ThesisProject-Completedpaper

MOVEMENT PATTERN AS MATH INTERVENTION 1
Running Head: MOVEMENT PATTERN AS MATH INTERVENTION
Cross Lateral Movement Pattern as Math Intervention
A Collaborative Action Research Study Thesis
By
Robert Eric Ellingsen
Concordia University Irvine, California
School of Education
Submitted in Partial Fulfillment of the
Requirements for the
Degree of
Master of Arts in Education
in
Educational Administration
April, 2015
Faculty Advisor Dr. Francine Stewart

Chapter 1
Problem
American public education has been perceived to be in crisis since the publication of A
Nation at Risk in 1983. Pundits rebuke public education as having failed American children.
The most recent data from the National Assessment of Educational Progress (2013) seems to
confirm this. The NAEP is a biannual measure of students knowledge and skill in
English/language arts and mathematics in grades 4, 8, and 12. In 2013 nearly two-thirds of
fourth graders and eighth graders failed to reach the level of proficiency in mathematics. More
than half of fourth graders could not accurately read the scale of a thermometer. Seventy-five
percent of fourth graders could not solve a simple word problem requiring them to add double
the amount to the original amount (Green, 2014). The 2013 California Standards Test in
Mathematics displays similar results. Just over half of California students scored proficient or
advanced (California Department of Education [CDE], 2013).
Since the Soviets launched Sputnik in 1957 Americans have been grappling with how to
improve mathematics instruction. The New Math movement of the 1960s, epitomized by the
School Mathematics Study Group out of Yale University, sought to shift mathematics from the
memorization of formulas to abstract reasoning (Phillips, 2014). The 1980s was the era of brain
compatible instruction with its emphasis on children creating meaning (Hart, 1983). These
attempts to reform mathematics instruction were met with confusion and a return to traditional
methods.
No Child Left Behind in 2001, the Common Core State Standards initiative in 2008, and
Race to the Top in 2009 are the most recent federal programs to reform public education. With
the emphasis on high-stakes standardized testing, schools have invested more and more time on

academic instruction, teaching only those skills being tested. The result is that an already
sedentary student body has only become more so. Only 42% of school-aged children get the
recommended 60 minutes of physical activity recommended (Erwin, Fedewa & Soyeon, 2012).
When a student is dependent only upon a school setting for that physical activity, the opportunity
declines greatly: In 2006, 4% of elementary schools, 8% of middle schools, and 2% of high
schools provided daily physical education (Centers for Disease Control [CDC], 2010).
Historically, motor development and cognitive development have been studied
separately. They have been seen as independent phenomena. Cognitive development was seen
as the last aspect of mental development. But the development of the prefrontal cortex and the
neocerebellum proceed in a parallel fashion through adolescence. Motor functions and mental
functions are more intertwined than has been previously understood. Most cognitive tasks that
require the prefrontal cortex also require the neocerebellum (Diamond, 2000). All learning is
performatory, thus learning, by necessity, requires the active engagement of the neocerebellum
(Rosenbaum, Carlson & Gilmore, 2001).
In 2010 the Centers for Disease Control and Prevention reported 50 studies on the impact
of physical activity (including physical education classes) on academic achievement and
academic behavior. Of all the associations examined, slightly more than half were positive, 48%
were not significant, and only 1.5% were negative. One part of the report is especially applicable
to this research. Nine of the studies focused exclusively on physical activity within the
classroom: activity breaks of between five and twenty minutes. Eight of these studies (88%)
found positive associations between classroom based physical activities and cognitive skills
(CDC, 2010).
There is an abundance of research touting the relationship between physical activity and
cognition. The benefits begin with certain physiological processes: increased blood flow to the
brain, increased mental arousal, increased production of neurotransmitters, and even structural

changes in the central nervous system. However the benefits of movement are not only
physiological. Movement is intricately connected to brain development separate and apart from
the physiology of movement (Sibley & Etnier, 2003). Thus, regardless of physical and health
benefits, the movement itself makes a difference, not just the physical exertion. Crossing the
midline (i.e. left hand to the right side of the body and vice versa) is a developmental milestone.
The inability to attain this developmental milestone is called midline crossing inhibition and is
prevalent in children identified as learning disabled (Surburg & Eason, 1999).
James R. Bloedel and Vlastislav Bracha (1997), in their research paper “Duality of
Cerebellar Motor and Cognitive Functions” best summarize the conclusions made by this wealth
of research: “There is not movement without cognition and there is not cognition without
movement.” (p 620)
Despite the research supporting the link between the cerebellum and cognitive thought
and despite the clear need for a reform of traditional instructional practices evidenced by
standardized test scores, interventions are rarely physical. In the 2012-13 academic school year,
a local school district implemented Response to Intervention (RTI) as a pedagogical approach to
improve academic achievement. RTI provides early, systematic, and intensive assistance to
students at risk or with established skill deficits. Of the interventions promoted on the Response
to Intervention website, none involve the bodily-kinesthetic intelligence (Intervention Central,
2014). It is time to consider a more holistic approach to academic interventions, one in which
mind and body are integrated, what happens to one happens to the other.
Given that bodily kinesthetic interventions are rarely used despite the preponderance of
evidence as to the benefits, the purpose of this study is to design an intervention that links
movement to cognition. The hypothesis is that the intervention will have a measurable effect.
Participants will include 64 3rd grade students from one California elementary school
with a demographic ratio of 44.7% Hispanic/Latino, 45.6% White, 9.7% Other (SARC, 2014).

