The Effect of Instrumental Music Instruction on the Standardized Mathematics Assessment
Achievement of Elementary School Students in Grades 3 through 5
By Kristina Gillmeister
Submitted in Partial Fulfillment of the Requirements for the
Degree of Master of Education
July 2008
Graduate Programs in Education
Goucher College
Acknowledgements
I am grateful to Dr. Adam Milam and Dr. Bess Rose for the care with which they reviewed the
manuscripts of each chapter; and for conversations that clarified my thinking, writing and
research approach. Their professional collaboration meant a great deal to me. Amy Cohn,
Deborah Derrickson, Christopher Lerch, Mary Ferguson and the Division of Accountability,
Assessment and Research from Anne Arundel County Public Schools also graciously conferred
with me and provided assistance with data collection at critical and opportune times: my thanks
to them too. In preparing this research, my professors and fellow students in the Goucher
Graduate Programs in Education have been characteristically generous in taking time to support
me on the journey to the completion of this research and my master’s degree program. As
always it was my husband Michael who provided the guidance under which this work could take
place; many thanks to him for having the patience to assist me with statistics, technical writing,
editing and many other aspects of my research and writing process. I hope that you will very
much enjoy this work as well as find it immensely educative and that it will stimulate insights
and new trains of thought into the relationships between music and mathematics.
Table of Contents
List of Tables
i
List of Figures
i
Abstract
ii
I. Introduction
Overview
Statement of Problem
Hypothesis
Operational Definitions
1
1
3
3
4
II. Review of the Literature
Introduction
The Biological Relationship Between Mathematics and Music
Biology of Mathematical Processes
Biology of Music Processes
The Relationship between Musical Training and Mathematics Processing and
Achievement
Summary
6
6
6
7
8
10
13
III. Methods
Design
Participants
Instrument
Procedure
14
14
15
18
20
IV. Results
Within Grade Comparisons
Total Music Instruction Comparisons
23
24
27
V. Discussion
33
References
38
List of Tables
1. Student Demographics by Elementary School
2. Student Demographics by Years of Instrumental Music Instruction
3. Within Grade Comparison of Mean Total Test Scale Score and Subscores by
Grade for Students Who Did and Did Not Participate in Instrumental Music
Instruction
4. Group Statistics for Each MSA Section by Years of Instrumental Music
Instruction
5. One-way ANOVA Statistics for the Total Music Instruction Comparison of
Years of Instrumental Music Instruction Versus MSA Total Test Scale Score
and Subscores
6. Tukey-Kramer Method Post Hoc Test Analysis for the Total Music Instruction
Comparison of Years of Instrumental Music Instruction Versus MSA Total
Test Scale Score and Subscores
17
17
25
28
29
30
List of Figures
1. Brain views of arithmetic tasks showing common patterns of activation in the
conjunction view
2. Anne Arundel County map noting the location of schools participating in the
study
3. The structure of test items on the Maryland School Assessment
4. 3rd, 4th and 5th grade MSA Mathematics scale and subscores are reported,
grouped by those who participated in music that year and those who did not.
Significance is based on t-test values of no music versus music for each year
5. 5th grade MSA Mathematics scale and subscores are reported, grouped by years
of instrumental music instruction. Significance is based on Tukey–Kramer post
hoc p-values for no music versus one year, two years and three years of
instrumental music instruction
i
8
16
18
26
31
Abstract
In order to avert a decrease in the allocation of both time and funding resources to pullout instrumental music education programs in elementary school, this study aimed to determine
the effect of instrumental musical instruction on mathematics achievement for elementary school
students. A causal-comparative study was completed using a sample of 240 elementary students
from three Anne Arundel County Public Schools elementary schools.
The effect of instrumental music instruction on mathematical achievement was
determined using data from the Maryland School Assessment (MSA) in grades 3, 4 and 5. This
study showed that there was a statistically significant increase in mathematical achievement with
participation in instrumental music instruction from both within grade comparisons, showing the
effect of receiving instrumental music instruction in a given year, and a total music instruction
comparison, showing the effect of the total number of years of instrumental music instruction in
elementary school on mathematics achievement. Data was analyzed using GraphPad Prism 5.00
statistical analysis tools. Two-tailed unpaired Student’s t-tests and Analysis of Variance
(ANOVA) with a 95% significance interval were conducted on the raw data.
The mean total test scale score or subscore was higher in all cases for the within grade
comparison of students who received instrumental music instruction versus those who did not.
