the known impact of such behaviors on academic engagement and learning outcomes ([<reflink idref="bib1" id="ref26">1</reflink>]; [<reflink idref="bib18" id="ref27">18</reflink>]). While prior studies using the <emph>Early Numeracy Curriculum</emph> ([<reflink idref="bib11" id="ref28">11</reflink>]) have demonstrated consistent academic gains (e.g., [<reflink idref="bib8" id="ref29">8</reflink>]; [<reflink idref="bib9" id="ref30">9</reflink>]), they have not addressed how individualized behavior supports may interact with academic instruction to influence outcomes.</p> <p>To address this gap, this study evaluated the effects of the <emph>Early Numeracy Curriculum</emph> ([<reflink idref="bib11" id="ref31">11</reflink>]) on early numeracy skill acquisition for students with MSDD and significant behavior challenges. Unlike prior research, this study was conducted in a classroom setting where participants received individualized behavior supports as part of their ongoing special education services. These supports were not part of the intervention itself but reflected the students' typical school-day routines and were intended to help them access instruction. The research question investigated was: What are the effects of the <emph>Early Numeracy Curriculum</emph> on the acquisition of early numeracy skills in students with MSDD and significant behavior challenges?</p> <p>Graph: Figure 1. Student Independent Correct Responses on Early Numeracy Curriculum Unit One Assessment. Note : Each tier represents an individual participant. Solid vertical lines Indicate the start of the intervention phase. Data are shown using a multiple probe across participants design with independent timelines for each student. The maximum possible score is 26 correct responses. Eloise's baseline includes a gap due to illness and school breaks. Gaps in intervention data reflect scheduled assessment intervals and student absences related to school and health-related disruptions.</p> <hd id="AN0189916318-2">Method</hd> <p></p> <hd id="AN0189916318-3">Setting</hd> <p>The study took place in a self-contained special education classroom located within a PreK–8 Title I public school in a small rural community in the southeastern USA. The school served 563 students, nearly half of whom (46%) qualified for free or reduced lunch. The student population was predominantly Caucasian (64%), with 28% identifying as Hispanic, 4% as African American, and another 4% identifying as two or more races. Instruction was delivered at a small group table in the classroom, which was arranged to minimize distractions and support one-on-one instruction.</p> <hd id="AN0189916318-4">Participants</hd> <p>Three elementary students with MSDD and significant behavior challenges participated in the study. All students were enrolled in a self-contained "AU" classroom, a state-designated setting for students with educational classifications of autism and intellectual disability. This dual classification aligns with the research label of MSDD, which reflects the combination of cognitive, communication, and adaptive support needs commonly associated with these eligibility categories. To participate, students met the following criteria: (a) documented classifications of autism and intellectual disability; (b) instructional goals related to early numeracy; (c) engagement in behaviors that interfered with instruction, as reported by teachers and confirmed through review of school records (e.g., behavior intervention plans, functional behavior assessments, individualized education plan [IEP]); and (d) regular school attendance (i.e., at least 90% of scheduled school days during the prior year). Participants were recruited through purposeful sampling from an eligible classroom in a local public school. Written informed consent was obtained from families and the study was approved by the university's Institutional Review Board. Students were assigned pseudonyms to protect their identity. Participant profiles are summarized in Table 1. Additional information was collected through teacher interviews, IEP records, and cumulative files to describe each student's academic, communication, and behavior profiles. All three participants required individualized behavior supports (e.g., token reinforcement, preferred activities, sensory breaks) to participate in instruction.</p> <p>Table 1. Participant Characteristics.</p> <p>Graph</p> <p> <ephtml> <table><colgroup><col align="left" /><col align="char" char="." /><col align="left" /><col align="left" /><col align="char" char="." /><col align="left" /><col align="left" /><col align="left" /><col align="left" /></colgroup><thead><tr><th align="left">Participant</th><th align="left">Age</th><th align="left">Grade</th><th align="left">Race/ethnicity</th><th align="left">IQ (WISC-V)</th><th align="left">Diagnosis</th><th align="left">Communication</th><th align="left">Academic IEP goals</th><th align="left">Behavioral supports</th></tr></thead><tbody><tr><td>Claire</td><td>10</td><td>5th</td><td>White</td><td>50</td><td>Autism</td><td>Limited speech; uses Proloquo2Go AAC</td><td>Numeral identification; one-to-one correspondence</td><td>Deep breathing chart; foam chin press for self-injury</td></tr><tr><td>Ben</td><td>11</td><td>6th</td><td>Hispanic</td><td>40</td><td>Autism, ADHD</td><td>Nonverbal; uses Proloquo2Go AAC</td><td>Numeral identification; counting with one-to-one correspondence; shape recognition</td><td>Token economy for attending behaviors</td></tr><tr><td>Eloise</td><td>5</td><td>K</td><td>White</td><td>32</td><td>Autism, ADHD, ODD</td><td>Verbal (mild articulation difficulty)</td><td>Numeral Identification; counting with one-to-one correspondence</td><td>Calming strategies; reduced distractions; split sessions</td></tr></tbody></table> </ephtml> </p> <p>1 <emph>Note</emph>: Diagnoses and IQ scores were based on school records and WISC-V ([<reflink idref="bib27" id="ref32">27</reflink>]) assessments. AAC = augmentative and alternative communication; ADHD = attention deficit hyperactivity disorder; K = kindergarten; ODD = oppositional defiant disorder.