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The Effects of a Supplemental Explicit Counting Intervention for Preschool Children

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Title: The Effects of a Supplemental Explicit Counting Intervention for Preschool Children
Language: English
Authors: Hinton, Vanessa M., Flores, Margaret M., Schweck, Kelly, Burton, Megan E.
Source: Preventing School Failure. 2016 60(3):183-193.
Availability: Routledge. Available from: Taylor & Francis, Ltd. 325 Chestnut Street Suite 800, Philadelphia, PA 19106. Tel: 800-354-1420; Fax: 215-625-2940; Web site: http://www.tandf.co.uk/journals
Peer Reviewed: Y
Page Count: 11
Publication Date: 2016
Document Type: Journal Articles
Reports - Research
Education Level: Preschool Education
Early Childhood Education
Descriptors: Mathematics Instruction, Computation, Preschool Children, Mathematics Skills, Teaching Methods, At Risk Students, Special Education, Inclusion, Preschool Education, Developmental Delays, Intervention, Rural Schools, Instructional Effectiveness, Questionnaires
Assessment and Survey Identifiers: Leiter International Performance Scale
DOI: 10.1080/1045988X.2015.1065400
ISSN: 1045-988X
Abstract: Counting skills are foundational for young children to build number concepts in mathematics. Multitiered instruction that involves core instruction as well as supplemental interventions is implemented to support young children in the learning process and promote early intervention of basic skills. Researchers show that explicit instruction is successful in teaching students in preschool. More research needs to be conducted on brief explicit mathematic interventions that target the skill of counting and are supplemental to preschool mathematics core instruction. In this study, researchers examine the effects of using explicit instruction as an intervention to teach counting skills for four children who were at risk for mathematics difficulties or who received special education services for developmental delay in an inclusive preschool setting. The researchers find a functional relation for a 15-minute supplemental explicit intervention and counting skills. Implications of these findings are also discussed.
Abstractor: As Provided
Number of References: 17
Entry Date: 2016
Accession Number: EJ1100004
Database: ERIC
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  Value: <anid>AN0115578960;psf01jul.16;2019Mar15.12:12;v2.2.500</anid> <title id="AN0115578960-1">The Effects of a Supplemental Explicit Counting Intervention for Preschool Children. </title> <p>Counting skills are foundational for young children to build number concepts in mathematics. Multitiered instruction that involves core instruction as well as supplemental interventions is implemented to support young children in the learning process and promote early intervention of basic skills. Researchers show that explicit instruction is successful in teaching students in preschool. More research needs to be conducted on brief explicit mathematic interventions that target the skill of counting and are supplemental to preschool mathematics core instruction. In this study, researchers examine the effects of using explicit instruction as an intervention to teach counting skills for four children who were at risk for mathematics difficulties or who received special education services for developmental delay in an inclusive preschool setting. The researchers find a functional relation for a 15-minute supplemental explicit intervention and counting skills. Implications of these findings are also discussed.</p> <p>Keywords: counting; explicit instruction; intervention; mathematics; preschool</p> <p>Multitiered instructional frameworks based on student progress monitoring are increasingly being implemented to teach young children in preschool settings. A multitiered approach encourages early intervention to prevent students from failing before receiving the help they need (Vaughn & Fuchs, [<reflink idref="bib17" id="ref1">17</reflink>]). Toll & Luit ([<reflink idref="bib13" id="ref2">13</reflink>]) explain that there is ample evidence to support the need for and various ways of implementing early numeracy instruction, yet there is little information on the effects of interventions designed especially for younger students. An important aspect of mathematics instruction in preschool involves counting because it is linked to young children developing fluidity and flexibility with numbers, the sense of what numbers mean, and the ability to perform mental mathematics and observe the world and make comparisons (Berch, [<reflink idref="bib2" id="ref3">2</reflink>]; National Council of Teachers of Mathematics, [NCTM], [<reflink idref="bib7" id="ref4">7</reflink>]).</p> <p>To date there is a need to examine supplemental mathematic interventions designed to teach counting skills for preschool and taught in conjunction with the core mathematic instruction offered in an inclusive preschool classroom (Gersten et al., [<reflink idref="bib4" id="ref5">4</reflink>]). The purpose of this study is to investigate the effects of using explicit instruction as a supplemental intervention for counting combined with a preschool classroom's Tier I core instruction for students with a disability or identified as at risk.</p> <hd id="AN0115578960-2">Counting</hd> <p>The most common numerical activity in young children's homes and in preschool is counting (Ramani & Siegler, [<reflink idref="bib11" id="ref6">11</reflink>]). Researchers show there are stages of development that outline the learning trajectory of young children learning to count. Van de Rijt & Van Luit ([<reflink idref="bib14" id="ref7">14</reflink>]) explain the developmental process of learning to count and the order in which counting skills are acquired as an essential foundation in mathematics. Children first learn acoustic counting. Acoustic counting involves speaking numbers but not connecting numbers with objects, also known as rote counting. The next stage is counting asynchronously, which is when young learners realize that numbers are used to count things, but they are not able to point to one object while enumerating one number. This is demonstrated when students miss an object or point to the same object twice while counting. In the next stage, counting synchronously, children are capable of counting and pointing to objects at the same time, making a one to one relation. After synchronous counting, children demonstrate resultative counting, or seriation. Counting synchronously demonstrates the principle of