The total music instruction comparison showed that the mean fifth grade total test scale score
and all fifth grade subscores showed incremental improvement as total years of instrumental
music instruction increased. The mean scores of students who had three years of instrumental
music instruction by the fifth grade saw an additional 18 to 27 points on their total test scale
score or subscores over those who had zero years of instrumental music instruction and an
additional 19 to 25 points over those who had only one year of instrumental music instruction.
ii
CHAPTER 1
OVERVIEW
“During most of the 20th century, the United States possessed peerless mathematical
prowess—not just as measured by the depth and number of the mathematical specialists who
practiced here but also by the scale and quality of its engineering, science, and financial
leadership, and even by the extent of mathematical education in its broad population. But without
substantial and sustained changes to its educational system, the United States will relinquish its
leadership in the 21st century” (National Mathematics Advisory Panel, 2008, p. xi). Knowledge
and proficiency in mathematics is of the most fundamental importance if the U.S. is to compete
in a 21st century global economy. According to the National Assessment of Educational
Progress (NAEP) and the National Report Card for Mathematics in 2007, just 33% of students in
grade 4 achieve at a proficient level and only 6% achieve at the advanced level. This means that
61% of elementary school students in the United States fail to grasp the most fundamental of
mathematical concepts needed in order to achieve at a proficient level (National Assessment of
Educational Progress, 2007).
At a time when the nation is facing such a crisis in mathematics achievement, a greater
amount of time is being devoted to mathematics instruction in the elementary school program.
This is often to the detriment of courses of study deemed to be “not as academic,” such as
instrumental music programs. In many cases instrumental music programs have been moved
into before- or after-school time slots or in extreme cases they have been cut from the curriculum
altogether. Whether this is rationalized through the impact of No Child Left Behind or
tightening economic times, a Harris poll indicates that the public does not support such cuts. In
fact, a 2005 survey of over 1,000 Americans showed that 93 percent agreed that “the arts are
1
vital to providing a well-rounded education for children. Additionally, 54 percent rated the
importance of arts education a ‘ten’ on a scale of one to ten” (Americans for the Arts, 2005).
Music programs offered during the school day have been the object of a significant
amount of scrutiny, especially programs that are termed “pull-out” music programs. These
music programs remove students from the classroom for a portion of the school day in order to
provide them with instrumental music lessons and ensemble practice time. Critics of such
programs say that they take time away from fundamental instruction such as lessons in reading
or mathematics. In a time when principals, administrators and superintendents are being held
responsible for standardized test achievements and articles and news stories about “getting back
to the basics” abound, instrumental music instruction has fallen by the wayside.
Several options for addressing the challenge of instrumental music instruction taking
away from academic achievement have been proposed. They include moving the instrumental
music programs outside of school hours, providing integrated arts instruction or eliminating the
instrumental music program altogether. Moving the program outside of school hours severely
limits access to the program, especially for students from homes where transportation and other
resources cannot be provided outside of the school day. However, more time during the school
day can be devoted to the core academic pursuits. An integrated arts curriculum eliminates the
barrier of access, but often provides a more generalized approach to music and arts instruction.
It may not allow time for instrumental music instruction as well. Finally, the societal and
personal costs of the elimination of an instrumental music program are significant to individuals,
communities and the nation as a whole. Although these options are most often considered, a
better solution would be to support the continuation of instrumental music programs. This
solution is supported by both national and local studies linking participation in instrumental
2
music education programs to increased academic achievement, especially in the areas of reading
and mathematics.
With the convergence of these two crises in both musical and mathematics education, it is
critical to determine the impact of musical training specifically on mathematics achievement.
Socially and biologically, there are strong correlations between mathematical and musical skill
sets. Several research studies have shown a positive correlation between mathematical
achievement and instrumental music instruction (Geoghegan & Mitchelmore, 1996; Rauscher &
Zupan, 2000; Gardiner, Fox, Knowles & Jeffrey, 1996; Haley, 2001; Whitehead, 2001; & Cheek,
1999).
Statement of Problem
In order to avert a decrease in the allocation of both time and funding resources to pullout instrumental music education programs in elementary school, this study aimed to determine
the effect of instrumental musical instruction on mathematics achievement for elementary school
students. While the understanding clearly exists that success in mathematics programs is vital
for providing students options in their future education and careers, the elevation of mathematics
skill and ability does not need to occur at the expense of instrumental musical instruction. If
there is empirical evidence based upon local data as well as national studies that there is a
statistically significant relationship between mathematics achievement and musical instruction,
districts are likely to take notice of the impact of musical training on their own students’
mathematics achievement. Such empirical evidence also provides districts with a foundation for
continuing to provide instrumental music programs and will encourage further research in this
area.
3
Hypothesis
The specific purpose of this study was to determine the effect of instrumental music
instruction on mathematical achievement on the Maryland School Assessment (MSA) in grades
3, 4 and 5. The research hypothesis was that students who received instrumental music
instruction were predicted to have a higher level of mathematics achievement as measured by
their performance on the MSA than those who did not receive instrumental music instruction. In
summary, this study was designed to show that there was a statistically significant effect of
instrumental music participation on mathematical achievement from both a within grade
comparisons perspective, showing the effect of receiving instrumental music instruction in a
given year, and a total music instruction comparison perspective, showing the effect of the total
number of years of instrumental music instruction in elementary school on mathematics
achievement. Null hypotheses were created to test the statistical significance of each comparison
where it was stated that there would be no difference in scores between the groups being
compared.
