Creat ive Educati on
2010. Vol.1, No.3, 149-153
Copyright © 2010 SciRes. DOI:10.4236/ce.2010.130 23
Using an Exploratory Approach to Help Children with Autism
Learn Mathematics
Hui Fang Huang “Angie” Su1, Lean ne L ai 2, Herminia Janet Rivera1
1Nova Southeastern University, North Miami Beach, Flori da, USA;
2Nova Southeastern University, Davie, Fl orida, USA.
Email: {shuifang, Leanne, hr176}
Received June 1st, 2010; revis ed September 23rd, 2010; accepted September 3 0th, 2010.
The exploratory study was carried out at a Choice school located in Davie, Florida. Thirty-four pre-sch ool stu-
dents with autism and their integrated, typically developing peers received 3 months of mathematics instruction
during their regular school day. The purpose of the study was to identify the eff ective uses of inst ructiona l strat-
egies that will impact students’ learning. Instruction consisted of both direct and embedded instruction derived
from the Project MIND curriculum (Su, 2002). A comparing of the rates of acquisition of math skills for stu-
dents with autism who received interven tion with students with autism who did not receiv e in ter ven t i on revealed
information about the specific learning abilities of students.
Keywords: Autism and Mathematics, Preschool Mathematics, Effective Mathematics Strategies for Children
with Autism, Mathe m a t i cs fo r Pre-School Age Children with Autism
Introduction (What is Autism?)
Autism is a complex neurological disorder which impairs
one’s ability to socialize, communicate, process sensory infor-
mation, and experience the full range of interests common to
most people. In addition to the severe nature of the disorder, the
prevalence of autism is increasing. The Centers for Disease
Control (2007) reports that as many as 1 in every 150 persons
has autism. The severity of the disability coupled with the in-
creasing prevalence rate makes autism a priority among re-
searchers whose focus is to uncover etiologies and effective
treat ments .
Early Intervention
While there is no known cure for autism, experts agree that
the positive outcomes are highly associated with comprehend-
sive, early intervention programs (National Research Council
2001). The importance of early intervention for young chil-
dren with autism has been documented in the literature (Hurth,
Shaw, Izeman, Whaley, & Rogers, 1999; National Research
Council, 2001; Rogers, 1999). Rogers (1999) found that some
types of early intervention appeared to reduce the debilitating
impact of autism and those young children with autism may
make gains more quickly than young children with other severe
neurodevelopmental disorders. At present, early intervention
programs di ffer mar kedl y in terms of th e specific strat egies an d
interventions which are implemented. While the National Re-
search Council broadly recommends early intervention, they
also not e that less is known ab out the effi cacy of specific str at-
egies for facilitating learning in children with autism. In partic-
ular, little attention has been paid to developing programs and
evaluating treatment as related to academic skills and the
achievement of specific school readiness skills. While some
research has b een condu cted in the area of read ing, research on
strategies for teaching mathematics to students with autism is
limited (National Research Council 2001). A good example is
the study conducted by Stahmer, Collings, and Palinkas (2005)
where they wanted to provide data on early interventions prac-
tices in the classroom and they found special education teach ers
describing interventions related to speech therapy and occupa-
tional therapy/sensory integration. The study provided an im-
portant analysis of usage practices however; the authors rec-
ommended future investigations to gain a broader understand-
ing of methods and teaching strategies used in Early Childhood
Teaching mathematics is an important and critical area for
several reas on s. For one, with the advent of federal legislation
including No Child Left Behind Act (2001) there is an in-
creased focus on including children with special needs in gen-
eral education settings. All children are increasingly expected
to participate in high stakes testing and their sco r es ar e included
in school performance scores. Identification of effective ma-
thematical instructional strategies for students with autism may
facilitate success in both standardized testing and inclusion
within the regular classroom setting.
Prepare Students in Lif e Skills
Second, the ultimate goal of educating children with autism
(IDEA 2004) is to prepare students to achieve independence in
life functioning and become successful members of the com-
munity. Knowledge of basic math skills such as money, mea-
surement, and time are critical for independent functioning (Su,
2003). It is also necessary to p erfor m basic co mputatio nal math
for independent-living skills such as purchasing, banking, and
budgeting. According to Brown and Snell (2000) a key area of
academic instruction for students with multiple and severe
H. F. H. SU ET AL.
disabilities, including autism, is mathematics; functional math
enhances an individuals participation in daily routines and
increases opportunities for jobs, volunteer activiti es, and leisu re
enjoyment later in life.
Because of the considerable evidence that many students
with severe and multiple disabilities, including autism, have
difficulty acquiring knowledge of mathematical concepts, it is
important that educators use the most effective methods for
teaching students mathematical skills. Butler (2001) found in
their literature review of mathematics instruction that students
benefited from interventions emphasizing frequent feedback,
explicit instruction, and practice.
