Is TouchMath an Effective Intervention for Students with Autism?

Stephen F. Austin State University Stephen F. Austin State University

SFA ScholarWorks SFA ScholarWorks

Electronic Theses and Dissertations

7-2019

Is TouchMath an Effective Intervention for Students with Autism? Is TouchMath an Effective Intervention for Students with Autism?

April M. Huckaby

Stephen F Austin State University

, [email protected]

Follow this and additional works at: https://scholarworks.sfasu.edu/etds

Part of the Educational Psychology Commons

Tell us how this article helped you.

Repository Citation Repository Citation

Huckaby, April M., "Is TouchMath an Effective Intervention for Students with Autism?" (2019).

Electronic

Theses and Dissertations

. 256.

https://scholarworks.sfasu.edu/etds/256

This Thesis is brought to you for free and open access by SFA ScholarWorks. It has been accepted for inclusion in

Electronic Theses and Dissertations by an authorized administrator of SFA ScholarWorks. For more information,

please contact [email protected].

Is TouchMath an Effective Intervention for Students with Autism? Is TouchMath an Effective Intervention for Students with Autism?

Creative Commons License Creative Commons License

This work is licensed under a Creative Commons Attribution-Noncommercial-No Derivative Works 4.0

License.

This thesis is available at SFA ScholarWorks: https://scholarworks.sfasu.edu/etds/256

IS TOUCHMATH AN EFFECTIVE INTERVENTION FOR STUDENTS WITH

AUTISM?

By

APRIL M. HUCKABY, Bachelor of Science in Biology

Presented to the Faculty of the Graduate School of

Stephen F. Austin State University

In Partial Fulfillment

Of the Requirements

For the Degree of

Master of Arts

STEPHEN F. AUSTIN STATE UNIVERSITY

August 2019

Is Touchmath an Effective Intervention for Students with Autism?

By

APRIL M. HUCKABY, Bachelor of Science in Biology

APPROVED:

__________________________________________

Dr. Daniel McCleary, Thesis Director

__________________________________________

Dr. Jillian Dawes, Thesis Co-Director

__________________________________________

Dr. Frankie Clark, Committee Member

__________________________________________

Dr. Summer Koltonski, Committee Member

__________________________________________

Pauline M. Sampson, Ph.D.

Dean of Research and Graduate Studies

iii

ABSTRACT

The TouchMath program was created in 1976 to help students struggling with basic

mathematical computations (Bullock, 2005). Although the research has found

TouchMath to be an effective intervention for students in the general and special

education populations, only four studies have found the program to be effective for

students with Autism Spectrum Disorder (Berry, 2009; Cihak & Foust, 2008; Fletcher,

Boon, & Cihak, 2010; Yıkmış, 2016). The purpose of the study was to determine how the

intervention can affect accuracy and fluency for students with ASD. The study focused

on single-digit plus single-digit addition problems with three participants diagnosed with

ASD in grades 5-6, all of whom attended rural school districts in East Texas. A multiple-

probe design was used for progress monitoring, using cold and hot probes, with three

phases to the intervention: baseline, intervention, and generalization. An additional

modification was made to the TouchMath curriculum involving faded TouchPoints that

were used to aid in generalization. An analysis of results showed the TouchMath program

to likely be ineffective for students with ASD, however more research is warranted.

Limitations to the study are discussed.

iv

TABLE OF CONTENTS

ABSTRACT

……………………………………………………………...

iii

CHAPTER 1

1. Introduction …………………………………………….

1

CHAPTER 2

2. Review of Literature …………………………………....

4

CHAPTER 3

3. Method …………………………………………………

26

CHAPTER 4

4. Results ………………………………………………….

36

CHAPTER 5

5. Discussion ………………..…………………………….

41

REFERENCES

……………………………………………………………...

49

APPENDICES

……………………………………………………………...

61

A. Assessment Data …..…………………………………..

61

B. Teaching the TouchPoints 1-5...………………………..

62

C. Practice with TouchPoints 1-5………………………….

63

D. Criterion Data Collection – TouchPoints 1-5… ………

64

E. Teaching the TouchPoints 6-9….………………………

65

F. Practice with TouchPoints – 6-9………………….…….

66

G. Criterion Data Collection – TouchPoints 6-9 ………….

67

H. Counting ALL Practice………..………………………..

68

I. Criterion Data Collection – Counting ALL……………..

69

J. Counting ON Practice……………………………………

70

v

K. Criterion Data Collection – Counting ON………………

71

L. Counting ON with Faded TouchPoints Practice…………

72

M. Criterion Data Collection – Counting ON Faded……….

73

N. Counting ON without TouchPoints Practice……………

74

O. Criterion Data Collection – Counting ON without

TouchPoints………………………………………………...

75

P. Generalization Assessment………………………………

76

Q. Inter-rater Reliability Checklist………………………….

77

R. Social Validity…………………………………………..

82

VITA

……………………………………………………………...

83

1

CHAPTER 1

Introduction

As the number of students with Autism Spectrum Disorder (ASD) increases,

general and special education teachers will need to continue their search for new and

innovative methods of educating this group of students in a way that is effective and

beneficial for student success. Many students with ASD have exceptional mathematics

skills, while others continue to struggle with basic mathematical computations (Adkins &

Larkey, 2013). Often, students struggling with basic math skills fail to naturally acquire

math strategies. They are also unable to apply strategies effectively and do not

consistently use the same strategy for problem solving (Wendling & Mather, 2009). Due

to changes in state assessment, special education students are now, more than ever,

expected to acquire math computation abilities and perform on the same level as

nondisabled peers (Texas Education Agency, n.d.).

The state of Texas administered the State of Texas Assessments of Academic

Readiness (STAAR) Modified Exam for the final time during the 2013-2014 academic

year (Texas Education Agency, n.d.). Previous STAAR Modified exam accommodations

included larger print, fewer items per page, as well as three answer choices to multiple

choice questions (Texas Education Agency, 2011). Students who receive special

education services and accommodations are now required to complete the same state

exam as those enrolled in general education. According to the Spring 2017 Texas

2

Education Agency report for the STAAR 7

th

grade mathematics scores (Texas

Education Agency, 2017), 72% of all special education students in the State of Texas did

not meet the Approaching Grade Level performance standard. When comparing the

percentages of correctly answered questions from the reporting category Computation

and Algebraic Relationships, the total average for all students was 57% state wide. While

economically disadvantage students averaged 51%, English as a second language (ESL)

achieved 44%, At-Risk scored 45%, and all special education students only attained 37%.

Students receiving special education services continue to fall below the projection

curve of general education students in academic performance, with students with ASD

being among the lowest in 11 out of 13 federal disability categories (Wei, Lenz, &

Blackorby, 2013). With the standards of academic performance being raised for those

with special needs, general and special education teachers need strategies and curriculum

that can reach every student. Students with ASD exhibit more difficulties in calculation

and basic mathematical skills than students with other disabilities due to deficits in

executive functioning abilities, especially when paired with weaknesses in working

memory (Doobay, Foley-Nicpon, Ali, & Assouline, 2014). Interventions in mathematical

instruction are limited (King, Lemons, & Davidson, 2016). Research has found that the

most effective learning strategies for students in elementary grades with special needs

includes direct teaching of basic skills with the ability to practice through self-instruction

(Kroesbergen & Van Luit, 2003). The purpose of this study is to determine the

3

effectiveness of a modified TouchMath program for teaching basic mathematics

computation skills in addition for those students diagnosed with ASD in 5

th

and 6

th

grade.

4

CHAPTER 2

LITERATURE REVIEW

The number of children being diagnosed with Autism Spectrum Disorder (ASD)

is increasing every year. In fact, the percentage increased from 1.47% in 2010 to 2.76%

in 2016 (Xu, Strathearn, Liu, & Bao, 2018). According to The American Psychiatric

Association’s Diagnostic and Statistical Manual, Fifth Edition (DSM – 5; American

Psychiatric Association, 2013), ASD is described as a developmental disorder

demonstrating continual deficits with social interactions and communication skills across

different environments (American Psychiatric Association, 2013). Although the etiology

of ASD is still unknown, researchers have studied the anatomy and physiology of the

brains from people with autism over the past 20 years (Akshoomoff, 2005).

Neuroimaging has detected several regions of the brain from people with autism to be

enlarged in volume for certain areas and in other areas the volume is decreased when

compared to neurotypical brains (Akshoomoff, Pierce, & Courchesne, 2002; Getz, 2014).

Areas with consistent abnormalities across wide populations of adults and children with

ASD include the cerebellum, corpus collosum, amygdala, and hippocampus.

Abnormalities in the function of these specific brain regions tend to coincide with the

typical characteristic behaviors associated with ASD (Akshoomoff et al., 2002;

Akshoomoff, 2005).

5

The increased brain volume is due to an overgrowth of neurons, resulting in an

abundant amount of inefficient connections that reduces the efficiency of neural

pathways (Getz, 2014). Brain regions exhibiting a decrease in volume is due in part to a

diminution in neuron connections (Campbell, Chang, & Chawarska, 2014). An inverse

relationship has been found with the length and strength of neuron connections: the lower

the connection efficiency, the higher the severity of ASD symptoms (Lewis et al., 2014).

Zilbovicius et al. (1995) reported evidence of a delay in the development of the pre-

frontal cortex due to a reduction in functional connections between brain regions in

children with ASD, which can lead to potential problems with executive functioning.

Results from the comparison of cognitive, adaptive, and psychosocial differences

between neurotypical youth and students with high functioning ASD have found students

with ASD have a relative weakness in processing speed when compared to neurotypical

students (Doobay et al., 2014). This weakness could relate to deficits in executive

functioning, which is the necessary cognitive process needed for cognitive flexibility,

planning, self-regulation, response inhibition, task initiation, and working memory (Blijd-

Hoogewys, Bezemer, & van Geert, 2014). As children grow, the connections between

synapses can then increase in strength, as they are used more often, allowing for faster

processing speeds (Getz, 2014). This is an important factor in early intervention in both

behavioral and academic areas for students with ASD (Dawson et al., 2010).

Students with ASD demonstrate a wide range of strengths and weaknesses in

mathematic skills. All students receiving special education services tend to fall below the

6

performance levels of their peers in general education in both applied problems and

calculations. When comparing students within the 11 federal disability categories,

students with ASD scored in the lowest three disability groups, along with intellectual

disabilities and multiple disabilities (Wei et al., 2013). Researchers have studied the

growth trajectories for each disability category and students with ASD were found to

have significantly slower growth rates in calculation when compared to their peers in

special education (Wei et al., 2013). These results suggest that students with ASD

demonstrating weaknesses in mathematical computations will require more

individualized instruction with effective computation strategies in place to increase their

rate of performance.