Operational Definitions
For the purposes of this study, students receiving instrumental music instruction were
those who participated in a school-based band or orchestral programs. Instrumental music
instruction was specifically defined as students receiving one hour of instrumental music
instruction per week in two half-hour sessions. The instruction was conducted in group classes
according to instrument type and level of expertise. Mathematics achievement was operationally
measured by the results of the mathematics portion of the Maryland School Assessment (MSA).
Elementary school student was defined as a student in grades 3 through 5 who had the option of
4
participating in an instrumental music program and who was assessed yearly in mathematics
using the Maryland School Assessment (MSA).
5
CHAPTER 2
REVIEW OF THE LITERATURE
Introduction
The relationship between academic achievement and music listening or participation
has been the subject of a significant number of studies. This topic lends itself to numerous
explorations of the previously mentioned variables such as the relationship between
mathematical achievement and instrumental music participation, the focus of this study. In order
to fully understand the biological and anecdotal association between these two variables, the
theories of how they were connected was investigated. In addition, the biology of mathematical
processes and the biology of music processes were each explored individually. Finally the
relationship between musical training and mathematics processing and achievement is
considered. First, studies relating general academic achievement are examined and then the
discipline specific relationship between mathematics achievement and music participation is
further explored.
The Biological Relationship between Mathematics and Music
There are several brain-based theories relating mathematics achievement and musical
training. Two general types of theories, the neuroscientific and the near transfer theories,
dominate the theoretical framework for the relationship between musical and mathematical
processes. The neuroscientific, or trion, model theorizes that “music ‘resonates’ with inherent
neuronal firing patterns throughout the brain: thus, music listening and instruction can ‘prime’
the brain for improved performance on spatiotemporal and other cognitive tasks” (Crncec,
Wilson & Prior 2006, p. 584). The second theory, the near transfer theory, postulates that the
related cognitive skills required in musical and spatiotemporal reasoning would allow learning
6
that occurs in musical instruction to be transferred to mathematical or other similar tasks. The
neuroscientific theories “imply that there is something special or unique about the interaction
between music and the functioning of the brain, while transfer theories can apply to many types
of learning and cognitive domains” (Crncec et al., 2006, p. 585). Utilizing these theories, one
can begin to unravel the many relationships between mathematics and music.
Several mathematical aspects show a strong relationship to music. These include rhythm,
which is a numerical pattern of beats that can be counted, and musical pitch and harmony, which
are related to ratios and frequencies (often taught in trigonometry) as well as rational and
irrational numbers and their relationship to the musical scale. Finally, it is evident that music can
be composed based on a series of numerical calculations. In fact, “even Mozart is said to have
spent an occasion or two composing according to the roll of a dice” (Bahna-James, 1991, p. 479).
Other non-mathematical aspects of mathematics have also been shown to have at least a modest
relationship to music. These include spatial ability as well as temporal skills (Crncec et al.,
2006).
Biology of Mathematical Processes
PET and fMRI-BOLD activity indicates that for all arithmetic calculations, there are
common brain regions activated. Dehaene suggests that there are “different brain regions
responsible for the processing of spoken numbers, recalling numerical knowledge, calculation
and comparing magnitudes” (Fehr, Code & Herrmann, 2007, p. 94). Since each of these tasks is
necessary for arithmetic operations, each would be activated during arithmetic problem-solving.
The bi-hemispheric parietal regions of the brain are noted to be activated automatically
when the stimulus involves numbers. The parietal regions are activated in several different areas
including the “superior posterior parietal lobe, which is associated with visuo-spatial processing,
7
the left angular gyrus where verbal processing of numbers takes place and the horizontal segment
of the intraparietal sulcus where numerical quantity is processed” (Fehr et al., 2007, p. 94). The
left perisylvian region is activated during processes where “numbers are represented in written or
spoken form” (Fehr et al., 2007, p. 94) and this region is also used to access mathematics facts
that have been stored in the basal ganglia. Figure 1 shows clearly the commonly activated areas
in each operation as well as the areas activated only for performing certain tasks.
Figure 1. Brain views of arithmetic tasks showing common patterns of activation in the
conjunction view (Fehr et al., 2007).
When compared to simple rote tasks, complex tasks require greater operant memory capacity,
which is seen as greater activation in the frontal lateral and parietal regions of the brain. This is
true across all mathematic operations. In addition, “activation patterns due to mental arithmetic
reflect activation in the working memory and in a neural network related to finger movement
(counting on one’s fingers)” (Fehr et al., 2007, p. 93).
Biology of Music Processes
While the biology of mathematical processes is less fully understood, the biology of the
auditory process has been studied in detail and is generally accepted to include the outer ear,
inner ear, auditory nerve, brainstem, thalamus and auditory cortex. Sound waves are collected
and carried to the brainstem and ultimately to the auditory cortex. In addition to the biological
musical processing pathways, neurotransmitters also play a role in the “perceptual and emotional
8
processing of music in the brain” (Boso, Politi, Barale & Enzo, 2006, p. 189). Dopamine,
endorphins and endocannabinoids have been demonstrated to be released into the brain and
bloodstream while music listening is occurring (Boso et al., 2006).