Just over half of students come from socioeconomically disadvantaged home environments, as
measured by those students qualifying for free and reduced lunch. The school is in year four of
program improvement.
Researcher One is a curriculum coach in Santa Cruz City Schools and has 38 years
teaching experience working as a multi-subject teacher in elementary education, spanning grades
kindergarten through eighth. He has a bachelor’s degree in elementary education and a master’s
degree in curriculum and instruction. Researcher Two is a secondary mathematics teacher in the
Gilroy Unified School District with 8 years teaching experience working in grades seven through
twelve. She has an associate’s degree in mathematics and a bachelor’s degree in psychology.
Purpose of Study
The purpose of this study is to integrate cross-lateral movement patterns into mathematics
instruction and evaluate its effect in improving mathematical accuracy and fluency. We will
address the following research question:
Will the inclusion of cross-lateral movement patterns in mathematics instruction lead to
improvement of computational accuracy and fluency?
Teachers are a unique profession in that we are raised in the profession. We are interns
from the moment we first enter the classroom and each year our teachers become our models and
mentors. For that reason it is more difficult for us than for other professionals to shift to new
paradigms of practice. Our routines have become habitualized from a very early age. We have
been undergoing a period of educational reform for nearly half a century. Yet schools are still,
by and large, similar to what they were at the beginning of this process. Students are still
segregated by age, teachers still teach in isolated classrooms, periods of learning are still dictated
by time. These practices are major obstacles to reform and cannot be impacted by individual
classroom teachers. For the gestalt of education to shift, much greater societal and governmental

influences must be brought to bear. However, an individual classroom teacher can implement
reform in an individual classroom.
One of the ways teachers are apprenticed in the profession is our definition of appropriate
behavior. Despite the importance of movement and communication to the cognitive process, the
definition of being good in many classrooms is still students sitting still and being quiet. When a
student cannot sit still or be quiet, the student is labelled as bad, and that label often becomes part
of that student’s own perception of self. It is often these students who need to move and talk,
who have difficulty with academics. If they are referred to an intervention, that intervention
involves more of the same. The setting may have changed, the group may be smaller, but the
protocol often remains sitting still and being quiet. A student we shall call Alex best personifies
this disconnect. At the risk of being literary in an academic thesis, we nonetheless include a
poem that forms a key part of our personal reflection:
Quantifying Alex
By quantifying Alex
In reading he is a one
Have they determined yet how to measure fun?
In writing he is a two
Have they discovered yet how to glue
Disparate numbers into a child
A boy wonderfully wild
Resisting being styled
Into a three or a four
Dare I say more?
They say a five is where to be
Have they graphed yet how he loves to fly free
Beyond their artificial constraints
To a heaven peopled with saints
Fully alive and never measured
Instead being pleasured
By what is real
With a zest and a zeal
They will make the bells peal
By qualifying Alex

A student similar to Alex could possibly thrive in a classroom that purposefully puts into
practice the research concerning the relationship between physical activity and cognition in
children. The research begins in infancy when rhythmic movements accompany rhythmic
vocalizations (Iverson & Fagan, 2004). While motor impairment is not the most prominent
characteristic, autistic children, dyslexic children, and children with attention deficit
hyperactivity disorder generally have movement deficits (Diamond, 2000). Neuroimaging data
and cerebral lesion studies offer further evidence that movement should be given far more
credence when planning instruction: Portions of the prefrontal cortex associated with attention,
control, language, memory, and learning all have neural pathways connecting to the cerebellum
(Strick, Dum, & Fiez, 2009). For too long, the cerebellum has been relegated to the backwaters
of learning theory and educational practice.
This study has been designed to access the cerebellum and test the premise that linking
repetitious, coordinated motor activity to mathematics will result in improved achievement as
measured by objective evaluation. Three third grade classes will learn a complex movement
pattern. Once mastered it will be performed rhythmically to music daily at the onset of
mathematics instruction. Immediately after, a three-minute timed test of grade level appropriate
arithmetic covering the topics of addition, subtraction, and multiplication will be given or the
math lesson for the day will commence. Adhering to the California State Common Core
standards (2012), addition and subtraction will involve regrouping to the thousands place.
Multiplication will be knowledge of the basic facts. The test is designed to determine if accuracy
and fluency improve when preceded by a physical activity. While the skills being tested remain
the same, the computations will change on each test to control for the variable of mere
memorization of the sum, difference, or product. Tests will be administered, collected and
scored weekly to analyze for improvements in accuracy and fluency.

A corollary proposition is that concept formation also improves with physical activity.
The test as designed is measuring only accuracy and fluency. Might the benefits of physical
activity influence this larger sphere of understanding as well? The district being studied posts
mathematics benchmark scores each trimester. Second trimester marks are posted by the
beginning of the research project but third trimester marks will not yet be posted when the data
for accuracy and fluency is analyzed. Teachers will record observations of student learning in
journal format and those observations will be analyzed to determine whether concept
development in mathematics has also been impacted by physical activity.
Definition of Terms
Certain terms and their definitions will be used repeatedly during this research project:
Cognitive development refers to mental development: the processing of information, the
forming of concepts, the development of perception. In children, cognitive development is the
growing ability to think and understand (Schacter, Gilbert, Wegner, & Nock, 2014). Piaget
(1952) first formed his theory of cognitive development in the mid 20th century when he first
defined the developmental stages of children as sensorimotor, preoperational, concrete
operational, and formal operational.
The prefrontal cortex is that part of the brain critical for the complex cognitive activities
most associated with education. The cerebellum is the portion of the brain most closely related
to the brainstem and spinal cord. It acts as an intermediary between the autonomic and
cognitive neurological functions (Gray, 2008). Autonomic functions are those physiological
activities such as digestion and respiration not under conscious control. Historically the
cerebellum has been considered the center of all motor skills. But like the whole brain, the
cerebellum has continued to evolve. Research now shows that most thinking processes of the
brain require both the prefrontal cortex and the cerebellum. (Diamond, 2000). The term
neocerebellum is a term that describes that portion of the cerebellum that has continued to

involve in primates and humans (Medical Dictionary for the Health Professions and Nursing,
2012).
When researching physical education and physical activity there is a distinction made
between physiological mechanisms and developmental mechanisms. Physiological benefits to
cognition relate to changes brought about by exercise such as increased blood flow, heightened
mental arousal, and increased production of neurotransmitters. Both physical education and
physical activity create these physiological benefits. For the purpose of this study, physical
education refers to an actual curriculum concerned primarily with benefiting student fitness and
health. Recent research also confirms the cognitive benefits of physical activity. Physical
activity is defined as short breaks of movement that happen within the classroom for the purpose
of focusing attention (Caspersen, Powell & Christenson, 1985). The mathematics intervention of
this study is a physical activity.
Developmental mechanisms are the benefits of movement separate and apart from
exercise. (Sibley & Etnier, 2003). Crossing the midline is one such developmental
mechanism. Crossing the midline, or cross lateral movement is defined as the ability of the
limbs on one side of the body to reach across to the opposite side (Schofield, 1976). It is a
developmental milestone reached by most children at eight or nine years of age (Surburg &
Eason, 1999). Cross lateral inhibition effect (CIE) is the inability to do so and is found in brain
damaged adults, autistic and dyslexic children, and children with attention deficit hyperactivity
disorder (Diamond, 2000). Attention deficit hyperactivity disorder is a psychiatric disorder of
the neurodevelopmental type in which level of attention is reduced and impulsivity is increased
(Sroubek, Kelly, & Li, 2013).
Historically executive function has been defined as a management system of all
cognitive functions. The most current brain research refines that definition as a system

