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Dyscalculia:

Math and Learning Disabilities in
Education

Pati Brown

Math G, Final

Dr. Ian Walton

30 November 2009

Table of Contents

Introduction. 1

Catherine’s Story. 2

Learning Disabilities:  The ABC’s and the 1, 2, 3’s. 4

What is Dyscalculia?. 6

Advice to Parents. 9

Building a Healthy
Relationship with Numbers. 9

If You Suspect a Math
Learning Disability. 10

A Visit to the
Pediatrician. 10

Testing. 11

Advice to Adults. 12

It’s Not Too Late. 12

Don’t Give Up. 13

A Look at the Education
System.. 14

Conclusion:  Healing a Wounded Educational System.. 16

Works Cited. 20

Images Used. 22

Dyscalculia:

Math and Learning Disabilities in Education

Introduction

There was little known about math anxiety until 1978 when Sheila
Tobias wrote her groundbreaking book: Overcoming
Math Anxiety.  Indeed, math anxiety
is a real issue that has a significant impact on millions of people.  It is usually triggered by a traumatic
experience in a math class in elementary school and eventually results in
underperformance in mathematics and poor self esteem; and though math anxiety stands
alone as a serious issue, it is also a symptom of an educational system that
doesn’t fully embrace different learning styles or clearly understand learning differences.

While researching
this paper, I was astonished to find the research on dyscalculia and math
learning disabilities still in its infancy; in fact it wasn’t until earlier
this year that I even heard the word dyscalculia. The first evidence of
epidemiological studies of dyscalculia I could find was a study performed in
Slovakia in 1974.  It wasn’t until 1983
that the epidemiology of mathematical disorders was studied in the United
States by N.A. Badian, and after Badian’s research another 20 years passed
before any other documented studies were published.  What is promising however is that since the
early 1990’s we are seeing a more steady flow of research coming from not only
the United States, but other parts of the world, such as Europe and India.[1]

This paper
defines dyscalculia, explores its causes, ways to manage it, and its impact on
those who have it.  Additionally, this
paper looks at what the mainstream mathematics classroom can learn from special
education techniques.

Catherine’s Story

Catherine is in
her mid-forties and her difficulties in learning math have held her back
throughout her life.  She decided to
return to school to complete her AA degree:

“…I
received a letter [from my college] stating that I am not eligible for a
degree, [though I had just] walked across the stage in cap and gown.  I have taken five Algebra classes in two
years.  I have never worked harder at
anything in my life only to come away with an “F.”  I had perfect attendance; I went to the math
lab for a minimum of two hours after class, did my homework every night.  [In one class] I even went to the professor’s
home for tutoring.  Before failing these
math classes my GPA was 3.7, I was awarded the Academic Achievement Award in
recognition of my accomplishments.  I am
beyond frustrated.”[2]

Catherine is not alone.  She not
only suffers from a learning disability in mathematics, but additionally
suffers from a poorly structured system that neither understands her
frustration nor offers much help.  The
system fails to see the incongruity of her situation.  Students who achieve academic awards and
maintain 3.7 grade point averages don’t repeatedly fail math classes because
they aren’t trying or because they have math anxiety alone.  These students have fallen into a dark void
in our educational system.  Students like
Catherine often can’t get into four-year universities without meeting specific
math requirements.  While trying to take
math classes they will never be able to pass, they often experience severe
anxiety and depression, ending up with a string of failures, disproportionately
lowered GPA’s, and facing closed doors to higher education.

What does
Catherine do?  Does she continue to take
math classes, knowing she will continue to fail and her GPA will suffer?  Does she drop out of school and give up her
dream of a bachelor’s degree? It seems the roadmap to college success excludes
those with mathematics learning differences.
Realistically, someone who suffers from dyscalculia – or even a less
severe math learning difference – isn’t likely to enter a profession that requires
higher mathematics skills.