one-to-one correspondence in which one and only one number is assigned to each object in a given set. Resultative counting means young students are aware that counting has to begin with the number one, that every object has to be counted once, and that the last number gives the total number of objects. Counting resultatively demonstrates the principle of stable order and cardinality. The stable order principle affirms that number words always progress in the same order, and the cardinal principle means that the last number word counted represents the sum of the set. After resultative counting, children learn shortened counting. Shortened counting is demonstrated when young students count on from a representation of a number they see. For example in a pair of dice, the student would see four dots on one piece and three dots on the other piece. Instead of touching each dot, the student would say four and continue to count the remaining dots on the other piece. After children become fluent in shortened counting, they are able to count in a flexible way. Counting in a flexible manner shows the principle of irrelevance and the principle of abstraction. The irrelevance principle affirms that the order of objects in a set does not influence the final number counted, and the principle of abstraction means that the principles of one-to-one correspondence, stable order, cardinality, and irrelevance are employed when counting any set, irrespective of what the collection of objects look like.</p> <hd id="AN0115578960-3">Counting Instruction</hd> <p>Promising research exists about effective curricula for young children with disabilities and counting skills. Studies probe the effects of instruction that requires children to count through classification of numbers, focusing on counting skills such as subitizing, and counting to solve meaningful problems. Instruction for students in kindergarten involves core instruction that utilizes discovery-oriented techniques, but it is important that explicit instruction supplement core counting instruction for students who struggle and need targeted interventions. Providing early intervention in numeracy and number sense may ensure that students will be successful in more complex mathematical concepts such as understanding the base ten system and mathematical operations.</p> <p>Toll & Luit ([<reflink idref="bib13" id="ref8">13</reflink>]) investigate two kindergarten remedial programs to build number sense. The first program is a comprehensive systematic program and the second is an accelerated version of the comprehensive systematic program. Students who were identified as at risk for mathematics difficulties and received the remedial interventions made greater gains for both remedial programs investigated. Although the study addresses the need for intensive remedial numeracy instruction, more research should be conducted that inspects the numeracy instruction taught in conjunction with core teaching in the general education setting.</p> <p>Mononen, Aunio, & Koponen ([<reflink idref="bib6" id="ref9">6</reflink>]) conducted a pilot study to examine the effects of early numeracy skill instruction for students in kindergarten with specific language impairments (SLI). Numeracy instruction encourages students to use subitizing skills and find groupings of numbers within larger quantities. For example, seven can be taught as two and five, and students use manipulatives to see that two and five make up the amount of seven. Nine students with SLI received the instruction and their performance was compared to 32 students without SLI who received instruction that did not include the numeracy program. The students with SLI improved their counting skills to the level of their peers and performed similarly to their peers in addition and subtraction, but also showed weaker skills in arithmetic reasoning and in matching spoken and printed multi-digit numbers.</p> <p>Another curriculum shown to be effective is the Additional Early Mathematics (AEM) program (Van de Rijt & Van Luit,[<reflink idref="bib14" id="ref10">14</reflink>]). AEM uses guided or structured instruction, with the teacher choosing the materials and activities that fit with the abilities of the student. Guided instruction involves the teacher observing students solving problems and providing feedback. Throughout instruction, the teacher makes suggestions and models solving problems. Results of Van de Rijt and Van Luit's study indicate that both experimental groups who received the AEM instruction made significant gains compared to the control groups. Young Children with Special Education Needs Count Too (Van Luit & Schopman, [<reflink idref="bib15" id="ref11">15</reflink>]) is another curriculum that builds counting skills. This curriculum involves guided instruction (i.e., observing students and providing feedback) and structured instruction (i.e.., making suggestions and modeling) in which students connect new material they learned with prior knowledge by repeating, organizing, and arranging information. Participants were 124 kindergarten students between the ages of 5 and 7 with special education needs. Young Children with Special Education Needs Count Too was found to be more effective in teaching young students who scored below the 25th percentile on a mathematics achievement test to count (Van Luit & Schopman, [<reflink idref="bib16" id="ref12">16</reflink>]). In a different study, Ramani and Siegler investigated the effects of playing an informal linear board game to build number line estimation, magnitude comparison, numerical identification, and arithmetic learning for preschoolers from low-income backgrounds. Ramani and Siegler found that the linear board game improved children's knowledge of numeral identification, and the ability to solve novel arithmetic problems. They also found that students with low socioeconomic backgrounds made more gains than students with upper socioeconomic backgrounds.</p> <p>In summary researchers have shown that effective instruction can improve number knowledge for young students. Instruction can range from informal games in preschool to more structured instruction in kindergarten. To date there needs to be more research that investigates the effects of a more structured supplemental mathematic intervention in a preschool setting that is implemented in conjunction with preschool classroom mathematics instruction. One way of providing a structured mathematics intervention in preschool is through explicit instruction. Explicit instruction and preschool is described in the next section (Adams & Engelmann, [<reflink idref="bib1" id="ref13">1</reflink>]; Engelmann & Carnine, [<reflink idref="bib3" id="ref14">3</reflink>]; Stanton-Chapman, Denning, & Jamison, [<reflink idref="bib12" id="ref15">12</reflink>]).