continuously interacting with sensorimotor functions to control behavior, strongly connected to
action and movement (Koziol, 2012).
There are many reports one can cite to build an argument that a new way of thinking
about mathematics instruction might be required. We have cited international comparisons,
Trends in International Mathematics and Science Study (2011), national studies, National
Association of Educational Progress (2013), and local reports, School Accountability Report
Card, (2013). The School Accountability Report Card is an annual report required by
California law. It reports to the community about the teaching, learning, and measures of
progress at each public school in the state. These reports measure achievement levels of students
as defined by agreed upon standards. The newest iteration is called the Common Core State
Standards (2015), a national effort begun in 2008 by the National Governors Association with
the aim of raising achievement levels of students across the country (Bidwell, 2014).
Another federal initiative, the Disabilities Education Improvement Act reauthorization
of 2004 fundamentally changed the way in which interventions were delivered to those students
in need. The discrepancy model that required data to corroborate a significant gap between
ability and achievement was replaced with a multi-tiered approach. This new approach was
designed to identify and support students at appropriate levels and degrees of intensity with
assignment to special education as the final level of intervention for a relatively small percentage
of students. This has come to be known as Response to Intervention.

Chapter 2
Review of Relevant Literature
“We do not simply inhabit our bodies; we use them to think” (Seitz, 2000, p. 23).
Purposeful precise movement in a regular rhythmic beat can have a strategic impact on
cognition, is the thesis of our Action Research Project. The prefrontal cortex as the center of
cognition has long held a preeminent position in public education. Historically, the emphasis in
traditional education has been to influence the development of learning, memory, and executive
function. Executive function has been defined as a management system of all cognitive
functions. The most current brain research refines that definition as a system continuously
interacting with sensorimotor functions to control behavior, strongly connected to action and
movement (Koziol, 2012).
The cerebellum is the portion of the brain most closely related to the brainstem and spinal
cord (Gray, 2008). As such, the cerebellum controls the motor activity necessary for purposeful
movement, and also influences the cognition that develops congruently with purposeful
movement. This thesis posits that real education reform will acknowledge the fundamental role
the cerebellum plays in cognition and will include the development of strategies that utilize the
cerebellum’s untapped potential.
When studying the relationship between movement and cognition there are two broad
categories to consider. Directed and coordinated movement has both physiological effects and
developmental effects. Physiological effects on cognition relate to changes brought about by
exercise, such as increased blood flow, hormonal balances, increased production of
neurotransmitters, and heightened mental arousal (Penedo & Dahn, 2005).

Developmental effects on cognition relate to changes brought about by movement
separate and apart from exercise. (Sibley & Etnier, 2003). By far the greatest number of
research studies have been conducted to determine the physiological effects of movement.
Physical education benefits society in general and education in particular in several
significant ways. Aerobic fitness benefits brain structure, brain function and school
achievement. The brain volumes of physically fit children are larger in the basal ganglia and
hippocampus (Chaddock-Heyman, Hillman, Cohen, & Kramer, 2014). Research shows students
who are physically fit process language faster than their less-fit peers. Their neurons fire more
quickly and their brain waves have greater amplitude (Scudder, Federmeier, Raine, Direito,
Boyd, & Hillman, 2014). There are statistically significant relationships between cognition,
achievement, and fitness (Chomitz, Slining, McGowan, Mitchell, Dawson, & Hacker, 2009).
The aerobic argument is clear: A more rapid heartbeat causes greater oxygenation of the blood
and increased cerebral capillary growth (Illinois Public Health Institute, 2013).
In two separate studies, Gabbard and Barton (1979) and McNaughten and Gabbard
(1993) focused specifically on computational fluency. Aerobic exercise enhanced mathematical
performance. However, there is a significant difference between the research of Gabbard,
Barton, and McNaughten and this Action Research Project. This study does not examine the
aerobic benefits of the movement, but the benefits of the movement itself.
Child development specialists have long recognized the importance of direct, coordinated
movement. Piaget (1952), in particular, researched how these movements directly impacted the
development of cognition. He theorized all representational thought begins with infants relating
to and manipulating objects. For example, an infant’s shift in coding systems from self to
landmarks happens once the infant begins to creep, crawl, or walk. Thus the beginnings of some
aspects of cognitive thought are linked to motor abilities. Movement aids cognitive ability, and
may even be necessary (Sibley & Etnier, 2003).

An example of a developmental mechanism is crossing the midline, the ability for limbs
on one side of the body to reach across to the other. It is first evidenced as infants begin to crawl
and is a developmental milestone usually attained at 8 or 9 years of age (Surburg & Eason,
1999). Until then, young children have difficulty with movements that cross from one side of the
body to another. This is a characteristic that brain damaged adults have in common with young
children. In adults it is identified as cross lateral inhibition effect (CIE). Children with attention
deficit hyperactivity disorder, autistic and dyslexic children often have movement deficits as well
(Diamond, 2000).
Research has linked directed, coordinated movement to cognitive thought. Embodied
cognition posits the brain works with the movement of the body (Petrick-Smith, King, & Hoyte,
2014). At the University of Vermont, Petrick-Smith and her research team have had students use
their arms to form angles and work with coordinate planes on the dance floor. Researchers at
Indiana University are studying the congruence of body gestures and speech (Yoshida, Smith,
Ping, & Davis, 2009). Even blind people communicating with other blind people use gestures to
convey meaning (Abdulla, 1998).
Seitz (2000) states in his article, The Bodily Basis of Thought, that we think with our
bodies. Current brain research supports this concept with the renewed emphasis on the
cerebellum. Being the portion of the brain most closely related to the brainstem and spinal cord,
it acts as an intermediary between autonomic and cognitive neurological functions (Gray, 2008).
Historically, the cerebellum has been considered the center of all motor skills. Current research
validates that we think with our bodies, linking motor skills to cognition and specific movements
to specific thoughts (Abdulla, 1998).
In 2010 the Centers for Disease Control released its report The Association Between
School-Based Physical Activity, Including Physical Education and Academic Performance.