Our classrooms are
seeing many students like Catherine, students with extremely high intelligence
who underachieve in math.  As soon as
they hit a certain discipline or level of math, their brains seemingly cease to
function efficiently and they are left behind as their classmates forge
forward.  Math comes more easily to their
peers, but for some reason their brain is different, they lag behind, and are
eventually labeled an “under-performer” or “slow.”  They experience embarrassment, fear, and will
do almost anything to avoid doing math.

Learning Disabilities:  The
ABC’s and the 1, 2, 3’s

It has long been thought that if a person is good with reading and
language skills they should have no difficulties in math.  Historically there has been far more research
done on children who experience difficulty in reading than in math.  Currently reading scores are used to compute
discrepancies in ability-achievement, but math scores are seldom used.  Because of this misinformation, many who have
issues learning math are passed over and fall through cracks in the
system.  Imagine the conflicted feelings
of a child who does well in all subjects, only to get into a math class and
find they just can’t do the work.[3]

Studies in dyslexia
– a condition that affects a person’s ability to read and write – were originally
noted in Germany in the 1860’s in patients who suffered brain or cerebral
vascular      injuries.  By the turn of the 20th century,
physicians began to see that dyslexia – or “word-blindness” – was sometimes
apparent in children who never experienced brain injuries.  It was in the early 1900’s that dyslexia was
acknowledged as a congenital defect.[4]

Conversely, there
is much less known about dyscalculia than dyslexia; our collective knowledge
bank is still anemic in what it knows about the cognitive skills that serve
mathematics learning.   Studies in
dyscalculia are currently where dyslexia studies were thirty years ago.  We know that children with limited spatial
abilities suffer limited geometry skills.  And those with poor auditory and visual memory
can’t achieve success in math if they can’t remember the numbers.  Additionally we know that language abilities
do play an important role in solving math problems in double-digit addition.

Let’s look at the
example below:

3

9

+

2

6

6

5

This problem involves at least five
steps which require language ability to process:

1.
Add the 9 and the 6 to get the answer 15

2.
Write the first digit for the answer “5” under
the “6”

3.
Hold the 10’s place digit “1”

4.
Write that digit above the “3”

5.
Add the three digits in the 10’s column

As straight-forward as this problem
seems, it is very complicated for a child with math learning disabilities.  And the math problems only become more
complicated as he gets older.[5]

What is Dyscalculia?

Perhaps part of
the misunderstanding in the treatment and education of those who have
dyscalculia is the lack of a consistent definition.  There seem to be as many definitions of
dyscalculia as there are sources for those definitions.

The Diagnostic and
Statistical Manual of Mental Disorders, fourth edition (DSM-IV) is the standard
psychiatric handbook used in the United States.
This handbook gives the following diagnostic guidelines for “Mathematics
Disorder”:

“Mathematical ability, as measured by
individually administered standardized tests, is substantially below that
expected given the person’s chronological age, measured intelligence, and
age-appropriate education, which significantly interferes with academic
achievement or activities of daily living that require mathematical ability.”

(American Psychiatric
Association, 1994, Section 315.1) [6]

This is a sterile
and inaccurate definition, one that isn’t adequate to sort out those who have a
math learning disability from those who had an exceptionally bad teacher or who
experienced situational problems in their life at a crucial time in their math
education.

Researchers Karin
Landerl, et al, define dyscalculia as a deficiency in the number module in the
brain.[7]  Additionally, researchers from Bed-Gurion
University in Israel state that those with developmental dyscalculia usually
have difficulty keeping their attention on task as well as difficulties
processing numbers.[8]  In yet another limited but comprehensive study
of 7 children in Israel, researchers Ruth S. Shalev and Varda Gross-Tsur found
neurological conditions present in addition to dyscalculia.  The conditions they recognized were petit mal
seizures, Gerstmann syndrome, number dyslexia, and attention deficit disorder.[9]