Students with ASD who demonstrate mathematical strengths can also have

difficulties utilizing consistent methods of calculation. One method often utilized by

students with ASD is the recall strategy, also known as rote memory. Although students

with ASD can perform well with rote memory, researchers have found they generally are

unable to fully explain how they solved a problem 66% of the time, as this requires

executive functioning skills (Haas, 2010). As the curriculum increases throughout the

student’s educational career and becomes more complex, eventually rote memory can

become less effective as the amount of information required to remember significantly

increases. By applying mathematical strategies provided by the TouchMath curriculum,

students with ASD can begin to develop executive functioning skills (Kroesbergen et al.,

7

2003). TouchMath also provides students with other means of problem solving that do

not rely solely on rote memory alone.

As the number of students with ASD increases, teachers and school staff will

continue to look for effective ways to support these students within the classroom. The

research in mathematic interventions for students with ASD has been limited. Barnett

and Cleary (2015) conducted a literature review for effective evidence-based

interventions focusing on mathematics interventions for students with ASD. The review

only involved 11 articles, three of which included the TouchMath program. A similar

review was conducted by King, Lemons, and Davidson (2016) who found many of the

articles were related to behavioral interventions, with few effective interventions for

mathematic instruction for students with ASD and only one article pertaining to

TouchMath. Of those interventions, many of them pursued general mathematic function

or computation skills and one-to-one student/teacher ratio of direct teaching strategies.

Researchers have found that when working with elementary age students with special

needs, interventions involving the learning of basic skills of mathematics are more

effective than problem-solving based skills (Kroesbergen et al., 2003). Students also

benefit more from direct instruction from a teacher than a computer-based program or

mediated/assisted instruction (Kroesbergen et al., 2003). With limited research involving

mathematical instruction for students with ASD, there is a significant need for

researchers to provide effective interventions and curriculum that can accommodate this

population.

8

Basic math computation is the foundation for all math problem solving abilities

given that mathematics is a cumulative and hierarchical process (Wendling et al., 2009).

The foundation for all higher-level mathematics is number sense (Feikes &

Schwingendorf, 2008). Number sense refers to the overall knowledge of numbers and

operations and the ability to apply this knowledge to make mathematical decisions and

develop efficient and useful strategies for problem analysis (Reys et al., 1999). Students

who have a firm understanding of number sense are successful in understanding the

meaning of numbers and the relationship numbers can have through different operations

such as the difference in 3 + 2 versus 3 x 2 (Schneider & Thompson, 2000). Once this

understanding is acquired, fluency can begin to develop. Fluency is based on the ease

and accuracy in which basic math calculations are carried out (Locuniak & Jordan, 2008).

Calculation deficits and mathematical difficulties in fluency have been linked to

poorly established number sense abilities (Gersten, Jordan, & Flojo, 2005; Mazzocco &

Thompson, 2005). Locuniak and Jordan (2008) conducted a study to determine if the

level of number sense acquisition found in kindergarten students can predict calculation

fluency in second grade better than cognitive abilities. The study found that the most

successful students in second grade were those who had developed a firm understanding

of number sense at the acquisition stage in kindergarten. One of the defining

characteristics of students with math difficulties is a deficiency in calculation fluency,

which stems from the ability to comprehend number sense (Locuniak et al., 2008). In

9

order to develop fluency, students must acquire number sense and then be provided

opportunities to work with numbers in many different ways (Boaler, 2015).

The complexity of math continues to increase as students move up in grades, so

the demand for students to obtain knowledge and reasoning abilities substantially

increases (Wendling et al., 2009). Eventually, math evolves from the concept of

numerals and their relationships, to more complex word problems that require problem

solving abilities. According to Ferrini-Mundy and Martin (2000), "Problem solving

means engaging in a task for which the solution method is not known in advance (p. 52).”

Students use prior knowledge to solve problems and in doing so, they can develop new

understandings, making successful problem solving the ultimate goal for students in

mathematics (Ferrini-Mundy et al., 2000).

In a survey completed by Bryant, Bryant, and Hammill (2000), teachers reported

that students with learning disabilities rated word problems in mathematics as the most

difficult type of problem for those students. Wendling and Mather (2009) stated an

effective problem solver requires the abilities to: “(a) represent the problem accurately,

(b) visualize the elements of the problem, (c) understand the relationships among

numbers, (d) use self-regulation, and (e) understand the meaning of the language and

vocabulary” (p. 198). The researchers also specified that the most difficult issues

students with math difficulties demonstrate with problem-solving is understanding what

the question is asking and then following the multiple steps required to answer the

10

question. Regardless of the difficulties found with problem-solving, efficiency in basic

number sense and fluency are necessary for success in higher-level mathematics.

The instructional hierarchy, described by Haring and Eaton (1978), is based on

four stages of learning. The hierarchy is utilized to assist teachers in determining the

stage of learning their students are in, their proficiency in obtaining new skills, and

guidance in choosing academic interventions that are the most appropriate and relative to

their proficiency level (Burns, VanDerHeyden, & Boice, 2008; Daly & Martens, 1994).

During the first stage, known as acquisition, students learn new skills with performance

focusing on getting the correct answer (Cates & Rhymer, 2003). Students’ performance

is often inaccurate and slow during this phase, and they can benefit from interventions

involving explicit teaching, modeling, and an increase in immediate feedback (Ardoin &

Daly, 2007). Once accuracy is acquired, the focus shifts to fluency during the second

stage of learning. Students benefit most from interventions providing opportunities for

repeated practice and immediate feedback during the fluency stage. This allows students

to focus on accuracy while increasing their response time (Daly, Hintze, & Hamler,

2000).

The third stage of learning is generalization, in which performance conditions

offer different stimuli that were presented during the fluency stage. For example, instead

of answering 3 x 5 on a flash card, the student is now expected to apply their knowledge

of 3 x 5 in real world situations. To attain skill generalization, students should be given

ample opportunities to practice their acquired, fluent skills across diverse situations

11

(Cates & Rhymer, 2003). Adaptation is the fourth and final stage of the instructional

hierarchy and is the most complex stage (Hall, 2016). Adaptation is achieved by

applying a learned skill to a new concept, such as applying the knowledge of

multiplication to the process of long division (Cates & Rhymer, 2003). Students will

need support in breaking down problems that require multiple operations to solve into

smaller steps and will benefit from immediate feedback and opportunities for repeated

practice (Cates & Rhymer, 2003).

According to Kroesbergen and Van Luit (2003) direct instruction focusing on

basic skills of mathematics is the most effective means of working with children with

special needs. The TouchMath curriculum provides effective strategies for students with

ASD by strengthening their foundational skills and building their executive functioning.

This can give students with ASD a strong platform to support them as the hierarchical

and cumulative mathematics curriculum increases in complexity. In 1976, the

TouchMath program was created to aid struggling students with mathematical

computation. According to the TouchMath manual (Bullock, 2005), the program

provides tactile reference points, known as TouchPoints, to form connections between the

concrete and abstract concepts of the numeral. TouchMath can be used as a supplemental

program for those struggling with basic mathematical computation in addition,

subtraction, multiplication, and division (Bullock, 2005).

12

The TouchMath Program

Students with ASD who have demonstrated proficiency in computation abilities

have only been successful through the use of rote memory (Haas, 2010). Kramer and

Krug (1973) discussed the difference between the advantages and disadvantages of rote

addition versus the use of manipulatives. Rote addition is based on the ability to

memorize basic math facts. This allows for fast paced work, and does not require the

need for manipulatives, which overall allows for less conspicuous problem solving as

opposed to counting on fingers. A disadvantage that Kramer and Krug found with rote

addition, was that it does not teach the process of addition, nor does it aid in

generalization. Rote addition was simply based on memorization, and if students could

not understand the meaning of 2 + 5, they could not comprehend using this form of

problem solving.

For those students who could not memorize the math facts, Kramer and Krug

(1973) allowed for the use of manipulatives during problem solving. The researchers

mentioned that some students were incapable of memorizing fundamental combinations

and “these students may never be able to depend on rote: therefore, they must rely upon

an alternative system if they are to use addition” (p. 141). The researchers sought to find

a curriculum that allowed for a progressive transition to rote memory, but no such

curriculum was found. One of the researchers devised a reference point pattern placed on

the numbers, which allowed students to count all or count on to solve the math problems.

13

In 1976, Janet Bullock developed the program called TouchMath that modified Kramer

and Krug’s reference points and called them “TouchPoints” (Bullock, 2005).

Bullock’s (2005) TouchMath program focuses on students learning the value of a

number by placing points, known as TouchPoints, onto the numeral. TouchPoints are the

reference points that correspond to the value of the number. The TouchPoints are

systematically placed on the numerals with numerals 1 through 5 having single

TouchPoints. Students are to touch and count each single TouchPoint one time, while

numerals 6 through 9 contain double TouchPoints requiring the student to touch and

count twice (How it works, n.d.).

By combining tactile, visual, and auditory sensations, the TouchMath approach is

multisensory in nature and allows for the numerals to be presented simultaneously in a

concrete, semi-concrete, and abstract manner. Students first learn the position of the

TouchPoints on each numeral, then touch and count the TouchPoints to form a concrete

understanding of the value of the number (Yıkmış, 2016). For addition, students can

either count all TouchPoints to find the sum or apply the counting on strategy: saying the

highest value number and continuing to count the TouchPoints (Bullock, 2005). This is

similar to students using their fingers as references; however, the TouchPoints allow for

the student’s counting to be less conspicuous. For subtraction, students are to count

14

backwards from the highest numeral in the problem, and for multiplication and division

the students utilize skip counting, visual cues from the TouchPoints, and multisensory

step by step strategies to acquire accuracy with these higher-level math skills (How it

works, n.d.).

The program is derived from Piaget’s preoperational stage and Bruner’s enactive

theory of development in which students are actively engaged through touching the

points while counting aloud, allowing them to understand the concept being taught

(Green, 2009). As the TouchPoints are faded out with practice, students eventually

understand the abstract meaning of the number and how it can be used to solve problems,

coinciding with Bruner’s symbolic stage and Piaget’s formal operational stage (Green,

2009). It also breaks down the process of addition, subtraction, multiplication, and

division into smaller, logical steps that prohibits the need for storage of mathematical

facts (Scott, 1993).

The TouchMath program also aligns with Haring and Eaton’s (1978) instructional

hierarchy. Students begin with acquiring knowledge of the meaning of numerals, and the

foundational computation skills of addition and subtraction utilizing TouchPoints. With

direct teaching, modeling, opportunities to practice, and immediate feedback, students

become more accurate and eventually the TouchPoints are removed to build and increase

fluency (Yıkmış, 2016). With repeated practice, and immediate feedback, fluency is

accomplished and then students can generalize the TouchMath strategies to more

complex math problems with different stimuli. When students are introduced to the

15

concept of multiplication and division, students can adapt their knowledge of the

TouchPoints from sequential counting to skip counting.