This report distinguishes between physical education and physical activity. Physical education is
considered a separate curriculum and is concerned primarily with benefiting student fitness and
health. Physical activity is defined as periods of movement within the classroom lasting from
between 5 and 20 minutes (Caspersen, Powell & Christenson, 1985). The CDC’s report
referenced nine studies of physical activity. Eight of the nine studies found a positive correlation
between the physical activity and academic achievement (CDC, 2010)
This Action Research Project can be considered a physical activity, not physical
education. It is a short movement break within the classroom. The research for this project will
analyze the benefit of the movement itself, not the aerobic benefits.
Movement and music are intertwined. Infants only a few days old recognize drumming
patterns and can discern a missed beat and their heart rate slows to the sound of a lullaby
(Rodrigues, 2008). Oliver Sacks (2007) even invented a new term, musicophilia, to describe
how innately ingrained music is into our consciousness. Neuroscience has found that from
drumming to singing, animals make music. Birds produce brain cells at higher rates during the
period in which they learn new songs (Rodrigues, 2008). Research suggests that the active
learning of music benefits brain development (Sparks, 2013). Spelke (2008), neuropsychologist
at Harvard University, has found a clear benefit from musical training. Wandell (2008) of
Stanford University used brain imaging to study how the brain was influenced by music and
noted improvements in reading fluency in students receiving musical training. The research can
be so specific as to note that studying musical notation helps children learn difficult fraction
concepts (Courey, Balogh, Siker, & Paik, 2012). The research is also general enough to suggest
that musical training enhances verbal memory, reading ability, and executive functions
(Miendlarzewska & Trost, 2014). That music’s reach is so broad should come as no surprise
when one understands that there is no single area of the brain responsible for music. Music
requires the involvement of a dozen networks (Sacks, 2007) scattered throughout the brain.

Pitch, timbre, harmonics, volume, and rhythm are all components of music. For the
purpose of this research, the cognitive benefit of rhythm is the core interest. Rhythm is defined
by the Oxford Dictionary (2015) as a strong, regular, repeated pattern of movement or sound.
Rhythm exists not only externally, outside our bodies, but within as well. Researchers have
recorded the rhythmic fluctuations of brain waves since the 1920s (Cossins, 2012). Different
brain rhythms correlate with different thought processes (Cossins). Child development
specialists have concluded vocal and motor systems are linked and that infants’ rhythmic arm
shaking is closely involved in the development of speech (Iverson & Fagan, 2004). Beat and
rhythm impact attention (Geist, Geist, & Kuznik, 2012). The intent of this study is to determine
whether a rhythmic movement pattern done to music, and crossing the midline, will access the
underutilized learning potential of the cerebellum and impact computational accuracy and
fluency.
Achievement in mathematics in America’s public schools still lags behind that of other
nations (Trends in International Mathematics and Science Study [TIMSS], 2011). This is a
specific concern as the future becomes more and more digitized. Digital computation requires an
understanding of base 2, the binary system used internally in nearly all modern digital devices.
Yet many students still struggle to understand base 10.
An even greater concern is the persistent achievement gap between white students and
students of color as represented by scale scores. Scaled scores are a conversion of a student's
raw score to a common scale that allows for a numerical comparison between students. The
National Association of Educational Progress identifies the gap between scale scores of whites
and blacks as 32 in 1990. Despite modest gains overall during the interval, the gap remained 32
in 2013. The gap between scale scores of whites and hispanics was 20 in 1990 and 19 in 2013
(NAEP, 2013). The School Accountability Report Card (SARC) for the school represented in
this study reveals the same discrepancy as documented by the 2013 STAR Mathematics test

scores: white students, 78% proficient or advanced; hispanic or latino students, 47% proficient
or advanced.
Challenged by these startling statistics, America is called upon once again to reform
education. Reformations have been an ongoing event in American history. In the eighteenth
century, Thomas Jefferson (1785) described his ideas for a system of public education. In the
nineteenth century, Oliver Wendell Holmes, Sr. stated, “Every now and then a man’s mind is
stretched by a new idea or sensation, and never shrinks back to its former dimension” (1873, p.
225) and Horace Mann established public education for the public good (Finkelstein, 1990). In
the mid twentieth century, spurred by the Soviet launching of the first space satellite Sputnik,
America sought to improve mathematics instruction (Phillips, 2014). In the twenty-first century
it is time to stretch our model of mind and its effects on cognition and learning.
The New Math movement of the 1960s, epitomized by the School Mathematics Study
Group out of Yale University, sought to shift mathematics from the memorization of formulas to
abstract reasoning (Phillips, 2014). The 1980s was the era of brain compatible instruction with
its emphasis on children creating meaning (Hart, 1983). These attempts to reform mathematics
instruction were met with confusion and a return to traditional methods.
No Child Left Behind in 2001, the Common Core State Standards initiative in 2008, and
Race to the Top in 2009 are the most recent federal programs to reform public education. The
Common Core State Standards (2015) is a national effort begun in 2008 by the National
Governors Association with the aim of raising achievement levels of students across the country
(Bidwell, 2014). Mathematics instruction is now being represented in much the same way as the
New Math of the 1960s. Then our nation was spurred by the ideological competition with the
Soviet Union. Terms such as precision, relevance, and discovery learning were as prevalent then
as now (Phillips, 2014). Now the challenge is global economic competition. America is asking
itself what is required to be prepared mathematically for this new digitally dominated world.