Perhaps the best,
most comprehensive definition of dyscalculia comes from neuropsychologist,
Brian Butterworth, and is included in the evaluation test he developed
specifically for dyscalculia, the Dyscalculia Screener. In this text Butterworth
describes dyscalculia, sometimes called “number-blindness,” as a persistent
congenital condition.  He quotes the
Department of Education in Great Britain:

“[Dyscalculia] is a condition that affects
the ability to acquire arithmetical skills.
Dyscalculic learners may have difficulty understanding simple number
concepts, lack an intuitive grasp of numbers and have problems learning number
facts and procedures.  Even if they
produce a correct answer or use a correct method, they may do so mechanically
and without confidence.” (Butterworth’s Dyscalculia Screener)  [10]

Researchers differ
slightly in their definitions of dyscalculia and the reasons for it.  Some believe dyscalculia is a result of
congenital deficiencies, others believe it results from delayed rather than
abnormal development,[11]
and still others believe there is a sort of pseudo-dyscalculia,
a result of poor math instruction.[12]
However all agree that many experience
a serious problem developing proper math skills.  There is significant evidence that many
children with dyscalculia experience other learning disabilities as well.  Butterworth estimates that between 3.4% and 10%
of the population suffers from dyscalculia (as defined in DSM-IV).  This is a significant portion of our
population.

Advice to Parents

Building a Healthy Relationship with Numbers

A deficit in math
can affect many academic skills.
Therefore it is very important to maintain frequent and open
communication with your child and
your child’s teacher about school, and particularly about math.  Look for signs of stress when your child
brings math work home, and be careful not to feed into your child’s math stress
by getting angry or telling them how much you hated math as a child.

Listen to what
your child has to say about math, and watch how they problem-solve.  Are

they counting on their fingers when they should know how to mentally
count?  Are they being taught
multiplication before they fully know how to add and subtract?  Be sensitive to how they feel about going to
school in the morning.  Do they feel sick
often or complain about having to go to school?

It is also
important to understand that teaching to different learning styles can be very
anxiety-provoking for some teachers.  If
you sense that your child’s math teacher is not a good fit, get your child help
immediately.  Speak with the principal to arrange for
alternative teaching or classroom options.
Understand that a strong foundation in mathematics plays a vital role in
your child’s lifelong educational success, and most importantly, her
self-esteem.

If You Suspect a
Math Learning Disability

First, speak with
your child’s teacher.  What behaviors has
she observed in your child in relation to math lessons?  Has she seen evidence of any of the
following?

·
In addition to problems in math, are there
observed issues in listening, speaking, reading, writing, or reasoning?

·
Is your
child’s general intelligence higher than his performance indicates?

·
Does the child withdraw or daydream during math
lessons?

·
Does she hear what the teacher says and then
immediately forget?

·
Does she have trouble retaining a concept she
once understood?

·
Has the child developed escape behaviors like
tantrums, depression, difficulty starting or completing homework, or inattention?

A Visit to the Pediatrician

Have the following evaluated by your child’s pediatrician:

·
Birth history

·
Medical history

·
Developmental and behavioral history

·
Family and social history

·
Physical examination to determine prenatal,
genetic, or environmental risk factors

·
Evaluation from teacher and educational
professionals

·
Hereditary factors such as dyscalculia present
in a parent or sibling

·
Sleep habits[13]

Testing

If
your child’s teacher believes he has a learning disability, she may request
professional testing.  Testing is the
tool that gives educators guidance in attaining accommodations for your
child.  The accommodations a child
receives are aimed at changing the educational experience for the better,
relieving the stress and imparting skills designed to help children compensate
for their disabilities.