Coleman and Lamb’s (1985) review and evaluation of TouchMath noted several

strengths and weaknesses of the program. Strengths of the program included offering

hands-on, visual aids to promote the ease of learning the value of numbers and

fundamental computation skills, which in turn reduces the dependency of rote memory.

This aspect is particularly beneficial for students with special education needs, who have

issues with memorization. TouchMath visuals allow these students to proceed to new

skills, instead of being held back due to the inability to memorize math facts. There were

also some weaknesses mentioned by the authors, concerning gaps in the program that

were not sufficiently explained in the teacher’s manual; including, the concept of more

than, and the use and comprehension of a number line. The worksheets provided in the

program can also be overstimulating for some students with special needs, due to the

amount of artwork used for visual appeal, and the amount of problems per page. Place

value is also not incorporated as part of the curriculum, which is another concern, given

that this is a skill needed to understand computation.

Despite the weaknesses found in the curriculum, there have been several studies

that have found TouchMath to be effective across many grade levels and academic

abilities. Aydemir (2015) conducted a review of 27 articles relating to the TouchMath

program published between the years of 1990 and 2014. Many of those articles

determined the TouchMath curriculum was effective over a wide spectrum of educational

16

populations, such as students in general education, gifted and talented (GT), and special

education programs. It has also been found that TouchMath can be effective for specific

special education populations including students with learning and intellectual

disabilities, physical disabilities, Down Syndrome, and Autism. Only four TouchMath

studies were found that included students with ASD. All four studies were effective and

all of them focused on addition, with one study targeting subtraction. Participants ranged

in age from 7–10 years, with one participant being 14 years of age and in the eighth grade

(Berry, 2009; Cihak & Foust, 2008; Fletcher, Boon, & Cihak, 2010; Yıkmış, 2016).

TouchMath in General Education

The results from studies involving TouchMath and the general education

population have demonstrated overall increases in computation accuracy for elementary

students and generalization into secondary level mathematics. All studies focused on

addition, with two studies also involving subtraction (Calik & Kargin, 2010; Mays, 2008;

Mostafa, 2013; Rudolph, 2008; Strand, 2001; Ulrich, 2004; Uzomah, 2012; Velasco,

2009). Improving computational accuracy and increasing overall mathematic

performance is a vital asset to those involved in the education system.

For general education students in grades Kindergarten through 2

nd

grade, research

has found the TouchMath program assists young elementary students in acquiring the

concept of addition and increases accuracy, which is required to develop fluency

(Mostafa, 2013; Strand, 2001; Uzomah, 2012; Velasco, 2009). Uzomah (2012)

recommended kindergarten instructors seek out programs and methods that have

17

manipulatives associated with the curriculum but are also within the student’s

developmental level. The TouchMath program meets Uzomah’s criteria as an effective

curriculum based on Piaget’s theory of cognitive development.

The TouchMath program is also an effective supplemental resource to the general

education curriculum, especially for students requiring more individualized instruction in

a general education setting (Calik et al., 2010; Rudolph, 2008; Ulrich, 2004). Students

have displayed marked improvement in basic computation skills within a one-week time

frame, and those students found to exhibit low levels of improvement during instruction,

including those considered GT, were able to increase their computation speed (Rudolph,

2008). Results from teacher surveys have reported that students learn more, understand

mathematics better, and are more accurate when using TouchPoints (Jarrett & Vinson,

2005).

Students in the general education population display diverse abilities in

mathematical learning requiring teachers to differentiate their instruction to meet the

needs of all their students, especially in an inclusion classroom setting. While working

with two 2

nd

grade inclusive classrooms during a six-week period, Mays (2008) found

that the TouchMath curriculum can benefit all students, including low performing

students, those with learning disabilities, and gifted students. This provides evidence that

the TouchMath curriculum is effective for student success, regardless of their level of

learning abilities, and can also be effective within a short period of time.

18

Although the TouchMath curriculum has been successful for some elementary age

students, some students continue to use TouchPoints at the secondary education level.

Despite the TouchMath research demonstrating positive outcomes for middle school

students in grades 6-8 (Fletcher et al., 2010), a common concern for teachers is their

student’s ability to generalize the acquired skill to problems without TouchPoints.

Vinson (2005) investigated these concerns by surveying 772 college students, in which

68% of the participants were found to have used TouchMath or similar strategies during

high school or in current math courses. Vinson found that having achieved higher

educational mathematic instruction, using TouchMath techniques prevented students

from depending on memorization of math facts, which at times can lead to errors.

Vinson also stated that secondary students, still using touchpoints would not have any

other support methods to succeed without this technique and concluded the results

provide credibility to the TouchMath curriculum.

Research has found the TouchMath program to increase academic performance

for students in the general education population, including GT students, at both the

elementary and secondary levels (Calik et al., 2010; Mostafa, 2013; Strand, 2001; Ulrich,

2004; Uzomah, 2012; Velasco, 2009). It has also been shown to decrease the number of

errors made during calculation, increase mathematical accuracy and speed, can be

implemented within a short period of time, and benefits students with diverse learning

abilities (Jarrett et al., 2005; Mays, 2008; Rudolph, 2008). The evidence supports the

19

premise that the TouchMath program can help students identified with disabilities

improve their basic mathematic foundational skills.

TouchMath in Special Education

Several studies have found the TouchMath program to benefit students in special

education settings as a supplement to the core curriculum and as an intervention focusing

on individual performance. Most of these studies (8) focused on the effects of the

TouchMath program in teaching addition, four studies examined subtraction, and two

studies demonstrated positive student outcomes for all four mathematical operations

(addition, subtraction, multiplication and division) for students receiving special

education services (Dombrowski, 2010; Dulgarian, 2000; Green, 2009; Scott, 1993;

Ronquillo, 2017; Waters & Boon, 2011). All studies provided evidence of an increase in

student performance in mathematical computation using the TouchMath program as

either a core curriculum, supplemental resource, or intervention (Aydemir, 2015).

When used as the core curriculum, the TouchMath program increased 75% of

participants receiving special education services performance levels from below grade

level to above grade level after one year of implementation, resulting in no longer

qualifying for special education services (Dev et al., 2002). Researchers followed up

with the student’s progress three years later and all students were able to maintain general

education status and continued with success in mathematic computation (Dev et al.,

2002). Many students receiving special education services lack skills to help them be as

successful as students in general education. By providing them with effective strategies,

20

such as the TouchMath program, special education students can decrease problematic

behaviors due to elevated frustration levels from the lack of ability to perform basic

arithmetic (Green, 2009).

Students receiving special education services for mild intellectual or learning

disabilities have become more successful in mathematic abilities after receiving

TouchMath instruction. TouchMath has increased fluency and accuracy; is

generalizable; and is considered socially valid by both students and teachers (Calik et al.,

2010; Dulgarian, 2000; Scott, 1993; Simon & Hanrhan, 2004; Wisniewski & Smith,

2002). Researchers have also found the TouchMath curriculum to be successful for

students with physical disabilities and Down Syndrome and were able to successfully

generalize the TouchMath technique to subtraction (Avant & Heller, 2011; Newman,

1994). The aforementioned qualities of the TouchMath program provide an effective

method for teachers and staff to intervene on behalf of students receiving special

education services that require more individualized instruction and assistance.

TouchMath and Autism. The research on the effectiveness of the TouchMath

program benefiting students with ASD is extremely limited. Two studies have compared

the TouchPoints strategy to the use of a number line. In both studies, elementary and

middle school students with ASD demonstrated significant increases in addition

computation and preferred the TouchPoint strategy over use of the number line (Cihak et

al., 2008; Fletcher et al., 2010). The research also has demonstrated effective

generalization for students with ASD in which participants were able to solve mathematic

21

equations without the need for TouchPoints over an extended period of time (Berry 2009;

Yıkmış, 2016). This is important because as the mathematical curriculum becomes more

complex and abstract, the need for a solid foundation of basic computation skills,

provided by the TouchMath program, becomes all the more important.

Although the research is limited, not all students with ASD have benefited from

the TouchMath program. In a study completed by Berry (2009), eight out of 10

participants with ASD benefited from using TouchPoints while performing addition and

subtraction problems and made significant math fluency gains. Two of the participants

were unsuccessful with the TouchMath program because they were unable to

comprehend the double circle TouchPoints and because of self-stimulatory behaviors

exhibited from another participant. Results from this study suggest teachers should

consider specific instructional needs and behavioral limitations of their students when

planning the implementation of the TouchMath program.

Aydemir’s review of the TouchMath program in 2015 found only 7% of the

participants in the studies analyzed were diagnosed with ASD, while 30% had learning

disabilities. The literature review conducted for this study found 36 articles within the

literature involving the TouchMath program and only four studies, including one study

conducted in Turkey, involved participants with ASD for a total of 18 students ranging in

age from 7-10 years, 13-14 years, and 10 participants identified only as elementary age

(Berry, 2009; Cihak et al., 2008; Fletcher et al., 2010; Yıkmış, 2016). Eight of the 36

articles, including one article pertaining to students with ASD (Berry, 2009), only

22

appeared on the TouchMath website and no other publication forms of the article could

be found elsewhere (e.g., thesis, dissertation, peer-review publication; Bedard, 2002;

Berry, 2009; Dulgarian, 2000; Mays, 2008; Rudolph, 2008; Strand, 2001; Vinson, 2004;

Vinson, 2005). Therefore, more research is warranted given the scarcity of TouchMath

research including participants with ASD. In fact, more research overall is needed as

TouchMath does not appear on the What Works Clearinghouse website (“WWC

Summary,” n.d.).

Other Findings. Of all the published research, there was only one article that

found the effectiveness of the TouchMath curriculum to be inconclusive. The results

from the study conducted by Velasco (2009) were considered inconclusive due to

limitations involving the post-test treatment integrity when comparing the TouchMath

program to the California Math and Phonemic Awareness programs. Nonetheless, the

researchers concluded that students in the TouchMath group improved their math fluency

skills by performing problems with more accuracy and speed on the post-test compared

to their pre-test.