Music has been noted to have an effect on the biology of the brain. The synapses have
been shown to be strengthened when students learn and perform music and the brain’s capacity
for information is thus subsequently increased. In addition, the area of the brain connecting the
left and right hemispheres has been shown to be larger in musicians as opposed to non-musicians
(Cox & Stephens, 2006). There are also known biological differences between musicians and
non-musicians in areas of the brain associated with musicality. Heschyl’s gyrus, which is
located in the primary auditory complex, shows an increase in volumetric measurements as
musical training and musicality increase (Limb, 2006).
Musical memory has also been studied and showed significant activation in the right
hippocampus and bilateral lateral temporal regions, as well as the left inferior frontal gyrus and
left precuneus which were also noted as being active in the attentional and stimulation demands
of algebraic problem solving (Watanabe, Yagishita & Kikyo, 2008; Lee, Lim, & Yeong et al.
2007). Other studies also imply that “areas traditionally thought to be involved in single-domain
processing have far greater flexibility than previously understood” (Limb, 2006, p. 438). This is
especially seen in the activation of the frontal operculum (located in the inferior frontal gyrus)
when subjects without musical training were presented with listening to a series of chords that
occasionally contained out-of-key notes. The activation of the frontal operculum was surprising
because this area was previously known for being active only in processing language. In a
peripheral study musical passages were also seen to activate the middle temporal gyrus as well as
to “cause a priming effect for certain words” (Limb, 2006, p. 439)
9
The Relationship between Musical Training and Mathematics Processing and Achievement
Studies involving students at several levels of schooling, from elementary through
secondary school, were analyzed to determine if a relationship between musical training and
mathematics achievement existed. Some studies, related to school-age music programs from
elementary and middle school have indicated no correlation between instrumental musical
training and mathematics achievement. In 2003, Rafferty studied the effect of providing piano
lessons to second graders and the relationship of this training to mathematical achievement. This
program, the Music Spatial-Temporal Math Program, showed no significant effect on the math
achievement of those who participated over those who did not (Rafferty, 2003). A study by Cox
and Stephens (2004) compared the number of music credits a student had successfully completed
to both their mathematics and overall GPA. Their findings indicated no statistically significant
differences in either GPA of students with no musical training compared to those who had
received musical training. Their study, however, was limited by sample size and the types of
music instruction offered at the school being studied (Cox & Stephens, 2004).
However, there is a stronger case that instrumental music instruction participation has a
positive correlation with mathematics achievement. In students of preschool age, participation in
a music program showed a positive correlation with scores on a mathematics achievement test.
However, these higher scores may have resulted from the students’ background in music from
the home rather than participation in the school-based music program (Geoghegan &
Mitchelmore, 1996). In kindergarten, the effect of keyboard instruction on spatial-temporal
ability (a necessary precursor to mathematical achievement) was studied. Students either
received no music instruction or keyboard instruction. Benchmarks at four and eight months
showed that the students in the keyboard group had scored considerably higher on the spatial-
10
temporal tasks than the students who received no music and that at eight months the achievement
gaps between the groups had grown considerably (Rauscher & Zupan, 2000).
The effect of musical training on mathematics achievement continues through elementary
school. In a study by Gardiner, Fox, Knowles, and Jeffrey (1996), one group of first-grade
students was instructed in a music and visual-arts curriculum while the control group received no
such instruction. The students chosen for instruction in the music and visual-arts curriculum had
lower achievement at the beginning of the study than the students who did not participate. After
instruction in the music and visual-arts curriculum for seven months, students showed higher
scores on the mathematics achievement test than those students who had no instruction. Students
were retested at the beginning of the following year and still showed increased math
achievement. Instruction in the music and visual-arts curriculum was continued for a second
year and students continued to produce the same results. They concluded that students who had
no instruction in the visual-arts curriculum had the lowest test scores, those who participated for
one year had higher mathematics achievement and those who participated for two years had the
highest math achievement scores of students involved in the study (Gardiner et al., 1996).
Similar effects were noted in upper-elementary and secondary students. Three sets of
fourth-grade students, those who had begun music instruction prior to fourth grade (where it was
introduced at the school level), those who began studying an instrument in fourth grade and those
with no formal instrumental training, were tested for mathematics achievement. The strongest
mathematics achievement occurred in students who began instrumental instruction prior to fourth
grade (Haley, 2001). In secondary students, the effect of music instruction (using the OrffSchulwerk approach) on math scores was studied by Whitehead (2001). This approach teaches
music through singing, chanting rhymes, keeping a beat, clapping and dancing. The study
11
concluded that the greater the amount of music instruction, the greater the gains in mathematics
achievement over a given time period. Those with the greatest amount of music instruction
showed the greatest gain in mathematics, followed by those with limited music instruction,
followed by those with no music instruction (Whitehead, 2001).
