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USING THE MULTISENSORY APPROACH OF TOUCH MATH TO
TEACH BASIC MATHEMATICAL OPERATIONS TO STUDENTS
WITH SIGNIFICANT DISABILITIES
by
Rebecca Hood
A Thesis
Submitted to the
Department of Language, Literacy, and Special Education
College of Education
In partial fulfillment of the requirement
For the degree of
Master of Arts in Learning Disabilities
at
Rowan University
May 15, 2014
Thesis Chair: S. Jay Kuder, Ed.D
Rebecca Hood
iii
Abstract
Rebecca Hood
USING THE MULTISENSORY APPROACH OF TOUCH MATH TO TEACH BASIC
MATHEMATICAL OPERATIONS TO STUDENTS WITH SIGNIFICANT
DISABILITIES
2013/14
S. Jay Kuder, Ed.D
Master of Arts in Learning Disabilities
The current study examines how the multisensory approach of the Touch Math
program is used in a school that educates students with significant disabilities to improve
their basic operation addition skills. The students who participated in this study struggled
with traditional teaching of basic operation skills, and they were having difficulty
maintaining fact knowledge, with modifications to their current instruction. The study
was conducted in a school in Atco, New Jersey over an eight-week period. The current
study used baseline assessments, which the two single digit addends without touch points,
to determine the student participant’s individual single digit addend knowledge. Then the
students explicitly taught the multisensory approach of how to use touch points to count
up and all to create a sum of two single digit addends. After being taught how to use the
touch points to help add two single digit addends, students were given post-intervention
assessments, with touch points on the two single digit addends to determine their
individual progress and possible improvement in basic operation addition skills.
Although an individual’s results varied, all students showed improvement in their basic
operation addition facts, by using the multisensory approach from the Touch Math
program to add two single digit addend.
iv
Table of Contents
Abstract iii
Chapter 1 Introduction
1.1 Purpose of the study 1
1.2 Key terms 2
1.3 Implications 4
Chapter 2 Review of the Literature
2.1 Mathematical learning disabilities: difficulties and deficits 6
2.2 Multisensory approach to teach mathematics to students with
learning disabilities
10
2.3 Instructional strategies and techniques to teach basic operations to
students with significant disabilities
18
2.4 Using the Touch Math program as a multisensory approach to teach
basic operations
28
2.5 Summary 30
Chapter 3 Methodology
3.1 Subjects 32
3.2 Setting 37
3.3 Methods 38
3.4 Materials 38
3.5 Instruments 40
3.6 Assessments 40
3.7 Intervention 42
v
Table of Contents Continued
Chapter 4 Results
4.1 Premise of the study 45
4.2 Procedures 45
4.3 Results of baseline and post-intervention assessments for each
student participant
46
4.4 Comparison of the assessment results for each student participant 53
4.5 Group achievement of each individual addend 65
Chapter 5 Discussion
5.1 Current study 68
5.2 Limitations of the current study 73
5.3 Implications of the current study 75
Reference 78
vi
List of Figures
Page
Figure A 55
Figure B 58
Figure C 60
Figure D 63
Figure E 65
Figure F 67
1
Chapter 1
Introduction
1.1 purpose of study. Many students with significant disabilities, including those with
cognitive impairments, autism spectrum disorders, severe and specific learning
disabilities, and multiple disabilities, have difficulty learning basic mathematical concepts
and operations. These significant disabilities affect the students’ abilities to both develop
basic operation skills and maintain basic operation facts in a meaningful and consistent
way. In my classroom I have noticed that my students’ abilities and skills in the area of
basic operations is inconsistent and scattered. Therefore, I decided to study whether the
use of the multisensory Touch Math program will help students with significant
disabilities learn and maintain skills in basic operations and basic operation facts.
This study is of importance to special educators who teach students with
significant disabilities because basic operations can be incorporated into skills that
students can apply both inside and outside of the classroom. Basic operations skills can
a bill, counting change to give and receive a payment, measuring an object, determining
elapsed time, following a recipe, counting forward and backwards, and skip counting.
Therefore, this study will investigate whether using a multisensory approach as an
instructional technique, in the area of basic operations improves this skill for students
with significant disabilities. Using a multisensory approach for instructional approaches
for students with significant disabilities will provide an opportunity for them to use more
than one sense to obtain a skill or concept in multiple and varying lessons.
Overall, the pencil and paper method does not appear to be meaningful to my
students, and the students do not have mastery of basic operations skills and facts.
Therefore, this study will investigate whether using the multisensory approach of the
2
Touch Math program will improve the mathematics skills of students with significant
disabilities. It is hypothesized that the Touch Math program will lead to an improvement
in students with significant disabilities’ mastery of basic operations skills and facts.
1.2 key terms. Touch Math: according to the program’s website, (www.touchmath.com,
found on 10-28-13) is a multisensory program that uses its signature touch points to
engage students of all abilities and learning styles. The Touch Math program is intended
for students in grade range of pre-school through second grade, as well as, the use of this
program is intended for special education students and intervention purposes.
Multisensory approach instruction: is when instructors incorporate techniques and
strategies to engage students’ learning on multiple levels. Instructors encourage students
to use multiple senses to gather information to complete a task, link prior knowledge to
new learning, problem solve, incorporate non-verbal skills, create an understanding
between concepts, and store information and use information in recall.
(www.lexiconreadingcenter.org retrieved on 10-28-13)
Basic operations: are mathematical problems that incorporate number facts that
are created through addition, subtraction, multiplication, and division. According to
www.mathisfun.com (retrieve on 10-28-13) definitions of basic operations, addition is
bringing two or more numbers (or things) together to make a new total. Subtraction is
taking one number away from another. Multiplication is repeated addition, and division
is splitting into equal parts or groups.
Significant disabilities: According to the New Jersey’s Administrative Code,
Chapter 6A:14 (www.nj.gov/education/code/current/title6a/chap14.pdf, retrieved on 10-
3
28-13) definitions of significant disabilities falls under the following special education
classification categories:
Autistic: a pervasive developmental disability that significantly impacts a
student’s verbal and nonverbal communication, which adversely affects a student's
educational performance. The onset of a student’s pervasive development disability is
evident before the age of three. Other characteristics of a student who is classified as
Autistic is the student may engage in often are repetitive activities and stereotypical
movements, the student may be resistant to environmental changes or changes in their
daily routine, as well as, the student may have an unusual response to sensory
experiences and have a lack of responsiveness to others.
Cognitively impaired: refers to a student with a below average general cognitive
functioning that coexists with significant deficits in adaptive behavior. This impairment
in cognitive functioning and adaptive behavior is manifested during the developmental
period in utero and it greatly affects a student's educational performance. It is broken
into three categories based on the severity of both the student’s cognitive functioning and
adaptive behavior in a school, home and community setting: mild cognitive impairment,
moderate cognitive impairment, and severe cognitive impairment.
Multiply disabled: refers to a student who has two or more disabling conditions,
and these disabling conditions interfere with their educational needs, as well as, their
educational needs cannot be met in a special education program that only addresses one
of their disabling conditions.
Specific learning disability: refers to a student who has a disorder in one or more
of the basic psychological processes that pertains to the understanding or use of
4
expressive and receptive language, and their disorder may manifest itself and interfere
with a student’s ability to listen, think, speak, write, spell, or the ability to perform
mathematical calculations. A student’s specific learning disability can be determined
when there is a severe discrepancy between a student’s current academic achievement
and intellectual ability in one of the following areas: basic reading skills, reading
comprehension, oral expression, listening comprehension, mathematical calculations,
mathematical problem solving, written expression, or reading fluency.
1.3 implications. The intention of this study is to show an improvement in the
achievement of learning facts of basic operations using the multisensory approach of the
Touch Math program, specifically for students with significant disabilities.
This study is not to promote of the Touch Math program as the only multisensory
approach to improve basic operations skills for students with significant disabilities. The
results of this study could be applied in classrooms with students who have less
significant disabilities, such as a mild to moderate learning disability in either an
inclusion or resource classroom setting. This study would provide these instructors a
multisensory approach mathematical program to use to help improve students’
achievement in the area of basic operations.
This study will be conducted in a school for students with significant disabilities
educational and related services needs, but this study is intended to show a variety of
teachers how to use a multisensory approach and strategies to improve students’
achievement in the area of basic operations.
Overall the purpose of this study is intended to show whether using the
multisensory approach of the Touch Math program will demonstrate achievement and
knowledge in the area of basic operations for students with significant disabilities.
5
Therefore this study could be a useful tool in the future for educators who instruct
students with significant disabilities to provide a resource in the area of basic operation
skills using a multisensory approach. The materials used in this study could also be used
in the future as a possible positive link between students with significant disabilities’
improved state standardized test score and the use of a multisensory approach for
instructional purposes. This study’s use of a multisensory approach could be used in not
only helping improve basic operation skills, but this approach could be used in other
areas of instruction and improving skills to help students’ with significant disabilities
transition into adulthood with a set routine of strategies to help with solving problems in
an environment outside of a classroom.
6
Chapter 2
Review of the Literature
The intention of this study is to investigate whether the use of the multisensory
approach of instruction within the Touch Mat h program will lead to an improvement in
the achievement of basic mathematical operations for students with significant
disabilities. The literature is reviewed for difficulties and deficits students have with a
mathematical disability. The literature is also reviewed to determine if using a
multisensory approach of instruction improves the achievement of students with special
needs in the area of basic operations. Also, the literature is reviewed that discusses
instructional strategies and techniques to teach basic operations to students with both
mild and significant disabilities, and to improve their skills and achievement in this area.
The last area of literature that is reviewed examined the use of the Touch Math program
and how its use improves students’ with significant disabilities achievement in the area
of basic operations.
2.1 mathematical learning disabilities: difficulties and deficits. In Geary’s (2004)
article describing the difficulties and weaknesses a student with a mathematical learning
disability has, the following were cited: counting, arithmetic, working memory
difficulties, weak conceptual knowledge, semantic memory deficits, and visual-spatial
deficits.
A student with a mathematical learning disability who has a weakness within the
area of counting displays the following types of difficulties: one-to-one correspondence,
stable order, counting cardinally, abstract counting, and order irreverence.
7
Within Geary’s article, he featured a counting procedure and a study regarding
counting. Geary and colleagues’ (Geary, Bow-Thomas, and Yao, 1992) procedure, for
students with both mathematical and reading disabilities, featured the use of a puppet to
count a set of objects. The puppet would count objects correctly, and at times the puppet
counted the objects incorrectly. It was for the student to identify if the puppet counted
correctly or not. The puppet would perform the procedure of counting cardinally,
abstract, and order irreverence, and the student’s responses would indicate their
understanding of counting principles.
After discussing this counting procedure, Geary also discussed another study that
he performed regarding counting weaknesses. In this study, students who were in first
and second grade, with an IQ score range of 80-120, and had either or both a
mathematical and reading disability, participated in this study. The student participants
were assessed in a series of experimental and achievement tests. Results from these
experimental and achievement tests found that student participants did not fully
understand all of the counting principles. Results from the assessments, also showed that
the student participants have had difficulties within the counting notation of their working
memory when monitoring the counting process. Poor counting knowledge appears to
contribute to the student participants’ delayed competency in using counting to solve
arithmetic problems.
Continuing with Geary’s 2004 article, a student with a mathematical learning
disability who has a weakness within the skill area of arithmetic, is unable to or struggles
with counting on or counting all to solve basic addition problems. This inability to count
on or all to solve basic addition problems is connected to a student’s understanding of
counting. Students with this inability have trouble making memory representations
8
through direct retrieval and/or decomposition of basic facts and storing them into their
long-term memory. It is suggested that students with this inability to count on or all
when solving basic addition problems would benefit from both rigorous and lenient
criterion. A rigorous criterion is where a student would state answers they were certain
are correct. A lenient criterion is where a student would state any answer correct or not,
to automatize basic facts. When both types of criterion are implemented in their
arithmetic instruction, it will lessen both students’ error in answering more complicated
questions and relying on their working memory.