From Butterworth’s
Dyscalculia Screener

Though highly specific information on testing is beyond the scope of
this paper; I have discovered two tests that are comprehensive in diagnosing

dyscalculia.  The first is Brian Butterworth’s Dyscalculia
Screener.  The Dyscalculia Screener is
designed as a quick and reliable way to isolate dyscalculia from other causes
of poor understanding of numbers.  The
Screener uses timed tests to measure the capacity for numerosity, thus
minimizing the effects of educational influence and giving a true sense of how
well numbers are understood.[14]

Another battery of
tests aimed specifically at identifying problems with number processing is the
Neuropsychological Test Battery for Number Processing and Calculation in
Children (NUCALC). This test “assesses counting, dictation of numbers, mental
calculations, reading numbers, positioning of numbers on an analog scale, oral
and written comparisons of number pairs, and number and contextual estimation,
and problem solving.”[15]

Advice to Adults

It’s Not Too Late

Many students make their way through high school without even being
diagnosed with a learning disability.  By
the time these students reach college, their learning disability has often
combined with math anxiety and created an obstacle that is seemingly impossible
to maneuver.  Some simply give up and
drop out of school despite their high intelligence level.  These scenarios are neither uncommon nor are
they impossible to deal with.

Unfortunately,
getting through college with a learning disability isn’t easy, but you are your
own best advocate.  Carol Toppel,
Learning Specialist at Mission College, encourages students to understand the
emotional component of math learning disabilities, and to go back and review their
math knowledge to see what skills have been lost or never learned.  She stresses how easy it is to fall behind in
math because mathematics lessons build on the essence of skills that are taught
sequentially.  If a student forgets or
never learns a basic skill, they can suffer anxiety that looks exactly like a
learning disability. [16]  An evaluation with a disabilities specialist
can differentiate a learning disability from math anxiety or trauma resulting
from concepts missed during early education.

Every college or
university has a department dedicated to students with learning
disabilities.  If you suspect you have
dyscalculia or an undiagnosed learning disability, contact the disability
services office of your college and ask to meet with a counselor.  You will find a place that understands your
situation and offers free testing, emotional support, and proper accommodations
to help you though the classes you find difficult.  The disability services departments in
colleges employ counselors and tutors who are highly trained in a variety of
learning differences in addition to dyscalculia.  The accommodations you may receive as a
result of a learning disability include: extended time for tests, note-takers,
counseling, priority registrations, and tutors trained to work with students
with learning differences,

Don’t Give Up

Catherine, whose interview appears in the beginning of this paper,
isn’t giving up.  She has experienced
considerable disappointment and remains frustrated, however she is not giving
up until she receives her degree.  This
means writing letters, meeting with counselors and professors, and gathering as
many advocates within the college system as she can.  It is unfortunate that students like Catherine
have to go through so much red tape to attain the goals that come easily to so
many other students.

For students that
continually fail math classes despite using special accommodations, some
college counselors may be able to help students find alternative classes that
build a similar skill-set taught in a math class. Unfortunately this is a
difficult process and not always possible.
Some four-year universities may waive math requirements only when a
student repeatedly fails math classes, but again only after suffering
substantial failures in the classroom and a diminished GPA.

A Look at the Education System

Indeed there seems to be more of a problem in the educational system
than with the special-needs student. There needs to be more variety in course
selection within math departments.  Math
education has historically followed the path of the “average” learner, and
awkwardly and reluctantly bends itself to accommodate those who learn
differently.  However even within the
realm of “normal” we have a broad spectrum of learning styles.  When only one style of learning is
acknowledged, some students don’t learn as well – or at all.  Howard Gardner, a neurologist and professor
in the Harvard Graduate School of Education, developed a “theory of multiple
intelligences” based upon the evolution of humans to perform using different
forms of analysis.[17]

The following is a list of the
intelligences noted by Howard Gardner:[18]

Linguistic/Verbal
intelligence (as in a poet); has strong language skills, excels in
reading, speaking, and vocabulary.

Logical-mathematical
intelligence (as in a scientist); reasons logically and mathematically,
recognizes patterns and enjoys puzzles and experiments.

Musical/Rhythmic
intelligence (as in a composer); possesses strong appreciation of music
and aptitude for creating music; remembers sounds and rhythmic patterns.