</p> <hd id="AN0189916318-5">Special Education Teacher</hd> <p>The special education teacher who implemented the study was in her second year of teaching students with MSDD. She held a degree in special education and a valid teaching license. During the study, she was also working on a master's degree in special education focused on students with behavior and emotional disabilities.</p> <hd id="AN0189916318-6">Materials</hd> <p>The <emph>Early Numeracy Curriculum</emph> ([<reflink idref="bib11" id="ref33">11</reflink>]) was used to guide instruction and assessment in this study. Designed for students with MSDD, the curriculum included four units with six scripted lessons each. This study used lessons from Unit One (excluding the sixth lesson because it was a review lesson). Each lesson featured a theme-based math story and structured activities to support early numeracy instruction. Instructional materials included a set maker, line counter, pattern board, blank calendar, magnetic number and symbol tiles, a whiteboard, and themed manipulatives. Instruction and assessment sessions took place at a small group table in the students' special education classroom.</p> <hd id="AN0189916318-7">Procedures</hd> <p>All instruction was delivered one-on-one by a certified special education teacher trained in delivering the <emph>Early Numeracy Curriculum</emph> ([<reflink idref="bib11" id="ref34">11</reflink>]) and prompting procedures used in the curriculum. Each session followed the curriculum's scripted routine and was delivered across five lessons from Unit One. Sessions began with an interest-building activity aligned with the lesson theme and included a teacher-read math story, guided practice on targeted skills, and student engagement with curriculum manipulatives. Sessions lasted approximately 20 min and were repeated three times per lesson. The same instructional format and materials were used across all participants. Session fidelity was monitored using a task analysis checklist, and one out of three sessions were video-recorded for interobserver agreement and procedural reliability. As part of their existing IEPs, students continued to receive individualized behavior supports (e.g., token boards, preferred activities, and sensory breaks) during instruction. These supports were not components of the experimental intervention but may have supported student participation.</p> <hd id="AN0189916318-8">Dependent Variable</hd> <p>The primary dependent variable was the number of correct independent responses on a 26-item early numeracy assessment provided with the curriculum (i.e., Unit One Assessment, [<reflink idref="bib11" id="ref35">11</reflink>]). The same teacher who taught the lessons administered the assessment in the classroom in a one-on-one setting and collected data on each test item. Items were scored as correct or incorrect. A correct response was defined as an accurate, independent answer for test items and the assessment had a possible total score of 26.</p> <p>The Unit One assessment included two types of items: demonstration items and test items across the 12 targeted skills, and were the same for baseline and intervention probes. Assessment procedures began with a demonstration trial for all early numeracy skills assessed except identifying the symbol for equal (=). Demonstration items helped ensure that participants understood what was going to be asked by the upcoming test items and were not scored. To illustrate, when administrating the demonstration trial for counting 1–5 movable objects in a line, the teacher placed the counting line in front of the student, then put two pennies on the counting line and modeled counting by pushing the pennies above the line, one at a time, saying 1, 2 as the pennies were moved. The pennies were moved back to the line and the teacher said to the student, "Your turn. Count the pennies. How many pennies are there?" When students responded correctly, they received general verbal praise (e.g., "Nice work answering that question!"). When participants did not respond, an additional model along with another opportunity to respond was given. If there was still no response, the teacher physically guided the student to count the pennies (or whatever the item was demonstrating). In this example, the test item asked the learner to count a different number of pennies using the same materials. All assessment sessions were video-recorded for procedural fidelity monitoring.</p> <hd id="AN0189916318-9">Independent Variable</hd> <p>The independent variable was a multi-component instructional package based on the <emph>Early Numeracy Curriculum</emph> ([<reflink idref="bib11" id="ref36">11</reflink>]). The intervention targeted 12 early numeracy skills: count 1–5 movable objects in a line, count 1–5 nonmovable objects in a line, rote count from 1–5, make sets of 1–3, add premade sets with sums to 5, compare sets for same/equal, identify the symbol for equal, identify an ABAB pattern, use a nonstandard unit of measurement to measure 1–5, identify dates from first to fifth on a calendar, identify 1–5 days later in a week using a calendar, and identify numerals 1–5. Each lesson included a theme-based math story and embedded instructional trials on all 12 skills. Instruction was delivered using systematic prompting procedures (constant time delay [CTD] and SLP), and curriculum materials were integrated into each activity to support access and engagement. Skills remained consistent across lessons to provide repeated practice and promote fluency.