Within the area of skill area of arithmetic it was noted that (Geary, 1990; Hanich,
et al, 2001;) (Geary, et al 1999; Geary et al., 2000) students with either a mathematical
and reading learning disability or both, use the same types of problem solving strategies
to solve arithmetic problems as their non-disabled peers, however they differ in how they
develop strategies to solve arithmetic problems. Students with learning disabilities in
both the areas of mathematics and reading commit more counting errors, and use
developmentally immature counting-all procedures more than non-disabled peers. The
immature counting-all procedures that these types of students tend to rely on include
counting on their fingers, verbal counting, and retrieval strategies with weak connections,
when solving arithmetic problems.
Students with mathematical learning disabilities also have procedural deficits.
They have difficulties with solving multi-step arithmetic problems. They tend to use
immature strategies when solving an arithmetic problem, such as counting on their
fingers. Students that have procedural deficits not only tend to commit more errors in
solving multi-step problems, based on their immature strategy development, but in their
9
alignment of numbers, when they are writing down partial errors, including errors when
carrying or borrowing.
These types of procedural errors are linked to difficulties with a student’s working
memory. A student who has difficulties with working memory, struggles with
information representation and manipulation of number words, as well as, poor attention,
which could interrupt their execution of mathematical procedures. A student who has
working memory difficulties, displays weak problem solving procedural strategies that
include counting on their fingers and the tendency to over or under count. Both of these
types of strategies place high demands on a student’s working memory, when solving
arithmetic problems. When students are working on multi-step problems, they tend to
miscount, loose track of where they are in solving the problem, and how they process the
language of the problem.
Students with a mathematical learning disability, have difficulties with conceptual
knowledge. Students have a poor understanding of both concepts and procedures. They
tend to have a developmental delay in more complicated multi-step problems, and have a
difficult time detecting errors. Overall this is due to a student’s frequent counting errors.
Students with a mathematical learning disability also frequently, have difficulties
with semantic memory. Students with semantic memory weaknesses have difficulty
storing and retrieving arithmetic facts from their long term memory. They tend to
commit more errors when solving arithmetic problems, and have slower reaction time
patterns, which is associated with dyscalculia. Students with this type of memory storage
difficulty are unable make a connection between the problem and generating an answer
quickly. Students also have difficulties with language retrieval, which will interfere with
their ability in solving both simple and complicated arithmetic problems.
10
Students with a mathematical learning disability may also have visual-spatial
difficulties. They have a performance deficit on spatial working memory tasks, either
through their ability to represent information or the ability to maintain their attention on a
spatial task. These difficulties occur with multi-step problems and complex mathematical
problems.
More importantly, Geary’s 2004 article discusses the difficulties and deficits
within the skill areas of mathematics that students with learning disabilities have. It
shows that students’ mathematical deficits and difficulties are based in number sense, and
how they use and generalize various strategies to solve both simple and complex
problems. This article indicates that students who have mathematical difficulties and
deficits could benefit from instructional strategies that help them generalize mathematical
skills that are based in number sense and counting, and rely less on their processing skills
and working memory.
Geary’s 2004 article, can be connected to the current study’s student participants
who have significant disabilities, who are struggling with fact automaticity, and will
benefit from the multisensory approach to instruction from the Touch Math program, of
counting up or all of the touch points to complete basic operation addition problems. The
students who participate in this current study will be explicitly taught how to count up
and all, and how to strategize to solve problems, without relying on weak strategies, such
as counting on their fingers, where they tend to loose track or miscount.
2.2 multisensory approach to teach mathematics to students with learning
disabilities. In a longitudinal study of the multisensory approach to improve basic
operation skill achievement of students with mild learning disabilities, by Dev, Doyle,
and Valente’s 2002, eleven students, ranging in age from six to seven years old,
11
participated in this two-year study. Before the intervention of the study was conducted,
the eleven student participants were assessed using the WRAT-III. After the formal
assessment, the researchers examined how to improve developmental language and
mathematical skills using the Orton-Gillingham and Touch Math program as intervention
tools in this study. (For the purposes of this review, only the results of the Touch Math
program will be discussed.)
The authors of this study used the Touch Math program in a general education
classroom setting for students in first and second grade. During the intervention, the
instructional use of this program was performed daily, and lessons for first grade students
varied in length from twenty to twenty-five minutes. For students in the second grade,
the teachers reviewed concepts of the Touch Math program, but the teachers did not
reteach the skills of this program to these students on a daily and consistent basis.
At the end of this longitudinal study, the eleven students were assessed on the
WRAT-III. For student participants, their results of this assessment were compared to
their initial assessment WRAT-III scores, conducted two years prior. In their initial
scores, seven of the participants’ scores in the area of mathematical skills were at the pre-
first grade (primer) level, three of the participants’ scores were at the early first grade
level, and one participant’s score was at the intermediate first grade level. After the
participants received the instruction in the Touch Math program over the two-year period,
three-fourths of the student participants scored above grade level within the area of
mathematical skill development. It was also noted that after the study was completed the
authors found that those students that participated in this study were no longer in need of
special education services.
12
In Kaufmann and Pixner’s (2012) replication study, they examined previous
studies that used the multisensory approach and its use in combination with number fact
training. The authors reviewed various studies that displayed strong evidence that
indicated that the use of a multisensory approach is superior to instructing students using
one modality when teaching basic facts. They placed a heavy emphasis on a particular
study, by Domahs, et.al, (2004) that examined the effectiveness of the multisensory
approach within a remediation study that was directed to re-teach number fact knowledge
in neurological patients with acquired calculation disorders by linking multiplication
problems with color. Multiplication factors were presented in different colors, and each
color was to be associated to a unit or digit of its respective problem. This reviewed study
was conducted over a five-month period, and instruction was conducted three times per
week. The results of this reviewed study found that a designated color representation of
multiplication problems were proved to be a important cue in facilitating the patient’s
performance of the given multiplication problems, but the patient who participated in the
study did not generalize using this strategy in non-multiplication basic operation
problems.
Therefore, the authors of this article wanted to replicate this study and provide a
similar type of cueing system to use for elementary students. Kaufmann and Pixner
conducted a pilot study dividing twenty-two students in third and fourth grade into two
groups. Twelve students participated in the experimental group, and ten students
participated in the control group. The experimental group was given an intensive
training period of visual cueing strategies once per week, over an eight week period.
Within this intensive training period, student participants were instructed on using a
number/color association to solve multiplication problems. It was noted in the study that
13
the number/color association was consistently used during the entire intensive training
period. Multiplication facts were presented visually to student participants. Each factor
of the problem was printed in its designated color associate, when students were solving
the problem’s product. When products were being visually presented they were given a
color association, and the factors within the problem were not color associated.
The
control group was given attention and memory instruction to learn multiplication facts
during the eight week instructional period. These student participants were not given a
number/color association to solve multiplication problems.
The effectiveness of this intensive intervention was evaluated through a pre-
intervention and post-intervention standardized arithmetic test, as well as, a standardized
assessment being given eight weeks after the intervention ended to determine the
intervention’s stability.
The students that participated in the pilot program were given a
rating scale and questionnaire to determine their perception of the program.
Kaufmann and Pixner compared the experimental and control group results by
both the student participants’ age and intellectual ability. Results of the standardized
assessment after the intervention was conducted showed a significant increase in the area
of standardized calculations for students in both groups. Also, student participants in both
groups showed improvement in their performance of solving multiplication facts after the
intervention period ended. However, students in the experimental group displayed a
higher performance increase compared with the control group. Kaufmann and Pixner’s
study produced promising results, and these results will encourage further research that
should include a larger sample size and different types of control groups. Further
research should also explore different types of multisensory approaches to basic
operations, and determine if other approaches improve students’ basic operation skills.
14
In Mancl, Miller, and Kennedy’s (2012) multiple-probe-across-participants study
design, they examined the effectiveness of explicit instruction along with the use of the
concrete-representational-abstract sequencing with integrated cognitive strategies to
instruct students how to subtract when regrouping is involved. There were five fourth
and fifth grade student participants, and they were chosen to participate based on their
school’s personnel identifying that each of them had a learning disability in mathematics.
Also, student participants were screened before the intervention was conducted. The
screening examined their ability to solve both computation and word subtraction
problems that involved regrouping. Students who scored below 50% were eligible to
participate in the intervention of the study.
The students that participated in this study received thirty minutes of a Tier-3
mathematics intervention that used direct instruction in a resource classroom. The
student participants were placed in this type of classroom setting during the study, due to
their low achievement in specific grade level academic skills. Student participants were
given a baseline assessment before intervention instruction began. During the
intervention, student participants were probed during the intervention to monitor their
progress, and the effectiveness of the intervention.
Within the intervention, student participants were provided with the following:
eleven teacher scripted lessons that provided explicit regrouping instruction, graphic
organizers for the students to use as both a cueing system and a graphic organizer to solve
the subtraction problems, manipulatives, place value charts, student folders, and a chart to
show students’ their progress in obtaining regrouping skills. The intervention’s scripted
lessons included concrete lessons, representational lessons, a strategy lesson, and abstract
lessons. In each lesson, the same five explicit teaching components consistently used to
15
teach previously taught skills, included: advanced organizers, describing and modeling,
guided practice, independent practice, and practicing problem solving skills.
The students that participated in this study produced the following results: In the
baseline assessment, scores for the participants ranged from 0% to 40%. In the probes
during the intervention, their scores ranged from 40% to 100%.
Based on these articles, it appears that a multisensory approach can be used in
developing mathematical skills. This approach to instruction needs to be done daily and
consistently, and students need to be given multiple modalities to learn and review
mathematical concepts. When reviewing these articles, it can also be noted that when
students are given strategies within the multisensory approach to instruction that students
are given can be faded, skills areas should improve, and students should be able
generalize the multisensory strategies in other settings.
In Witzel and Allsopp’s (2007) article, they discussed how to engage students
with high incidence disabilities, and their use of manipulatives to learn mathematical
skills. The disabilities that were included were the following: specific learning
disabilities, attention deficit disorder, and mild to moderate cognitive impairments. They
felt that the use of manipulatives would allow students with these types of disabilities
have the opportunity for a multisensory experience to learn and achieve skills, with
confidence and success.
Witzel and Allsopp (2007) felt that there are three instructional techniques that
allow the use of manipulatives to teach mathematical skills: linking prior knowledge to
new concepts, an emphasis on thinking-aloud modeling, and applying multisensory
cueing. These three instructional techniques were applied in two sixth grade inclusion
16
classroom settings. They used these techniques in these two classroom settings to teach
the addition of fractions.
This article stated how the three instructional techniques were used, but it did not
provide statistical data to say that it improved their skills in adding fractions. The authors
concluded that these instructional techniques were a good resource for teachers to use.
However, it was noted that students with low incidence disabilities, severe cognitive
impairments and multiple disabilities, would benefit from statements of relevance, during
instruction. Teachers should provide manipulatives with application that can be useful,
and meaningful connections, along with the stated instructional strategies.
In Strand’s (2001) experimental control group study, she examined the effects of
the multisensory approach within the Touch Math program versus a non-intervention
based mathematical program for first grade students.
There were two control groups of student participants. In the first control group
the student participants were from two different schools, thirty-seven student
participants in School A and twenty-two students in School B. There were three teachers
who taught the student participants. In this control group, 95% of the student
participants were Caucasian, and came from a middle class socioeconomic background.
In the second control group, student participants were from one large school, and there
were sixty-one first graders, who were taught by three teachers. Within this control
group, 95% of the student participants were Caucasian, and came from a middle class
socioeconomic background.
Both control groups were established at the beginning of the school year, and the
teachers in both control groups were given specific parameters to implement
mathematical instruction to the students. The teachers in the first control group were
17
instructed how to use the Touch Math program in their classroom. The student
participants in this control group were exposed to the method of using touch points, in
addition to their standard mathematical curriculum, which included the Addison Wesley
textbook series. In the second control group, the teachers taught the student participants
through their standard mathematical curriculum. The student participants in this control
group were not given any interventions, and were taught strategies that were based on
previously learned skills within the Addison Wesley textbook series.