Visual/Spatial
intelligence (as in a sculptor or airplane pilot); thinks in pictures and
understands relationships between objects in space.

Bodily
kinesthetic intelligence (as in an athlete or dancer); uses body with
skill and grace, makes things with hands, excels in sports, dance, and
communicating in body language.

Interpersonal
intelligence (as in a salesman or teacher); embraces strong understanding
of others feelings and desires.

Intrapersonal
intelligence (exhibited by individuals with accurate views of themselves);
has a solid understanding of inner feelings and desires.

Naturalist
Intelligence; has the ability to identify plant life and animals in
nature.

Carrying Gardner’s theory into the classroom provides us insights
into new ways to acknowledge and teach a variety of learners or all ages.  If we know how a student learns, we can
present materials in an engaging manner.
For instance, a linguistically oriented student does well with words and
word problems, a logically oriented learner enjoys forming concepts and looking
for patterns and relationships, someone who is musically oriented enjoys rhythm
and melody.  Likewise kinesthetic
learners learn by using physical manipulatives and games and the
interpersonally oriented student likes to work in with others in groups.[19]
In addition to effectively teaching
students without learning differences, teachers who are well-versed in
educational styles can more easily spot dyscalculia in the classroom

Just because
students advance in school, doesn’t mean all learning styles merge at a given
time.  Even in colleges, students learn
differently.  Perhaps if all schools
committed to teach to the student, we
would see fewer cases of math anxiety disguised as a learning disability, and
those with learning disabilities would find efficient ways to learn that were
acceptable in the mainstream classroom.

Conclusion:  Healing a
Wounded Educational System

In an interview on Dystalk.com, Matthew Taylor, Chief Executive of
the Royal Society for the Encouragement of the Arts in the U.K. and former
advisor to Tony Blair, gives an insightful approach for improving the school
system in Great Britain.  His approach is
well worth noting for schools in the U.S. as well.  In the Dystalk.com interview, Mr. Taylor
encourages the government to “build a school system around the needs of the
child rather than the child having to have their provision built around the
rigidities of the system.”   Further, he
says that if we fail the special-needs children, we fail the society, and will
eventually end up with an entire society of struggling children who become
struggling adults.

Taylor points out
that special-needs children aren’t getting “Cinderella service” in their
educations; they are getting accommodations that are as important in mainstream
schools as they are in special-education environments.  What special-needs programs understand is the
“complex and… plural nature of children’s abilities,” they don’t just look at
the child who fits the “normal” model, rather they have to look at the whole
child and how that child learns.  Special
education works because it breaks the narrow focus of limited learning styles;
this style of teaching can only enhance the mainstream educational process.[20]

There is no arguing that math is an essential part of a balanced
education – yet how do we manage to get intelligent students who struggle with
math successfully through school, and give them equal opportunities in higher
education?  There is plenty of evidence
that suggests early signs of difficulties in math should be addressed
immediately.  Indeed too many students
fall through the cracks.  With enormous
budget cuts and teachers stretched to near breaking points, it’s time to
seriously consider not just how many
we teach, but how we teach.  Not only do we need more research on
dyscalculia and its detection, but we need additional research and curriculum
for training teachers that stresses the many differences in how our students
learn.

Math is a subject that is normally taught once a day, yet students
read constantly throughout the day.
Since students learn math differently, they require sufficient
non-threatening reinforcement in math throughout the school day.  Teachers in mainstream classrooms can find
ways of incorporating mathematics throughout the day by using games, music, and
other techniques to help students with a variety of learning styles
thrive.  It is also vital for teachers to
maintain strong communication with parents, alerting them to any potential
problems in math processing that a student may be experiencing. When students
are diagnosed with dyscalculia, they require special accommodations as soon as
possible.  Teachers and parents must
understand that, if not treated properly, math can erupt into an emotionally
charged subject that has the potential to limit a child for life.