</p> <hd id="AN0115578960-4">Explicit Instruction and Preschool</hd> <p>Researchers have demonstrated explicit instruction to be effective in teaching students with disabilities in preschool settings (Adams & Engelmann, [<reflink idref="bib1" id="ref16">1</reflink>]; Engelmann & Carnine, [<reflink idref="bib3" id="ref17">3</reflink>]; Stanton-Chapman et al., [<reflink idref="bib12" id="ref18">12</reflink>]). There are specific steps in the provision of explicit instruction. The steps include: (a) provide an advance organizer, (b) demonstrate and model the skill, (c) provide guided practice, (d) provide independent practice, and (e) provide a post-organizer (Miller, [<reflink idref="bib5" id="ref19">5</reflink>]; Peterson, Mercer, & O'Shea, [<reflink idref="bib9" id="ref20">9</reflink>]). In the advance organizer, the instructor ensures that students have the prerequisite knowledge to learn the skill, tells students what they are going to learn, and makes what they are going to learn relevant. In the demonstration phase of instruction, the teacher shows the new concept or how to perform a skill. In the guided practice phase, the instructor and students together demonstrate the concept or perform the skill. Once students show understanding of the new concept or skill, they are to demonstrate the concept or perform the skill without teacher assistance. In the independent practice phase of instruction, the teacher provides students with feedback on their performance, and will give assistance if it is warranted. Finally in the post-organizer the teacher and the students reflect and review what they learned.</p> <p>The following questions guided the study. What are the effects of supplemental explicit instruction on the resultative counting performance of preschool students who were identified as at risk for mathematics failure? What are the effects of supplemental explicit instruction on the graphic counting performance of preschool students who were identified as at risk for mathematics failure? What are the effects of supplemental explicit instruction on the counting performance of preschool students who were identified as at risk for mathematics failure?</p> <hd id="AN0115578960-5">Method</hd> <p></p> <hd id="AN0115578960-6">Participants</hd> <p>The participants in this study include four students who received a 15-minute explicit intervention for counting, three days a week. All participants were referred by their classroom teacher because they were to start kindergarten the next school year, and at mid-year did not show adequate progress based on their performance on the school district's informal kindergarten readiness assessment that measures number identification and requires students to count and match numbers to their quantities. The students were not demonstrating cardinality of numbers or using one-to-one correspondence during mathematics core instruction (Table 1).</p> <p>Table 1. Participants Characteristics</p> <p> <ephtml> <table><tbody><tr><td>Pseudo name</td><td>Age</td><td>Race</td><td>Gender</td><td>Category</td><td>Reason for referral reported by the teacher</td><td>Baseline skill</td><td>Leiter-R</td></tr><tr><td>Aiden</td><td>5</td><td>White</td><td>Male</td><td>DD<xref ref-type="fn" rid="t1fn0001" /></td><td>At mid-year did not count synchronously or resultatively to demonstrate cardinality of numbers 1–10</td><td>Rote counted to ten</td><td>74</td></tr><tr><td>Jason</td><td>5</td><td>White</td><td>Male</td><td>At-risk</td><td>At mid-year did not count quantities larger than five synchronously or resultatively</td><td>Rote counted to ten</td><td>91</td></tr><tr><td /><td /><td /><td /><td /><td /><td>Demonstrated cardinality quantities up to five</td><td /></tr><tr><td>Kat</td><td>5</td><td>African American</td><td>Female</td><td>At-risk</td><td>At mid-year did not count synchronously or resultatively to demonstrate cardinality of numbers 1–10</td><td>Rote counted to ten</td><td>97</td></tr><tr><td /><td /><td /><td /><td /><td /><td>Counted objects using asynchronous counting</td><td /></tr><tr><td>Ned</td><td>5</td><td>African American</td><td>Male</td><td>DD<xref ref-type="fn" rid="t1fn0001" /></td><td>At mid-year did not count synchronously or resultatively to demonstrate cardinality of numbers 1–10</td><td>Rote counted to ten</td><td>95</td></tr></tbody></table> </ephtml> </p> <p>10001 DD stands for the special education label of developmental delay.</p> <hd id="AN0115578960-7">Setting</hd> <p>The study took place in an inclusive preschool classroom located in a public elementary school in a rural county in the southeastern United States. The preschool class included students with and without disabilities. The classroom teacher was certified in early childhood special education and taught in an inclusive preschool classroom for eight years.</p> <p>The study lasted 15 weeks, which included collection of baseline data and maintenance data. The intervention was implemented for 12 weeks and instructional sessions occurred on Mondays, Wednesdays, and Fridays every week. Core mathematics instruction was provided in the morning first as a whole-group activity. All students received core instruction, including the participants of the study. The teacher would introduce the number of the day, write out representations of the number (numerals, and circles to represent the quantity using a tens frame) for students, and model counting to that number. Students would count to the number as a whole group, and then count objects with the teacher. The teacher would then have students take turns and count individually. Afterward, whole-group students broke into small groups to participate in small-group sessions. A typical mathematics small-group session involved students counting objects or pictures, and matching the quantity to the number of the day. There were three tables and students were at each table in groups of four or five. An assistant was at each table to provide prompts in the order of least intrusive to most intrusive (i.e., hand over hand). The teacher rotated among the tables and implemented guidance or enrichment through modeling or by asking questions. Supplemental instruction was provided by the primary researcher within the classroom during regularly scheduled instructional rotations after all literacy and mathematics instruction took place. These rotations