At the end of the school year, both control groups were given a one-page
worksheet. This worksheet had sixteen problems, and the problems ranged in the degree
of difficulty. When analyzing the results of the student participants’ worksheet, Strand
looked at eight comparative scores. The comparative score categories that she examined
included: problems with the same process, single digit addition, single digit subtraction,
double digit addition with and without regrouping, double digit subtraction with and
without regrouping, and the students’ overall total score. It was noted that when she
analyzed the students’ skills that there were skills more challenging than expected for
them, however, their performance in mathematical computation areas could be assessed.
It was found that, when comparing the performance of the eight mathematical
operations problems, the first control group responded more accurately to all of problems
on the worksheet, with 80% accuracy. The second control group achieved 44% accuracy
with their responses to all of the problems on this summative assessment. Overall, the
first control group did better than the second control group on all of the mathematical
skills assessments, except simple addition. Therefore, this study reflects that use of the
touch points within the Touch Math program as an intervention to either stand-alone or
coincide with standard mathematical curriculum. This study also shows that the use of the
18
touch points is a universal intervention that can be applied in various basic operation
skills.
Overall, the studies that were reviewed indicated that students with mild
disabilities benefitted from a multisensory approach of the touch points within the Touch
Math program, either as a stand-alone program or when it coincides with a standard
mathematical curriculum. The more opportunities that a student has to learn and review
mathematical skills through the systematic and explicit use of this intervention, the better
a student becomes at being able to solve problems and generalize basic operation skills.
2.3 instructional strategies and techniques to teach basic operations to students with
significant disabilities. In Browder, Jimenez, Spooner, Saunders, Hudson, and
Bethune’s (2012) conceptual model, they examined how the instruction of early
numeracy skills was given to students with moderate and significant disabilities. The
early numeracy skills that they included in their conceptual framework for instruction to
students with these types of disabilities included: number identification, rote counting,
representation of numbers through one-to-one correspondence, number conversation,
composing and decomposing numbers, magnitude of numbers, early measurement
concepts, understanding the effect of basic operations, and patterning.
Within this conceptual framework for instruction in these early numeracy skills,
they wanted students, with both high and low incidence disabilities, to gain access to
skills through the targeting of specific early numeracy skills, the use of systematic
prompting and feedback, varying daily instruction through story-based lessons, and to
promote the generalization of the skills to grade-level content through inclusive
embedded content.
19
When developing this conceptual framework, Browder, et. al., (2012), had three
special education teachers and five students in second through fifth grade in both an
inclusive and self-contained classroom environment participate. The student participants
had moderate to significant disabilities which included intellectual disabilities or autism.
The student participants received instruction in early numeracy skills three to four times
per week. Lessons were taught in a repeated manner, and each lesson was taught to the
student participants three times. Students were assessed at the end of each unit of
instruction, and there were a total of four units taught to the student participants.
When the students were assessed, the researchers decided to use inter-rater
reliability to compare the intervention of repeated instruction of the same concept within
early numeracy skills, and its consistent use. Inter-rater reliability had high fidelity, and
it showed that this intervention and it consistent use was valid, at 97%, over 60% of
lessons. Overall, the researchers felt that the student participants benefitted from repeated
instruction of targeted skills. The three teachers that participated in this conceptual
framework plan to use this type of instruction in the future. The teachers also stated that
this type of instruction for early numeracy skills was easy to implement. It prepared the
student participants for the state alternate math assessment based on alternate
achievement, and directly prepared them for the end of the unit assessments.
This article is important because it shows how students with both moderate and
significant disabilities should be provided with systematic prompting and feedback,
within varied and repeated teaching of concepts, given access to linking skills in a
meaningful manner, and be frequently assessed to determine their progress in concepts
and skills. This type of repeated instruction of concepts and skills and frequent
assessment will be applied in the current study. Students will be taught how to apply
20
touch points to numbers, count up using touch points to solve addition problems in
repeated lesson, and will be frequently assessed to determine progress their automaticity
of the addition of basic facts.
Browder, Spooner, Ahlgrim-Delzell, Harris, and Wakeman (2008) conducted a
meta-analysis of sixty-eight studies that examined teaching mathematical skills to
students with significant cognitive disabilities. They grouped together studies based on
mathematical skills and study methodology components. Mathematical skills that were
reviewed included: numbers, computation, and/or measurement. The study methodology
components that were included in groupings were the following: the National Council for
Teachers of Mathematics components and mathematical skills represented in included
studies, evidence that individuals with significant cognitive disabilities can learn
mathematics, and evidence-based practices for single subject designed studies. Studies
that involved computation focused on how to instruct students with significant cognitive
disabilities to perform counting, calculation, and/or number matching skills. Studies that
involved measurement focused on how to instruct students with these types of disabilities
to perform money skills
.
Overall, their literature review and meta-analysis found that the methodology
components indicated strong evidence for teachers to use systematic instruction to teach
specific mathematical skills. Researchers found in their review that they were concerned
with the components of mathematics and specific types of skills that have been acquired
by students with significant disabilities. They felt that there was a limitation in current
research on teaching mathematics to this population. They felt that there was a gap in
how students in this population had access to the general curriculum. They question
21
whether all of the components of mathematical skills were relevant for students with
significant cognitive impairments. The researchers of this literature review and meta-
analysis felt that giving this student population access to the general curriculum requires
setting priorities for students who need intensive instruction to master and generalize
skills, and should include targets in each of the five major component areas of
mathematics.
This literature review and meta-analysis highlighted the fact that students with
significant cognitive impairments benefit from systematic and explicit instruction.
Therefore, students would benefit from this type of instruction to improve upon, to
hopefully master, and generalize mathematical skills.
Browder, Wakeman, Flowers, Rickelman, Pugalee, and Karvonen (2007)
discussed the importance of developing a curriculum and assessments for students with
significant disabilities that are linked to the general education curriculum. The authors of
this article stated that very few guidelines exist for teaching and assessing skills that are
linked to grade-level content curriculum, and that there is a lack of guidelines to teach
students of this population. This article also provides a conceptual framework linking
instruction and assessment for grade-level content skills for these students.
After the authors of this study discussed the various challenges that students with
significant disabilities have in being asked to preform general education skills, they
agreed upon criteria and assessment requirements that would be linked to general
education content area skills, and that truly reflect their students’ mastery of these skills.
Browder, et. al, (2007) felt that curriculum for students in this population have
targets of achievement in academic content areas. These targets of achievement should
be linked to the student’s assigned grade level, which is based on their chronological age.
22
They also mentioned that functional activities and materials should be used to promote
understanding, and that these activities should focus on prerequisite skills and some
partial attainment of grade level curriculum. They also felt that students in this
population should have the opportunity to meet high expectations, be able to demonstrate
a range in their depth of knowledge, show achievement within their symbolic level, and
to show growth across grade levels.
The authors of this conceptual framework then discussed criteria of instruction
and assessment for teachers to use to link the framework to grade level content areas.
They stated that curriculum for students in this population, have academic content that is
linked to both state and national standards. Curriculum should be linked to the student’s
assigned grade level, which is based on their chronological age. It should be linked to
general education grade level content, but it should differ in its depth and complexity.
Curriculum should focus on prerequisite skills or skills learned at a different grade
level, and it should be stated in a student’s individual education plan, and be able to be
applied in state-level alternative assessments. There should be a distinction in
achievement across grade levels. The focus of students’ achievement within the
curriculum should promote access to activities and materials, along with accommodations
and modifications to support progress. The targets of achievement within the curriculum
should maintain fidelity with original grade-level standard, as well as specify student’s
performance. Lastly, there should be multiple levels of access to the general curriculum
to allow students use different forms of symbolic communication to demonstrate their
learning.
These studies, literature reviews, guidelines, and frameworks all mentioned
creating a guideline for curriculum and instruction in mathematical skills that should be
23
systematic, explicit, and broken into smaller tasks, for students with significant
disabilities. Curriculum and instructional approaches should be linked to general
education. It should be relevant to their needs and skill acquisition. Also, the skills that
students are working on should be individualized and monitored frequently to indicate
both acquisition and generalization.
Browder, Lee, and Woods (2013) discussed and presented a guideline to teach
mathematical skills that are delegated by the United States Department of Education’s
Common Core, to students with significant cognitive disabilities. Browder, Lee, and
Woods stated that the mathematical skills delegated by the Common Core should be
taught in each grade level. Mathematical skills that should be taught within kindergarten
through eighth grade should include: counting, operations and algebraic thinking,
numbers and operations in base 10, numbers and operations in fractions, measurement
and data, geometry, ratios, and proportional relationships. The authors of this
presentation also felt that students in these grade levels should be instructed in skills that
include the following: the number system, expressions and equations, statistics and
probability, and functions. Students in high school should be taught the following
mathematical skills: numbers and quantity, algebra, functions, modeling, geometry, and
statistics and probability.
Browder, Lee, and Woods then discussed in their presentation how to teach the
mathematical skills of the Common Core to students with significant disabilities. They
stated that those educators who teach mathematical skills to students with significant
disabilities should instruct them in the following way: initially present new information
or skills with a personal or relevant story, then provide students with a graphic organizer
to complete newly learned information or demonstrate a newly learned skill, and finally
24
present students with a task analysis so students can demonstrate skill and/or complete
the stages of a multiple step skill or process.
Browder’s, et al, (2013) presentation also included a pilot study that they
conducted to examine instructional techniques to teach mathematical skills that were
delegated by the Common Core to students with significant disabilities. In their study,
there were twelve students with various significant disabilities’ whose intelligence
quotients were indicated as 74 or less. It was noted in their presentation that the student
participants used various modes of communication and accommodations within their
classroom setting, while participating in this study. Six special education teachers
participated in this study. They provided the student participants with systematic and
scripted lessons that reinforced evidence-based practices of systematic prompting and
task-analysis instruction. The special education teachers also used data tracking sheets to
monitor the students’ task analysis accomplishments within each lesson.
The content that was systematically taught to the student participants included:
algebraic equations, data analysis, geometry: area and volume, geometry: coordinate
planes, basic operations, fractions, decimals, as well as, exponents.
In the area of algebraic equations, the following instruction was conducted in this
pilot study: within the elementary and middle school grade levels student participants
were instructed to solve one-step algebraic equations with a missing variable, and high
school student participants, were instructed to solve two-step algebraic equations with
two missing variables, and incorporate their work within a table, which was based on a
word problem with a real world application.
In the area of data analysis, the following instruction was conducted in this pilot
study: within the elementary grade level, student participants were taught how to collect
25
data and ask questions, organize and record data in a table, create and graph data using a
bar graph, and interpret the data, by answering questions. Within the middle school grade
level, student participants were instructed how to determine the number of outcomes, the
probability of events, as well as, describe probability as less/more, or likely to occur.
Within the high school grade level, student participants were instructed on how to solve a
two-step equation with two variables using a table, and the table was to be used to solve
for y, if x was provided for.
Within the area of geometry: area and volume, the following instruction was
conducted in this study: at the elementary grade level, student participants were
instructed on how to find area using formulas and tile manipulatives. In the middle
school level, student participants were instructed on how to find the area of a two
dimensional objects and the volume of a three dimensional objects using both formulas
and a calculator. In the high school level, student participants were instructed on how to
find the appropriate unit of measure and how to find the volume of a box.
In the area of basic operations, students that participated in this pilot study were
explicitly and systematically taught the following: in the elementary grade level,
participants were instructed on how to solve a one-step word problem using one of the
four basic operations and use of a calculator. In the middle school grade level,
participants were instructed on how to solve a multi-step ratio and percent problems, and
how to calculate percentages within a realistic application. In the high grade school level,
participants were instructed on how to solve two-step equations with a rational number.
Within the area of fractions, decimals, and exponents, students that participated in
this pilot study were systematically and explicitly taught the following: in the elementary
grade level, participants were taught how to identify, order, and compare fractions. In the
26
middle grade school level, student participants were instructed on how to convert
fractions into decimals, solve problems involving fractions, and locate and compare both
decimals and fractions on a number line. In the high school grade level, student
participants were instructed on how to convert fractions to decimals, and how to write
decimals using scientific notation.