Summary and Critique of the Literature

A review of the literature suggests the TouchMath curriculum successfully

increased student accuracy and fluency of basic mathematics skills in addition and

subtraction for students in general education, GT programs, and special education

(learning disabilities, mild intellectual abilities, physical disabilities, Down Syndrome,

and ASD; Avant et al., 2011; Aydemir, 2015; Bedard, 2002; Berry, 2009; Jarrett et al.,

23

2005; Mays, 2008; Newman, 1994; Rudolph, 2008; Scott 1993; Simon et al., 2004;

Uzomah, 2012; Vinson, 2005; Wisniewski et al., 2002; Yikmis, 2016). The program

allows multiple opportunities to build executive functioning skills and strengthen

student’s mathematic skills foundation for future abstract and complex mathematics

curriculum found at the secondary level and is developed at the appropriate cognitive

development level for elementary students (Uzomah, 2012). Vinson (2004) demonstrated

that the TouchMath program related to the cognitive theories of Piaget and Bruner, and

offers a visual, auditory, and tactile/kinesthetic approach for learners. Students with a

wide spectrum of cognitive abilities have improved mathematic performance with the use

of the program, regardless of their fine motor abilities (Avant et al., 2011; Newman,

1994). By fading the TouchPoints out during the learning process, participants in two

studies were able to generalize these learned skills to solve mathematical problems

without the need for visual TouchPoints. Researchers accomplished this by removing the

TouchPoints and had the participants continue touching the numerals with their pencil in

the same places where the TouchPoints had been. Over a significant amount of time,

students began solving problems automatically (Berry, 2009; Yıkmış, 2016). By

providing students in special education with the needed skills to be successful at math,

the TouchMath program aided in increasing proficiency levels and improving

problematic behaviors within the classroom (Green, 2009).

The research has shown the TouchMath curriculum can be an effective program,

even as a supplement to the existing curriculum, for elementary students, and it also

24

allows students to generalize the skill in higher education with less errors compared to

those using rote memory (Aydemir, 2015; Vinson, 2005). Nevertheless, the TouchMath

curriculum can only be effective if teachers and educational staff have access to the

curriculum. Rains, Durham, and Kelly (2009) conducted a study involving kindergarten

through 3rd grade teachers from the United States focusing on teacher awareness of the

TouchMath program. The authors found that teachers who taught in the lower grades

were familiar with the program, but as the grade level increased the teachers became

increasingly unaware of the TouchMath instructional strategies. The study suggests

teachers are more willing to utilize supplementary math materials; however, knowledge

of availability of these resources can be limited.

There is a dearth of effective mathematic interventions for students with ASD

(King et al., 2016). Due to deficits in executive functioning, many students with ASD

will continue to struggle with basic computation and will require more individualized

direct teaching instruction at the elementary level (Doobay et al., 2014). The four studies

using the TouchMath program with students with ASD have shown significant increases

in mathematical performance (Berry, 2009; Cihak et al., 2008; Fletcher et al., 2010;

Yıkmış, 2016). As high stakes testing continues to increase, and the performance

trajectory of students with ASD continues to fall below proficiency levels, there is a need

for more research to find effective mathematic interventions for this population.

Furthermore, it is important for the instructional strategies being taught to students with

ASD allow for generalization to novel problems and skills.

25

Purpose and Research Question

The purpose of this thesis was to add to the limited research-base of the

TouchMath program. The study investigated if the TouchMath strategies could increase

the accuracy and fluency of single-digit plus single-digit problems for students with ASD

in grades 5-6. The study also explored the generalizability of performing calculations

without the use of TouchPoints by slowly fading the TouchPoints out during the

intervention process. Unique to this study, smaller versions of TouchPoints were used

and termed “faded” TouchPoints to remind the participants where to touch the numerals

as they count. In the closing stages of the intervention sessions, all visible TouchPoints

were removed from the integers and participants were asked to use their “imaginary”

TouchPoints to solve the problem. Successful generalization occurred when participants

could effectively perform an addition problem without using visual TouchPoints by

transferring stimulus control from overt to covert. The following research questions were

addressed:

R1: Can TouchMath increase the accuracy and fluency of single-digit plus single-

digit, problems of students with ASD in grades 5-6?

R2: Can the TouchPoints be successfully faded while maintaining stable

responding?

26

CHAPTER 3

Method

Participants

School principals from eight different rural school districts around East Texas

were contacted about the study with a request to send prepared recruitment letters to all

parents/guardians of potential participants. A total of five students with documentation

of a diagnosis of ASD were recruited for the study in grades 5-6, but only three students

met the criteria to participate. To be included in the study, students had to be able to

recognize and write numbers 0-18, to count forwards to 18, as well as focus and remain

on task for 10-minute increments. Students with prior exposure to the TouchMath

curricula were excluded from the study. Other exclusionary factors included: students

displaying limited verbal abilities and severe problematic behaviors, and high rates of

absenteeism in a school setting which could lead to potential limitations for the study

(Martínez-Mesa, González-Chica, Duquia, Bonamigo, & Bastos, 2016).

Data gathered prior to the beginning of the study indicated two participants did

not meet criteria for the study. One student did not have a firm understanding of

numerals and could not write the correct number when prompted. Another student was

nonverbal and exhibited severe sensory and problematic behaviors that prevented

participation in the study. Participant one, Anna, a fifth-grade Caucasian female, spent

her entire day in the general education setting with accommodations and modifications

27

set in place through special education services. Participant two, Sam, a fifth-grade

Caucasian male, was also mainstreamed in the general education setting with similar

special education services provided. Participant three, John, a sixth-grade Caucasian

male spent his entire day in a self-contained life skills classroom.

None of the students had prior exposure to TouchMath or its procedures. Anna

and Sam used rote memory (i.e., memorized addition math facts) during baseline to

answer the addition problems, while John used a “100’s chart.” While in intervention,

the researcher strongly encouraged Anna to utilize the TouchMath strategies for all

assessment probes. In spite of this, she continued to primarily use rote memory and only

used TouchMath as a supplement. Sam continued to use rote memory for all cold probes

but then used the TouchMath strategies during the hot probes. Throughout the

intervention, John was unable to complete the assessment probes utilizing the learned

TouchMath strategies and reverted back to the 100’s chart he used during baseline.

Materials

Materials used in the study included assessment data using “addition: sums to 18”

probes from the Measures and Interventions of Numeracy website ("MIND: Facts on

Fire", n.d) to collect data during baseline, intervention, and generalization phases to

determine the effectiveness of the program (See Appendix A). Intervention worksheets

used in the study included: TouchMath worksheets for each step in the procedure

provided by the TouchMath company and worksheets created by the researcher (See

Appendices B-H). The researcher-created worksheets were formatted in a word

28

processer using a similar font as the TouchMath curriculum and contained numerals with

TouchPoints that were needed for criterion data collection and for introducing and

implementing the faded TouchPoints. Visuals and manipulatives for the intervention

sessions included: Magnetic 3D Numerals and Student Number Cards provided by the

TouchMath company. Additional materials included: pencils, counters, verbal praise and

tangible rewards for positive behavioral supports, and a computer for tracking data.

Procedure

Participants that met the inclusion criteria each worked in a one-on-one session

with the researcher three times per week for five consecutive weeks. To obtain a stable

trend of data points during baseline, MIND probes were administered prior to the

intervention phases. Participants were asked to complete each probe within a two-minute

time frame and were scored for digits correct per minute and percent of digits correct per

digits attempted.

Practice worksheets and manipulatives were used during each intervention session

to introduce the TouchPoints and new concepts (See Appendix B). At the beginning of

each session, each participant independently completed a “cold probe” to monitor

between-session growth., and a “hot probe” was also given post-session to measure

within-session growth. Each probe was obtained from the MIND website and was

identical in procedures to the baseline assessment. For sessions two through seven, data

were collected to determine if the participant met the criterion of 80% concept mastery to

move on to the next session. Once the TouchPoints were introduced at the conclusion of

29

session two, students reviewed the TouchPoints before learning the next concept in each

session with visuals and manipulatives, such as the Student Number Cards.

All intervention session procedures were derived from the TouchMath program.

Session five involved the generalizability component, which was added to the curriculum

for this study, termed faded TouchPoints, to aid in gradually fading out the need for

TouchPoints represented on the numbers in the problem. The term imaginary

TouchPoints was also developed for this study and is not a term associated with the

TouchMath curriculum. Finally, in sessions four and five, the directions to “circle the

largest number” was added to the curriculum to emphasize the importance of identifying

the largest integer to apply the counting on strategy.

Throughout the sessions, participants were given positive reinforcement for

exhibiting on-task behaviors (e.g., actively engaging in task, following directions).

Immediate feedback and verbal praise (i.e., “nice job, good working”) were offered

during the learning and practice intervals based on on-task behaviors. Tangible rewards

including edibles and/or toys from a treasure box were given to participants at the end of

each session. Feedback was not provided during or after the two-minute progress

monitoring probes. The least-to-most hierarchy prompting system was utilized during the

learning and practice sessions. Each prompting level ranged from the unassisted

independent level to sequenced levels ranging from minimum to maximum amounts of

prompting (Neitzel & Wolery, 2009). Participants were first asked to complete the task

with a verbal prompt. Then visuals from the TouchMath Student Number Cards were

30

offered for more assistance. If further prompting was required, the researcher would then

model the task to be completed. Finally, if the participant continued to require

prompting, physical hand-over-hand prompting was utilized (Neitzel & Wolery, 2009).

Intervention sessions proceeded as follows:

Session 1 - Teaching the TouchPoints 1-5

A cold probe was administered at the beginning of the session. Participants first

became acquainted with the single TouchPoints for each numeral 1-5 by touching and

counting the TouchPoints by first placing counters on the manipulative placement

worksheets from the TouchMath program. Then, Magnetic 3D Numerals manipulatives,

provided by the TouchMath program, were used during this session. Participants then

practiced touching and counting each TouchPoint on the practice worksheet (See

Appendices B-D). At the end of the session, a hot probe was administered.

Session 2 - Teaching the TouchPoints 6-9

A cold probe and criterion assessment were administered at the beginning of

session two. Participants meeting the 80% criterion proceeded to the second session and

became acquainted with the double TouchPoints for each numeral 6-9 by touching and

counting the TouchPoints. Similar worksheets and manipulatives from session one were

used to practice the double touch concept. Participants then practiced touching and

counting each TouchPoint on the practice worksheet (See Appendices E-G). Last,

participants completed a hot probe for progress monitoring.

31

Session 3 – Counting ALL – Single-digit plus Single-digit Addition Problems

A cold probe and criterion assessment were administered at the beginning of

session three. Participants meeting the 80% criterion were introduced to the counting all

strategy by counting all TouchPoints for single-digit plus single-digit addition problems

to form single-digit and double-digit sums. Participants first practiced with the Magnetic

3D Numerals and then completed a practice worksheet (See Appendices H-I). The

session concluded with a hot probe for progress monitoring.

Session 4 – Counting ON with TouchPoints

A cold probe and criterion assessment were administered at the beginning of

session four. Participants meeting the 80% criterion were introduced to the counting on

strategy with the use of TouchPoints. Then, participants were asked to identify and circle

the largest numeral in the problem. To solve the addition problem, participants said the

name of the numeral they circled and then continued to count on with TouchPoints on the

lowest numeral. (See Appendices J-K). Participants were then administered a hot probe.