were a mix of structured and discovery-oriented activities, and involved small-group and one-to-one instruction with the classroom teacher and learning centers (dramatic play, gross motor skills, art, numeracy, writing, and literacy). Every 15 minutes, students rotated among the centers that were usually self-chosen for the duration of about an hour each morning. Although centers were usually self-chosen, for at least one rotation, the teacher and the primary researcher would pull students to work on skills that required remediation at a designated station (i.e., a table located in the front of the classroom or a table located in the back of the classroom). The teacher also conducted discrete trial training for specific IEP goals at one table and the students who participated in the study worked with the primary researcher on counting skills at the other table. Assistants rotated among the stations in the center of the room and implemented incidental teaching, which often engaged students in conversations; participated with students in play activities; and promoted learning through asking questions.</p> <hd id="AN0115578960-8">Materials</hd> <p>Lesson materials included work mats, bowls, counting objects such as cars, pretend jewels, and cubes, and lesson sheets that had drawings of circles students could count. Work mats consisted of construction paper or a blank sheet of paper the researchers and students placed objects on to count. The work mats and bowls helped students organize the objects they were counting and see the numeric amounts. Lesson sheets included numeric pictorial representations of circles, which ranged from numerical representations of one to ten. The first three lessons for each counting skill involved objects students counted using work mats or bowls. Flash cards were used at the beginning of the lessons for graphic and shorten counting, in which each card had a specific number of circles that represented a certain number. Students would say the amount of circles on the cards without touching and counting each circle. Instructional procedures that utilized the work mats, bowls, lesson sheets, objects, and flash cards are discussed in the following section.</p> <p>The progress monitoring probes were administered before instruction began. Probes assessed resultative counting, subitizing, and shortened counting. Resultative counting probes had ten sets of circles drawn out for students to see. Each set ranged from one to ten circles. Students were to touch and count then answer how many for each set. Probes for subitizing involved ten sets of drawings of circles that were encompassed by a square. The sets ranged from one to five circles in each square. The square was a visual for students to say how many without touching the circles. Shortened counting probes were similar to the subitizing probes, but additional circles were outside the squares. Students would say the amount inside the square and continue counting by touching and counting the circles outside the square.</p> <p>The Leiter International Performance Scale–Revised (Leiter-R) was used to obtain a nonverbal composite score for students' cognitive functioning. The Leiter-R was correlated with the Wechsler Abbreviated Scale of Intelligence-III full-scale intellectual quotient score with a correlation of.85. Reliability for the Leiter-R was.88.</p> <hd id="AN0115578960-9">Resultative Counting Lessons</hd> <p>Resultative counting lessons consisted of three lessons that utilized concrete materials and seven lessons that utilized pictures of circles. Lessons built on each other and became more complex. When teaching students how to count resultatively, the researchers reviewed orally counting to ten, told the students that counting is a way of knowing how many, and explained that when counting, you start with the number one and the last number you say is the amount you have. When completing lessons with objects, the researchers placed objects on a work mat (the amount started with a small number such as three and all lessons never exceeded the amount of ten) and said "I want to know how many objects there are. Watch me, I will count to find out." The researchers placed the objects on the work mat one by one and said the respective number as the object was placed on the mat. After modeling counting, the researchers would clear the mat, put another amount of objects on the table, and say "Let's all count together." The researchers placed the objects one by one and the students said the corresponding number simultaneously with the researchers. The researchers then gave students mats and objects and allowed students to count objects with feedback. To review, the researchers asked students to demonstrate how they count. The same procedures were followed with the lesson sheets, except the researchers and children counted pictures of circles instead of objects.</p> <hd id="AN0115578960-10">Graphic Counting</hd> <p>Graphic counting—also referred to as subitizing—was used to identify how many without touching the objects or pictures. Students identified how many with quantities between one and five. When graphic counting, students found amounts within the numbers presented to identify the quantity instead of counting each object or picture. For example, the amount of four could be two and two or one and three. Graphic counting would provide another way for students to determine how many and prepare students for shortened counting. Similar to resultative counting, the first three lessons utilized objects and the following seven utilized pictures.</p> <p>When completing lessons with objects, the researcher placed objects on the work mat (the amount started with a small number such as one and all lessons never exceeded the amount of five) and said "I have three objects. I can count the objects without having to touch each item. Watch me, two and one. Three is the same as two and one." After modeling, the researcher would clear the mat, put the same amount previously modeled and say "Let's find out together how many objects there are without having to touch each item." The researcher would touch two objects and have students say two then touch one object and have students say one, and then ask how many. After completing problems together, the researcher gave students mats and objects and allowed students to count objects with feedback. After students counted on their own with feedback, the researcher reviewed the lesson. To review, the researcher asked students to demonstrate how they count without having to touch each item. The same procedures were followed with the lesson sheets, except the researcher and children counted pictures of circles instead of objects.