Precision in computation is one such requirement. This Action Research Project is designed to
improve precision in mathematics.
The New Math was ultimately rejected in favor of traditional approaches. Now, in the
present day, the Common Core is becoming less common. The goal was for 50 states to reach
agreement about a unified set of national standards. In 2011 the goal seemed within reach as 45
states had adopted the new standards. Since then Indiana and Oklahoma have opted out of
Common Core and four other states are reviewing the standards to potentially replace them
(Brown, 2015). But with all the ebb and flow of philosophy and pedagogy two things have
remained constant: a traditional model of mind limited to the cerebral cortex as the center of
learning and low test scores in mathematics.
When the Individuals with Disabilities Education Improvement Act (IDEA) was
reauthorized in 2004, changes were made in how struggling students could be identified. The
old model of intervention, the discrepancy model, relied on a significant difference between
ability and aptitude. Instead a new model was proposed: a multi-tiered system of increasingly
intense interventions to meet the needs of all sub-groups. It has come to be known as Response
to Intervention, or RTI (Hoover, 2008). This new model changed the way in which interventions
were delivered to those students in need. Protocols were designed to identify and support
students at appropriate levels and degrees of intensity with assignment to special education as the
final level of intervention for a relatively small percentage of students.
This study’s survey of interventions promoted under the RTI heading reveal a
fundamental flaw. While the concept of interventions is admirable, the interventions continue to
be logical and mathematical in their approach, with a reliance on drill. What is presented as new,
computer-based interventions offering immediate feedback, are digitized worksheets. There has
been no fundamental redesign of interventions. They offer more of the same to students facing

difficulties with mathematics. The irony is obvious: For students struggling in mathematics,
interventions provide more time for students to practice their failure.
This survey of mathematics interventions is admittedly small. A complete survey of
mathematics interventions is worthy of its own Action Research Project. However, the results
are illustrative of the cognitive bias of mathematics in general and interventions in particular:
Intervention Central (2015) promotes 10 interventions, none of which involve music or
movement. Jim Wright (2015) promotes 15 interventions, none of which involve music or
movement. Math Wire (2015) has nine online interventions, none of which involve music or
movement. The University of Missouri School of Psychology (2015), on what it states is a “full
list” of math interventions, lists 16, none of which involve music or movement.
These interventions subsist under the old paradigm of teaching and learning, one that
places the prefrontal cortex in an exalted state without tapping into the vast resources of the
cerebellum. The cerebellum is small, but contains over half the neurons of the central nervous
system (Munoz, 2015). These neurons are interconnected with all regions of the brain, including
the prefrontal cortex. Despite the popularity of left/brain, right/brain and triune brain models, we
are whole-brained creatures. It is time for a new paradigm: one that taps the cognitive potential
of the cerebellum by accessing its strengths of movement and rhythm processing to improve
academic achievement.
The traditional idea that the cerebellum’s responsibility is to control autonomic and motor
functions alone no longer appears to be valid (Schmahmann, 2006). Neuroimaging data and
cerebellar lesion studies prove the cerebellum’s output targets many other regions of the brain.
For example, it is now known that there is increased activity in the cerebellum associated with
the syntax of predictive speech, previously thought to be only centered in the neocortex. In his
book This is Your Brain on Music, Levitin (2006) describes the brain as an organ designed for
predictions. Predictive speech is speech in which what is going to be said next can be

anticipated. The brain waves of the cerebellum are amplified when it responds to sentence
structure such as: It was so cold outside the rain turned to ___. Levitin (2006) also describes the
brain as an organ that responds to novelty. The cerebellum’s response is equally as intense when
a sentence violates the rules of predictive speech: I was so tired and sleepy that I danced all
night.
As we look at the basic survival needs of our ancestors, it is clear the brain evolved for
the control of action. The cerebellum is the center of that action. The cerebellum has continued
to evolve over time along with the neocortex. It is not merely an old structure as described in
MacLean’s (1990) triune brain theory. The term “neocerebellum” is now seen as often in the
literature as “neocortex.” It is that portion of the cerebellum that has continued to evolve in
primates and humans and is dominated by nerves linking it to the cerebral cortex (Medical
Dictionary for the Health Professions and Nursing, 2012). The neocerebellum has evolved to
control actions. The neocortex, as the center of cognitive thoughts, evolved to influence those
actions (Koziol, 2012).
According to Diamond (2000), human development in the individual mirrors human
evolutionary history. The common idea is motor development begins and ends early, whereas
cognitive development continues to evolve throughout adolescence. Current research disproves
this. The cerebellum’s development is similar to the prefrontal cortex in that both continue to
develop through adolescence.
The study of mental disabilities and their causes provide further evidence the cerebellum
should not be disregarded during a discussion of cognitive thought. Structural abnormalities are
found in the cerebellums of people with schizophrenia, autism, and attention deficit hyperactivity
disorder (Munoz, 2015). Mental abilities and their causes provide further evidence of the central
role the cerebellum plays in regards to thought. Neuroimaging data and cerebellar lesion studies

confirm that what are known as executive functions, such as attention, control, and memory are
neurally connected to the cerebellum (Strick, Dum, & Fiez, 2009).
Fundamental facts of brain research make obvious the numerous studies that link aerobic
exercise to improved cognition. The ancient Greeks first alluded to “mens sana in corpora sano”
- sound mind and a sound body. In our recent history, California became the first state to
legislate physical education in the public schools in 1866 (Tomporowski, Lambourne, &
Okumura, 2011). There was a great deal of research about the relationship between movement
and thought during the 1950s and 1960s. This research was done to justify the presence of
physical education programs in the schools (Sibley & Etnier, 2003). By the 1970s the practice of
physical education became widely accepted and there seemed little need for justification.
Now there is a renewed emphasis on physical education and physical activity. This
renewed emphasis goes beyond the fitness and health benefits. Physical education and physical
activity exist for the benefit of the brain as well as the body. Physical education is also mental
education; physical activity is also mental activity. This study uses the physical activity of fluid,
defined, and precise movement to develop the mental activity of computational accuracy and
fluency.
Humans need patterned, repetitive, and rhythmic activity (Brous, 2014). It has been an
essential part of our culture for millennia, from tribal dance rituals, through Woodstock to the
raves of today. People, especially children, need to move. It is essential to the development of
thought and attention. Despite years of reform, schools are still primarily a place where students
sit and listen. Real educational reform might benefit from utilizing all we have learned about the
cerebellum’s central role in learning and advocate strategies such as rhythmic beat to increase
learning.