</p> <hd id="AN0189916318-10">Research Design</hd> <p>A single-case multiple probe across participants design ([<reflink idref="bib16" id="ref37">16</reflink>]) was used to demonstrate experimental control. The study phases included baseline and intervention. Once baseline was established for all participants, the first participant began the intervention phase and the other participants continued in baseline conditions. When the first participant showed an increased trend and level, the next participant entered the study. Each participant continued to enter the study in a time lagged manner until all participants received the intervention. Visual analysis was used to determine changes in level, trend, and variability within and across phases for each participant. The number of sessions per phase varied based on each participant's performance and school-related constraints (e.g., absenteeism and school breaks).</p> <hd id="AN0189916318-11">Assessment Timing and Probe Spacing</hd> <p>During the intervention phase, each participant received three instructional sessions per lesson prior to completing the assessment probe. As a result, data points in the intervention phase were typically collected once per week. This pacing reflects the practical scheduling constraints in the classroom. Gaps between graphed data points in the intervention phase represent these intervals between assessment probes rather than missing data.</p> <hd id="AN0189916318-12">Procedural Fidelity and Interobserver Agreement</hd> <p></p> <hd id="AN0189916318-13">Fidelity Tools and Scoring Procedures</hd> <p>To evaluate fidelity, the research team created two task-analyzed checklists based on the instructional procedures outlined in the <emph>Early Numeracy Curriculum</emph> teacher's guide ([<reflink idref="bib11" id="ref38">11</reflink>]): (a) an 82-step checklist for delivering the Unit One assessment, and (b) a 26-step checklist for delivering an early numeracy lesson. These researcher-developed forms outlined the expected sequence of instructional and assessment actions. In contrast, the curriculum-provided <emph>Early Numeracy Unit One Assessment</emph> form was used to measure student skill acquisition and was not altered by the research team. Procedural fidelity was calculated using the method described by [<reflink idref="bib2" id="ref39">2</reflink>] ‒ dividing the number of steps completed by the total number of steps planned, then multiplying by 100%.</p> <hd id="AN0189916318-14">Observer Training and Data Collection</hd> <p>The second observer was trained to use the two researcher-created fidelity checklists and the <emph>Early Numeracy Unit One Assessment</emph> form. Training included scoring video-recorded lessons and assessment sessions not used for the study. No training videos were used in reliability calculations. To evaluate implementation fidelity, the second observer independently scored 35% of all instructional and assessment sessions using the checklists. Missed steps most commonly involved omitted instructions or generic praise. Across observations, mean fidelity was 97% for assessments (range = 94–99%) and 99% for lessons (range = 95–100%). As part of the fidelity plan, any session scored below 90% would have triggered booster coaching. However, this threshold was never reached.</p> <hd id="AN0189916318-15">Interobserver Agreement (IOA)</hd> <p>IOA was calculated for at least 30% of all baseline and intervention probe sessions. The second observer independently recorded student responses on the <emph>Early Numeracy Unit One Assessment</emph> form, indicating whether responses were correct (+) or incorrect (–). Item-by-item agreement was defined as both observers recording the same score for an item. IOA was calculated by dividing the number of agreements by the total number of agreements plus disagreements, then multiplying by 100% ([<reflink idref="bib16" id="ref40">16</reflink>]). Mean IOA across participants was 96% (range = 90–100%), indicating strong reliability of scoring procedures.</p> <hd id="AN0189916318-16">Experimental Design Procedures</hd> <p></p> <hd id="AN0189916318-17">Baseline</hd> <p>To obtain baseline data, the teacher collected a minimum of five data points per student by administering the <emph>Early Numeracy Unit One Assessment</emph>. After initial stability was observed, multiple additional probes were conducted to confirm baseline levels remained consistent before each student began intervention. Baseline probe sessions were administered individually in the special education classroom and followed the same procedures as intervention probes. Baseline probe sessions typically took 10–20 min.</p> <hd id="AN0189916318-18">Intervention</hd> <p>The intervention provided instruction on the targeted early numeracy objectives. First, the teacher began the lesson with an interest building activity (i.e., anticipatory set) related to the lesson. For a story about a day spent at the beach, the interest building activity might include asking the student if they have ever been to the beach followed by a brief conversation about the experience. The teacher might also share a time when they went to the beach and offer a seashell or some sand for the students to explore for the purpose of activating their background knowledge about the lesson's theme.