Further studies on the duration and type of musical instruction were noted by Cheek
(1999) who surveyed students in eighth grade to collect information about their musical
background. The information collected included demographics, number of years in school music
lessons, number of years in private music lessons and the type of musical instrument they played.
Analysis of the data from these surveys as well as student achievement data in mathematics on
the Iowa Tests of Basic Skills (ITBS) showed that students with two or more years of private
music lessons had a significantly higher mean mathematics score than students with no private
lessons. In another interesting finding, students who had keyboard lessons had significantly
higher ITBS mathematics scores than students who had music lessons on other instruments
(Cheek, 1999).
Further analysis by Vaughn (2000) of 20 correlational studies relating mathematics
achievement and voluntary music participation did show a modest positive correlation between
the two. A separate analysis of six experimental musical training studies where the subjects were
elementary school students did show a statistically significant increase in achievement on a
mathematics assessment. Vaughn also noted that the connections between music and
mathematics are numerous in terms of skill sets. Both involve numbers, ratios and patterns
(Vaughn, 2000). This connection between skill sets laid the groundwork for further research
noting that participation in instrumental music programs can result in increased achievement in
12
mathematics due to the fact that students have a stronger understanding of the concepts used in
both disciplines.
Summary
Strong biological evidence exists for a fundamental brain-based relationship between
music and mathematics. Whether the trion model, the near transfer theory, or a combination of
the two is responsible for the effect of musical training on mathematics achievement, there is a
notably significant relationship between them. This relationship has been documented from preschool through secondary students who have undergone a variety of musical experiences. While
the research supports a strong correlational evidence of the relationship between music and
mathematics, the cause-and-effect relationship is still unproven. However, many of the skill sets
in these two arenas overlap and it is likely that the acquisition of skill sets in music would enable
higher achievement in mathematics.
13
CHAPTER 3
METHODS
Instrumental music participation, especially the use of pull-out programs, has often been
criticized as taking students away from more academic subjects. It is argued that while students
are out of the classroom, they can not benefit from the instruction taking place. Instrumental
music programs, however, do not hinder the academic achievement of the child, particularly in
mathematics (Geoghegan & Mitchelmore, 1996; Rauscher & Zupan, 2000; Gardiner et al., 1996;
Whitehead, 2001; Cheek, 1999; Vaughn, 2000). The purpose of this study was to determine the
effect of instrumental music instruction at the elementary school level on mathematics
achievement.
Design
This study was designed as a causal-comparative study. The purpose of the study was to
determine the effect of instrumental music instruction on standardized mathematics achievement
by looking at students’ overall total test scale scores and subscores on the mathematics portion of
the Maryland School Assessment. Specifically, this study tested the hypothesis that students
who received instrumental music instruction were predicted to have a higher level of
mathematics achievement as measured by their performance on the MSA than those who did not
receive instrumental music instruction. Both within grade comparisons, which showed the effect
of receiving instrumental music instruction in a given year on mathematics achievement, and
total music instruction comparison, which related the total number of years of instrumental
music instruction in elementary school to fifth grade mathematics achievement, were used to test
the research hypothesis.
14
The independent variable in this study was participation in and years of instrumental
music instruction, while the dependent variable was mathematics achievement on the Maryland
School Assessments in mathematics. The control group included students who had zero years of
instrumental music instruction while the experimental group included students who had one or
more years of instrumental music instruction. The anticipated effect that was investigated was
derived from both biological and anecdotal theories relating the two variables.
Participants
Schools participating in the study volunteered from the larger sample of all elementary
schools in the Anne Arundel County Public School System. The Anne Arundel County Public
Schools (AACPS) school system is the 5th largest in Maryland and among the 50 largest school
systems in the country. It is located between the major cities of Baltimore, MD and Washington,
DC. The district contains 77 elementary schools, 19 middle schools, 12 high schools, 1
alternative high school, 1 charter school, 2 applied technology centers, 3 special education
centers, 1 middle school learning center and 1 special education regional program. Within these
schools approximately 74,000 students are served in the following demographics: 22% African
American, 4% Asian, 68% Caucasian, 5% Hispanic, and 1% other. The specific schools
participating in this study were Bodkin Elementary, Glendale Elementary and Solley Elementary
School. The boundaries of the school system as well as the locations of schools participating in
this study can be seen in Figure 2. Tables 1 and 2 contain demographic data for these schools.
15
SOLLEY ELEMENTARY
GLENDALE ELEMENTARY
BODKIN ELEMENTARY
Figure 2. Anne Arundel County map noting the location of schools participating in the study
(Google Maps, 2008)
Bodkin Elementary School is located in Pasadena, MD and is a part of the Chesapeake
High School Feeder System which serves the eastern central portion of Anne Arundel County in
a generally suburban to rural setting. Bodkin is located within a quarter mile of the Chesapeake
Bay and is a National Blue Ribbon School of Excellence. In 2007, Bodkin was also awarded
Green School Status and also named a School of Character for its environmental practices and
character education programs. In addition to these achievements, for the 2006-2007 school year,
Bodkin had an overall 96.5% attendance rate, an enrollment of 603 students, 6.5% of students in
special services, 4.6% of students receiving free and reduced meals (FARMS) and a 3.3%
student mobility rate.