Session 5 – Counting ON with Faded TouchPoints

A cold probe and criterion assessment were administered at the beginning of

session five. Participants meeting 80% from the previous intervention session were

asked to identify and circle the largest numeral in the problem and then continue to count

on with the faded TouchPoints for the first part of the practice worksheet. During the

second part of the session, students simply identified and said the largest numeral and

continued counting the faded TouchPoints on the lowest numeral to aide in the

32

generalization in identifying the largest numeral (See Appendices L-M). Participants

were then administered a hot probe.

Session 6 – Counting ON Strategy without TouchPoints

A cold probe and criterion assessment were administered at the beginning of

session six. Participants meeting the 80% criterion were asked to identify the largest

number in a problem and use their “imaginary” TouchPoints to continue counting and

solve the problem without using TouchPoints (See Appendices N-O). The session

concluded with a hot probe.

Session 7 – Generalization Assessment

Criterion assessment probes were administered at the beginning of session seven.

Participants meeting the 80% criterion were given a generalization assessment without

TouchPoints, similar to the baseline assessment (See Appendix P).

Research Design

A multiple-probe design was used to determine the effectiveness of the

TouchMath program for students with ASD for addition problems with single-digit plus

single-digit problems to form single-digit and double-digit sums. A multiple-probe

design is a combination of the techniques of probe procedures and multiple-baseline

(Horner & Baer, 1978). Versions of multiple-baseline and multiple-probe designs allow

for replication of a condition across multiple participants with staggered implementation

across subjects and account for practice effects (Riley-Tillman & Burns, 2009). Instead

of collecting data simultaneously for all participants throughout baseline, as in a multiple-

33

baseline design, the multiple-probe design intermittently collects baseline data with

probes to determine the performance level of each participant (Cooper, Heron, &

Heward, 2014).

The multiple-probe design consists of phase A (baseline) and phase B

(intervention). During phase A, data are collected for all participants under the same

conditions until stability within the data is reached. Once baseline data are stable, the

intervention phase B is introduced to the first participant and continues until stability is

reached again for the phase B data (Riley-Tillman et al., 2009). In addition to the

primary phases, the current study also included a third phase, C (generalization).

Due to time constraints related to the end of the school year, stabilized data during

phase B was unattainable and only two consecutive sessions were concluded for each

participant before the next participant entered phase B. Participants began the

intervention phase B once a stable baseline was established and an A-B pattern continued

for all participants until they completed intervention sessions 1-6. The generalization

session, phase C, consisted of the assessment in session seven to determine if the

participants were able to maintain accurate and stable responses of single-digit plus

single-digit problems forming single-digit and double-digit sums without visual

TouchPoints.

When utilizing forms of multiple-probe designs, it is critical for all participants to

display similar characteristics of academic and behavioral functioning (Riley-Tillman et

al., 2009). This was considered when selecting participants for the study. Experimental

34

control occurs when three demonstrations of effect are observed. For multiple-probe

designs and variants, this can occur when effects are replicated across at least three

participants. Stronger experimental control can be achieved by involving more

participants, allowing for greater opportunities for replication. A minimum of three

participants are required for multiple-probe design studies (Riley-Tillman et al., 2009).

Statistical analysis

Data were analyzed using visual analysis of changes in level, trend, variability,

and percentage of nonoverlapping data (PND) of digits correct per minute (DC/PM)

between phases. PND is found by calculating the percentage of data points in Phase B

(intervention) that exceed the highest data point in Phase A (baseline; Parker, Vannest, &

Davis, 2011). This percentage was used to estimate the effect size of the intervention.

An effect size of 80% and greater is considered large (Scruggs & Mastropieri, 1998).

DC/PM served as a dependent variable and was calculated by dividing the number

of correct digits divided by the total amount of time (2 min; Shinn, 1989). For example:

in the problem 2 + 9, a participant who answers 11 would have two digits correct. If they

had responded 12, the digits in the ones column would be incorrect, whereas the digit in

the tens column would be considered correct (Deno & Mirkin, 1977). An increase in the

total number of correct digits per minute indicate improved skill fluency. For students in

grades 4-6 solving addition problems, 24 – 49 DC/PM is considered to be within the

instructional level, and less than 24 DC/PM would indicate a need for academic

intervention (Burns, VanDerHeyden, & Jiban, 2006). Hence, this study will refer to 23

35

or fewer DC/PM as being in the frustrational range, 24 - 49 DC/PM as being in the

instructional range, and 50 or more DC/PM as being in the mastery range. Due to student

response patterns, the percentage of digits correct for assessment probes was also

calculated as a dependent variable to observe possible changes in accurate responding.

Inter-rater reliability was conducted for 25% of the intervention sessions. Staff

from the local school districts completed an observation checklist for treatment integrity

(See Appendix Q). A total of five sessions were conducted (one with Anna, one with

Sam, and three with John) for observation inter-reliability. All observation checklists

resulted in 100% agreement. The probe assessments from all sessions were also scored

by a second rater to calculate inter-rater reliability. Twenty-five percent of the

assessment probes, three from each participant, were chosen randomly for inter-rater

reliability in which scores for DC/PM were compared for accuracy. All assessment

probes resulted in 100% agreement between the researcher and the second rater.

36

CHAPTER 4

Results

During baseline, Anna demonstrated stable responding for three consecutive

sessions and her performance was within the frustrational level for fluency (M = 18.1;

range = 18 to 18.5 DC/PM; see Figure 1). While in the intervention phase, Anna’s

responding on both cold and hot probes remained stable across all sessions with no

change in variability (M = 17.0; range = 11 to 22.5). Her intervention data showed a

slight increase in level and trend from the baseline phase (PND = 33% for cold probe;

50% for hot probe). Similar patterns of responding were observed during the

generalization phase (M = 18.6; range = 14 to 26; PND = 40%). Throughout the study,

Anna maintained accuracy of 100% for all sessions (see Figure 2).

Sam’s baseline data showed some instability in responding, requiring the need for an

additional session. Baseline data indicated Sam performed at the instructional level for

fluency (M = 37.3; range = 30.5 to 42.0). During the intervention phase, Sam’s

performance on the cold probes remained stable throughout all sessions (M = 36.7; range

= 28.0 to 43.0). He also demonstrated minimal changes in level, trend, or variability

from the baseline phase (PND = 17% for cold probe). However, his hot probes indicated

a negative effect on his level of responding (M = 12.8; range= 9.5 to 17; PND = 0%).

Sam demonstrated a similar pattern throughout the generalization phase (M = 25.4; range

37

= 19 to 37; PND = 0%). For accuracy, Sam maintained sufficient accuracy, greater than

95%, throughout all phases.

John performed at the frustrational level during all phases. While in baseline,

John maintained stable responding (M = .67 DC/PM; range = 0.50 to 1.00). During the

intervention phase, John’s responding on the cold and hot probes varied over the six

sessions with no change in level (M = 2.29 DC/PM; range = 1 to 3.5). His intervention

data showed an increase in trend with variable levels of responding from the baseline

phase (PND = 100%). The time allotted with John for data collection only consisted of

five weeks and due to end of year time constraints, only one session was available to

collect data for generalization. John showed a decrease in data during the generalization

phase with results similar to baseline patterns (M = 0.50; range = 0.50; PND = 0%).

Throughout the entire study, John showed extremely variable rates of accuracy. During

baseline, accuracy ranged from 14 to 33% and during the intervention phase he scored

between 36 - 70%.

38

Figure 1

Fluency – Digits Correct per Minute

39

Figure 2

Accuracy – Percent Digits Correct

When assessing the effectiveness of the TouchMath intervention by comparing

baseline and intervention phase data, PND effect sizes are classified as follows: very

effective (scores above 90), effective (70-90), questionable (50-70), ineffective (below

50; Scruggs & Mastropieri, 1998). Johns’ PND for fluency between the baseline and

intervention phases fell in the very effective range with a score of 100% for cold probes,

while Anna’s and Sam’s were in the ineffective range with a score of 33% and 13%,

40

respectively. For accuracy, John exhibited a PND of 100% for cold probes, which is in

the very effective range. The PND scores for both Anna and Sam were in the ineffective

range with 0%. Both participants maintained stable accuracy of 95% or greater for all

phases.

Participants provided a generally positive review of the intervention on a social

validity questionnaire (See Appendix R). The questionnaire consisted of six questions

and were measured using a Likert-type scale ranging from 1 (strongly disagree) to 6

(strongly agree). Participants scored 83% of the items as a 4 or a 5. They expressed they

liked the study, thought the study was helpful, and that they would continue to use

TouchMath over other strategies they had learned in the past. In contrast, participants did

not agree that the TouchMath strategies were easy to use or that they improved their math

calculation skill when using TouchMath strategies.

41

CHAPTER 5

Discussion

Researchers have found the TouchMath curriculum to be an effective intervention

at increasing the math accuracy and fluency of students in general and special education.

Four studies found in the literature pertained to students with ASD, all of which found

TouchMath to be an effective intervention for students with ASD (Berry, 2009; Cihak &

Foust, 2008; Fletcher, Boon, & Cihak, 2010; Yıkmış, 2016). The purpose of this study

was to add to the limited TouchMath literature by focusing on single-digit plus single-

digit addition problems and how the intervention can affect math accuracy and fluency

for students with ASD. The study also sought to add to the research base by modifying

the TouchMath curriculum, wherein faded TouchPoints were used to aid in

generalization.

The current study obtained mixed results when comparing participants’ baseline

and intervention phase data. PND ranged from ineffective to very effective, with the

intervention being effective for only one participant. In the beginning of each

intervention session, a cold probe was administered to monitor between-session growth,

while within-session growth was measured with a hot probe at the conclusion of the

session. Anna’s PND score for the cold probes, when comparing intervention to baseline,

was 33% and Sam’s PND was 17%, placing both Ann and Sam’s PND in the ineffective

range. In contrast, John’s PND was 100%, which is in the very effective range.

42

Prior to intervention, Sam performed in the instructional range, while Anna and

John were in the frustrational range. Sam’s fluency remained level with baseline in the

instructional range. Throughout intervention, Anna was able to perform at higher rates of

fluency during intervention for two cold probes; however, she stayed within the

frustrational level throughout intervention. John demonstrated the greatest increase in

fluency and his PND score was in the very effective range, although his overall fluency

remained in the frustrational range. When comparing cold probes to hot probes, Anna’s

PND score increased while Sam and John’s decreased, demonstrating less learning for

within-session growth than between-session growth. The difference in scores may have

resulted from the use of prior strategies to complete the addition problems during cold

probes, despite being reminded by the researcher to use TouchMath. Once the

interventions session was complete, the researcher reminded the participants for a second

time to use TouchMath, in which Anna and Sam were more compliant to do so.