</p> <p>Next, the teacher read a theme-based math story aloud from beginning to end without stopping to promote comprehension. Then the teacher used the scripted lesson to guide students through the math story again, stopping at predetermined points in the story to teach the 12 early numeracy skills. For example, in a story about a day at the beach, the script guided the teacher to reread the first four lines of the story that introduced the date Amber and her family were going to the beach. The teacher used the designated prompting procedure indicated in the script for finding the date on the calendar graphic organizer (identify dates from first to fifth on a calendar) with the participant. Multiple opportunities were provided during the lesson for participants to practice using early numeracy skills, either with prompted support or independently. In another example from the math story about the speedway, the story talked about the seats being arranged in an ABAB pattern (i.e., red, blue, red, and blue). Red and blue cubes were then set up to create an ABAB pattern and a non-ABAB pattern and participants were asked to point to the ABAB pattern. They would also identify another ABAB pattern during the after-lesson activity.</p> <p>All skills were taught using the SLP strategy except for numeral identification which was taught using the CTD prompting strategy. The steps for teaching numeral identification were described in the lesson script. Students were provided small whiteboards with magnetic number tiles one through five. During the first round (i.e., 0-s), the teacher simultaneously selected a number from an array on her whiteboard to show students and said, "Find the number 4." During the second round (i.e., 10 s delay), the teacher said, "Find the number "4" and waited 10 s for participants to find the number on their number boards. Claire touched the number on the number board and said "4," Ben pointed to the number on his number board and used his AAC device to say "4," and Eloise touched the number on her number board. After students found the number 4, the teacher delivered descriptive verbal praise, "Good job! You're right. That is the number 4." When students made an error or did not respond, the teacher delivered an error correction where she said and showed the correct response (e.g., "This is the number 4") and asked students to find the number again ("Show me 4").</p> <p>For all other early numeracy skills, participants were given a chance to independently respond and, when they were unable to answer on their own, a model prompt was provided using the SLP. Specific verbal praise was given for correct responses (e.g., "Great work! You counted to 3!") and error correction was given for incorrect or no responses (e.g., "Count to 3 like this: 1-2-3. Now, it is your turn. Count to 3"). Manipulatives related to the story (e.g., flip flops for the beach story) helped participants actively engage in the lessons and solve the math problems. The teacher repeated a lesson three times before introducing the next lesson for that unit. The Unit One assessment was administered in between these lessons to monitor students' progress on early numeracy skill acquisition. The early numeracy skills remained constant in each lesson in Unit One but the materials and order of responding varied. For example, in the pirate treasure story, the students rote counted to five first while, in the class trip story, the students identified dates from first to fifth on a calendar first.</p> <hd id="AN0189916318-19">Social Validity</hd> <p>After the study concluded, the special education teacher completed a 10-item social validity questionnaire developed by the research team to evaluate the acceptability and feasibility of the intervention. The form assessed perceptions of the curriculum's usefulness, effectiveness, alignment with IEP goals, and feasibility for students with MSDD. The teacher strongly agreed or agreed that the curriculum met her students' needs, supported participation, aligned with IEP goals, and contributed to skill gains. She also indicated that she would use the curriculum again, viewed early numeracy instruction as important for students with MSDD, and found the lessons appropriately timed and engaging. The only item marked "disagree" related to the time required to create adaptations, indicating that the curriculum's materials were not time consuming to adapt. Overall, her responses indicated high social validity for the curriculum in a real-world classroom setting.</p> <hd id="AN0189916318-20">Data Analysis</hd> <p>Visual analysis served as the primary method for evaluating the presence of a functional relation in this multiple probe across participants design (see Figure 1). Following the recommendations of [<reflink idref="bib14" id="ref41">14</reflink>], graphs were examined for changes in level, trend, variability, immediacy of effect, and consistency of data patterns across phases and participants. The presence of a functional relation was judged based on (a) changes in performance following intervention, (b) consistency of effects across participants, and (c) stability of baseline data prior to intervention.