Within the area of geometry: coordinate planes, students that participated in this
study were systematically and explicitly taught the following: in the elementary grade
level, student participants were taught how to define and identify both the x-axis and y-
axis, a point of origin, and a number line. These students were taught how to locate and
graph points within the first quadrant of a coordinate plane. In the middle school level,
student participants were taught how to plot points on a coordinate plane, and form line
segments within a coordinate plane to create polygons. In the high school level, student
participants were taught how to identify different types of transformations including:
reflections, rotations, and translations, as well as, congruency when a two-dimensional
shape is transformed.
After this systematical and explicit instructional period, a total of sixty-nine
lessons, Browder, Lee, and Woods indicated that students with significant disabilities
could learn mathematical concepts within the Common Core State Standards. However,
the overall performance results of the student participants, varied by content and by the
type of student who completed the task analysis of each lesson. The authors of this pilot
study noted that students’ rate of learning concepts varied, as well as, their previous
knowledge of mathematical concepts. It impacted their performance of the task analysis
within each lesson.
27
In Browder, Jimenez, and Trela’s (2012) single subject design study, they
examined the effect of grade-aligned mathematical instruction on skill acquisition within
a large urban school system, for middle school students with moderate cognitive
disabilities. A special education teacher, who taught in a self-contained classroom,
instructed middle school aged students with either moderate or severe cognitive
disabilities executed the intervention in this study. Within this single subject design
study, student participants were probed intermittently to determine their acquisition of
skills through the demonstration of task-analysis instruction. Their teacher nominated
students that were chosen to participate, after meeting specific study criteria. The criteria
that student participants needed meet included: having a specific intelligence quotient,
being able to interact with the intervention materials, and the ability to communicate
either verbally or with an augmentative communication device.
The researchers gave four student participants that met the study’s criteria for
participation a pre-test before intervention instruction, a unit of study test based on a
mathematical standard after instruction, and a maintenance test one to three weeks after
the unit of study was completed. The student participants received task-analysis
instruction on each mathematical standard for five weeks, and then were assessed on that
unit of study. After the end of unit assessment, student participants were given
intermittent maintenance assessments to determine if they acquired and maintained
previously learned skills.
The results from this study indicate that there is mutual relationship when
comparing task-analysis instruction, to the pre unit, post unit, and maintenance testing
results of the student participants. Therefore before instruction began, a baseline was
established, instruction in needed areas should be given, and frequent assessments should
28
be given to determine the student’s rate of skill acquisition and their generalization of
skill application.
2.4 using the Touch Math program as a multisensory approach to teach basic
operations. In Wisniewski and Smith’s (2002) action research study, they examined the
effectiveness of the Touch Math program to improve mathematical achievement for
special education students in third and fourth grade. There were four students, who
attended a resource room class for academic services for a part of the school day that
participated in this study. Before the intervention of the Touch Math program, students
were given a pre-test of forty problems. After an extended period of explicit instruction
with this program, the students were given a post-test with the same amount of problems.
They received instruction in the Touch Math program twenty minutes each day, and were
probed using a Mad Minute computation probe once a week, over a fourteen-week
period. The weekly probe that was given to the students did not have a time limit, and
students could use manipulatives, such as touch points or a number line to complete the
assessment.
The following results were shown of the students’ achievement and progress
based on the pre-test and posttests. Student #1 achieved the following: in the pre-test of a
five minute interval 85%, and on the post-test of a five minute interval, 100%. Student
#2 achieved the following: 98% in the pre-test of a ten-minute interval, and on the post-
test of a four-minute interval 95%. Student #3 achieved the following: on the pre-test
within a seven minute interval 100%, and on the post-test of a four minute interval 100%.
Student #4 achieved the following: on the pre-test within an eight-minute interval, 23%,
and on the post-test, 93%, within a four-minute interval.
29
Overall results show that the specific strategies of the Touch Math program can be
used to aide in the automaticity of basic operation facts.
This article relates to the current study because student participants will be
instructed on how to place touch points on numbers, and to count up or all touch points to
solve addition problems. The students will then be intermittently probed on fact families
using the strategy of counting up or all touch points. These intermittent probes will
determine their attainment of mathematical facts. Also, these intermittent probes will
determine if the student participants are using the strategy efficiently.
In Fletcher, Boon, and Chiak’s (2010) study, they examined three middle school
students with significant disabilities, and the use of the Touch Math program, in an
alternating-treatment design. In this study, the participants were instructed how to solve
single-digit addition problems using both a number line and the Touch Math program.
Within the alternating-treatment, the authors of this study compared participants’
achievement of solving single-digit problems with a number line versus their
achievement of solving single-digit problems with the Touch Math program, and the
effectiveness of both strategies.
After a baseline assessment and intermittent probes during the intervention
process, the following results were reported: student participants achieved 4% accuracy
in the baseline assessment. There were significant improvements in the students’ use of
touch points compared to their use of a number line to solve single-digit addition
problems. All three of the student participants were able to utilize touch points to solve
addition problem more quickly and accurately than the use of the number line. After
being given the strategy of using touch points to aide in solving the addition problems,
the students averaged 92% accuracy on a probed assessment. When the students were
30
given the strategy of using a number line to aide in solving the addition problems, the
students averaged 30% accuracy. Finally, when the authors replicated their study, the
student participants averaged 96% accuracy.
This article relates to the current study, because student participants will be
instructed explicitly and systematically to use touch points and to count up or all to solve
basic addition problems. Through the eight-week length of the current study, it is
intended that the students will be able to generalize the strategy of using touch points, to
solve basic operation addition problems.
Both of these studies indicate that students’ mathematical skills improve with the
use of the Touch Math program versus traditional techniques including a number line or a
manipulative. Students were able to use the touch points in aiding them to solve basic
operation problems. The Touch Math program provides a meaningful strategy for
students to solve basic operation problems.
2.5 summary. The current research study uses the Touch Math program as a strategy to
provide visual, auditory, and tactile cues to improve students with significant disabilities
achievement of basic operation addition facts. Student participants use touch points as a
visual, auditory, and tactile cue to help them count up to solve answers to addition
problems. Before this strategy is taught to the student participants, they will be given a
baseline assessment to determine their basic operation fact knowledge. Then the strategy
of counting up with touch points will be explicitly taught to the students over an eight
week period, with intermittent assessments each week within the intervention period, to
determine if there is an improvement in student participants’ achievement in addition
basic operations. The studies that were mentioned that used the Touch Math program as a
strategy, indicated improvement in students’ with mild, moderate, or significant
31
disabilities, achievement in basic operations. Hopefully, the student participants will
display achievement in their basic operation skills, when using the Touch Math program.
32
Chapter 3
Methodology
In this study, I used the Touch Math program as a multisensory approach to teach
basic addition operations to students with significant disabilities in a small group setting,
within a self contained classroom setting. This intervention took place over an eight-week
period, in a self-contained classroom setting, in a non-profit private Special Education
school in Atco, New Jersey.
3.1 subjects. Five students participated in this study. The students ranged in ages from
eleven through sixteen years of age, with a mean age of thirteen years, eight months.
Student participants are in various grades, with a range of fifth through ninth grade, with
a mean grade of seventh grade.
Student A (I.O.): is an African American, eleven years, three month old, fifth grade
male. I.O. resides in a large urban area in Camden County, with his mother, and three
siblings, one of which is his twin. His twin attends the same non-profit Special
Education school, but is not in the same classroom.
He has asthma, which requires the use of an inhaler before a physical activity, and
he needs breathing treatments if an asthma attack occurs. He also has severe allergies to
bee stings and insect bites, which would require the use of an epi-pen if he were having
anaphylaxis. His medical conditions do not affect his academics.
I.O. has been attending this school since December 2012, after having severe
academic difficulties, due to attention and lack of academic progress, in the public school
that he previously attended. He has been in this current self-contained classroom setting
since July 2013. He is classified as Multiple Disabled, with an IQ of 58, based on his
most current Special Education evaluations.
33
He receives all academic skills in this self-contained classroom setting, and group
speech services one time per week. His related service schedule does not affect his
academics, and he receives instruction in mathematical concepts five days per week.
Student B (G.M.): is a Caucasian, thirteen years, six month old, seventh grade male. He
resides in a small suburban area within Camden County, with his parents, and four other
siblings.
G.M. has been attending this non-profit private Special Education school since the
beginning of the 2007 school year, due to his severe medical issues and lack of academic
progress. He has been in this current self-contained classroom setting since July 2013.
He is classified as Multiple Disabled, with an IQ of 48, based on his current Special
Education evaluations. He receives all academic services in this classroom setting, and
has a one-on-one assistant. The one-on-one assistant helps G.M. with remaining on task,
reinforces and reviews academic concepts, and helps keep him safe when a medical
emergency occurs.
G.M.’s severe medical issue is a seizure disorder with grand mal types of seizures.
If G.M. does have a seizure at school, and the seizure continues for ten minutes, he
receives anti-seizure medication. If a seizure occurs at school, his one-on-one aide, one
other classroom staff member, and the school nurse will help make sure he is safe during
the seizure, clean up anything, and give him any needed medical attention. If the seizure
activity has ceased within ten minutes, he will be picked up by his mother, and goes
home for the remainder of the school day. If he has seizures after he gets home, he will
not attend school until the seizure activity has ceased. If his seizures have not ceased after
ten minutes, a medical emergency service will be called, he will be escorted to the
hospital, by his one-on-one aide, the school nurse, and his mother.
34
The seizure activity does affect his continuous daily attendance at school, and the
length of his school day. His continuous seizure activity not only affects his school day,
but it has a tremendous impact on his academic progress and retention of academic skills.
He receives individual speech services three times per week, group speech
services once per week, individual OT services once per week, group OT services once
per week, individual PT services once per week, and group PT services once per week.
His related services schedule is quite full, and he only receives instruction in
mathematical concepts, three times per week.
Student C (A.D.): is an African American, fourteen years, six month old, eighth grade
female. She resides in a suburban area of Camden County, with other similar aged peers
in a residential group home.
This residential group home setting is temporary. This residential group home
setting is for children and teenagers with various special education needs, who do not live
with their biological families, due to domestic issues. Services for these children are
provided through New Jersey’s Department of Yout h an d Fa mil y Se rv ic es . A.D . me nt io ns
frequently that she wants to go back home, and her case manager expressed that she will
be returning to live with her biological family, who reside in an urban area of Union
County, towards the end of the school year.
Due to her temporary group home setting residential setting, Student C, attends
meetings and appointments regarding progress towards returning to live with her
biological family, which affects her attendance throughout the length of the school day,
and continuous daily attendance.
A.D. has been in this self-contained classroom setting since May of 2013, due to
her residential situation. Before entering this classroom setting, she was in a self-
35
contained classroom setting in the public school she attended in Union County. She is
classified as Multiple Disabled, with an IQ of 46, based on her current Special Education
evaluations. She receives all academic services in this classroom setting, and has a one-
on-one assistant. A.D.’s one-on-one assistant helps her remain on task, reinforce and
review academic skills, as well as, reinforce appropriate behavior modifications to shape
her behavior.
She receives multiple medications for mood deficits, anxiety, attention, and anger
displacement. The medication that she takes is on a scheduled daily routine that occurs at
home. The medication affects her academic progress and retention, as well as, her
personal affect.
She receives individual speech services once per week, group speech services
once per week, individual OT services once per week, group OT services once per week,
individual PT services once per week, group PT services once per week, individual
counseling services once per week, and group counseling services once per week. Her
related service schedule is quite full, and it impacts her instruction in mathematical
concepts, and she receives instruction in this area three times per week.
Student D (D.S.): is a Caucasian, fourteen years old, seven month, ninth grade male. He
resides in a large suburban area in Burlington County, with his parents, and three younger
siblings, who happen to be triplets.
D.S. has been attending this school setting, and had been a student in this specific
classroom, since July 2013. Previously, D.S. attended a county wide special services
school, but no longer attends this special services school, due to his parents concern
regarding the lack of his academic progress. He is classified as Autistic, with a non-verbal
intelligence composite of 79, based on his current Special Education evaluations. An
36
overall IQ was not reported, due to his limited communication and achievement in
completing tasks within an evaluation. He receives all academic services in this self-
contained classroom. D.S. has a one-on-one assistant who helps him remain on task,
complete tasks, reinforce and review academic skills, and reinforce appropriate behavior
modifications to shape his behavior.