Due to time constraints, only five days were permitted for Anna to be in the

generalization phase, three days for Sam, and only one day for John. Anna primarily

used rote memory, with TouchMath as a supplement, during the first generalization

session, but then used the TouchMath strategies for the remainder of the generalization

sessions. Her fluency rate decreased to below baseline levels, but then gradually began to

trend upward towards the end of the study. During the three days of generalization with

Sam, his fluency decreased significantly when compared to baseline. John performed

below baseline for both accuracy and fluency during the only generalization session that

43

was conducted. Although the data indicate the TouchMath program to be very effective

for John during the intervention sessions, all PND scores for all participants fell within

the ineffective range for the generalization sessions indicating they were unable to

transfer the skill to novel problems.

Treatment integrity was compromised throughout the study as participants

continued to use previously learned strategies during assessment probes, despite being

repeatedly encouraged by the researcher to use the TouchMath strategies. Although

treatment procedures were implemented by the researcher with 100% fidelity, the

observation checklist did not consider the use of other types of strategies used by the

participants. Anna continued to use rote memory for problems she was confident about

but used the TouchMath counting on strategy for items that she could not recall the

answer. Sam used rote memory for the cold probes but used the TouchMath strategies

during the intervention hot probes. During hot probes, Sam’s fluency dropped into the

frustrational level, indicating the TouchMath strategies had a negative effect on his

fluency rate. Although John was able to use the TouchMath strategies correctly during

intervention practice, he still reverted back to using a 100’s chart for cold and hot probes

during intervention. When the researcher encouraged John to utilize the TouchMath

strategies, he quickly voiced that he could not do it and began showing physical signs of

frustration. Due to adherence to IRB procedures and the ethical duty of the researcher to

prevent any participant from having adverse consequences as a result of being in the

study, John was allowed to use his previously learned method during assessment probes.

44

It was not until after practicing the TouchMath strategies without visible TouchPoints in

session six, that he agreed to try the hot probe with the TouchMath strategy of counting

all. All participants were able to perform the generalization assessments probes using

only the TouchMath strategies.

King et al. 2016 addressed the dearth of research for effective math interventions

that exists with the population used in the current study. Many of the reasons for why

there is a limited research base for students with autism were also encountered in this

study. Issues involved during the study included: inclusion/exclusion criteria that affects

the limited available research samples and the willingness of the participants to

participate and adhere to procedures that are needed for adequate research to be

conducted.

TouchMath is an acquisition intervention, which requires time and multiple

opportunities to practice the new skills. Another limitation to this study was the limited

amount of time that was available for the researcher to work with the participants. In

previous studies performed with students with ASD involving TouchMath, one study was

conducted over a two-year period (Berry, 2009) and the other study had participants

remain in intervention between 7 - 21 days (Yıkmış, 2016). Only five weeks were

available for data collection because it was the end of the school year. Three weeks were

needed to successfully complete the baseline and intervention sessions. The study

required at least three days to collect baseline data and six consecutive days to complete

six sessions of intervention for each participant. Unfortunately, the time constraints did

45

not allow for each participant to demonstrate growth during the intervention phase.

While all participants met each intervention session criteria and successfully

demonstrated understanding and application of the TouchMath strategies during each

intervention session, they showed little-to-no growth during the intervention and

generalization phases for accuracy and fluency. Avant et al. (2011) and Newman (1994)

conducted a study using a multiple-probe design to see how TouchMath can affect

student’s accuracy with addition problems. Both studies utilized 2-3 days of pre-training

sessions between baseline and intervention in which participants were taught the

TouchMath strategies prior to collecting intervention data. The current study required six

days of instruction, due to an additional session added to include “faded” TouchPoints,

all of which occurred during intervention. By performing pre-training sessions, the

amount of time needed to complete the intervention session can be reduced by half,

allowing more time for each participant to demonstrate growth. However, these pre-

training sessions should still be considered when determining one’s rate of improvement.

Another limitation of the study was the limited population sample available.

Eight rural East Texas school districts were approached for potential participants, and

only five students with ASD were available for recruitment. All five participants varied

in abilities from severe to mild levels of ASD and only three students qualified for the

study. A key element when using a multiple-probe design is for participants to

demonstrate similar behavioral and academic functioning (Riley-Tillman et al., 2009).

While Anna and Sam displayed similar abilities, John demonstrated much lower

46

academic and behavioral functioning. Throughout the study, Anna and Sam were able to

follow directions from the researcher very well, transitioned from one session to the next

with ease, and worked diligently with little prompting to complete the math problems.

John, however, struggled to remain on-task without frequent reminders and required

more prompts from the researcher. At times, the length of the practice worksheets

seemed too long, requiring frequent breaks and encouragement from the researcher in

order to finish the session. Once John demonstrated understanding the concept being

taught, he was unable to generalize that concept to the assessment probe. The

intervention procedures were also presented to John at a much faster pace than he was

comfortable with. Although he met the 80% criterion on each criterion assessment probe,

he still required more supports than the other participants, (i.e., prompts from the

researcher for each step in solving the problem with the TouchMath strategies) as the

TouchPoints were faded.

Even though the participants’ academic and behavioral abilities were not as

similar as the design required, the study may provide some insight into the type of student

that may benefit the most from TouchMath. While John struggled with performing the

TouchMath strategies without the visible TouchPoints, he demonstrated the greatest

increase in fluency. Relatedly, Fletcher, Boon, and Cihak (2010) found participants with

ASD and moderate intellectual disability who were functioning within the frustrational

range benefited more from the TouchMatch curriculum than from use of a number line.

Given the pre-existing data coupled with John and Anna’s performance, future research

47

should examine whether TouchMath is only beneficial for those students performing in

the frustrational range.

An additional limitation that should be considered is Anna and Sam’s successful

use of rote memory for addition problems. Both Anna and Sam maintained sufficient

accuracy, greater than 95%, throughout baseline and the intervention phases with rote

memory and TouchMath. During baseline, Sam was performing at an average rate of 37

DC/PM and was considered to be well within the appropriate instructional level for a 5

th

grade student. During the generalization phase, it took longer for Sam to count the

“imaginary” TouchPoints causing a decrease in DC/PM when compared to baseline.

This suggests that the TouchMath program is not an effective intervention for those

students performing at or above the instructional level. In fact, the use of TouchMath, as

an acquisition intervention, may be contraindicated and create learning delays for

students already functioning at these levels.

Overall, the current study may have found different results over a greater length

of time. Future studies should examine the comparative benefit of TouchMath when

accounting for students’ instructional levels during baseline. The current study suggests

that TouchMath may be beneficial for students in the frustrational range as an acquisition

intervention but contraindicated for students within the instructional range. Furthermore,

a comparison study between TouchMath and other acquisition interventions (e.g., taped

problems, flash cards) is warranted given the available data. In particular, researchers

should focus on the rate of learning over time when comparing studies.

48

In conclusion, the results of this study indicate TouchMath is likely an ineffective

strategy for students with ASD. However, given the use of alternate strategies for all

participants during intervention, more research is warranted, particularly for students

within the frustrational range. Researchers may consider the instructional level of each

student prior to implementing the intervention, as students within the frustrational level

may show greater improvements than students within the instructional or mastery levels.

Students exhibiting lower academic abilities than typically developing peers will likely

require more intensive supports over a prolonged period of time. In the current study,

only one of three participants demonstrated an increased rate of accuracy and fluency.

Although John’s data showed the intervention to be very effective, treatment integrity

was a limitation throughout the intervention as John also used other problem solving

strategies. Therefore, it cannot be determined what the effects of each strategy produced.

Future researchers should consider other strategies students have previously learned

before implementing the TouchMath strategy and how those learned strategies may affect

the intervention.

49

References

Adkins, J., & Larkey, S. (2013). Practical mathematics for children with an autism

spectrum

disorder and other developmental delays. London, UK: Jessica Kingsley Publishers.

Akshoomoff, N. (2005). The neuropsychology of autistic spectrum disorders.

Developmental Neuropsychology, 27(3), 307-310.

doi:10.1207/s15326942dn2703_1

Akshoomoff, N., Pierce, K., & Courchesne, E. (2002). The neurobiological basis of

autism from a developmental perspective. Development and Psychopathology, 14,

613–634.

American Psychiatric Association. (2013). Diagnostic and statistical manual of mental

disorders (5th ed.). Arlington, VA: American Psychiatric Publishing.

Ardoin, S. P., & Daly, E. J. (2007). Introduction to the special series: Close encounters of

the instructional kind-how the instructional hierarchy is shaping instructional

research 30 years later. Journal of Behavioral Education, 16(1), 1-6.

doi:10.1007/s10864-006-9027-5

Avant, M. T., & Heller, K. W. (2011). Examining the effectiveness of TouchMath with

students with physical disabilities. Remedial and Special Education, 32(4), 309-

321.

50

Aydemir, T. (2015). A review of the articles about TouchMath. Procedia-Social and

Behavioral Sciences, 174, 1812-1819.

Barnett, J. E. H., & Cleary, S. (2015). Review of evidence-based mathematics

interventions for students with autism spectrum disorders. Education and training

in autism and developmental disabilities, 50(2), 172-185.

Bedard, J. M. (2002). Effects of a multi-sensory approach on grade one mathematics

achievement. Retrieved from

https://www.TouchMath.com/about/researchPapers.cfm?rID=141

Berry, D. (2009). The effectiveness of the touch math curriculum to teach addition and

subtraction to elementary aged students identified with autism. Retrieved from

https://www.TouchMath.com/about/researchPapers.cfm?rID=135

Blijd-Hoogewys, E. A., Bezemer, M. L., & van Geert, P. C. (2014). Executive

functioning in children with ASD: An analysis of the BRIEF. Journal of Autism

and Developmental Disorders, 44(12), 3089-3100. doi:10.1007/s10803-014-

2176-9

Boaler, J. (2015). Fluency without fear: Research evidence on the best ways to learn

math facts. Retrieved from https://www.youcubed.org/evidence/fluency-without-

fear/

Bryant, D. P., Bryant, B. R., & Hammill, D. D. (2000). Characteristic behaviors of

students with LD who have teacher-identified math weaknesses. Journal of

Learning Disabilities, 33, 168-177.

51

Bullock, J. (2005). TouchMath teacher training manual. Colorado Springs, CO:

Innovative Learning Concepts.

Burns, M. K., VanDerHeyden, A. M., & Jiban, C. L. (2006). Assessing the instructional

level for mathematics: A comparison of methods. School Psychology Review,

35(3), 401.