Strategies Used
Embedded instruction has also been suggested as one
strategy that could be used with young children with disabilities
in inclusive early childhood special education programs
(Harrower, 1999; McDonnell, Johnson, Polychronis, & Riesen,
2002). In embedded instruction, students are taught skills
within the ongoing routines of the classroom setting. Embedded
instruction is similar to traditional teaching fo rmats, the teacher
implements instructional procedures designed to support the
student's acquisition of the target skill. It differs in that the
instruction is distributed across the activities that typically
occur in the classroom setting rather than being presented one
after another with short intertriai intervals. This is accomp-
lished by presenting the instruction when teaching opportunities
occur naturally during activities like music, movement, art,
cooking, circle time, transition activities and outdoor play.
Object ive of Study
The objective of this study is to evaluate the impact of sys-
tematic instruction in mathematics on preschool children with
autism. Specifically, this study will aim to answer the follo wing
Does systematic instr uction in mathematical co ncepts, u ti-
lizing direct and embedded instruction, lead to increased
knowledge of mathematical concepts and the language of
mathematical concepts in preschool-aged children with
What are the relative cont ributions of cogni tive and visual
spatial abilities on the ability to acquire knowledge of ma-
thematic al concepts?
How does t he rate o f acquisi tion of mathematic al con cepts
made by students with autism compare to the rate of
progres s made by same-aged, typically developing peers?
What modifications to the Project MIND Math Is Not
Difficult® mathematics activities are useful when teaching
mathematical concepts to students with autism?
Methodological Design/Data Analysis of
Four preschool classes serving students with high-function-
ing autism (> 70 on measures of cognition) at the Pre-school
were selected to participate. Two of the selected classes were
those which exclusively served students with autism. The other
two class es were int egrated presc hool class rooms which served
students with autism as well as typically developing peers.
For the purpose of this study, one autism class and one inte-
grated class were randomly assigned to a study group. The
other two classes served as the control group. In all, 25 students
with autism and 10 typically developing peers participated in
the study.
Pre-training: Prior to implementation of mathematics instruc-
tion, al l teachers recei ved inst ruction and training on u sing The
Project MIND approach (Su, 2002) a multi-sensory math cur-
riculum, and on direct instruction of math. Classroom teachers
participated in after-school training sessions from September
through January and received frequent coaching visits and
support by project staff to trouble shoot, provide resources, and
to insure the curriculum was properly implemented.
Treatment: For students in the study group, systematic in-
struction in mathematics using strategies based on The Project
MIND approach was implemented for a period of 3 months.
Systematic instruction was provided using both direct and em-
bedded instructional strategies teaching mathematical concepts
such as number sense, an d numerical operation s .
For direct instruction, students participated in 15-minute,
teacher-led instruction sessions daily. Specific objectives taught
were individually determined based on the results of pre-as-
sessment data and student’s performance level in mathematics
at the time of the study.
For embedded instruction, mathematical instruction was em-
bedded into a variety of preschool activities including music,
movement, art, cooking, circle time, transition activities and
outdoor play utilizing strategies described in th e Project MIND
approach. The base 10 concept was taught through pairing up
number “buddies” (Figure 1).
The students were taught the base ten concepts utilizing a
multi-game approach. Students used number tiles to match up
numbers which add up to ten (Figure 2). This lays the founda-
tion for algebraic thinking. The students were asked, “Who is
4’s b est friend?” Then a number senten ce was constru cted (e.g.
4 + ____ = 10) or (_____+ 8 = 10).
Figur e 1.
Best friend large number tiles.
H. F. H. SU ET AL.
Concept building continued with a game called “Object Grab
Game” (Su, 1988). Students were given three different methods
to identify a number objects, number cards, pictures cards
(concrete, semi-concrete, abstract) (Figure 3) and (Figure 4).
When prompted, students used any of the three ways to identify
the number. For example, the teacher calls “7,” the student
must quickly find its best Friend 3 using the objects, number
cards, o r picture card s. If the emphasi s was on abstract thinking,
then the student who used concrete objects to identify the best
friends would receive the highest points.
Students were also given everyday objects to compare (Fig-
ure 5) and (Figure 6). Here students identified the larger, small-
er, shorter, and or longer of the two objects.
One of the mo re difficult skills that the stu dents were able to
accomplish was to insert missing numbers when given a se-
quence of numbers. For example, _____, 8, 9 (Figure 7) and
(Figure 8).
Figur e 2.
Number tiles.
Figur e 3.
Object grab game.
Figur e 4.
Student selects a strategy to respond.
Figur e 5.
Longer or s horter.
Figur e 6.
Larger or smaller.
H. F. H. SU ET AL.
Figur e 7.
What number is missing?
Figur e 8.
Students worked o n double digits.
The Design
A quasi-exp e rimental, pre- and post- with control group de-
sign was used in the study (Shadish, Cook, & Campbell, 2002).