Additionally,
universities and community colleges need to develop math courses that build
math thought-processes and linear thinking in a variety of ways, while helping
students with learning differences attain college degrees.  Perhaps algebra isn’t the only way.  A course like Math G., an overview of
mathematical principals and theories, is a wonderful way to teach math.  Likewise there must be a multitude of options
for math classes based on theories and mathematical history.

Finally, prevention of math anxiety is of critical
importance, and teaching to a variety of learning styles is sure to foster
positive math experiences.  If we have a
country that is falling behind in math, we need to examine and mend our broken
education system.  Millions of people
experience math as a subject that exists within a barbed wire cage.  In order for this outlook to change, our
system has to change.  We have to learn
to separate the learning disabilities from the anxiety disabilities. And it is
vital to diagnose and develop early treatment programs for those who suffer
dyscalculia in order to support and foster healthy “math esteem.”

Works Cited

Bender, William
N. Learning Disabilities:
Characteristics, Identification, and Strategies. Needham Heights:
Allyn & Bacon, 1995. Print.

Berch, Daniel
B., Ph.D., and Michele M.M. Mazzocco. Why Is Math So Hard for Some Children?
The Nature and Origins of Mathematical Learning Difficulties and Disabilities.
Baltimore: Paul H. Brookes Publishing Co., 2007. Print.

Butterworth,
Brian. Dyscalculia Screener. London: NferNelson Publishing Company
Limited, 2003. c2k Schoolbox. Web. 15 Nov. 2009.
<http://c2kschoolbox.granada-learning.com/‌pdf/‌manuals/‌Specialmanuals/‌Dyscalculia_Screener_Manual.pdf>.

Butterworth,
Brian, and Brian Butterworht. What Counts:
How Every Brain is Hardwired for Math. New York: The Free Press,
1999. Print.

Catherine.
Personal interview. 13 Nov. 2009.

Curtain-Phillips,
Marilyn, M. Ed. Math Attack: How to Reduce Math Anxiety in the Classroom, at
Work and in Everyday Personal Use. Kearney: Morris Publishing, 1999. Print.

Gardner,
Howard, Ph. D. “Intelligence in Seven Steps.” Creating the Future. New
Horizons for Learning, 1991. Web. 15 Nov. 2009. <http://www.newhorizons.org/‌future/‌Creating_the_Future/‌crfut_gardner.html>.

Gwynn, Hilary,
M.D. “Learning disabilities:  the
pediatircian’s role (Special Needs: Realizing Potential).” Pediatric News
42.4 (2008) (2008): 32 (1). General OneFile. Web. 1 Nov. 2009.
<http://0-find.galegroup.com.catalog.oaklandlibrary.org/‌gtx/‌start/‌do?prodId=ITOF&userGroupName=oakland_main>.

Landerl, Karin,
et al. “Dyslexia and Dyscalculia: Two learning disorders with different cognitive
profiles.” Journal of Experimental Child Psychology (July 2009): 309+. General
OneFile. Web. 2 Nov. 2009.
<http://0-find.galegroup.com.catalog.oaklandlibrary.org/‌gps/‌start.do?prodId=IPS&userGroupName=oakland_main>.

“New
Communication Disorders Research Reported from Bed-Gurion University.” Biotech
Week 19 Aug. 2009: 735. General OneFile. Web. 2 Nov. 2009.
<http://0-find.galegroup.com.catalog.oaklandlibrary.org/‌gps/‌start.do?prodId-IPS&userGroupName=oakland_main>.

Shalev, Ruth
S., and VArda Gross-Tsur. “Developmental Dyscalculia and Medical Assessment.” Journal
of Learning Disabilities 26.2 (1993): 134-137. Sage Journals Online.
Web. 8 Nov. 2009. <http://online.sagepub.com/‌cgi/‌searchresults>.

Taylor,
Matthew. Interview. Dystalk.com. Dystalk.com, 2009. Web. 5 Nov. 2009.
<http://www.dystalk.com/‌talks/‌99-special-educational-needs-policy>.