</p> <p>To supplement visual analysis, Tau-U effect sizes were calculated to quantify the magnitude of intervention effects ([<reflink idref="bib19" id="ref42">19</reflink>]; [<reflink idref="bib21" id="ref43">21</reflink>]). Tau-U is a nonparametric index for single-case designs that measures the degree of nonoverlap between baseline (A) and intervention (B) data and can adjust for positive trends in baseline. For each participant, we calculated across-phase nonoverlap (Tau-AB) by making all pairwise comparisons between A and B data points in chronological order, scoring concordant pairs as 1, discordant pairs as 0, and ties as 0.5. Tau-AB was computed as (Concordant − Discordant) ÷ (nA × nB), where nA and nB are the number of baseline and intervention observations. Baseline trend was estimated using Kendall's tau between session order and baseline data values; positive trends were subtracted from Tau-AB to yield baseline-corrected Tau-U, while negative or zero trends were not adjusted.</p> <p>All calculations were performed directly from the study dataset (Excel) using a custom Python script replicating the formulas from <emph>SingleCaseES</emph> (R package, [<reflink idref="bib20" id="ref44">20</reflink>]). Baseline and intervention data for each participant (Claire, Ben, Eloise) were analyzed separately, and corrected Tau-U values were aggregated using the weighted mean, with weights equal to the number of A × B pairwise comparisons per participant.</p> <hd id="AN0189916318-21">Results</hd> <p>Overall, visual analysis indicated mixed evidence of a functional relation between the intervention and improved early numeracy performance across participants. One participant (Claire) demonstrated a clear and consistent increase in correct independent responses following the introduction of the intervention, consistent with a strong functional relation. For the other two participants, performance improved during the intervention phase, but patterns such as pre-intervention upward trends (Ben) and gradual or variable gains (Eloise) limited confidence in attributing change solely to the intervention.</p> <hd id="AN0189916318-22">Claire</hd> <p>During baseline probe sessions, Claire demonstrated low and variable performance (<emph>M</emph> = 4.2; range = 0–9). After the introduction of the intervention, her correct independent responses increased substantially (<emph>M</emph> = 14; range = 9–22), with consistent improvement across sessions. Although the first intervention data point overlapped with a baseline data point, her performance increased steadily thereafter, demonstrating a strong upward trend and a clear change from baseline to intervention.</p> <hd id="AN0189916318-23">Ben</hd> <p>Ben's baseline performance was low (<emph>M</emph> = 1.5; range = 0–3), with a slight upward trend observed across sessions. Following the start of the intervention began, his correct responses continued to increase (<emph>M</emph> = 8.8; range = 4–13). However, because this upward trend began before the intervention was introduced and improvement occurred gradually as scores moved upward over multiple sessions rather than as an immediate level change, visual analysis does not support a functional relation between the intervention and changes in performance.</p> <hd id="AN0189916318-24">Eloise</hd> <p>Eloise demonstrated consistently low and stable responding during baseline (<emph>M</emph> = 0.1; range = 0–1). During the intervention phase, her correct responses increased (<emph>M</emph> = 5.4; range = 3–11), though performance fluctuated across sessions. The pattern reflects a moderate, gradual upward trend in performance rather than a distinct or sustained level change, providing limited evidence for a strong functional relation.</p> <hd id="AN0189916318-25">Magnitude of Effect</hd> <p>After adjusting for positive baseline trend, the weighted mean Tau-U across participants was 0.77, which represents a strong level of nonoverlap between baseline and intervention phases and indicates substantial improvement in performance during the intervention. Individual baseline-corrected Tau-U values ranged from 0.47 to 1.00, all in the positive direction, indicating that each participant demonstrated improvement and none showed a neutral or negative effect. By participant, baseline-corrected Tau-U values were Claire = 0.47, Ben = 0.50, and Eloise = 1.00. According to [<reflink idref="bib19" id="ref45">19</reflink>] guidelines, values between 0.40 and 0.60 indicate a moderate effect and values above 0.60 indicate a strong effect, placing Claire and Ben in the moderate range and Eloise in the strong-to-maximum range. In practical terms, moderate effects reflect noticeable gains that are likely to be meaningful for the learner, while strong effects indicate highly consistent improvement across intervention sessions.</p> <hd id="AN0189916318-26">Discussion</hd> <p>Previous research on the <emph>Early Numeracy Curriculum</emph> ([<reflink idref="bib11" id="ref46">11</reflink>]) has consistently demonstrated positive academic outcomes for students with MSDD (e.g., [<reflink idref="bib8" id="ref47">8</reflink>]; [<reflink idref="bib9" id="ref48">9</reflink>]; [<reflink idref="bib10" id="ref49">10</reflink>]; [<reflink idref="bib12" id="ref50">12</reflink>]; [<reflink idref="bib13" id="ref51">13</reflink>]); however, these studies generally included students whose learning was not significantly affected by behavior support needs that might disrupt instruction or require targeted behavioral interventions. This study expands the evidence base by demonstrating that students with MSDD and significant behavior challenges can make gains in early numeracy when provided systematic instruction aligned with their individual learning needs. This is an important addition to the literature, as students with combined academic and behavioral needs are often excluded from intervention research due to concerns about fidelity, data variability, or session completion. In this study, participants continued receiving their typical individualized behavior supports, and results indicate that the curriculum can be implemented effectively in classrooms where such supports are necessary alongside academic instruction. By addressing this underserved population, the study provides practical implementation insights and reinforces the value of designing interventions that integrate both instructional and behavioral considerations within the same educational context.