In this design, both the study and control groups were given
pre- and post-mathematics achievement tests using sub-tests
from the Hawaii Early Learning Profile (HELP) (which as-
sesses a student’s mathematical reasoning and problem solv-
in g), an d t h e B r ac ken Ba si c Co n ce p t S c al e Revised (BBCS-R),
(which assesses student’s knowledge of the language of mathe-
matical co ncepts).
Analysis of Covariables
In addition to a pre- and post-test comparison, students were
assessed (prior to intervention) on their cognitive and visual-
spatial abilities. Cognitive abilities were assessed using the
Mullen Scale of Early Learning (MSEL), a comprehensive,
individually administered measure of cognitive functioning.
Visual-spatial abilities were assessed using the Beery Deve-
lopmental Test of Visual Motor Integration (VMI). The VMI
and the M SE L were used t o id entify the r elati ve ef fects o f these
variables on acquisition of knowledge of mathematical con-
Statistica l A nalysis
The Wilcoxin Signed Ranks Test was used to test for a sta-
tistical ly significant difference b etween pr e and post t est scores
in stud ents’ mathe matical concep ts, rel ative effects o f cognit ive
ability, and visual spatial ability when exposed to systematic
instruction in math. The comparison of the scores of mathe-
matics and cognitive funct ioning between the st udy and control
groups were made using the Mann-Whitney U test for continu-
ous data and the Chi Square test for discrete data. Additional
descriptive trend analyses were used to demonstrate the time
series data of each outcome variable. For every test that was
conducted, the significance level was 0.05. Statistical analysis
was performed using the Statistics Package for Social Science
(SPSS) software program.
Statistically significant differences between pre and post test
scores indicated that students with high-functioning autism
were able to increase knowledge of mathematical concepts
when exposed to systematic instruction in math. In addition, a
significant difference between the study and control group
showed that systematic instruction in mathematics accelerated
learning as compared to student’s educated within the guide-
lines of their typical preschool curriculum.
Statistically significant differences in acquisition of math
skills between students with autism and students without autism
revealed patterns about the acquisition of math among students
with autism. If typically developing peers acquired math skills
more readily than students with autism, then results yielded
evidence that autism impaired student’s ability to acquire aca-
demic skills.
The Mann-Whitney U test was primarily used in this study
due to a relatively small sample size in this pilot study. In the
paper base assessments, the results show that a significant dif-
ference was observed between the study group (with project A+
intervention) and control group (without intervention) in the
overall M ullen score (Man n-Whitn ey U, P = 0.000). I n particu-
lar, a significant difference was shown on all subtests of the
Mullen test including visual test (Mann-Whitney U, P = 0.002),
fine motor test (Mann-Whitney U, P = 0.000), expressive lan-
guage test (Mann-Whitney U, P = 0.002), and receptive lan-
guage test (Mann-Whitney U, P = 0.001). A statistically signi-
fycant difference was also found on the H.E.L.P. mathematics
scale (Mann-Whitney U, P = 0.036) between the study group
and control group after intervention. Further, we used the Wil-
coxon Signed Rank test to compare the pre- and post-int e rven-
tions of each test scores to those children with autism assigned
to the study group. A significant improvement was shown only
on the H.E.L.P. mathematic test (Wilcoxon Signed Rank, P =
Prior to the start of the project, we anticipated several chal-
The teachers in the study group may potentially share in-
H. F. H. SU ET AL.
formation with teachers of the control group. Therefore,
teachers in both groups agreed (in writing) not to share
teaching strategies during the study period.
Parents may request switching from the control group to
the study group. For this reason, parents had agreed (in
writing) to the guidelines of the study.
Potential attrition of student participants poses a concern.
Therefore, any child leaving the center before the project
is completed was assessed at the time of departure (when
possible) to determine progress, using the assessment in-
strument d esigned by the researc h team. In our study, thir-
ty-four pre-school students with autism and their inte-
grated, typically developing peers received 3-months of
mathematics instructions during their regular school day.
Implication of the Study
Results from this pilot study will h elp reform the way special
and general educators provide mathematics instructions to
young children with autism. The strategies can be replicated in
other programs serving students with autism. The second stage
of the study will include older students with autism, and those
with concomitant intellectual disabilities. School districts will
be able to implement the program in a variety of classrooms
serving children with autism and other severe disabilities.
Acknowledgement s
We wish to thank Dr. Wendy Masi, who allowed the study to
be carried out at the Mailman Segal Institute of Nova South-
eastern University. Dr. Masi was the former Dean of Mailman
Segal Institute for Early Childhood Studies. We also wish to
thank the co-principal Investigato rs of the study, Dr. Melissa N.
Hale, Mi chel e Kapl an, and Dr . Sue Kabo t for their as sistan ce in
selecting sample groups, adjusting activities to help fit the
needs o f the stu dent s, and execut ing assess ments an d col lectin g
assessmen t d ata o f the studen ts invol ved. We are grate ful for al l
the assistance and guidance provided by the Institute.
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