Burns, M. K., VanDerHeyden, A. M., & Boice, C. H. (2008). Best practices in intensive

academic interventions. In A. Thomas & J. Grimes (Eds.), Best practices in

school psychology V (pp.1151-1162). Bethesda, MD: National Association of

School Psychologists.

Campbell, D. J., Chang, J., & Chawarska, K. (2014). Early generalized overgrowth in

autism spectrum disorder: Prevalence rates, gender effects, and clinical outcomes.

Journal of the American Academy of Child & Adolescent Psychiatry, 53(10),

1063-1073.e5. doi:10.1016/j.jaac.2014.07.008

Cates, G. L., & Rhymer, K. N. (2003). Examining the relationship between mathematics

anxiety and mathematics performance: An instructional hierarchy perspective.

Journal of Behavioral Education, 12(1), 23-34. doi:10.1023/A:1022318321416

Cihak, D., & Foust, J. (2008). Comparing number lines and touch points to teach addition

facts to students with autism. Focus on Autism and Other Developmental

Disabilities, 23, 131–137.

52

Calik, N.C. & Kargin, T. (2010). Effectiveness of the touch math technique in teaching

addition skills to students with intellectual disabilities, International Journal of

Special Education. 25(1):195.

Coleman, M. C., & Lamb, C. (1985). Touch math. Techniques, 1(5), 337-341.

Cooper, J. O., Heron, T. E., & Heward, W. L. (2014). Applied behavior analysis (2

nd

ed.).

Harlow: Pearson Education.

Daly, E. J., III, Hintze, J. M., & Hamler, K. R. (2000). Improving practice by taking steps

toward technological improvements in academic interventions in the new

millennium. Psychology in the Schools, 37 (1), 61-72.

Daly, E. J., III, & Martens, B. K. (1994). A comparison of three interventions for

increasing oral reading performance: Application of the instructional hierarchy.

Journal of Applied Behavior Analysis, 27(3), 459-469. doi:10.1901/jaba.1994.27-

459

Dawson, G., Rogers, S., Munson, J., Smith, M., Winter, J., Greenson, J., ... & Varley, J.

(2010). Randomized, controlled trial of an intervention for toddlers with autism:

The early start Denver Model. Pediatrics, 125(1), e17-e23.

Deno, S.L, & Mirkin, P.K. (1977). Data-based program modification: A manual. Reston,

VA: Council for Exceptional Children.

Dev, P.C., Doyle, B.A., & Valente, B. (2002). Labels needn’t stick: “At-Risk” first

graders rescued with appropriate Intervention. Journal of Education for Students

Placed At Risk, 7(3), 327-332. doi:10.1207/S15327671ESPR0703_3

53

Doobay, A. F., Foley-Nicpon, M., Ali, S. R., & Assouline, S. G. (2014). Cognitive,

adaptive, and psychosocial differences between high ability youth with and

without autism spectrum disorder. Journal of Autism and Developmental

Disorders, 44(8), 2026-2040. doi:10.1007/s10803-014-2082-1

Dombrowski, C. (2010). Improving math fact acquisition of students with learning

disabilities using the" Touch Math" method. (Master’s thesis). Retrieved from

https://rdw.rowan.edu/etd/104

Dulgarian, D. (2000). TouchMath intervention vs. traditional intervention: Is there a

difference? Retrieved from

https://www.TouchMath.com/about/researchPapers.cfm?rID=140

Feikes, D. & Schwingendorf, K. (2008). The importance of compression in children’s learning of

mathematics and teacher’s learning to teach mathematics. Mediterranean Journal for Research in

Mathematics Education, 7(2).

Ferrini-Mundy, J., & Martin, W. G. (2000). Principles and standards for school

mathematics. Reston, VA: National Council of Teachers of Mathematics.

Fletcher, D., Boon, R. T., & Cihak, D. F. (2010). Effects of the "TouchMath" program

compared to a number line strategy to teach addition facts to middle school

students with moderate intellectual disabilities. Education and Training in Autism

and Developmental Disabilities, 45(3), 449-458.

54

Gersten, R., Jordan, N. C., & Flojo, J. R. (2005). Early identification and interventions

for students with mathematics difficulties. Journal of Learning Disabilities, 38,

293–304.

Getz, G. E. (2014). Applied biological psychology. Springer Publishing Company.

Green, N. D. (2009). The effectiveness of the touch math program with fourth and fifth

grade special education students. Retrieved from

https://eric.ed.gov/?id=ED507708

Haas, S. (2010). Differences in estimation and mathematical problem solving between

autistic children and neurotypical children (Unpublished master's thesis).

Carnegie Mellon University, Pennsylvania.

Hall, M. (2016). A comparison of targeted and multicomponent small-group reading

interventions in early elementary grades (Doctoral dissertation). Retrieved from

https://conservancy.umn.edu/handle/11299/178961

Haring, N. G., & Eaton, M. D. (1978). Systematic instructional technology: An

instructional hierarchy. In N. G. Haring, T. C. Lovitt, M. D. Eaton, & C. L.

Hansen (Eds.), The fourth R: Research in the classroom. Columbus, OH: Merrill.

Horner, R. D., & Baer, D. M. (1978). Multiple-probe technique: A variation on the

multiple baseline. Journal of Applied Behavior Analysis, 11(1), 189-96.

How It Works. (n.d.). Retrieved June 29, 2018 from

https://www.TouchMath.com/index.cfm?fuseaction=about.how

55

Jarrett, R. M., & Vinson, B. M. (2005). A quantitative and qualitative study of a high

performing elementary school in mathematics: Does TouchMath contribute to

overall mathematics achievement? Athens, AL: Athens State University.

King, S. A., Lemons, C. J., & Davidson, K. A. (2016). Math interventions for students

with autism spectrum disorder: A best-evidence synthesis. Exceptional Children,

82(4), 443-462.

Kramer, T. & Krug, D. A. (1973) A rationale and procedure for teaching addition.

Education and Training of the Mentally Retarded, 8, 140–145.

Kroesbergen, E. H., & Van Luit, J. E. (2003). Mathematics interventions for children

with special educational needs: A meta-analysis. Remedial and Special

Education, 24(2), 97-114.

Lewis, J. D., Evans, A. C., Pruett, J. R., Botteron, K., Zwaigenbaum, L., Estes, A., . . .

Piven, J. (2014). Network inefficiencies in autism spectrum disorder at 24

months. Translational Psychiatry, 4(5), e388. doi:10.1038/tp.2014.24. Retrieved

from

https://www.researchgate.net/publication/262111596_Network_inefficiencies_in_

autism_spectrum_disorder_at_24_months

Locuniak, M. N., & Jordan, N. C. (2008). Using kindergarten number sense to predict

calculation fluency in second grade. Journal of Learning Disabilities, 41(5), 451-

459. doi:10.1177/0022219408321126

56

Martínez-Mesa, J., González-Chica, D. A., Duquia, R. P., Bonamigo, R. R., & Bastos, J.

L. (2016). Sampling: How to select participants in my research study?. Anais

brasileiros de dermatologia, 91(3), 326-30.

Mays, D. (2008). TouchMath: An Intervention that Works. Retrieved from

https://www.TouchMath.com/about/researchPapers.cfm?rID=133

Mazzocco, M. M., & Thompson, R. E. (2005). Kindergarten predictors of math learning

disability. Learning Disabilities Research and Practice, 20(3), 142–155.

MIND: Facts on Fire. (n.d.). Retrieved from http://brianponcy.wixsite.com/mind/copy-of-

mind-facts-on-fire

Mostafa, A. A. (2013). The effectiveness of touch Math Intervention in teaching addition

skills to preschoolers at-risk for future learning disabilities. International Journal

of Psycho-Educational Sciences,4(4), 15–22.

Neitzel, J., & Wolery, M. (2009). Steps for implementation: Least-to-most prompts.

https://autismpdc.fpg.unc.edu/sites/autismpdc.fpg.unc.edu/files/Prompting_Steps-

Least.pdf

Newman, T. M. (1994). The effectiveness of a multisensory approach for teaching

addition to children with down syndrome. (Master’s thesis). McGill University,

Montreal, Quebec.

Parker, R. I., Vannest, K. J., & Davis, J. L. (2011). Effect size in single-case research: A

review of nine nonoverlap techniques. Behavior Modification, 35(4), 303-322.

57

Rains, J., Durham, R., & Kelly, C. (2009). Executive summary multi-sensory materials in

K-3 mathematics: Theory and practice. Retrieved from

https://www.researchgate.net/publication/242770970_Executive_Summary_Multi

sensory_Materials_in_K-3_Mathematics_Theory_and_Practice

Reys, R. E., Reys, B. J., McIntosh, A., Emanuelsson, G., Johansson, B., & Yang, D. C.

(1999). Assessing number sense of students in Australia, Sweden, Taiwan and

the United States. School Science and Mathematics, 99(2), 61-70.

Riley-Tillman, T. C., & Burns, M. K. (2009). Evaluating educational interventions:

Single-case design for measuring response to intervention. New York: Guilford

Press.

Ronquillo, J. B. (2017). Effectiveness of Touch Math on the learning performance of

grade II pupils in mathematics. International Journal of Multidisciplinary

Approach & Studies, 4(1), 166-175.

Rudolph, A. C. (2008). Using Touch Math to improve computations. Retrieved from

https://www.TouchMath.com/pdf/RudolphResearch.pdf

Schneider, B., & Thompson, S. (2000). Incredible equations develop incredible number

sense. Teaching Children Mathematics, 7(3), 146-148.

Scott, K. S. (1993). Multisensory mathematics for children with mild disabilities.

Exceptionality, 4(2), 97-111. doi:10.1207/s15327035ex0402_3

Scott, K. S. (1993). Reflections on multisensory mathematics for children with mild

disabilities. Exceptionality, 4(2), 125-129.

58

Scruggs, T. E., & Mastropieri, M. A. (1998). Summarizing single-subject research: Issues

and applications. Behavior Modification, 22, 221-242.

Simon, R., & Hanrahan, J. (2004). An evaluation of the Touch Math method for teaching

addition to students with learning disabilities in mathematics. European Journal

of Special Needs Education, 19(2), 191-209.

doi:10.1080/08856250410001678487

Shinn, M. R. (Ed.). (1989). Curriculum-based measurement: Assessing special children.

New York: Guilford Press.