</p> <p>Another way this study advances the field is by contributing to the small but growing body of research in which the <emph>Early Numeracy Curriculum</emph> ([<reflink idref="bib11" id="ref52">11</reflink>]) is delivered by classroom teachers rather than researchers or trained research staff. Most prior investigations ([<reflink idref="bib8" id="ref53">8</reflink>]; [<reflink idref="bib10" id="ref54">10</reflink>]; [<reflink idref="bib12" id="ref55">12</reflink>]; [<reflink idref="bib13" id="ref56">13</reflink>]) were implemented by researchers or with researcher support (e.g., the researcher conducted the assessment probe sessions), which helped ensure high procedural fidelity but may not fully reflect the realities of daily classroom instruction. [<reflink idref="bib9" id="ref57">9</reflink>] demonstrated the feasibility of teacher-led implementation, though such examples remain rare. The present study strengthens this line of evidence by showing that a special education teacher, working within the demands of a real-world classroom, can successfully implement the curriculum with fidelity and achieve meaningful student outcomes.</p> <p>Taken together, the use of a practicing classroom teacher as the interventionist and the inclusion of students with significant behavior challenges illustrate that the <emph>Early Numeracy Curriculum</emph> ([<reflink idref="bib11" id="ref58">11</reflink>]) can be integrated into authentic, multifaceted instructional environments while maintaining procedural fidelity and producing positive learning gains for most participants. This combination reflects the realities of many special education classrooms and extends the literature beyond highly controlled research settings. More importantly, it provides a model for how evidence-based academic instruction can be sustained in real-world contexts where teachers must balance intensive behavioral supports with ambitious learning goals, offering a pathway for broader adoption and long-term impact.</p> <hd id="AN0189916318-27">Limitations and Future Directions</hd> <p>The results of this study should be considered in light of several limitations. One limitation was that only one student (Claire) reached the 80% mastery criterion on the curriculum-aligned assessment. The other two students demonstrated progress but did not achieve mastery within the study timeframe, underscoring the challenge of meeting high-performance benchmarks for students with MSDD and significant behavior challenges. These findings highlight the importance of aligning mastery criteria with both research-based expectations and the realities of school-based implementation. Future researchers might examine alternative mastery thresholds or incremental benchmarks that still promote high expectations while acknowledging the variability in learning trajectories for this population.</p> <p>Another limitation involved dosage, influenced by both the planned instructional schedule and unplanned absences. Lessons were delivered three times per week, fewer than the four to five days recommended by the <emph>Early Numeracy Curriculum</emph> ([<reflink idref="bib11" id="ref59">11</reflink>]), and implementation was occasionally interrupted by factors such as family travel and health-related absences. These interruptions reduced total instructional exposure and, for one student (Eloise), created gaps in the data record. Although all students made measurable gains, students with complex learning and behavioral needs may require more frequent opportunities to respond and additional practice to achieve and maintain mastery ([<reflink idref="bib16" id="ref60">16</reflink>]; [<reflink idref="bib24" id="ref61">24</reflink>]). Future research may want to explore feasible ways to boost instructional intensity and maintain continuity during unavoidable disruptions, such as embedding numeracy practice into daily classroom routines or using paraprofessionals to deliver brief review or catch-up sessions.</p> <p>A third limitation relates to the single-case multiple probe across participants design. The presence of a baseline trend for one participant (Ben) and a gradual, delayed effect for another (Eloise) reduced confidence in a strong causal interpretation for those students. Although Claire's data demonstrated a clearer change in trend and level, variation in response patterns across participants limits internal validity. While gains in performance were observed, they should be interpreted cautiously. These considerations highlight the need to balance rigorous methodological standards with the realities of school-based research, where factors such as variable attendance, ongoing behavior supports, and instructional pacing can influence both the fidelity and impact of an intervention. Future researchers should also consider design decisions that both strengthen experimental control and enhance the