D.S. takes medication for both attention and anxiety. He takes his medication at
home. The medication that he takes affects his attention, mood, and his retention of
academic skills and progress.
He receives individual speech services twice per week, group speech services
once per week, individual OT services once per week, and group OT services once per
week. His related services impact his mathematical instruction, and he is instructed in
mathematical concepts three times per week.
Student E (S.Y.): is a Caucasian, sixteen years, two month old, ninth grade male. He
resides in a small suburban area in Gloucester County, with his parents, and his younger
adopted sibling.
S.Y. has been a member of this classroom since September of 2012. Previously
S.Y. was instructed at home for several years, due to his parents being unhappy with the
special education services that he was receiving at various other county wide special
services schools. He is classified as Other Health Impaired, with an IQ of 40, based on
his current Special Education evaluations. S.Y. receives all academic services in this self-
contained classroom setting. He has a one-on-one aide/behavior support assistant. This
person helps S.Y. remain on task, reinforces and reviews academic skills, as well as,
implements and maintains a daily behavior modification plan to shape his behavior.
37
S.Y. has Fragile-X Syndrome. He has frequent medical appointments and
evaluations due to this genetic disorder. He does take medication related to the
characteristics of this disorder. These include medications for anxiety and attention. He
takes these medications on a daily basis at home. These medications affect his learning,
attention, and behavior. They also impact his academic progress and retention of
academic skills.
He takes medication for allergies and digestive tract issues. He takes these
medications on a daily basis at home, and it does not affect his academics or interrupt his
school day. S.Y. also has asthma and uses an inhaler, on an as needed basis.
He receives individual speech services twice per week, group speech services
once per week, individual OT services twice per week, and group OT services once per
week. His related service schedule is quite busy, and it affects his instruction in
mathematical concepts. He receives instruction in this academic area three times per
week.
3.2 setting. This single subject, multiple probe design study is taking place in a self-
contained classroom, within a non-profit Special Education school, in Atco, New Jersey.
This classroom serves eight students with various disabilities including: cognitive
impairments, autism spectrum disorders, specific learning disabilities, other health
impairments, and multiple disabilities. Seven out of eight students have a one-on-one
assistant. Each one-on-one assistant reinforces academic skills and behaviors, through
positive behavior support and modification, as well as, helps students with individually
based needs.
All of the students in this classroom setting receive academic instruction in all
curriculum areas both small and whole group settings. For the purpose of this study, I
38
will implement the multisensory approach of the Touch Math program in a small group
setting. There will be five students participating, and they were selected based on their
individual needs in the skill area of basic operations.
3.3 methods. In this classroom, mathematical skills are taught thirty minutes daily. Each
student is taught based on their individual needs, and they are either taught in a small
group or large group setting.
The baseline assessments, explicit teaching, and intermittent assessments took
place in a small group setting, over an eight-week period. The small group had at least
three of the student participants on a daily basis for instructional and assessment
purposes.
3.4 materials. During the intervention of applying and counting up touch points of the
Touch Math program the student participants used the following: candy, stickers, cereal,
highlighters, white boards, dry erase markers, erasers, pencils, Touch Math: touch point
flash cards, Touch Math: touch point addition worksheets on the first grade level, Touch
Math: touch point number lines, and the Touch Math application on the iPad.
The student participants used manipulatives such as candy, stickers, and cereal to
help make the concept of touch points more concrete, through number sense skills. The
students used dry erase markers and highlighters to help distinguish double touch points
that need to be touched twice, which are the numbers six through nine. Students were
given Touch Math: touch point flash cards, Touch Math: touch point number lines, and
the Touch Math application on the iPad, to practice counting the touch points on each
individual number, as well as, practice counting up a total of touch points when presented
with two single digit addends.
39
Before beginning the intervention the students were provided with baseline
assessments over a two-week period. Each baseline assessment was a teacher-made
addition worksheet. The worksheets had a mix of fact family single digit addition
problems, and each problem’s addends did not have touch points.
Example of Baseline Assessment:
During the initial portion of the intervention, the students were instructed on the
following: how to apply and use touch points by counting up and all, using various
materials, such as the Touch Math: touch point flash cards, Touch Math: touch point
number lines, markers, and white boards, to teach both the strategy and approach to
solving an addition problem. Students used the white boards and dry erase markers to
practice counting up touch points of two numbers, to create a sum. They practiced
various problems on their dry erase board. The students were given Touch Math: touch
point addition worksheets to reinforce counting up and all touch points for homework.
The students were given worksheets to complete for homework, four days out of the
school week. These worksheets were on the first grade level of the Touch Math program,
and were photocopied materials.
40
Within the eight-week intervention the students were provided with intermittent
assessments, once per week. The intermittent assessments had a mixture of two fact
family addition problems, with touch points.
Example of Intermittent Post-intervention Assessment:
3.5 instruments. Within the eight-week process of using touch points to aide in solving
addition problems, the students were given baseline and intermittent assessments.
Baseline assessments were given to the students to determine their knowledge of sums
with addition fact families one through nine. The intermittent assessments were given to
the students after four weeks of explicit instruction, and this determined their progress in
solving addition problems of fact families zero through nine, using touch points as an
aide.
3.6 assessments. Breakdown of baseline assessments: The five student participants
were given four baseline assessments. Each baseline assessment contained either two or
three fact families. The number of fact families that were being assessed determined the
number of problems contained on each of the assessments. The baseline assessments
with two fact families contained twenty addition problems, and the baseline assessments
with three fact families contained thirty addition problems.
41
The student participants were given one baseline assessment per class period. The
class period was thirty minutes, and was a daily instructional period, however the student
participants had various related services that impacted whether they received daily
instruction in the area of mathematics. After the students were given each a baseline
assessment, they were instructed to solve the addition problems to the best of their ability,
independently, to complete within the class period of thirty minutes to complete. There
were a total of four baseline assessments. The amount of fact families and problems
varied on each baseline assessment.
Example of a student participant’s baseline assessment:
Baseline assessments took over two weeks to give to the students, due to their
individual related service schedule, and inclement weather, which either caused school to
be delayed or closed for the day.
Breakdown of post-intervention assessment: After the four weeks of the explicit
instructional period of using the multisensory approach to instruction, where student
participants used touch points to count up and all to create a sum for a single digit
addition problem, they were given post-intervention assessments.
Each post-intervention assessment contained two fact families, with possible fact
families of zero through nine, with addends of zero through nine. Each post-intervention
42
assessment contained twenty problems, with touch points on each addend. When the
student participants were given a post-intervention assessment, they were instructed to
use the touch points on the assessment and touch point number line to help them count up
and solve for each problem. The students were given thirty minutes to complete each
post-intervention assessment.
Example of a student’s post-intervention assessment:
Overall the post-intervention assessments took two weeks to complete. This was
due to both student participant’s individual related service schedule, and inclement
weather, which was due to a delay or school closure.
3.7 intervention. After the student participants were initially assessed on the four
baseline assessments, over a two- week period, explicit instruction of counting touch
points and counting up all of the touch points began. The intervention was given daily,
for a thirty minute increment, and the group of student participants ranged from a group
of three to a group of five, depending on their individual related schedule or absences.
The intervention took place over a four-week period.
Breakdown of the intervention: In the initial phase of the intervention, the student
participants were instructed in placing the touch points on numbers and counting up all of
the touch points. Students learned how to do this by counting touch points on flash cards
43
with the touch points, or drawing touch points on a given number, as well as, placing
manipulatives, such as candy or stickers on a given number.
After the students were given several opportunities to place the touch points on
numbers physically or by drawing them and then counting the points, this skill was then
reinforced through the Touch Math program’s application on the iPad. This application
allowed the student participants the opportunity to review touch point placement and
counting the touch points up, through several multiple sensory input process, including
sight, touch, and sound. This portion of explicit instruction took place for one week.
After the student participants were instructed in how to place touch points on
numbers and how to count up the points, the second portion of the intervention began.
The student participants were instructed how to count all of the touch points on two
single digit addends in an addition problem. These concepts were modeled through
several teacher-provided examples on the white board, the students wrote the problems
on their own individual white board, and they went through each example step-by-step.
Students wrote each number and their touch points on the white board, and used the
Touch Math number line to help count up the touch points to create a sum. Then, as a
small group, they counted up all of the touch points for each addend to create a sum for
the teacher given examples. After being given the teacher examples that they worked on
together, the students were given independent work in the form of touch point worksheets
from the first grade level of the Touch Math program. These worksheets had various
single digit addition problems. Each problem’s addends had touch points already placed
on it. Student participants were given a Touch Math number line, with numbers that had
touch points on them as a visual reminder to help with counting up, if they were
struggling. Also for students who needed extra reinforcement of counting up all of the
44
touch points, there were three one-on-one assistants and the teacher to go over the touch
points, and both visually and verbally prompt the student participants to count up the
touch points.
As the students were practicing independently with these types of worksheets in
the classroom, they also reinforced the concept of adding two single digit addends with
touch points, by completing worksheets, at home. They were given homework four days
per week. The worksheets were similar to the worksheets that they completed
independently in the classroom. These worksheets contained various single digit addition
problems. Each problem’s addends had touch points on it. The process of independent
practice, including both in the classroom and at home, took place for three weeks. After
the intervention phase was completed, the student participants were given post-
intervention assessments.
45
Chapter 4
Results
4.1 premises of the study. In this current study, five students with severe and significant
disabilities, who attend a school that serves students with special education needs,
participated in the explicit use of touch points, as a multisensory approach of instruction
to improve their basic operation addition skills.
Students were given baseline assessments of addition facts, which include fact
families zero through nine, with addends zero through nine. Then, students were
explicitly taught how to use the touch points to both count up and count all, to create a
sum for an addition problem. After four weeks of explicit instruction of using touch
points as a strategy to solve addition problems, the students were given post-intervention
assessments. These post-intervention assessments included touch points that were placed
on fact family addends. Fact families that were included in these assessments were zero
through nine, with addends of zero through nine.
The baseline assessments, explicit instruction of the intervention, and post-
intervention assessments took place over eight weeks.
4.2 procedures. The five student participants were assessed on their basic operation fact
knowledge for addition problems. The facts families that they were assessed on included
facts zero through nine. The fact families were broken into groups of two, and students
were assessed on these groups of facts once per week.
After the student participants were given fact family baseline assessments, they
were instructed how to apply and count up touch points. First the students applied touch
points on flash cards using manipulatives, such as stickers and candy. Secondly, the
students reinforced applying touch points on the iPad, using the Touch Math application.
46
Finally, the students applied touch points by drawing touch points on numbers. After the
student participants practiced applying touch points they were instructed how to count up
touch points to create a sum for an addition problem. The students were provided with
addition problems without touch points, and then they placed touch points on each
number and counted up to create a sum.
After four days of practice counting up while applying touch points, the students
were assessed on fact families, two fact families at a time. These assessments did occur
once per week, and determined students’ progress in obtaining addition fact family
knowledge. During the intermittent assessments, students were able to use number lines
and flash cards, both of which have touch points, if necessary.
The baseline assessments, intervention of explicit teaching with intermittent
assessments, took eight weeks.
4.3 results of baseline and post-intervention assessments data for each student
participant. Student A (I.O.), Baseline Assessment: He was given four baseline
assessments, within a two-week period. On the first baseline assessment, Student A was
assessed on the following facts family addends: zero, one, and two. He was assessed on a
total of thirty problems, and he answered all of the questions correctly. He scored 100%
accuracy.
On the second baseline assessments, Student A was assessed on the following fact
family addends: four, five, and six. He was assessed on thirty questions, and answered
twenty-four out of the thirty questions, correctly. He scored 80% accuracy.
On the third baseline assessment, Student A was assessed on the following fact
family addends: three and seven. I.O. attempted all of the questions, and he answered
thirteen out of twenty questions correctly. He scored 65% accuracy.