</p> <hd id="AN0115578960-11">Shortened Counting</hd> <p>Shortened counting was taught by combining graphic counting with resultative counting. When teaching shortened counting, students were given objects in a bowl or a picture with circles that were inside a square. There were also objects outside the bowl or circles outside the square. Students were told to count the objects in the bowl or circles in the square without touching then touch and count objects outside the bowl or circles outside the square. Similar to resultative and graphic counting, the first three lessons utilized objects and the following seven utilized pictures.</p> <p>The researcher modeled shortened counting and would say, "I see two and one so I know there are three in this bowl. I will now touch and count the rest to see how many in all." After modeling, the researcher said "Let's find out together how many objects there are by saying how many are in the bowl then touching and counting the rest." After doing problems together, the researcher gave students bowls and objects and allowed students to count objects with feedback. To review, the researcher asked students to demonstrate how they count using shortened counting. The same procedures were followed with the lesson sheets, except the researcher and children counted pictures of circles instead of objects.</p> <hd id="AN0115578960-12">Research Design and Procedures</hd> <p>A multiple probe across three separate behaviors was designed to show a functional relation between the counting instruction and three behaviors. The behaviors were resultative counting, graphic counting, and shortened counting. The criterion for phase change was eight of ten problems correct; this was chosen based on the criterion for mastery used for classroom lesson objectives for mathematics.</p> <hd id="AN0115578960-13">Procedural Integrity and Inter-Observer Agreement</hd> <p>Data for procedural integrity were collected continuously throughout the study to ensure that the procedures were implemented correctly. Procedural integrity included: (a) probes were administered before mathematic instruction began and answers or help were not provided, (b) the teacher told students what they were going to learn, (c) the teacher modeled the counting skill, (d) the teacher counted objects or pictures with the students, (e) students counted objects or pictures independently, and (f) the teacher provided students feedback based on their performance. Integrity checklists were completed in which another researcher or a classroom assistant observed the administration of probes and instruction as it was taking place for at least 30% of baseline data collection and phases of the intervention. To calculate procedural integrity for assessments and instruction, a researcher other than the primary researcher or a paraprofessional would check yes or no if specific instructional behaviors occurred or did not occur. Practice sessions were held in which the researcher and paraprofessional identified behaviors and filled out the checklist while the primary researcher modeled a lesson. The researcher and paraprofessional practiced until both could accurately identify the behaviors and fill out the checklist with 100% agreement. Procedural integrity was calculated as 100% for the resultative counting phase, 100% for the graphic counting phase, and 100% for the shorten counting phase.</p> <p>Inter-observer agreement was conducted for 100% of the probes administered and integrity checklists. Probes were scored by the primary researcher and scored by the researcher previously mentioned. To calculate interrater reliability for the procedure checklists, the total number of agreements between the researcher and the classroom assistant was divided by the total number of observations, then multiplied by the number 100 (Poling, Method, & LeSage, [<reflink idref="bib10" id="ref21">10</reflink>]). The same process was completed to calculate interrater reliability for the probes; however, the total number of agreements between the primary researcher and the researcher were used. Interrater reliability was 100% for the procedural integrity, 100% for the resultative counting probes, 97% for the graphic counting probes, and 100% for the shorten counting probes.</p> <hd id="AN0115578960-14">Social Validity</hd> <p>Social validity was addressed through a closed and open-ended questionnaire after the study. The classroom teacher answered questions regarding the efficacy of the intervention and recommendations for the intervention. Questions were would you use the counting intervention in the future—why or why not, what are ways of improving the counting instruction, did the students make progress? The teacher's feedback indicated that she believed the counting instruction improved students' skills. She also said she liked having an option for instruction that could supplement the use of a five or ten frame when teaching number concepts. Last, the teacher stated she would like to use the counting instruction in the future.</p> <hd id="AN0115578960-15">Results</hd> <p>Instructional progress was monitored and graphed for each student. Figure 1 summarizes Aiden's performance, Figure 2 summarizes Jason's performance, Figure 3 summarizes Kat's performance, and Figure 4 summarizes Ned's performance.</p> <p>Graph: Fig. 1. Results from Aiden.</p> <p>Graph: Fig. 2. Results from Jason.</p> <p>Graph: Fig. 3. Results from Kat.</p> <p>Graph: Fig. 4. Results from Ned.</p> <hd id="AN0115578960-16">Aiden</hd> <p>Aiden's baseline were stable with zero quantities resultatively counted correctly, his baseline for graphic counting were stable with the last four data points showing one and zero quantities counted correctly, and his baseline for shortened counting were stable with zero quantities counted correctly. There was not an immediate change in performance from baseline to intervention for resultative counting. However, there was a change in level of performance in resultative counting between baseline and instruction from zero to 4.5. There were two overlapping data points, but there was an upward path during the instructional condition, which indicated steady improvement. Aiden reached criterion after nine probes that ranged from zero to nine. There was an immediate change in graphic counting between the last baseline data point and the first data point within instruction. Within intervention, the level was six and Aiden reached criterion after nine probes ranging from three to eight. There was only one overlapping data point, and the instructional phase data points showed an upward path that indicated steady improvement. Last, there was an immediate change in level of performance in shortened counting between baseline and instruction. Aiden reached criterion after four probes ranging from one to nine. There were no overlapping data points, and the instructional phase data points showed an upward path that indicated steady improvement. Maintenance data were taken two weeks after the shortened counting instructional phase indicating that Aiden maintained the counting skills.