Chapter 3
Methods
Demographics
This study was conducted at one elementary school site. The school is a public
elementary school and serves 544 students in grades kindergarten through 5th. Sixty-four
students in three 3rd grade classrooms participated in this study. The students are leveled for
reading instruction according to the multi-tiered approach of Response to Intervention (RTI) but
the students are in heterogeneous classrooms for mathematics instruction. The action research
was conducted only during mathematics class.
Every school in California is required by state law to publish a School Accountability
Report Card (SARC) annually. This report provides current data about the condition and
performance of the school. The data is due by February 1 of each year. The following statistics
were gathered from the SARC for the 2013-14 school year. At the time of this report, data was
not yet posted for the 2014-2015 school year. The school was 44.7% hispanic or latino, 45.6%
white, and 9.7% other. The school reported 53.7% of students qualified for the federal Free and
Reduced Lunch program. Proficient and advanced scores for the 2013 STAR test were 47% of
hispanic or latino students and 78% of white students. Forty percent of students are classified as
English Language Learners (ELL) and 38% of students are classified as Students with
Disabilities.
This Action Research Project is a study of physical activity as an academic intervention.
Since the review of the literature in chapter two analyzes the impact of physical education and
physical activity on academic performance, it is interesting to note that only 34.5% of fifth

graders at this site met all of the fitness standards as defined by the California Physical Fitness
Test (PFT).
The school has 29 fully credentialed teachers, two resource specialists, one library media
teacher, one speech and language specialist, and one half-time psychologist.
The city population is approximately 59,946, with a median age of 29.9 years. Population
demographics are 19.4% hispanic or latino, 74.5% white, and 6.1% other. There are 21,657
total households with an average household size of 2.39 residents. Median earnings range from
$17,150 for individuals with less than a high school degree to $53,542 for individuals with a
graduate or professional degree (U. S. Census Bureau, 2010, American FactFinder).
Participants
The participants in this study were 64 students enrolled in three 3rd grade classrooms,
48.4% male and 51.6% female. Six percent of students had Individual Education Plans due to a
discrepancy between ability and achievement as tested and determined by the school
psychologist. These students received additional services from the resource specialists. Fifteen
percent of students were classified as having Limited English Proficiency according to the
California English Language Development Test (CELDT). These are students who have
difficulty comprehending, speaking, reading, or writing English. They were placed in
mainstream English classroom but received 45 minutes daily instruction in English language
development.
Roles of the Researchers
This action research project was completed by two veteran teachers. Both researchers
designed the project. One researcher conducted the intervention on site. Both researchers
analyzed and reflected upon the data gathered.

Researcher One has thirty-eight years of teaching experience working with a wide range
of grade levels from kindergarten through eighth grade. He has extensive experience working
with both gifted and talented learners and English language learners. Researcher One is
currently serving his district as a Common Core curriculum coach specializing in mathematics
instruction at the elementary level.
Researcher Two has nine years of teaching experience working within grade levels seven
through twelve. She has worked in a wide variety of school settings, including middle school,
high school, and continuation high school, teaching all levels of math. She has extensive
experience working with students who struggle with mathematics. Researcher Two is currently
serving her district as a high school math teacher, and a member of her district’s math lead team.
Intervention Plan
We conducted a four week study to determine whether a complex, cross-lateral, rhythmic
movement done prior to mathematics instruction would increase fluency and accuracy with grade
level appropriate arithmetic computation. Prior to the first week of intervention Researcher One
taught the students the movement pattern. Based on the results of our literature review we knew
that students engaged in a physical activity prior to instruction would benefit more from the
instruction. Research has linked movement to cognitive thought. Embodied cognition posits
that the brain works with the movement of the body (Petrick-Smith, King, & Hoyte, 2014). The
intent of our study is to determine whether a rhythmic movement pattern done to music, and
crossing the midline, will benefit mathematics fluency and accuracy.
During the first week we surveyed students to assess their perceived competence
regarding the movement pattern and arithmetic achievement. We also conducted a three minute
test of basic third grade arithmetic to gather our baseline data. The arithmetic test covered grade
level appropriate computation as defined by the California State Common Core Standards

(2012): Using place value understanding to fluently add and subtract within 1000 (3.NBT.2) and
fluently multiply and divide within 100 (3.OA.7).
For the remainder of the first week and for the subsequent three weeks, students
performed the movement pattern daily. This was followed by mathematics instruction following
the district scope and sequence. Instruction was not directly linked to the arithmetic being tested.
However, arithmetic computation was often involved with the problems students were being
asked to solve. Each Wednesday, a new form of the three minute, basic arithmetic test was
presented directly after the movement pattern practice. This was a design element to prevent
memorization of a sequence of answers that would skew the data. Data identifying fluency and
accuracy rates was collected each Wednesday.
Data Collection
Accurate conclusions regarding research questions depend upon collecting and analyzing
appropriate data. Our research question was: Will the inclusion of cross-lateral movement
patterns in mathematics instruction lead to improvement of mathematical accuracy and fluency?
We collected a triangulation of data that included student surveys, observational data in the form
of teacher journaling, and quantitative data in the form of timed weekly tests of student
arithmetic computation. According to Hendricks (2013), quantitative research contends that this
hypothesis can be tested and measured amongst a random sample of individuals and that
generalizations can be made from the results. Our hypothesis is that cross-lateral movement
patterns done prior to instruction will improve mathematical accuracy and fluency.
During the first week students were given a survey to assess their perceived competence
regarding the movement pattern and arithmetic achievement. Students rated their responses on a
five-point Likert scale ranging from strongly agree to strongly disagree. Our second form of pre-

intervention data was a three-minute timed test of grade level appropriate arithmetic: addition
and subtraction with regrouping, and basic multiplication facts.
During the intervention period teachers in the participating classes observed student
behaviors and performance. Teachers were asked to determine which students had improved
attention, motivation, and accuracy of computation during daily assignments.
At the conclusion of the intervention students retook the same survey given at the
beginning of the intervention and a final timed test measuring arithmetic fluency and accuracy.
Plan for Increasing Validity
Our action research project has high truth-value validity. According to Hendricks (2013),
quantitative research allows for greater objectivity and accuracy of results. Quantitative research
allows for the testing of hypotheses that are constructed before the data is collected. Perhaps
most importantly, research results are relatively independent of the researcher, decreasing the
risk of personal bias impacting the analysis.
Carefully prescribed procedures ensured validity and reliability of the data collected. We
utilized accurate data recording when analyzing data collected. While the first researcher was
the most actively engaged in work with the students, the second researcher was not on site and
offered objective feedback based solely upon the data being analyzed. Triangulating our data
sources, we were able to determine whether one source of data would corroborate or contradict
findings of another data source. Quantitative measures of mathematical fluency and accuracy
were compared with student pre and post surveys and teacher journal observations.
Our study has catalytic validity as it has changed the teaching practices in the three third
grade classrooms involved in the study. Physical activity has continued to be included during
academic periods. Different movement patterns to different rhythms continue to be introduced.
We are so confident of the results that the results will be presented to the district administration