Glendale Elementary School is located northwest of Riviera Beach, MD and is a part of
the Northeast High School Feeder System which serves the northeast portion of Anne Arundel
16
County in a generally suburban setting. Approximately 40 students come from schools
throughout the northern end of Anne Arundel County to an outstanding special education center,
located within Glendale Elementary School. Glendale currently has an overall 95.1% attendance
rate, an enrollment of 477 students, approximately 20% of students in special services, 34%
FARMS students and a 7% student mobility rate.
Solley Elementary School is located in Glen Burnie, MD and is a part of the Glen Burnie
High School Feeder System which serves the north central portion of Anne Arundel County in a
generally urban setting. Glendale currently has an overall 95.7% attendance rate, an enrollment
of 570 students, approximately 8% of students in special services, 22.2% FARMS students, and a
5.9% student mobility rate.
Students who were in grade 5 in the 2005-2006 school year were selected as the sample.
This group of students had MSA mathematics testing data as well as instrumental music
instruction data for grades 3, 4, and 5. Only students with data regarding their instrumental
music instruction and mathematics scores for all three years were included in the sample.
Table 1. Student Demographics by Elementary School
School
Total # American Asian / African White HispanicFemaleMale Special 504 FARMS ELL
of
Indian / Pacific American (not of
Education
Students Alaskan Islander
Hispanic
Native
origin)
101
0
3
1
97
0
56
45
7
2
0
0
Bodkin
62
0
2
10
49
1
29
33
12
1
0
2
Glendale
77
0
1
9
65
2
51
26
3
2
11
1
Solley
240
0
6
20
211
3
136 104
22
5
11
3
Total
Table 2. Student Demographics by Years of Instrumental Music Instruction
Years of Total # American Asian / African White HispanicFemaleMale Special
Instrumental of
Indian / Pacific American (not of
Education
Music
Students Alaskan Islander
Hispanic
Native
origin)
62
0
2
3
57
0
32
30
8
0
49
0
0
9
39
1
33
16
4
1
54
0
1
4
48
1
29
25
6
2
75
0
3
4
67
1
42
33
4
3
240
0
6
20
211
3
136 104
22
Total
17
504 FARMS ELL
1
2
2
0
5
3
3
3
2
11
1
1
1
0
3
Instrument
The instrument chosen for this study was the Maryland School Assessment (MSA) in
Mathematics. The MSA is administered in reading and mathematics at the 3rd, 4th, and 5th grade
levels in elementary school. The MSA in mathematics was developed by CTB/McGraw-Hill in
collaboration with staff from the Maryland State Department of Education and local school
districts in Maryland and contains norm-referenced items from their Terra Nova series
mathematics assessment which is a norm-referenced test (Maryland State Department of
Education, 2006). Additional test items that correlated to Maryland mathematics content
standards were identified and new items were created to ensure coverage of all of the standards.
These items produced a criterion-referenced score for each student. Therefore, the math MSA
provided norm-referenced scores in the form of a total test scale scores, national percentile
rankings and stanine scores that compared students to their peers across the nation. The math
MSA also provided a criterion-referenced score that described how well a student had mastered
specific Maryland content standards in mathematics as well as their overall proficiency level
(Maryland State Department of Education, 2006). The structure of the MSA can be seen in
Figure 3.
18
Figure 3. The structure of test items on the Maryland School Assessment (Maryland State
Department of Education, 2002)
The mathematics MSA contains both selected-response (multiple-choice) and brief constructed
response items. On the 2005 and 2006 assessments students in grade 3 answered a total of 65
questions (51 selected response, 14 constructed response), students in grade 4 answered 64
questions (50 selected response, 14 constructed response) and students in grade 5 answered a
total of 65 questions (49 selected response, 16 constructed response) (Maryland State
Department of Education, 2005; Maryland State Department of Education, 2006). The MSA is
administered in the month of April each year over the course of two half-day sessions. The
mathematics total test scale score, national percentile rankings and the scores in several
subcategories are reported. The subcategories include patterns/algebra/functions,
geometry/measurement, statistics/probability, number relationships/computation, and math
processes (Maryland State Department of Education, 2006).
The reliability and validity of the mathematics MSA assessments is well documented in
the MSA technical reports. One type of reliability that is exhibited is rater agreement or
interrater reliability on the constructed response items. At least two raters scored each of these
19
items and if the raters differed by one point or less the higher of the two scores was reported. If a
greater discrepancy was reported than the dispute was resolved by a third rater. Rater agreement
was above 98.5% for all constructed response items (Maryland State Department of Education,
2005; Maryland State Department of Education, 2006). The MSA also exhibits equivalence
reliability between its various forms for the selected response items and the correlation value was
above 0.9 in all cases (Maryland State Department of Education, 2005; Maryland State
Department of Education, 2006). Internal consistency reliability was exhibited on the
mathematics MSA using Cronbach’s alpha since numbers are used to represent the response
choices. The reliability coefficients ranged from 0.92 to 0.96 (Maryland State Department of
Education, 2005; Maryland State Department of Education, 2006). The MSA also exhibits
several types of validity. It has undergone a significant analysis to ensure its content validity
which includes both item and sampling validity as indicated by the number of items correlated to
each Maryland mathematics standard. Classical item analysis was conducted on the MSA to
ensure construct validity as well (Maryland State Department of Education, 2005; Maryland
State Department of Education, 2006).