</p> <hd id="AN0115578960-17">Jason</hd> <p>Jason's baseline were stable with two, four, and three quantities resultatively counted correctly, his baseline for graphic counting were stable with the last four data points showing only one quantity counted correctly, and his baseline for shortened counting were stable with zero quantities counted correctly. For resultative counting, there was not an immediate effect. However, there was a change in level of performance in resultative counting between baseline and instruction from three to six. Jason reached criterion after nine probes ranging from two to nine. There were two overlapping data points and the instructional phase data showed an upward path that indicated steady improvement. For graphic counting, there was an immediate change in level of performance between baseline and instruction from 1.6 to 6.75. There were no overlapping data points and the instructional phase data points showed an upward path that indicated steady improvement. Jason reached criterion after four probes ranging from five to eight. Last there was an immediate change in performance from the last baseline data point in baseline to the first data point in instruction. There was a change in level of performance in shortened counting between baseline and instruction from zero to 6.5. There were no overlapping data points and the instructional phase data showed an upward path that indicated steady improvement. Jason reached criterion after four probes ranging from two to ten. Maintenance data were taken two weeks after the shortened counting instructional phase indicating that Jason maintained the counting skills.</p> <hd id="AN0115578960-18">Kat</hd> <p>Kat's baseline were stable with four, two, and two quantities resultatively counted correctly, her baseline for graphic counting were stable with the last six data points showing zero quantities counted correctly, and her baseline for shortened counting were stable with zero quantities counted correctly. There was a change in level of performance in resultative counting between baseline and instruction from 2.7 to 5.6. There were four overlapping data points, and the instructional phase data showed a variable but upward path that indicated steady improvement. For graphic counting, there was an immediate change in performance from the last baseline data point to the first instructional data point. There was a change in level between baseline and instruction from zero to six. There were no overlapping data points and the instructional phase data points showed an upward path. For shortened counting, there was an immediate change in level of performance from the last baseline data point to the first data point in instruction. There was a change in level from zero to 8.7 and Kat reached criterion after only three probes ranging from seven to ten. The instructional phase data showed an upward path that indicated steady improvement. Maintenance data were taken two weeks after the shortened counting instructional phase indicating that Kat maintained the counting skills.</p> <hd id="AN0115578960-19">Ned</hd> <p>Ned's baseline were stable with one quantity resultatively counted correctly on all assessments, his baseline for graphic counting were stable with the last three data points showing zero quantities counted correctly, and his baseline for shortened counting were stable with zero quantities counted correctly. There was a change in level of performance in resultative counting between baseline and instruction from one to 4.2. Ned reached criterion after seven probes ranging from zero to ten and his performance was variable and slow to change; however, the last three data points showed an upward path. For graphic counting, there was an immediate change performance from the last baseline data point to the first instructional data point. There was a change in level between baseline and instruction from 0.14 to six. There were no overlapping data points; however, his data path was variable prior to increasing. Ned reached criterion after nine probes ranging from two to nine. For shortened counting, there was an immediate change in performance from the last baseline data point to the first instructional data point. There was a change in level of performance between baseline and instruction from zero to eight. Ned reached criterion after four probes ranging from seven to nine with no overlapping data points. The instructional phase data showed an upward path. Maintenance data were taken two weeks after the shortened counting instructional phase indicating that Ned maintained the counting skills.</p> <hd id="AN0115578960-20">Effect Size</hd> <p>The effect of the explicit counting instruction was calculated using Tau-U for each student. Tau-U analysis combined non-overlapping data points between phases with trend within the intervention phases while accounting for any trend within baseline (Parker, Vannest, & Davis, [<reflink idref="bib8" id="ref22">8</reflink>]). Overall, a strong effect was found for Aiden, Jason, Kat, and Ned with a Tau-U of.94,.91,.89, and.86, respectively.