interpretability of findings in authentic school settings. While traditional approaches emphasize rigorous control through stable baselines and clear phase changes, other strategies can also address threats to validity ([<reflink idref="bib15" id="ref62">15</reflink>]). For example, including more than three participants, replicating effects with new participants in different settings, or embedding randomization procedures may strengthen the evidence base for early numeracy instruction with this population. Researchers might also explicitly compare observed changes to expected performance patterns, particularly when gradual, delayed improvements are anticipated rather than immediate level changes. This approach, as described by Ledford and colleagues, can guide analysis and interpretation in single-case research by clarifying how actual outcomes align with anticipated trends.</p> <p>A fourth limitation was the repeated use of the same 26-item assessment to measure student progress, which may have introduced practice effects. Without alternate forms or variations in assessment items, it is difficult to determine whether observed improvements reflect true skill acquisition or increased familiarity with the test content and format. Future researchers should consider using alternate assessment forms or rotating item sets to reduce the likelihood of practice effects influencing results.</p> <p>A further limitation was that individualized behavior supports were implemented throughout the study but were not introduced or manipulated as part of the intervention. As such, it is not possible to determine their individual contribution to student outcomes. Anecdotal reports suggested these supports helped reduce interfering behaviors and support participation but formal data were not collected. Future researchers should investigate how behavior supports interact with academic instruction and whether certain strategies are more effective in promoting engagement and learning.</p> <p>A final limitation was that social validity data were collected from only one stakeholder, the classroom teacher who also served as the interventionist. While her responses indicated strong support for the curriculum's utility, feasibility, and alignment with IEP goals, the perspectives of paraeducators, students, and family members were not collected. Including these voices in future research would provide a more complete picture of the intervention's acceptability and relevance in authentic school settings.</p> <ref id="AN0189916318-28"> <title> References </title> <blist> <bibl id="bib1" idref="ref26" type="bt">1</bibl> <bibtext> Adedipe D. T., Walton K. M. (2025). Telehealth parent training for challenging behavior in children with developmental disabilities: A systematic review and meta-analysis. Journal of Autism and Developmental Disabilities. Advance online publication. https://doi.org/10.1007/s40489-025-00501-5</bibtext> </blist> <blist> <bibl id="bib2" idref="ref39" type="bt">2</bibl> <bibtext> Billingsley F., White O. R., Munson R. (1980). Procedural reliability: A rationale and example. 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Hudson https://orcid.org/0000-0002-7673-4719</bibtext> </blist> <blist> <bibtext> The authors received no financial support for the research, authorship, and/or publication of this article.</bibtext> </blist> <blist> <bibtext> The authors declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.</bibtext> </blist> </ref> <aug> <p>By Melissa E. Hudson; Taylor L. Krueger and Tosha L. Owens</p> <p>Reported by Author; Author; Author</p> </aug> <nolink nlid="nl1" bibid="bib22" firstref="ref1"></nolink> <nolink nlid="nl2" bibid="bib26" firstref="ref2"></nolink> <nolink nlid="nl3" bibid="bib23" firstref="ref3"></nolink> <nolink nlid="nl4" bibid="bib25" firstref="ref8"></nolink> <nolink nlid="nl5" bibid="bib11" firstref="ref11"></nolink> <nolink nlid="nl6" bibid="bib10" firstref="ref15"></nolink> <nolink nlid="nl7" bibid="bib12" firstref="ref16"></nolink> <nolink nlid="nl8" bibid="bib13" firstref="ref17"></nolink> <nolink nlid="nl9" bibid="bib17" firstref="ref18"></nolink> <nolink nlid="nl10" bibid="bib18" firstref="ref27"></nolink> <nolink nlid="nl11" bibid="bib27" firstref="ref32"></nolink> <nolink nlid="nl12" bibid="bib16" firstref="ref37"></nolink> <nolink nlid="nl13" bibid="bib14" firstref="ref41"></nolink> <nolink nlid="nl14" bibid="bib19" firstref="ref42"></nolink> <nolink nlid="nl15" bibid="bib21" firstref="ref43"></nolink> <nolink nlid="nl16" bibid="bib20" firstref="ref44"></nolink> <nolink nlid="nl17" bibid="bib24" firstref="ref61"></nolink> <nolink nlid="nl18" bibid="bib15" firstref="ref62"></nolink>
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  Data: The Effects of an Early Numeracy Intervention Package for Students with Moderate to Severe Developmental Disabilities and Significant Behavior Challenges
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  Data: <searchLink fieldCode="AR" term="%22Melissa+E%2E+Hudson%22">Melissa E. Hudson</searchLink> (ORCID <externalLink term="https://orcid.org/0000-0002-7673-4719">0000-0002-7673-4719</externalLink>)<br /><searchLink fieldCode="AR" term="%22Taylor+L%2E+Krueger%22">Taylor L. Krueger</searchLink><br /><searchLink fieldCode="AR" term="%22Tosha+L%2E+Owens%22">Tosha L. Owens</searchLink>
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  Data: <searchLink fieldCode="SO" term="%22Education+and+Training+in+Autism+and+Developmental+Disabilities%22"><i>Education and Training in Autism and Developmental Disabilities</i></searchLink>. 2025 60(4):361-379.