and site principals as well as be included in the curriculum coaching model being developed in
the district.
Confidentiality and Informed Consent
Our study has been written without the names of the school, teachers, or students
involved in the research project. All survey materials and testing materials were reported
anonymously. The data was available only to the researchers and will be stored in a secure
location at the school district office for a period of three years before being destroyed.
Written permission of informed consent was received from the district administration,
site administrator, and parents of students involved. Copy of informed consent forms is included
in appendix A. Informed consent forms included an explanation of the purpose of the study,
assurances that participation was voluntary and confidential. All signed consent forms were
destroyed at the conclusion of the project to further ensure the confidentiality of the study.

Chapter 4
The purpose of this action research study was to evaluate the effect of Purposeful
Coordinated Rhythmic Physical Movements (PCRPM) on mathematical cognitive task
performance of eight to nine year old, third grade elementary school students in the Santa Cruz
City School District. PCRPM is a strategy that utilizes the link between directed, coordinated
movement to cognitive thought (Petrick-Smith, King, & Hoyte, 2014).
The Research Study
Over a two-week span of time preceding the start of data collection, 64 participating
volunteer students were taught a purposeful, coordinated rhythmic movement pattern in three 30
minute sessions by Researcher One using identical protocols.
At the beginning of the study, students completed a three-minute test of grade level
appropriate computation covering addition and subtraction with regrouping and basic
multiplication facts. Students were required to complete each equation in a consistent sequence
of addition, subtraction, and multiplication to ensure all operations were included in a measure of
accuracy and fluency. The test was scored and recorded by the researchers. Students were also
surveyed about their subjective perceptions of their achievement regarding the coordinated
rhythmic movement pattern and their self-perceived accuracy and fluency in the three
mathematical operations being measured.
The Sample
Sixty-four third grade students from three separate classrooms under the tutelage of three
different educators participated in the study. Of these 64 students, 43 students returned
permission slips allowing the use of the data. Constrained by the requirements of the Institutional

Review Board and honoring our commitment to confidentiality, the data being analyzed has been
restricted to these 43 students, the equivalent of two third-grade classrooms.
After the initial test of computational accuracy and fluency, students were placed into
three categories of proficiency: Below Basic, Basic, and Proficient, according to the number of
equations correctly completed. Below Basic represented 0-4 problems correctly completed.
Basic represented 5-9 problems correctly completed. Proficient represented 10 or more correctly
completed problems. Of the 43 participants being measured at the outset, 23% of students were
determined to be Below Basic, 60% of students were determined to be Basic, and 16% of
students were identified as Proficient. Within these categories we created subgroups using
students' self-ratings of movement pattern success on a Likert scale of 1 to 5: Low: (1-2),
Middle: (3-4), and High: (5). Initial results showed that the Below Basic and Basic groups had
an average rating of three whereas the Proficient group had an average score of four. This data of
average overall computation score and self-rated skill while performing the movement pattern
formed the baseline for the action research project study.
For three subsequent weeks, students began each daily math period performing the
movement pattern intervention and taking a three-minute math accuracy and fluency test.
Students measured their growth by graphing the results. Each week the test changed so as to
control for the variable of mere memorization of the sums, differences, and products.
Researchers collected weekly data from the new test on the day of its introduction to ensure a
measurement of skill as opposed to memorization. At the end of the final week, students were
again surveyed about their perceptions of achievement.
When analyzing the data, researchers were interested in measuring growth in
computational accuracy and correlating that measurement with the students’ subjectively rated
improvement of their movement pattern performance. At the end of three weeks of daily PCRPM

intervention in the three participating classrooms, progressive weekly testing results were
compared for the entire sample group of 43 subjects.
Data Results
Students had an average overall score of 79% on the first test. The overall score was
determined by the ratio of computations correct to computations attempted. The spread for
attempted calculations ranged from a low of one to a high of 23. The spread for computations
correctly completed ranged from a low of one correct to a high of 13 correct. Overall average
scores varied considerably depending upon this ratio. For example, Student 30 attempted only
one problem and completed it correctly for an average score of 100%. However, Student 41
tried 23 problems but answered only five correctly, for an average score of 22%. On the first
test, Below Basic students had an average overall score of 64%, Basic had a score of 81%, and
Proficient had a score of 90%. After the three-week intervention, Below Basic students had an
average overall score of 79% on the last test, a 52% increase over the first test. It was the Below
Basic group that benefited the most from the intervention. The Basic group and the Proficient
group had, respectively, an 83% and an 89% on the last test, showing little change.
It was interesting to compare those students for whom the researchers had complete data,
indicating that they were present for each part of the intervention, and those students for whom
the data was incomplete. The assumption was made that those students for whom the
information was incomplete were absent more frequently. The overall score for those students
present for the entire intervention grew from 78% on the first test to 86% on the last test. The
overall score for those students missing parts of the intervention decreased slightly from 79% in
the first test to 76% on the final test. This discrepancy presents a variable that was not
controlled, but merits further study: of what importance was student attendance to their
improved test scores?