47
On the fourth baseline assessment, Student A was assessed on the following fact
family addends: eight and nine. I.O. attempted all of the questions, and he answered
eleven out of twenty questions correctly. He scored 55% accuracy.
Student A (I.O.), Post-intervention assessment: He was assessed on five post-
intervention assessments, within a two-week period. On the first post-intervention
assessment, I.O. was assessed on fact family addends of one and two. He attempted all
twenty problems, answered all twenty problems correctly, and scored 100% accuracy.
On the second post-intervention assessment, I.O. was assessed on fact family
addends of three and four. He attempted all twenty problems, answered all twenty
problems correctly, and scored 100% accuracy.
On the third post-intervention assessment, I.O. was assessed on fact family
addends five and six. He attempted all twenty problems, answered all twenty problems
correctly, and scored 100% accuracy.
On the fourth post-intervention assessment, I.O. was assessed on fact family
addends of seven and eight. He attempted all twenty problems, answered all twenty
problems correctly, and scored 100% accuracy.
On the fifth post-intervention assessment, I.O. was assessed on fact family
addends of nine and zero. He attempted all twenty problems, and answered nineteen out
of twenty questions correctly. I.O. scored 95% accuracy.
Student B (G.M.), Baseline assessment: He was to be given four baseline assessments,
within a two-week period. Unfortunately G.M. had an influx of seizure activity, during
that two-week period, and was only able to complete one out of the four baseline
assessments.
48
On this baseline assessment G.M. was unable to complete the assessment. He
attempted fifteen out of thirty problems on the first baseline assessment. The first
baseline assessment contained fact family addends: zero, one, and two. He answered
eleven out of the fifteen questions that he attempted correctly, but was graded on all thirty
problems. Therefore he scored 37% accuracy.
Student B (G.M.), Post-intervention assessment: He was assessed on five post-
intervention assessments within a two-week period. On the first post-intervention
assessment, G.M. was assessed on fact family addends of one and two. G.M. attempted
eleven out of twenty problems within the class period. Due to him only finishing eleven
problems, the remaining problems within the assessment were voided and marked
incorrect. Therefore, his accuracy score was based out of the total number of questions
he answered correctly out of the total number of problems. He answered eleven
questions correctly out of twenty problems on this assessment, therefore G.M. scored
55% accuracy.
G.M. was given a second post-intervention assessment. On this assessment, he
was assessed on fact family addends of three and four. He attempted eleven out of
twenty problems within the class period. The remaining problems on the assessment
were marked incorrect, he answered those eleven problems accurately, and his accuracy
score was 55%.
On the third post-intervention assessment, G.M. was assessed on fact family
addends of five and six. He attempted fourteen out of twenty problems on this
assessment within the class period. The remaining problems were marked incorrect, and
his accuracy score reflects the problems that he did answer. He scored 70% accuracy.
49
On the fourth post-intervention assessment, G.M. was assessed on fact family
addends of seven and eight. He attempted twelve out of twenty problems on this
assessment within the class period. The remaining problems were marked incorrect, and
his accuracy score reflects the problems that he did answer. He scored 70% accuracy.
On the fifth post-intervention assessment, G.M. was assessed on fact family
addends of nine and zero. He attempted nine out of twenty problems on this assessment
within the class period. The remaining problems were marked incorrect, and his accuracy
score reflects the problems that he did answer. He scored 45% accuracy.
Student C (A.D.), Baseline assessment: She was assessed on four baseline assessments,
within a two-week period. On the first baseline assessment, with the fact family addends
of zero, one, and two were assessed. She attempted all of the questions, and answered
twenty-six out of thirty questions correctly. A.D. scored 87% accuracy.
On the second baseline assessment, where the fact family addends of four, five,
and six were assessed, she attempted all of the questions, and answered twenty-one out of
thirty questions correctly. A.D. scored 70% accuracy.
On the third baseline assessment, where the fact family addends of three and
seven were assessed, she attempted all of the questions, and answered eight out of twenty
questions correctly. She scored 40% accuracy.
On the fourth baseline assessment, A.D. was assessed on the fact family addends
of both eight and nine. She attempted all of the questions, and answered fourteen out of
twenty questions, correctly. She scored 70% accuracy.
Student C (A.D.), Post-intervention assessment: She was assessed on five post-
intervention assessments, within a two-week period. On the first post-intervention
assessments, A.D. was assessed on fact family addends of one and two. She attempted all
50
of the problems on this assessment. She answered nineteen out of twenty problems
correctly, and scored 95% accuracy.
On the second post-intervention assessment, A.D. was assessed on fact family
addends of three and four. She attempted all of the problems on this assessment. She
answered seventeen out of twenty problems correctly, and scored 85% accuracy.
On the third post-intervention assessment, A.D. was assessed on fact family
addends of five and six. She attempted all of the problems on this assessment. She
answered seventeen out of twenty problems correctly, and scored 85% accuracy.
On the fourth post-intervention assessment, A.D. was assessed on fact family
addends of seven and eight. She attempted all of the problems on this assessment. A.D.
answered fourteen out of twenty problems correctly, and scored 70% accuracy.
On the fifth post-intervention assessment, A.D. was assessed on fact family
addends of nine and zero. She attempted all of the problems on this assessment. A.D.
answered all twenty problems correctly, and scored 100% accuracy.
Student D (D.S.), Baseline assessment: He was assessed on four different baseline
assessments, within a two-week period. On the first baseline assessment, he was assessed
on fact family addends of zero, one, and two. D.S. attempted all of the problems on this
assessment, and answered two out of thirty questions, correctly. He scored 0.07%
accuracy.
On the second baseline assessment, he was assessed on fact family addends of
four, five, and six. He attempted all of the questions, answered zero out of the thirty
questions correctly, and scored 0% accuracy.
51
On the third baseline assessment, he was assessed on fact family addends of three
and seven. He attempted all of the questions, answered zero out of the twenty questions
correctly, and scored 0% accuracy.
On the fourth baseline assessment, D.S. was assessed on fact family addends of
eight and nine. He attempted all of the questions, answered zero out of the twenty
questions correctly, and scored 0% accuracy.
Student D (D.S.), Post-intervention assessment: He was assessed on five post-
intervention assessments within a two-week period. On the first post-intervention
assessment, D.S. was assessed on fact family addends of one and two. He attempted
sixteen out of the twenty problems on this assessment. The four problems that he did not
answer were marked incorrect. He scored 80% accuracy.
On the second post-intervention assessment, D.S. was assessed on fact family
addends of three and four. He attempted all of the twenty problems on this assessment.
He answered all of the questions correctly, and scored 100% accuracy.
On the third post-intervention assessment, D.S. was assessed on fact family
addends of five and six. He attempted all twenty problems on this assessment. He
answered nineteen out of twenty questions correctly, and scored 95% accuracy.
On the fourth post-intervention assessment, D.S. was assessed on fact family
addends of seven and eight. He attempted all twenty problems on this assessment. He
answered nineteen out of twenty questions correctly, and scored 95% accuracy.
On the fifth post-intervention assessment, D.S. was assessed on fact family
addends of nine and zero. He attempted all twenty problems on this assessment. He
answered eighteen out of twenty questions correctly, and scored 90% accuracy.
52
Student E (S.Y.), Baseline assessment: He was given four baseline assessments within
a two-week period. On the first baseline assessment, S.Y. was assessed on fact family
addends of zero, one, and two. He attempted all thirty questions, and answered fourteen
questions, correctly. S.Y. scored 47% accuracy.
On the second baseline assessment, S.Y. was assessed on fact family addends of
four, five, and six. He attempted all thirty questions, and answered eleven out of the
thirty questions correctly. He scored 37% accuracy.
On the third baseline assessment, S.Y. was assessed on fact family addends of
three and seven. He attempted all of the problems, and answered four out of the twenty
questions accurately. He scored 20% accuracy.
On the fourth baseline assessment, S.Y. was assessed on fact family addends of
eight and nine. He attempted all of the problems, and answer five out of the twenty
questions accurately. He scored 25% accuracy.
Student E (S.Y.), Post-intervention assessment: He was assessed on five post-
intervention assessments within a two-week period. On the first post-intervention
assessment, S.Y. was assessed on fact family addends of one and two. He attempted all
twenty problems on this assessment. He answered all of these questions correctly, and
scored 100% accuracy.
On the second post-intervention assessment, S.Y. was assessed on fact family
addends of three and four. He attempted all twenty problems on this assessment. He
answered nineteen out of twenty questions correctly, and scored 95% accuracy.
On the third post-intervention assessment, S.Y. was assessed on fact family
addends of five and six. He attempted all twenty problems on this assessment. He
answered all of these questions correctly, and scored 100% accuracy.
53
On the fourth post-intervention assessment, S.Y. was assessed on fact family
addends of seven and eight. He attempted all twenty problems on this assessment. He
answered all of these questions correctly, and scored 100% accuracy.
On the fifth post-intervention assessment, S.Y. was assessed on fact family
addends of nine and zero. He attempted all twenty problems on this assessment. He
answered all of these questions correctly, and scored 100% accuracy.
4.4 comparison of results for assessments for each student participant. When
comparing an individual’s achievement in the area of single digit addition, the percentage
of the number correctly answered questions for each fact family’s addend in a student
participant’s baseline assessment versus their post-intervention assessment was
examined. The result for ten problems per addend on the baseline was compared against
the ten problems on the post-intervention assessment.
Student A (I.O.): When examining the fact family addend of zero, I.O. answered all
addends on both the baseline and post-intervention assessment correctly. He achieved no
improvement on this addend, and there was no change in the development of this addend.
When examining the fact family addend of one, I.O. answered all addends on both
the baseline and post-intervention assessment correctly. He achieved no improvement on
this addend, and there was no change in the development of this addend.
When examining the fact family addend of two, I.O. answered all addends on
both the baseline and the post-intervention assessment correctly. He achieved no
improvement on this addend, and there was no change in the development of this addend.
When examining the fact family addend of three, I.O. answered all addends on the
baseline incorrectly and post-intervention correctly. Although a percentage cannot be
54
determined, I.O. showed an improvement from the baseline assessment to the post-
intervention assessment, and shows a positive change in the development of this addend.
When examining the fact family addend of four, I.O. answered seven out of ten
questions on the baseline correctly, and all ten questions on the post-intervention
assessment correctly. Therefore he achieved 43% improvement on this addend, and there
was a positive change in development.
When examining the fact family addend of five, I.O. answered all addends on
both the baseline and post-intervention assessment correctly. He achieved no
improvement on this addend, and there was no change in the development of this addend.
When examining the fact family addend of six, I.O. answered seven out of ten
questions correctly on the baseline, and all of the questions correctly on the post-
intervention assessment. He achieved 43% improvement on this addend, and there was a
positive change in the development of this addend.
When examining the fact family addend of seven, I.O. answered five out of ten
questions correctly on the baseline, and all of the questions on the post-intervention
correctly. He achieved 100% improvement on this addend, and there was a positive
change in the development of this addend.
When examining the fact addend of eight, I.O. answered five out of ten questions
correctly on the baseline, and all of the questions on the post-intervention correctly. He
achieved 100 % improvement on this addend, and there was a positive change in the
development of this addend.
When examining the fact family addend of nine, I.O. answered six out of ten
questions correctly on the baseline, and nine out of ten questions correctly on the post-
55
intervention assessment. Therefore, he achieved 50% improvement on this addend, and
there was a positive change in the development of this addend.
See Figure A, for I.O.’s achievement and development of each addend,
comparison between the baseline and the post-intervention assessment of each
addend.
Figure A
Student B (G.M.): When examining the fact family addend of zero, G.M. five out of ten
questions correctly on the baseline, and five out of ten questions correctly on the post-
intervention assessment. Therefore, he achieved no improvement on this addend, and
there was no change in development of this addend.
When examining the fact family addend of one, G.M. answered three out of ten
questions on the baseline correctly, and he answered seven out of ten questions on the
post-intervention assessment correctly. Therefore, he achieved 13.3% improvement on
this addend, and there was a positive change in the development of this addend.