Taymans,
Juliana M., Ph.D., Lynda L. West, Ph.D., and Madeline Sullivan, M.A. Unlocking
Potential: College and Other Choices for People with LD and AD/‌HD.
Bethesda: Woodbine House, Inc, 2000. Print.

Tobias, Sheila.
Overcoming Math Anxiety. New York: W.H. Norton Company, Inc., 1978.
Print.

Toppel, Carol.
Personal interview. 16 Nov. 2009.

Wiertelak,
Eric. “History of Dyslexia.” Dyslexia Homepage. Mcalester College, 30
Oct. 2003. Web. 15 Nov. 2009. <http://macalester.edu/‌psychology/‌whathap/‌ubnrp/‌dyslexia/‌history.html>.

Images Used

Open
Book/Introduction:

www.ehow.com

http://i.ehow.com/images/GlobalPhoto/Articles/5530396/3326060843178f99ba69_Full.jpg

Adult
Student/Catherine’s Story:

www.northweststate.edu

http://www.northweststate.edu/Community/images/adult_student.jpg

Dyslexia/Learning
Disabilities:

www.dyslexia-africa.com

http://www.dyslexia-africa.com/images/dyslexia-handwriting-pencil.jpg

Anxiety/What is
Dyscalculia?

www.schools.tdsb.on.ca

http://schools.tdsb.on.ca/jarvisci/jargonline/2006/ArticleImages/Dyscalculia.jpg

Crying Student/What is Dyscalculia:

www.About.com

http://z.about.com/d/learningdisabilities/1/0/Z/0/-/-/learning_disabilities.jpg

Adult and
Child/Advice to Parents:

www.dyslexia-teacher.com

http://www.dyslexia-teacher.com/teacher_with_boy1_smaller.jpg

Physician and Child/
A Visit to the Pediatrician:

http://www.siumed.edu/news/Photos-Graphics/Media/Batterman.jpg

Butterworth’s
Screener/Testing:

www.tatainteractive.com

http://www.tatainteractive.com/images/screenshot_nfernelson_big.png

Woman Studying/Advice
to Adults/It’s not Too Late:

www.cwti.org

http://www.cwti.org/images/pages/student.jpg

Getting a Boost/Don’t
Give Up:

www.greattraits.com

http://www.greattraits.com/images/perseverance2.jpg

Apple and
Spectacles/A Look at the Education System:

www.teacherpictures.com

http://teacherpictures.com/pictures-of-teachers.php

Dice/A Look at the
Education System:

www.ehow.com

http://i.ehow.com/images/GlobalPhoto/Articles/5331942/333766-main_Full.jpg

Teacher at Board/Conclusion:

www.teacherpictures.com

http://teacherpictures.com/pictures-of-teachers.php

Student/Conclusion:

www.todaysdrum.com

http://blogs.edweek.org/teachers/living-in-dialogue/upload/2009/04/racebased_test_prep_rallies_an/students-taking-test.jpg

Math Class
Board/Conclusion:

www.aaamath.com

http://www.aaamath.com/cd/cover4.jpg

Happy
Graduate/Conclusion:

www.stourbridge.ac.uk

http://www.stourbridge.ac.uk/info/news/images/access-to-h-e.jpg

[1] Daniel B. Berch, Ph.D., and Michele M.M. Mazzocco. Why
Is Math So Hard for Some Children? The Nature and Origins of Mathematical
Learning Difficulties and Disabilities. Baltimore: Paul H. Brookes
Publishing Co., 2007. Print.

[2] Catherine. Personal interview. 13
Nov. 2009.

[3] William N. Bender. Learning Disabilities:  Characteristics, Identification, and Strategies.
Needham Heights: Allyn & Bacon, 1995. Print.

[4] Eric Wiertelak. “History of Dyslexia.” Dyslexia
Homepage. Mcalester College, 30 Oct. 2003. Web. 15 Nov. 2009.
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