Math fluency for all students increased over the course of the intervention. Once again,
the Below Basic group benefitted the most from the intervention, with a 64% improvement in
computational fluency. The Basic group had a 37% increase, and the Proficient group had a 14%
improvement. The data indicates that the intervention was effective in increasing the speed of
problem completion. The effectiveness increased as the skill levels of the categories of the
student populations dropped, indicating that the intervention would best be targeted to students in
the lower skill brackets.
Math accuracy rates continued this same improvement pattern: Below Basic group had a
127% improvement in accuracy, the Basic group had a 43% improvement in accuracy, and the
Proficient group had a 16% improvement in accuracy.
By applying the same benchmark to determine group placement as at the beginning of
the study, the outcome data indicated that the population of the Below Basic group went from
23% to 16% of the sample, the population of the Basic group went from 60% to 38% of the
sample, and the population of the Proficient group went from 16% to 45% of the sample. Forty
percent of the Below Basic group had their raw score accuracy rate improve enough to move
them to the Basic group. Fifty percent of the Basic group had their raw score accuracy rate
improve enough to move them to the Proficient group. The quantitative analysis of the Action
Research Project confirmed the original hypothesis that the PCRMP strategy was an effective
intervention for computational fluency and accuracy.
At the beginning and end of the intervention, students were surveyed to provide a
subjective qualitative prism through which to view the data. All groups perceived themselves as
attaining significant improvement in performing the movement intervention. Initially, the Below
Basic and Basic groups both averaged a subjective rating of 3 on a Likert scale range from 1 to 5
while the Proficient group averaged a 4 rating. By the final individual survey, all three groups
had rated themselves as an average of 5 on the same Likert scale.

The analysis of the qualitative research regarding students self-perceptions about
accuracy and fluency during computation continues a pattern established by the quantitative
research. The survey of the Below Basic group reported a 43% growth in confidence. The Basic
group reported a 33% increase in confidence. The proficient group reported a 12% growth in
confidence. The group with the lowest achievement at the beginning of the study had the
greatest rate of growth when analyzed quantitatively, and the most significant rate of growth in
confidence when analyzed qualitatively. While overall confidence levels increased,
concomitantly, they did not increase at the same rate as quantitative measures.
Discussion
The first conclusion the researchers made is that the achievement and growth rate of the
Proficient group represented an acceptably accurate benchmark score for third-grade students.
These students began the study with an average accuracy/fluency rate of 12 correct computations
out of 12 attempted. After three weeks of practice, the accuracy rate changed to 12 correct
calculations out of 13 attempted, a statistically insignificant change. This group also rated
themselves as initially very high in movement pattern performance (4), with the lowest growth
rate of all the groups (25%) to a final self-rating of 5. Proficient students also had the lowest rate
of growth in confidence (12%), suggesting that these subjects began the study already competent
and confident regarding mathematical computations. The Proficient group, beginning the
research study with strong abilities and having the same amount of practice as the other groups,
made little growth. The conclusion of these researchers was that these scores were an accurate
representation of high achievement for third-grade students, and a goal to be reached by the
Basic and Below Basic students.
Another observation made by the researchers was that 43% of Proficient students missed
one test; however, no Proficient students missed more than one test. Nineteen percent of Basic

students missed one test, and 8% of Basic students missed more than one test. Fifty percent of
below basic students missed one test, and 20% of Below Basic students missed more than one
test. The 70% incomplete rate of the Below Basic group is in stark contrast to the 43%
incomplete rate of the Proficient group. This correlation between student achievement and task
completion merits further study. It suggests that attendance is a significant contributor to student
success. However, students who missed at least one test (i.e. minimum five percent of trial
period) had a 26% increase in overall score (number correct out of number attempted) in contrast
to a 15% increase for students who were present for all tests. The data once again suggested that
those students needed the intervention the most, profit the most.
The researchers concluded that the overall impact of the PCRPM intervention was
effective. This was not surprising in light of the most current research that movement needs to be
facilitated to maintain levels of alertness necessary for thinking and learning (Sarver et al.,
2015). Using the same benchmark to determine group placement as at the beginning of the
study, the raw score accuracy rate, Below Basic went from 23% to 16% of the total sample,
Basic went from 60% to 38% of the total sample, and Proficient went from 16% to 45% of the
total sample. Forty percent of the Below Basic group had an accuracy rate improve enough to
move to the Basic group. Fifty percent of the Basic group had an accuracy rate improve enough
move to the Proficient group.
The data analysis for this research project raised many new questions that merit further
study. With no control group, questions as to the ultimate factors contributing to improvement
remain to be considered and further investigated. Possible influences on outcome included
increased daily practice, increased student motivation, or even the presence of the researcher
measuring results. Other considerations such as effects of musical integration with the PCRPM
protocol warrant continued investigation. Research supports music’s impact on cognitive as well
as movement’s impact on cognitive function. Might one intervention have had a more

significant impact on the final result than the other? Might the combined effect have had a
greater impact than separate interventions? A project of much greater scope and duration
involving several control groups would be needed in order to study the distinct variables that
were necessary to refine the analysis.
The researchers acknowledge further studies must have clearer protocols for gathering a
greater number of permission slips. Neither of the researchers conducting the study was the
classroom teachers. Holding students accountable for permission slips was difficult. The Below
Basic group had a 16% return rate for permission slips. The Basic group had a 77% return rate
for permission slips. The Proficient group had a 100% return rate for permission slips. The
return rate of the parental endorsed permission slips informed the researchers of interesting data
separate to this particular study of PCRPM but still related to the research project. An
interesting insight was gained from the corollaries of the percentages of parental endorsement
and the level of student achievement to this unique PCRPM intervention. These corollaries
present an intriguing opportunity to gain additional insight into the sociological perspective
regarding the effect of parental compliance with necessary educational logistics on the cognitive
development and educational mastery of the individual student.
Summary
The data suggested that the PCRPM intervention model impacts student learning,
increasing both the fluency and accuracy rate of grade level appropriate mathematical
computations. The data indicated that those students most in need of intervention due to low
levels of achievement benefited the most from the intervention.
The absence of a control group left further questions to be studied. Was there a
correlation between good attendance and student achievement? Was there a relationship
between parental involvement and student achievement. What aspect of the PCRPM

intervention was having the greatest impact on fluency and accuracy: music or movement, or the
combination of both? Does the integration of other forms of multiple sensory stimuli produce
effects of such dynamic proportions as those tested in the PCRPM model of this action research
project?
The research has been shared with the Assistant Superintendent for Instructional services
and the Director of Curriculum and Assessment for Santa Cruz City Schools. They have
requested that the researcher assigned to the district write a mathematics intervention curriculum
to be used during a four-week summer school. The research has also been shared with teachers
in the district, many of whom are now implementing their PCRPM interventions.
The brain research documenting the intricate connections between the cerebrum and the
cerebellum and thus the relationship between learning and movement are profound. Preliminary
data obtained in this thesis project strongly suggests that assimilating to the core fundamentals of
this research and designing strategies that reflect this research can fundamentally change the
structure of the classroom as it exists today.

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