When examining the fact family addend of two, G.M. answered three out of ten
question on the baseline correctly, and he answered four out of ten questions on the post-
56
intervention assessment correctly. Therefore, he achieved 25% improvement on this
addend, and there was a positive change in the development of this addend.
When examining the fact family addend of three, G.M. answered zero out of ten
questions correctly on the baseline, and five out of ten questions on the post-intervention
assessment correctly. Although a percentage cannot be determined, G.M. showed an
improvement from the baseline assessment to the post-intervention assessment, and
shows a positive change in the development of this addend.
When examining the fact family addend of four, G.M. answered zero out of ten
questions correctly on the baseline, and answered six out of ten questions on the post-
intervention assessment correctly. Although a percentage cannot be determined, G.M.
showed an improvement from the baseline assessment to the post-intervention
assessment, and shows a positive change in the development of this addend.
When examining the fact family addend of five, G.M. answered zero out of ten
questions correctly on the baseline, and answered seven out of ten questions on the post-
intervention assessment correctly. Although a percentage cannot be determined, G.M.
showed an improvement from the baseline assessment to the post-intervention
assessment, and shows a positive change in the development of this addend.
When examining the fact family addend of six, G.M. answered zero out of ten
questions on the baseline, and answered seven out of ten questions on the post-
intervention assessment correctly. Although a percentage cannot be determined, G.M.
showed an improvement from the baseline assessment to the post-intervention
assessment, and shows a positive change in the development of this addend.
When examining the fact family addend of seven, G.M. answered zero out of ten
questions on the baseline, and answered seven out of ten questions on the post-
57
intervention assessment correctly. Although a percentage cannot be determined, G.M.
showed an improvement from the baseline assessment to the post-intervention
assessment, and shows a positive change in the development of this addend.
When examining the fact family addend of eight, G.M. answered zero out of ten
questions on the baseline, and answered four out of ten questions on the post-intervention
assessment correctly. Although a percentage cannot be determined, G.M. showed an
improvement from the baseline assessment to the post-intervention assessment, and
shows a positive change in the development of this addend.
When examining the fact family addend of nine, G.M. answered zero out of ten
questions on the baseline, and answered five out of ten questions on the post-intervention
assessment correctly. Although a percentage cannot be determined, G.M. showed an
improvement from the baseline assessment to the post-intervention assessment, and
shows a positive change in the development of this addend.
58
See Figure B, for G.M.’s achievement and progress in development of each
individual addend, comparison between the baseline and the post-intervention
assessment of each addend.
Figure B
Student C (A.D.): When examining the fact family addend of zero, A.D. answered eight
out of ten questions on the baseline, and answered all of the questions on the post-
intervention assessment correctly. Therefore she achieved a 25% improvement on this
addend, and showed a positive change in the development of this addend.
When examining the fact family addend of one, A.D. answered nine out of ten
questions on the baseline, and answered all ten questions on the post-intervention
assessment correctly. Therefore she achieved 11% improvement on this addend, and
showed that a positive change was made in the development of this addend.
When examining the fact family addend of two, A.D. answered nine out of ten
questions on the baseline, and nine out of ten questions on the post-intervention
59
assessment correctly. Therefore, she achieved no improvement on this addend, and there
was no change made in the development of this addend.
When examining the addend of three, A.D. answered three out of ten questions on
the baseline correctly, and eight out of ten questions on the post-intervention assessment
correctly. Therefore, she achieved 16.6% improvement on this addend, and there was a
positive change made in the development of this addend.
When examining the addend of four, A.D. answered eight out of ten questions on
the baseline correctly, and nine out of ten questions on the post-intervention assessment
correctly. Therefore, she achieved 12.5% improvement on this addend, and there was a
positive change made in the development of this addend.
When examining the addend of five, A.D. answered six out of ten questions on
the baseline correctly, and nine out of ten questions on the post-intervention assessment
correctly. Therefore, she achieved 50% improvement on this addend, and there was a
positive change made in the development of this addend.
When examining the addend of six, A.D. answered seven out of ten questions on
the baseline correctly, and eight out of ten questions on the post-intervention assessment
correctly. Therefore, she achieved 14% improvement on this addend, and there was a
positive change made in the development of this addend.
When examining the addend of seven, A.D. answered six out of ten questions on
the baseline correctly, and six out of ten questions on the post-intervention assessment
correctly. Therefore, she achieved no improvement on this addend, and no change was
made in the development of this addend.
When examining the addend of eight, A.D. answered eight out of ten questions on
the baseline correctly, and eight out of ten questions on the post-intervention assessment
60
correctly. Therefore, she achieved no improvement on this addend, and no change was
made in the development of this addend.
When examining the addend of nine, A.D. answered seven out of ten questions on
the baseline correctly, and nine out of ten questions on the post-intervention assessment
correctly. Therefore, she achieved 28.5% improvement on this addend, and there was a
positive change made in the development of this addend.
See Figure C for A.D.’s achievement and progress of each individual addend,
comparison between the baseline and the post-intervention assessment of each
addend.
Figure C
Student D (D.S.): When examining the addend of zero, D.S. answered zero out of ten
questions on the baseline correctly, and all ten questions on the post-intervention
assessment correctly. Although a percentage cannot be determined, D.S. showed an
improvement from the baseline assessment to the post-intervention assessment, and
shows a positive change in the development of this addend.
61
When examining the addend of one, D.S. answered two out of ten questions on
the baseline correctly, and nine out of ten questions on the post-intervention assessment
correctly. Therefore, he achieved 350% improvement on this addend, and there was a
positive change made in the development of this addend.
When examining the addend of two, D.S. answered zero out of ten questions on
the baseline correctly, and seven out of ten questions on the post-intervention assessment
correctly. Although a percentage cannot be determined, D.S. showed an improvement
from the baseline assessment to the post-intervention assessment, and shows a positive
change in the development of this addend.
When examining the addend of three, D.S. answered zero out of ten questions on
the baseline correctly, and all ten questions on the post-intervention assessment correctly.
Although a percentage cannot be determined, D.S. showed an improvement from the
baseline assessment to the post-intervention assessment, and shows a positive change in
the development of this addend.
When examining the addend of four, D.S. answered zero out of ten questions on
the baseline correctly, and all ten questions on the post-intervention assessment correctly.
Although a percentage cannot be determined, D.S. showed an improvement from the
baseline assessment to the post-intervention assessment, and shows a positive change in
the development of this addend.
When examining the addend of five, D.S. answered zero out of ten questions on
the baseline correctly, and nine out of ten questions on the post-intervention assessment
correctly. Although a percentage cannot be determined, D.S. showed an improvement
from the baseline assessment to the post-intervention assessment, and shows a positive
change in the development of this addend.
62
When examining the addend of six, D.S. answered zero out of ten questions on
the baseline correctly, and all ten questions on the post-intervention assessment correctly.
Although a percentage cannot be determined, D.S. showed an improvement from the
baseline assessment to the post-intervention assessment, and shows a positive change in
the development of this addend.
When examining the addend of seven, D.S. answered zero out of ten questions on
the baseline correctly, and all ten questions on the post-intervention assessment correctly.
Although a percentage cannot be determined, D.S. showed an improvement from the
baseline assessment to the post-intervention assessment, and shows a positive change in
the development of this addend.
When examining the addend of eight, D.S. answered zero out of ten questions on
the baseline correctly, and nine out of ten questions on the post-intervention assessment
correctly. Although a percentage cannot be determined, D.S. showed an improvement
from the baseline assessment to the post-intervention assessment, and shows a positive
change in the development of this addend.
When examining the addend of nine, D.S. answered zero out ten questions on the
baseline correctly, and eight out of ten questions on the post-intervention assessment
correctly. Although a percentage cannot be determined, D.S. showed an improvement
from the baseline assessment to the post-intervention assessment, and shows a positive
change in the development of this addend.
63
See Figure D, for D.S.’s achievement and progress in each individual addend,
comparison between the baseline and the post-intervention assessment of each
addend.
Figure D
Student E (S.Y.): When examining the addend of zero, S.Y. answered all of the
questions on the baseline correctly, and all of the questions on the post-intervention
assessment correctly. Therefore, he achieved no improvement on this addend, and there
was no change made in the development of this addend.
When examining the addend of one, S.Y. answered three out of ten questions on
the baseline correctly, and all of the questions on the post-intervention assessment
correctly. Therefore, he achieved 233% improvement on this addend, and there was a
positive change made in the development of this addend.
When examining the addend of two, S.Y. answered two out of ten questions on
the baseline correctly, and all of the questions on the post-intervention assessment
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correctly. Therefore, he achieved 25% improvement on this addend, and there was a
positive change made in the development of this addend.
When examining the addend of three, S.Y. answered one out of ten questions on
the baseline correctly, and all ten questions on the post-intervention assessment correctly.
Therefore, he achieved 90% improvement on this addend, and there was a positive
change made in the development of this addend.
When examining the addend of four, S.Y. answered five out of ten questions on
the baseline correctly, and nine out of ten questions on the post-intervention assessment
correctly. Therefore, he achieved 80% improvement on this addend, and there was a
positive change made in the development of this addend.
When examining the addend of five, S.Y. answered one out of ten questions on
the baseline correctly, and all ten questions on the post-intervention assessment correctly.
Therefore, he achieved 90% improvement on this addend, and there was a positive
change made in the development of this addend.
When examining the addend of six, S.Y. answered four out of ten questions on the
baseline correctly, and all ten questions on the post-intervention assessment correctly.
Therefore, he achieved 67% improvement on this addend, and there was a positive
change made in the development of this addend.
When examining the addend of seven, S.Y. answered two out of ten questions on
the baseline correctly, and all ten questions on the post-intervention assessment correctly.
Therefore, he achieved 25% improvement on this addend, and there was a positive
change made in the development of this addend.
When examining the addend of eight, S.Y. answered three out of ten questions on
the baseline correctly, and all ten questions on the post-intervention assessment correctly.
65
Therefore, he achieved 42.8% improvement on this addend, and there was a positive
change made in the development of this addend.
When examining the addend of nine, S.Y. answered three out of ten questions on
the baseline correctly, and all ten questions on the post-intervention assessment correctly.
Therefore, he achieved 42.8% improvement on this addend, and there was a positive
change made in the development of this addend.
See Figure E, for S.Y.’s achievement and development of each individual addend,
comparison between the baseline and the post-intervention assessment of each
addend.
Figure E
4.5 group of each individual addend. Addend 0: When examining the addend of zero,
there was a 36% increase in the number of correct answers from the baseline assessment
to the post-intervention assessment,
Addend 1: When examining the addend of one, there was a 70% increase in the number
of correct answers from the baseline assessment to the post-intervention assessment.
66
Addend 2: When examining the addend of two, there was a 67% increase in the number
of correct answers from the baseline assessment to the post-intervention assessment.
Addend 3: When examining the addend of three, there was a 975% increase in the
number of correct answers from the baseline assessment to the post-intervention
assessment.
Addend 4: When examining the addend of four, there was a 56% increase in the
number of the correct answers from the baseline assessment to the post-intervention
assessment.
Addend 5: When examining the addend of five, there was a 61% increase in the number
of the correct answers from the baseline assessment to the post-intervention assessment.
Addend 6: When examining the addend of six, there was a 67% increase in the number
of the correct answers from the baseline assessment to the post-intervention assessment.
Addend 7: When examining the addend of seven, there was an 87% increase in the
number of the correct answers from the baseline assessment to the post-intervention
assessment.
Addend 8: When examining the addend of eight, there was a 64% increase in the
number of the correct answers from the baseline assessment to the post-intervention
assessment.
Addend 9: When examining the addend of nine, there was 64% increase in the number
of the correct answers from the baseline assessment to the post-intervention assessment.
67
See Figure F, for the overall improvement percentage of each individual addend,
comparison between the overall percentage achieved on each addend on baseline
assessments versus the post-intervention assessments, based on group achievement.
Figure F
When looking at the average percentage for each individual addend based on the
student participants’ baseline and post-intervention assessments, it shows that their scores
improved after being explicitly taught the intervention of using the touch points.