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  Data: Division on Autism and Developmental Disabilities, Council for Exceptional Children. DDD, P.O. Box 3512, Fayetteville, AR 72702. Tel: 479-575-3326; Fax: 479-575-6676; Web site: http://www.daddcec.com/
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  Data: <searchLink fieldCode="DE" term="%22Numeracy%22">Numeracy</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematics+Skills%22">Mathematics Skills</searchLink><br /><searchLink fieldCode="DE" term="%22Intervention%22">Intervention</searchLink><br /><searchLink fieldCode="DE" term="%22Program+Effectiveness%22">Program Effectiveness</searchLink><br /><searchLink fieldCode="DE" term="%22Elementary+School+Students%22">Elementary School Students</searchLink><br /><searchLink fieldCode="DE" term="%22Students+with+Disabilities%22">Students with Disabilities</searchLink><br /><searchLink fieldCode="DE" term="%22Developmental+Disabilities%22">Developmental Disabilities</searchLink><br /><searchLink fieldCode="DE" term="%22Severe+Disabilities%22">Severe Disabilities</searchLink><br /><searchLink fieldCode="DE" term="%22Behavior+Problems%22">Behavior Problems</searchLink><br /><searchLink fieldCode="DE" term="%22Teacher+Attitudes%22">Teacher Attitudes</searchLink><br /><searchLink fieldCode="DE" term="%22Student+Needs%22">Student Needs</searchLink><br /><searchLink fieldCode="DE" term="%22Severe+Intellectual+Disability%22">Severe Intellectual Disability</searchLink><br /><searchLink fieldCode="DE" term="%22Moderate+Intellectual+Disability%22">Moderate Intellectual Disability</searchLink><br /><searchLink fieldCode="DE" term="%22Autism+Spectrum+Disorders%22">Autism Spectrum Disorders</searchLink><br /><searchLink fieldCode="DE" term="%22Self+Contained+Classrooms%22">Self Contained Classrooms</searchLink>
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  Data: 10.1177/21541647251399489
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  Label: Abstract
  Group: Ab
  Data: This study examined the effects of an early numeracy intervention package on the acquisition of foundational math skills in three elementary students with moderate to severe developmental disabilities and significant behavior challenges. The intervention package included the "Early Numeracy Curriculum" and systematic instructional strategies. A multiple probe across participants design was used to evaluate changes in correct independent responses on a curriculum-aligned assessment. All participants demonstrated improved performance during intervention, although gains were gradual and overlapped with baseline trends for some students. The teacher rated the intervention as feasible and effective and reported that it aligned with students' IEP goals. Findings support the use of structured early numeracy intervention packages that incorporate systematic instruction for students with complex learning and behavior needs.
– Name: AbstractInfo
  Label: Abstractor
  Group: Ab
  Data: As Provided
– Name: DateEntry
  Label: Entry Date
  Group: Date
  Data: 2026
– Name: AN
  Label: Accession Number
  Group: ID
  Data: EJ1496461
PLink https://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=eric&AN=EJ1496461
RecordInfo BibRecord:
  BibEntity:
    Identifiers:
      – Type: doi
        Value: 10.1177/21541647251399489
    Languages:
      – Text: English
    PhysicalDescription:
      Pagination:
        PageCount: 19
        StartPage: 361
    Subjects:
      – SubjectFull: Numeracy
        Type: general
      – SubjectFull: Mathematics Skills
        Type: general
      – SubjectFull: Intervention
        Type: general
      – SubjectFull: Program Effectiveness
        Type: general
      – SubjectFull: Elementary School Students
        Type: general
      – SubjectFull: Students with Disabilities
        Type: general
      – SubjectFull: Developmental Disabilities
        Type: general
      – SubjectFull: Severe Disabilities
        Type: general
      – SubjectFull: Behavior Problems
        Type: general
      – SubjectFull: Teacher Attitudes
        Type: general
      – SubjectFull: Student Needs
        Type: general
      – SubjectFull: Severe Intellectual Disability
        Type: general
      – SubjectFull: Moderate Intellectual Disability
        Type: general
      – SubjectFull: Autism Spectrum Disorders
        Type: general
      – SubjectFull: Self Contained Classrooms
        Type: general
    Titles:
      – TitleFull: The Effects of an Early Numeracy Intervention Package for Students with Moderate to Severe Developmental Disabilities and Significant Behavior Challenges
        Type: main
  BibRelationships:
    HasContributorRelationships:
      – PersonEntity:
          Name:
            NameFull: Melissa E. Hudson
      – PersonEntity:
          Name:
            NameFull: Taylor L. Krueger
      – PersonEntity:
          Name:
            NameFull: Tosha L. Owens
    IsPartOfRelationships:
      – BibEntity:
          Dates:
            – D: 01
              M: 12
              Type: published
              Y: 2025
          Identifiers:
            – Type: issn-print
              Value: 2154-1647
          Numbering:
            – Type: volume
              Value: 60
            – Type: issue
              Value: 4
          Titles:
            – TitleFull: Education and Training in Autism and Developmental Disabilities
              Type: main
ResultId 1