Procedure
Students were identified by their schools as either participating in an instrumental music
program or not participating in an instrumental music program. There is no school system
identification of students who participate in a music program until grade six when it is a
scheduled class. Since records of elementary instrumental music instruction are not centrally
kept by Anne Arundel County Public Schools, it was necessary to contact individual school
music teachers. The AACPS music office provided a list of instrumental music contacts. Two
music teachers responded and provided their class rosters for each year (2004-2005, 2005-2006
20
and 2006-2007) requested. Next, the mathematics MSA data for each school and grade level
was secured through the use of the educational data warehouse with the assistance of the AACPS
Division of Accountability, Assessment and Research. This data collected included: School
Name, Grade, Last Name, First Name, Pupil ID Number, Gender, Race, Special Education,
Limited English Proficiency, Free and Reduced Meals (FARMS), Math Total Test Scale Score,
Math Proficiency Level, Patterns/Algebra/Functions Subscore, Geometry/Measurement
Subscore, Statistics/Probability Subscore, Number Relationships/Computations Subscore, Math
Processes Subscore, and Total Math National Percentile Ranking. There was a separate
spreadsheet report for each year of data collected. Confidentiality of student and teacher
identification was maintained throughout this study.
Once the raw data was obtained, it was necessary to combine it into one document. A
spreadsheet was created such that the students in band or orchestra could be identified for each
year they participated and this was presented alongside their assessment data. Student data was
then sorted and analyzed for demographic information. Finally, the data was analyzed using
GraphPad Prism 5.00 statistical analysis tools. Specifically, two-tailed unpaired Student’s t-tests
and Analysis of Variance (ANOVA) with a 95% significance interval were conducted on the raw
data to determine whether there was a statistically significant relationship between instrumental
music instruction and mathematics achievement as measured by the mathematics portion of the
Maryland School Assessment.
Student’s t-tests were used for the within grade comparisons in order to compare two
specific groups at each grade level. This analysis method was chosen over ANOVA because
ANOVA would compare all possible combinations including across grades. However, this part
of the study was designed to show whether two groups, those who received instrumental music
21
instruction and those who did not, had a statistically significant difference in their total test scale
scores and subscores on the mathematics portion of the MSA at each specific grade level.
ANOVA was used to analyze data for the total music instruction comparison because there were
four different groups of students being compared and all comparisons were meaningful. The
students were grouped by their years of total instrumental music instruction in elementary school
through grade 5. This resulted in four groups: students with 0, 1, 2, or 3 years of total
instrumental music instruction. It was important to analyze comparisons between all of the
groups in this case.
22
CHAPTER 4
RESULTS
The effect of instrumental music instruction on mathematical achievement on the
Maryland School Assessment (MSA) in grades 3, 4 and 5 was examined in this study. The
research hypothesis was that students who received instrumental music instruction were
predicted to have a higher level of mathematics achievement as measured by their performance
on the MSA than those who did not receive instrumental music instruction. Two methods were
used to test the research hypothesis. One method used within grade comparisons to show the
effect of receiving instrumental music instruction in a given year on mathematics achievement.
The second method used a total music instruction comparison which related the total number of
years of instrumental music instruction in elementary school to fifth grade mathematics
achievement.
The first method compared the MSA mathematics performance of students within a
particular grade who received instrumental music instruction to students who did not. The null
hypotheses for these comparisons of students within each grade would state that there is no
difference between the total test scale scores and subscores on the mathematics portion of the
MSA of students who receive instrumental music instruction when compared to students who did
not receive instrumental music instruction in the same year.
The second method for testing the research hypothesis compared the total number of
years of instrumental music instruction students received in elementary school to their MSA
mathematics achievement in fifth grade. The null hypothesis for this method would state that the
mean total test scale scores and subscores on the mathematics portion of the MSA of students
23
who received 0, 1, 2 and 3 years of instrumental music instruction in elementary school would all
be equal.
Within Grade Comparisons
From a within grade comparison perspective, performing t-tests comparing the mean
total test scale scores and subscores earned in grades 3, 4, and 5 yielded the results shown in
Table 3 and Figure 4. This planned comparison determined if the two group means (the mean
score of students without music and the mean score of the students participating in music for
each year) were significantly different. It is important to note that in 2004-2005 (3rd grade),
number concepts were not tested on the Maryland School Assessment for Mathematics.