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Chapter 5
Discussion
5.1 current study. The current study was conducted in a school, located in Atco, New
Jersey, that serves students with severe and significant disabilities. There were five
student participants with various disabilities, including severe and specific learning
disabilities, cognitive impairments, autism spectrum disorders, and multiple disabilities,
ages eleven through sixteen years old, in a self-contained classroom that participated in
this study.
This study was conducted because the student participants’ basic operation
addition skills were varying, and their rate of progress towards mastering addition skills
was slow. The student participants were not responding to a paper and pencil method,
and learning their addition basic operation facts. Along with the use of manipulatives, a
number line, and the painful attempt of trying to memorize facts, the student participants
continued to struggle with strengthening their basic operation addition skills. A
multisensory approach to instruction was provided over an eight-week period to improve
basic operation addition skills. The student participants were explicitly taught the
multisensory approach of counting up touch points on two single digit addends, through
the use of the Touch Math program.
This multisensory approach to instruction through the Touch Math program were
chosen as the instructional strategy to use for these particular student participants, based
on previous research. There have been a number of studies that linked the multisensory
approach of the Touch Math program to improving, students with specific learning
disabilities, basic operation skills. There also have been previous studies conducted to
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determine the best approach to teach basic operation skills to students with severe and
significant disabilities. These studies indicated that using a multisensory approach to
instruction when teaching basic operation addition skills are the best instructional
approach for students with severe and significant disabilities. Therefore similar
instructional approaches would be used during the intervention of this current study.
Before the implementation of the intervention of using the touch points on two
single digit addends, the students were given baseline assessments of fact families, with
addends zero through nine. All of the student participants’ results on these baseline
assessments varied, and no one student’s results showed mastery across all of the
addends. Therefore the intervention of counting up all touch points was provided to the
student participants.
The intervention was provided to the student participants over a four-week period,
where they were explicitly taught how to count up all the touch points on two single digit
addends to create a sum. Initially, the student participants were taught how to apply the
touch points to numbers and count up the touch points to state a number. The student
participants were then taught how to count up the touch points on two single digit
addends to create a sum. The student participants used various materials during this
explicit teaching, including a number line with touch points, the Touch Math application
on the iPad, as well as, using manipulatives such as stickers and candy to create touch
points to solve single digit addition problems.
During the intervention period, it appeared that the student participants were
responding to the intervention, and were developing their basic operation addition skills.
Based on their response to the intervention, the student participants were assessed on
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post-intervention assessments. These assessments contained addends zero through nine,
with the touch points already being applied to the two single digit addends.
The student participants’ results show that they each made individual progress on solving
addition problems of each addend. Comparing the baseline assessment score to the post-
intervention assessment score, determined the percentage of improvement for each individual
addend. Although each student participant’s improvement percentage of an individual addend
varied, they all showed improvement in solving two single digit addends using touch points.
Therefore, the multisensory approach of instruction, of using touch points to help solve
basic operation addition problems appears to help students with severe and significant disabilities,
and can be linked to previous research.
This current study can be linked to Geary, et al’s, (2004) research that focused on
creating a strategy based intervention to improve students with learning disabilities’
arithmetic skills, using the Touch Math program. That study showed that students with
learning disabilities in the area of mathematics commit more counting errors, and use
developmentally immature counting-all procedures more than non-disabled peers.
Students with mathematical learning disabilities could benefit from instructional
strategies that help them generalize mathematical skills that are based in number sense
and counting, and rely less on their processing skills and working memory.
In a longitudinal study of the multisensory approach to improve basic operation
skill achievement of students with mild learning disabilities, by Dev, Doyle, and Valente’s
2002, eleven students, ranging in age from six to seven years old, participate in this two-
year study. Student participants were given a WRAT-III assessment before and after the
daily intervention of the Touch Math program to determine improvement in basic
operation skills over a two year period.
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This longitudinal study relates to the current study in its format of determining
achievement and improvement of basic operation skills. In Dev, et al’s 2002 longitudinal
study, they used formal assessment tools to determine if there was an achievement growth
in the student participants’ skills, after being explicitly instructed within the multisensory
approach of the Touch Math program over a two year period. This study showed that
there was improvement in their achievement of basic operation skills, based on the
baseline assessment, daily and explicit teaching of the multisensory approach of the
Touch Math program, and post-intervention assessment.
The current study had informal baseline and post-intervention assessments.
However the student participants were not explicitly taught the multisensory approach of
the Touch Math program over an eight-week period. Within this short intervention
period, the students that participated in the current study, their skills in basic operations,
improved. Therefore, Dev, et al’s 2002 and the current study both show that with
baseline, explicit intervention, and post-intervention assessment that student participants
skills improved.
In Strand’s 2013, experimental control group study, there were two groups of
student participants, one group received supplemental instruction through the Touch Math
program, and the other group did not receive supplemental instructional support. The
instructional support was provided to that particular control group for a year. At the end
of the school year, the students in both control groups were assessed on various basic
operation concepts. It was found that the students that received instructional support
from the Touch Math program achieved more accuracy on the various problems on the
assessment that their peers who did not receive instructional support.
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This study shows that students that were given supplemental instruction, and a
strategy based intervention, their skills in basic operations improved. Strand’s 2013 study
relates to the current study, in regard to providing student participants a strategy to count
up all of the touch points to add to single digit addends. This strategy improved the
student participants’ skills in solving single digit addends.
Regarding providing instructional materials and basic operation curriculum for
students with significant disabilities. There have been several meta-analysis studies and
curriculum guides for educators to provide mathematical instruction to students with
significant disabilities.
Within these studies and curriculum guides, the work of Browder, Jimenez,
Spooner, Saunders, Hudson, and Bethune’s (2012) conceptual model, they examined how
the instruction of early numeracy skills was given to students with moderate and
significant disabilities. They felt that students with significant disabilities struggles,
included: number identification, rote counting, representation of numbers through one-to-
one correspondence, number conversation, composing and decomposing numbers,
magnitude of numbers, early measurement concepts, understanding the effect of basic
operations, and patterning. They indicated that students with significant disabilities
would benefit from a multisensory approach to instruction to teach these skills. They
noted that the Touch Math program would be a beneficial instructional material for
students with significant disabilities.
The Touch Math program was used in the current study to help the student
participants improve their basic operation skills. The student participants used touch
points to help add and develop and strengthen the following skills: number identification,
rote counting, and composing number. Using the touch points when adding, improved
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the student participants basic operation skills, and indicates that the Touch Math program
and its instructional techniques are beneficial to students with significant disabilities.
5.2 limitations of the current study. Based on the current study, there were limitations
that affected the overall outcome. Limitations included the following: student
participants, the structure of the intervention, the structure of both the baseline and post-
intervention assessments, and the results of the interventions.
Within the limitations of the student participants, there were various constraints
that affected the current study, including the students’ schedules, their rate of learning the
strategy, and having it reinforced by other classroom staff members.
Four out of the five student participants had related services during the time that
mathematical instruction was given. These four student participants were not instructed
in mathematical concepts five days within a school week.
Another constraint included student participants’ rate of learning the intervention
and having it reinforced by other classroom staff. This was evident when examining
student participants that have a one-on-one assistant compared to student participants that
did not have a one-on-one assistant. Student participants that did have a one-on-one
assistant could have been more frequently monitored through out the process of learning
how to add numbers with touch points. Student participants that did have a one-on-one
assistant appeared to have more opportunities to have touch point concepts reinforced,
and monitoring during the entire intervention process. Therefore, this had a positive
affect on their learning and reinforcement of the touch point strategies to help them add
two single digit numbers.
Within the limitations of the structure of the intervention, the following occurred:
structure of the classroom where the intervention and assessments occurred, how the
74
assessments were structured, and the rate of the student participants’ consistent practice
of the intervention.
The student participants had a challenging environment to complete the baseline
assessment, intervention, and post-intervention assessment. The students were in a small
group within a classroom with students that did not participate in the current study.
Therefore, the non-participating students and classroom staff distracted the student
participants.
Also the assessments and intervention took place in the class period right before
lunch, and some of the student participants were focused on lunch. It appears that some
students rushed through assessments and independent practice to eat lunch.
The most glaring limitation of the structure of the intervention and its consistency
of implementation was the structures of the school day. This current study took place in
the height of the winter. Due to the frequency of the inclement weather, school was
either delayed or closed for the day. Students did not receive the consistency of the
intervention and assessments in a daily manner, and it affected the rate of learning and
maintaining the intervention.
When examining the limitations of the baseline and post-intervention
assessments, their structure and aides to complete theses assessments affected their
results. When the student participants completed the baseline assessments, the amount of
problems on these assessments varied. Two of the baseline assessments had twenty
problems, and two of the baseline assessments had thirty problems. Compared to post-
intervention assessments, where each assessment had twenty problems. Based on the
amount of problems on the type of assessment, it affected the percentage of achievement
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for each fact family addend both for the individual and the overall average for the addend
when comparing the group’s overall achievement of the group.
5.3 implications of the current study. After the current study was completed, and the
limitations of this study were examined, there are implications from those limitations.
Implications could be made in the following areas of limitations in student participants,
structure of the intervention, and the structure of the baseline and post-intervention
assessments.
Within the area of limitations of student participants, the following can be
implicated: students that participate in the study should receive the maximum amount of
instruction time to be thoroughly assessed and instructed in the assessment. For students
that do participate in a study on in an intense intervention, they should receive instruction
in that intervention every day at the same time, for the same amount of time. When
students do not consistently receive the intervention, it could affect their rate of learning
the intervention and progress towards maintaining a skill or concept.
The students that participated in this study had various rates of progress of using
the intervention of the touch points to help them solve single digit addition problems.
Due to their various rates of progress towards maintaining the use of the touch points to
solve single digit addition problems, there are two student participants that would not be
included in future studies. Those student participants are Student A and Student B.
Student A would not be included in a similar future study due to him having a majority of
the mastery of achievement in all of the addends, and it did not appear that he needed the
intervention to help with his addition skills. Student B would not be included in a similar
future study due to his seizure activity. His seizure activity affected his consistency of
the intervention and his percentage of achievement was affected due to his influx of
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seizures during the baseline assessment. Student B should receive an intervention to help
recall a strategy to help solve addition problems, but should not be assessed on the
strategy to see if it bettered his addition skills. Based on these two student’s rate of
achievement in improving their addition skills, students who almost have a skill mastered
and students who have consistent difficulties within a school day should not be included
in an intervention based study.
When examining the limitations of the structure of the intervention, the following
can be implicated: this intervention should be implemented at the beginning of the
school year. The students that participated in the current study struggled a majority of the
year before the intervention began. In future studies that provide similar interventions, it
would be best to be done in the beginning of the school year.
Also, this intervention was provided to the student participants right before lunch,
which was a major distraction for them. They were worried about lunch, and did not
appear focused during the instructional period. This type of intense instruction would be
best done at a different point in the school day, preferably earlier in the day.
In future studies, students that participate in similar future studies should be
assessed and instructed in a smaller and quieter area away from distractions.
When examining the limitations of the structure of the baseline and post-
intervention assessments, the following implications can be made: the baseline
assessments did not have the same number of problems on each assessment. The
baseline assessment should have been broken up into two fact addends, instead of either
two or three fact addends. It appeared that some student participants struggled with the
assessments with more questions. In future studies, student participants would benefit
from assessments that have a consistent amount of questions throughout the study.
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Also, it appears that during the post-intervention assessments some participants
rushed through the assessments, and their accuracy score is not truly reflected.
Specifically Student C appeared to rush through these post-intervention assessments, and
it appears that due to her rushing that her individual achievement score does not truly
reflect her maximum ability to add. In future intervention studies, there should be close
monitoring of students during the assessment period, and providing a quiet area to
complete the assessments.
The post-intervention assessments show that student participants benefitted from
intense intervention instructional approaches of using touch points to count up when
adding two single digit addends. Future studies that address increasing basic operation
skills should include baseline and post-intervention assessments to determine if the
intervention worked; but, more importantly, did the students make progress in both
obtaining and maintaining a skill?
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