</p> <hd id="AN0115578960-21">Discussion for Direct Application</hd> <p>The purpose of this study was to examine the effects of supplemental explicit instruction on the graphic counting performance of preschool students who were identified as at risk for mathematics failure. All students reached criterion across three counting skills, demonstrating a functional relation between explicit instruction and counting skills. The students' performance was variable and did not change immediately. This may be due to the nature of instruction. The first lessons involved manipulation of objects while the probes did not. Without the additional visual and physical aids, the students did not perform as well on probes as they did during instructional lessons. As the interventions moved from concrete to representational instruction, students' performance on probes increased; perhaps students' decreased dependence on physical objects during instruction led to this change in performance. To date, more research is needed on the effects of brief mathematics interventions designed to address specific skills and supplemental to core instruction that is provided to younger students in kindergarten or in preschool (Toll & Luit, [<reflink idref="bib13" id="ref23">13</reflink>]). Promising studies indicate that numeracy curriculum can be effective in teaching young children mathematics. Studies involved remedial and core mathematics instruction provided to students who were at risk or who had disabilities in kindergarten (Mononen et al., [<reflink idref="bib6" id="ref24">6</reflink>]; Toll & Luit, [<reflink idref="bib13" id="ref25">13</reflink>]; Van Luit & Schopman, [<reflink idref="bib16" id="ref26">16</reflink>]). Other studies included informal mathematic interventions that were implemented in addition to classroom instruction for students at risk in preschool (Ramani & Siegler, [<reflink idref="bib11" id="ref27">11</reflink>]).</p> <p>Teachers must have evidence-based interventions that can be implemented in practical and efficient ways. Counting is developmental and teachers need to provide instruction that builds children's ability to count amounts in fluid and flexible ways. Explicit interventions that target specific ways of counting can improve children's fluency with numbers, which increases mathematic skills. When implementing explicit instruction the teacher models the counting behavior (e.g., touching each item for resultative counting, visually counting without touching each item, or counting on to show shortened counting), implements the different ways of counting with the children, then lets children count on their own and provides feedback. In this study, a functional relation was demonstrated between the counting instruction and the behaviors of resultative, graphic, and shortened counting with all four participants.</p> <p>Explicit counting interventions supplement the core mathematics instruction that researchers have shown as effective for young students, and assist in building number knowledge so students can gain from the core instruction they receive. This is helpful for teachers because multitiered instruction requires educators to have a very broad array of educational programs they can use to implement instruction as well as various ways of targeting specific skills to implement supplemental interventions. The explicit counting intervention is one way of providing preschool teachers with limited resources a simple way of implementing targeted instructional counting support for preschoolers in addition to the core curriculum implemented in their classrooms.</p> <hd id="AN0115578960-22">Limitations and Future Recommendations</hd> <p>This study examined explicit instruction to teach counting skills for four students who were at risk or received special education services for a developmental delay in preschool. There were several limitations that need to be addressed. First, the primary researcher was the instructor in the study. Future research should include an instructor other than the primary researcher. Second, results cannot be generalized to a larger population. Future research should include a group design with a larger sample size to investigate the effects of supplemental preschool instruction that can be generalized. Also, the social validity question survey did not include a Likert scale and was not quantifiable. Future research should involve a social validity survey in which teachers' and students' perspectives on the intervention can be quantifiable. This study helps to build research that can give teachers and families more evidence-based instructional practices to teach young learners mathematics. Explicit instruction for counting can be one of the methods educators and families use to empower young children who need supplemental instruction in mathematics.</p> <hd id="AN0115578960-23">Implications</hd> <p>This study demonstrated positive effects of a counting intervention from preschool students. The counting intervention involved limited classroom time and resources, meaning that teachers could implement this type of instruction during daily center rotations with commonplace materials available in the classroom. For example, a teacher-directed center could include small group or one-on-one counting activities lasting 10 minutes. Counting activities similar to those implemented in this study could be modeled and guided during circle time and reviewed individually or within small groups as well. It is critical that young children enter kindergarten with numeracy experiences that prepare them for mathematical thinking and more complex mathematical concepts. The results of this study show the promise of incorporating explicit counting instruction within preschool settings in order to better prepare young children for future mathematical understanding.</p> <hd id="AN0115578960-24">Author Notes</hd> <p> <bold>Vanessa M. Hinton</bold> is a lecturer at the Department of Special Education, Rehabilitation, and Counseling at Auburn University. Her research interests include mathematics instruction and supported learning.</p> <p> <bold>Margaret M. Flores</bold> is an associate professor for the Department of Special Education, Rehabilitation, and Counseling at Auburn University. Her research interests include direct instruction and mathematics instruction in supported learning environments.</p> <p> <bold>Kelly Schweck</bold> is a field experience coordinator for the Department of Special Education, Rehabilitation, and Counseling at Auburn University. Her research interests include teacher education involving instruction and teacher dispositions.</p> <p> <bold>Megan E. Burton</bold> is an associate professor for the Department of Curriculum and Teaching at Auburn University. Her research interests include teacher education in mathematics instruction.</p> <ref id="AN0115578960-25"> <title> References </title> <blist> <bibl id="bib1" idref="ref13" type="bt">1</bibl> <bibtext> Adams, G. L., & Engelmann, S. (1996). Research on direct instruction: 25 years beyond DISTAR. Seattle, WA: Educational Achievement Systems.</bibtext> </blist> <blist> <bibl id="bib2" idref="ref3" type="bt">2</bibl> <bibtext> Berch, D. B. (Ed.). (1998, April). Mathematical cognition: From numerical thinking to mathematics education. Conference presented by the National Institute of Child Health and Human Development, Bethesda, MD.