Strand, L. (2001). The Touch Math program and it’s effect on the performance of first

graders. Retrieved from http://www.TouchMath.com/pdf/FirstGrade.pdf

Texas Education Agency. (n.d.). STAAR modified resources. Retrieved from

https://tea.texas.gov/student.assessment/special-ed/staarm/

Texas Education Agency. (2011) Technical digest 2011-2012: Chapter 5 STAAR

modified. Retrieved from

https://tea.texas.gov/student.assessment/techdigest/yr1112/

Texas Education Agency. (2017) STAAR statewide summary reports 2016-2017: Spring

2017 grade 3. Retrieved from

https://tea.texas.gov/Student_Testing_and_Accountability/Testing/State_of_Texas

_Assessments_of_Academic_Readiness_(STAAR)/STAAR_Statewide_Summary

_Reports_2016-2017/

59

Ulrich, C. (2004). The effects of mathematics instruction incorporating the TouchMath

program on addition computational fluency in a third-grade classroom. Retrieved

from https://eric.ed.gov/?id=ED507708

Uzomah, S. L. (2012). Teaching mathematics to kindergarten students through a

multisensory approach. Dissertation Abstracts International Section A, 73, 1718.

Velasco, V. (2009). Effectiveness of Touch Math in teaching addition to kindergarten

students (Doctoral dissertation). California State University, Long Beach,

California.

Vinson, B. M. (2004). A foundational research base for the TouchMath program.

Retrieved from https://www.TouchMath.com/about/researchPapers.cfm?rID=134

Vinson, B. M. (2005). Touching points on a numeral as a means of early calculation:

Does this method inhibit progression to abstraction and fact recall. Retrieved

from https://www.TouchMath.com/about/researchPapers.cfm?rID=131

Waters, H. E., & Boon, R. T. (2011). Teaching money computation skills to high school

students with mild intellectual disabilities via the TouchMath© program: A multi-

sensory approach. Education and Training in Autism and Developmental

Disabilities, 46(4), 544-555.

Wei, X., Lenz, K. B., & Blackorby, J. (2013). Math growth trajectories of students with

disabilities: Disability category, gender, racial, and socioeconomic status

differences from ages 7 to 17. Remedial and Special Education, 34(3), 154-165.

60

Wendling, B. J., & Mather, N. (2009). Essentials of evidence-based academic

interventions. Hoboken, NJ: John Wiley & Sons, Inc.

Wisniewski, Z. G., & Smith, D. (2002). How effective is TouchMath for improving

students with special needs academic achievement on math addition mad minute

timed tests? Retrieved from https://eric.ed.gov/?id=ED469445

WWC Summary. (n.d.) Retrieved from https://ies.ed.gov/ncee/wwc/Intervention/382

Xu, G., Strathearn, L., Liu, B., & Bao, W. (2018). Prevalence of autism spectrum

disorder among US children and adolescents, 2014-2016. JAMA: Journal of The

American Medical Association, 319(1), 81-82. doi:10.1001/jama.2017.17812

Yıkmış, A. (2016). Effectiveness of the Touch Math technique in teaching basic addition

to children with autism. Kuram Ve Uygulamada Eğitim Bilimleri, 16(3), 1005-

1025. doi:10.12738/estp.2016.3.2057

Zilbovicius, M., Garreau, B., Samson, Y., Remy, P., Barthelemy, C., Syrota, A., &

Lelord, G. (1995). Delayed maturation of frontal cortex in childhood autism.

American Journal of Psychiatry, 152, 248-252.

61

Appendix A

Assessment Data

Example:

62

Appendix B

Teaching the TouchPoints 1-5

63

Appendix C

Practice with TouchPoints 1-5

64

Appendix D

Criterion Data Collection – TouchPoints 1-5

65

Appendix E

Teaching the TouchPoints 6-9

66

Appendix F

Practice with TouchPoints – 6-9

Touch and count the Touchpoints out loud for each number.

67

Appendix G

Criterion Data Collection – TouchPoints 6-9

Touch and count the Touchpoints out loud for each number.

Touch & Count Correct: ______/16 x 100 = _______% correct

68

Appendix H

Counting ALL Practice

69

Appendix I

Criterion Data Collection – Counting ALL

Touch and count ALL TouchPoints to find the sum.

______/8 x 100 = _______% correct

70

Appendix J

Counting ON Practice

71

Appendix K

Criterion Data Collection – Counting ON

Circle the largest number and continue counting the TouchPoints to solve

the

problem.

______/8 x 100 = _______% correct

72

Appendix L

Counting ON with Faded TouchPoints Practice

73

Appendix M

Criterion Data Collection – Counting ON Faded

SAY the largest number then continue counting the TouchPoints to solve the problem.

______/8 x 100 = _______% correct

74

Appendix N

Counting ON without TouchPoints Practice

SAY the largest number and continue counting with your “imaginary” TouchPoints.

75

Appendix O

Criterion Data Collection – Counting ON without TouchPoints

SAY the largest number and continue counting with your “imaginary” TouchPoints.

______/8 x 100 = _______% correct

76

Appendix P

Generalization Assessment

Example:

77

Appendix Q

Inter-rater Reliability Checklist

Procedural Checklist for session 1 - Teaching the TouchPoints 1-5

1

2-minute Progress Monitoring Probe

√

Participants complete progress monitoring probe with a 2-minute time

limit

2

Introduce TouchPoints with Counters on manipulative worksheets.

√

- Participants place counters on circles of the worksheet

- Participants touch and count the counters out loud

- Participants touch and count the TouchPoints at the bottom of the

worksheet

3

Practice Counting TouchPoints on Magnetic 3D Numerals

√

- Participants touch and count the TouchPoints out loud

4

Practice worksheet

√

- Participants practice touching and counting the TouchPoints out loud

on the practice worksheet

5

2-minute progress monitoring probe

√

- Participants complete progress monitoring probe with a 2-minute time

limit

Procedural Checklist for session 2 - Teaching the TouchPoints 6-9

1

Assessment Probes

√

- 2-minute Progress Monitoring Probe

- Participants complete progress monitoring probe with a 2-minute

time limit

- Criterion assessment probe

- Score of < 80% Repeat Session 1

- Score of >80% Continue Session 2

2

Introduce TouchPoints with Counters on manipulative worksheets.

√

- Participants place counters on circles of the worksheet

78

- Participants touch and count the counters out loud

- Participants touch and count the TouchPoints at the bottom of the

worksheet

3

Practice Counting TouchPoints on Magnetic 3D Numerals

√

- Participants touch and count the TouchPoints out loud

4

Practice worksheet

√

- Participants practice touching and counting the TouchPoints out loud

on the practice worksheet

5

2-minute progress monitoring probe

√

- Participants complete progress monitoring probe with a 2-minute time

limit

Procedural Checklist for session 3 - Counting ALL – Single-digit plus Single-digit

Addition Problems

1

Assessment Probes

√

- 2-minute Progress Monitoring Probe

- Participants complete progress monitoring probe with a 2-minute

time limit

- Criterion assessment probe

- Score of < 80% Repeat Session 2

- Score of >80% Continue Session 3

2

Review TouchPoints

√

- Participants review TouchPoints on Student Number Cards

3

Introduce Counting All Strategy on Magnetic 3D Numerals

√

- Participants touch and count all TouchPoints out loud on Magnetic 3D

Numerals for single-digit plus single digit sums (1+3=4; 6+2=8;

3+4=7; 7+2=9; 8+0=8)

4

Practice worksheet

√

- Participants practice touching and counting the TouchPoints out loud

on the practice worksheet

79

5

2-minute progress monitoring probe

√

- Participants complete progress monitoring probe with a 2-minute time

limit

Procedural Checklist for session 4 - Counting ON with TouchPoints

1

Assessment Probes

√

- 2-minute Progress Monitoring Probe

- Participants complete progress monitoring probe with a 2-minute

time limit

- Criterion assessment probe

- Score of < 80% Repeat Session 3

- Score of >80% Continue Session 4

2

Review TouchPoints

√

- Participants review TouchPoints on Student Number Cards

3

Introduce the Counting ON Strategy

√

- Participants identify and circle largest numeral in the problem

- Participants say the name of the number they circled

- Participants continue counting the TouchPoints to solve problem

4

2-minute progress monitoring probe

√

- Participants complete progress monitoring probe with a 2-minute time

limit

Procedural Checklist for session 5 - Counting ON with Faded TouchPoints

1

Assessment Probes

√

- 2-minute Progress Monitoring Probe

- Participants complete progress monitoring probe with a 2-minute

time limit

- Criterion assessment probe

- Score of < 80% Repeat Session 4

- Score of >80% Continue Session 5

2

Review TouchPoints

√

- Participants review TouchPoints on Student Number Cards

80

3

Practice the Counting ON Strategy with Faded TouchPoints Part 1

√

- Participants identify and circle largest numeral in the problem

- Participants say the name of the number they circled

- Participants continue counting the TouchPoints to solve problem

4

Practice the Counting ON Strategy with Faded TouchPoints Part 2

√

- Participants identify and say the largest numeral in the problem

- Participants continue counting the Faded TouchPoints to solve problem

5

2-minute progress monitoring probe

√

- Participants complete progress monitoring probe with a 2-minute time

limit

Procedural Checklist for session 6 - Counting ON Strategy without TouchPoints

1

Assessment Probes

√

- 2-minute Progress Monitoring Probe

- Participants complete progress monitoring probe with a 2-minute

time limit

- Criterion assessment probe

- Score of < 80% Repeat Session 5

- Score of >80% Continue Session 6

2

Review TouchPoints

√

- Participants review TouchPoints on Student Number Cards

3

Practice the Counting ON Strategy without TouchPoints

√

- Participants identify and say the largest numeral in the problem

- Participants continue counting the “imaginary” TouchPoints to solve

problem

4

2-minute progress monitoring probe

√

- Participants complete progress monitoring probe with a 2-minute time

limit

81

Procedural Checklist for session 7 – Generalization Assessment

1

Assessment Probes

√

- 2-minute Progress Monitoring Probe

- Participants complete progress monitoring probe with a 2-minute

time limit

- Criterion assessment probe

- Score of < 80% Repeat Session 6

- Score of >80% Continue Session 7

2

Review TouchPoints

√

- Participants review TouchPoints on Student Number Cards

3

Generalization Assessment

√

- Participants complete assessment probe with a 2-minute time limit

82

Appendix R

Social Validity

83

VITA

April M.Huckaby completed her Bachelor of Science degree at Stephen F. Austin

State University in the Spring of 2007. She obtained a teaching certificate and taught

high school biology and chemistry for ten years at a rural school district in East Texas.

When her oldest son was diagnosed with Autism, she became aware of the struggles that

can occur between a special education student and a general education teacher. Mrs.

Huckaby realized the importance of supporting not only the students in special education,

but also the need to support teachers working with those students. In the fall of 2016, she

entered the School Psychology program at Stephen F. Austin State University in hopes of

making a greater impact for her students and their families.

Permanent Address: 124 West Henderson Street

Reklaw, Texas 75784

Publication Manual of the American Psychological Association (Sixth Edition)

This thesis was typed by April M. Huckaby