</bibtext> </blist> <blist> <bibl id="bib3" idref="ref14" type="bt">3</bibl> <bibtext> Engelmann, S., & Carnine, D. W. (1982). Theory of instruction: Principles and applications. New York, NY: Irvington.</bibtext> </blist> <blist> <bibl id="bib4" idref="ref5" type="bt">4</bibl> <bibtext> Gersten, R., Beckmann, S., Clarke, B., Marsh, L., Star, J. R., & Witzel, B. (2009). Assisting students struggling with mathematics: Response to intervention (RtI) for elementary and middle schools. U.S Department of Education. Retrieved from <ulink href="http://ies.ed.gov/ncee/wwc/pdf/practice%5fguides/rti%5fmath%5fpg%5f042109.pdf">http://ies.ed.gov/ncee/wwc/pdf/practice%5fguides/rti%5fmath%5fpg%5f042109.pdf</ulink></bibtext> </blist> <blist> <bibl id="bib5" idref="ref19" type="bt">5</bibl> <bibtext> Miller, S. P. (2009). Validated practices for teaching students with diverse needs and abilities (2nd ed.). Upper Saddle River, NJ: Pearson.</bibtext> </blist> <blist> <bibl id="bib6" idref="ref9" type="bt">6</bibl> <bibtext> Mononen, R., Aunio, P., & Koponen, T. (2014). A pilot study of the effects of RighStart instruction on early numeracy skills of children with specific language impairment. Research in Developmental Disabilities, 35, 999–1014. Retrieved from <ulink href="http://dx.doi.org/10.1016/j.ridd.2014.02.004">http://dx.doi.org/10.1016/j.ridd.2014.02.004</ulink></bibtext> </blist> <blist> <bibl id="bib7" idref="ref4" type="bt">7</bibl> <bibtext> National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston, VA: Author.</bibtext> </blist> <blist> <bibl id="bib8" idref="ref22" type="bt">8</bibl> <bibtext> Parker, R. L., Vannest, K. J., Davis, J. L. (2011). Effect size in single-case research: A review of nine overlap techniques. Behavior Modification, 35, 303–322. Retrieved from <ulink href="http://dx.doi.org/10.1177/0145445511399147">http://dx.doi.org/10.1177/0145445511399147</ulink></bibtext> </blist> <blist> <bibl id="bib9" idref="ref20" type="bt">9</bibl> <bibtext> Peterson, S. K., Mercer, C. D., & O'Shea, L. (1988). Teaching learning disabled children place value using the concrete to abstract sequence. Learning Disabilities Research, 4, 52–56.</bibtext> </blist> <blist> <bibtext> Poling, A., Methot, L. L., & LeSage, M. G. (1995). Fundamentals of behavior analytic research. New York, NY: Plenum.</bibtext> </blist> <blist> <bibtext> Ramani, G. B., & Siegler, R. S. (2011). Reducing the gap in numerical knowledge between low-and middle-income preschoolers. Journal of Applied Developmental Psychology, 32, 146–159. Retrieved from <ulink href="http://dx.doi.org/10.1016/j.appdev.2011.02.005">http://dx.doi.org/10.1016/j.appdev.2011.02.005</ulink></bibtext> </blist> <blist> <bibtext> Stanton-Chapman, T. L., Denning, C. B., & Jamison, K. R. (2012). Communication skill building in young children with and without disabilities in a preschool classroom. The Journal of Special Education, 46, 78–93. Retrieved from <ulink href="http://dx.doi.org/10.1177/0022466910378044">http://dx.doi.org/10.1177/0022466910378044</ulink></bibtext> </blist> <blist> <bibtext> Toll, S. W. M., & Van Luit, J. E. H. (2014). Effects of remedial numeracy instruction throughout kindergarten starting at different ages: Evidence from a large-scale longitudinal study. Learning and Instruction, 33, 39–49. Retrieved from <ulink href="http://dx.doi.org/10.1016/j.learninstruc.2014.03.003">http://dx.doi.org/10.1016/j.learninstruc.2014.03.003</ulink></bibtext> </blist> <blist> <bibtext> Van de Rijt, B. A. M., & Van Luit, J. E. H. (1998). Effectiveness of the additional early mathematics program for teaching children early mathematics. Instructional Science, 26, 337–358. Retrieved from <ulink href="http://dx.doi.org/10.1023/A:1003180411209">http://dx.doi.org/10.1023/A:1003180411209</ulink></bibtext> </blist> <blist> <bibtext> Van Luit, J. E. H., & Schopman, E. A. M. (1998). Als special kleuter tel je ook mee! Voobereidende rekenactiviteiten voor kleuters met een ontwlkkelingsachterstand [Young children with special needs count too! Early mathematics activities for young children with special educational needs]. Doetinchem, The Netherlands: Graviant.</bibtext> </blist> <blist> <bibtext> Van Luit, J. E. H., & Schopman, E. A. M. (2000). Improving early numeracy of young children with special educational needs. Remedial and Special Education, 21, 27–40. Retrieved from <ulink href="http://dx.doi.org/10.1177/074193250002100105">http://dx.doi.org/10.1177/074193250002100105</ulink></bibtext> </blist> <blist> <bibtext> Vaughn, S., & Fuchs, L. (2003). Redefining learning disabilities as inadequate response to instruction: The promise and potential problems. Learning Disabilities Research and Practice, 18, 137–146. Retrieved from <ulink href="http://dx.doi.org/10.1111/1540-5826.00070">http://dx.doi.org/10.1111/1540-5826.00070</ulink></bibtext> </blist> </ref> <aug> <p>By Vanessa M. Hinton; Margaret M. Flores; Kelly Schweck and Megan E. Burton</p> <p>Reported by Author; Author; Author; Author</p> </aug> <nolink nlid="nl1" bibid="bib17" firstref="ref1"></nolink> <nolink nlid="nl2" bibid="bib13" firstref="ref2"></nolink> <nolink nlid="nl3" bibid="bib11" firstref="ref6"></nolink> <nolink nlid="nl4" bibid="bib14" firstref="ref7"></nolink> <nolink nlid="nl5" bibid="bib15" firstref="ref11"></nolink> <nolink nlid="nl6" bibid="bib16" firstref="ref12"></nolink> <nolink nlid="nl7" bibid="bib12" firstref="ref15"></nolink> <nolink nlid="nl8" bibid="bib10" firstref="ref21"></nolink>
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  Data: Counting skills are foundational for young children to build number concepts in mathematics. Multitiered instruction that involves core instruction as well as supplemental interventions is implemented to support young children in the learning process and promote early intervention of basic skills. Researchers show that explicit instruction is successful in teaching students in preschool. More research needs to be conducted on brief explicit mathematic interventions that target the skill of counting and are supplemental to preschool mathematics core instruction. In this study, researchers examine the effects of using explicit instruction as an intervention to teach counting skills for four children who were at risk for mathematics difficulties or who received special education services for developmental delay in an inclusive preschool setting. The researchers find a functional relation for a 15-minute supplemental explicit intervention and counting skills. Implications of these findings are also discussed.
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