24
Table 3. Within Grade Comparison of Mean Total Test Scale Score and Subscores by Grade for
Students Who Did and Did Not Participate in Instrumental Music Instruction
p-value
MSA Section Grade
N
Mean
SEM
N
Mean
SEM t-value
(twotailed)
No Music
Total Test
Scale Score
Algebra/
Patterns
Subscore
Geometry/
Measurement
Subscore
Statistics/
Probability
Subscore
Number
Concepts/
Computation
Subscore
Process of
Mathematics
Subscore
Music
rd
3
4th
5th
3rd
4th
5th
3rd
4th
5th
3rd
4th
5th
3rd
4th
122
100
116
122
100
116
122
100
116
122
100
116
122
100
410.7
416.9
418.1
418.4
434.6
425.6
432.6
425.1
417.6
422.1
438.0
419.4
nd
453.0
3.7
3.7
2.6
6.5
7.4
3.4
7.7
6.5
3.1
6.4
8.4
3.6
nd
9.6
118
140
124
118
140
124
118
140
124
118
140
124
118
140
433.1
427.3
433.2
464.9
448.9
438.8
457.7
443.6
433.7
456.7
442.6
433.3
nd
459.1
4.1
2.7
2.8
8.6
6.2
3.1
8.9
6.3
3.4
8.8
5.8
3.6
nd
7.7
4.099
2.355
3.901
4.347
1.483
2.866
2.219
2.004
3.520
3.199
0.468
2.729
nd
0.495
<0.0001
0.0193
0.0001
<0.0001
0.1395
0.0045
0.0343
0.0462
0.0005
0.0016
0.6399
0.0068
nd
0.6213
5th
116
417.8
2.9
124
432.2
3.3
3.229
0.0014
3rd
4th
5th
122
100
116
423.2
403.9
414.6
6.4
4.4
3.5
118
140
124
448.0
418.8
431.2
5.7
3.9
3.1
2.865
2.511
3.561
0.0045
0.0127
0.0004
25
A.
B.
Scale Score by Grade
Algebra/Patterns Subscore by Grade
500
500
***
*
480
***
MSA Score
MSA Score
480
460
440
3rd
No Music
Music
4th
3rd
No Music
Music
D.
Test Grade
Statistics/Probability Subscore by Grade
500
*
*
480
***
MSA Score
MSA Score
5th
440
Test Year
500
460
440
420
**
ns
***
4th
5th
460
440
420
400
3rd
No Music
Music
4th
400
5th
3rd
Test Year
No Music
Music
Number Concepts/Computation Subscore by Grade
F.
Test Grade
Process of Mathematics Subscore by Grade
500
500
ns
480
**
MSA Score
480
MSA Score
4th
460
5th
C. Geometry/Measurement Subscore by Grade
460
440
420
**
400
400
E.
ns
420
420
480
***
400
No Music
Music
*
***
4th
5th
460
440
420
n.d.
3rd
**
4th
400
5th
3rd
Test Grade
No Music
Music
Test Grade
Figure 4. 3rd, 4th and 5th grade scale and subscores are reported, grouped by those who
participated in music that year and those who did not. Significance is based on t-test values of no
music versus music for each year (* p<0.05, ** p<0.01, *** p<0.001). Total Test Scale Score
(A), Algebra/Patterns subscore (B), Geometry/Measurement subscore (C), Statistics/Probability
subscore (D), Number Concepts/Computation subscore (E), and Process of Mathematics
subscore (F) by grade.
26
Based on a Student’s t-test at a 95% confidence interval, the null hypothesis stating that
students who receive instrumental music instruction do not achieve higher total test scale scores
and subscores on the mathematics portion of the MSA than students who did not receive
instrumental music instruction in the same year was rejected. In the comparisons between music
and non-music students for all total test scale scores and subscores in the 3rd and 5th grades
statistically significant differences were noted. In the 4th grade, statistically significant
differences were seen and the null hypothesis was rejected for total test scale score, geometrymeasurement subscore and process of mathematics subscore. These t-test results suggest that
there is a statistically significant difference in mathematics achievement in the aforementioned
categories between students who were currently receiving instrumental music instruction in the
year they were tested and those who were not. The null hypothesis could not be rejected for the
cases where a comparison of music and non-music students did not produce statistically
significant differences. This occurred in the 4th grade algebra-patterns subscore, number
concepts-computation subscore and statistics-probability subscore.
Total Music Instruction Comparisons
From a total music instruction comparison perspective, one-way analysis of variance
(ANOVA) was performed comparing the total test scale scores or subscores earned in grade 5 for
the groups described by 0, 1, 2, or 3 years of instrumental music instruction through grade 5.
There was no statistical significance between the variances according to Bartlett’s test, therefore
homoscedasticity or the assumption of equal variances across all groups was proven. The group
statistics for each MSA section by years of instrumental music instruction is shown in Table 4.
27
Table 4. Group Statistics for Each MSA Section by Years of Instrumental Music Instruction
Years of
Instrumental
MSA Section
N
Mean
SEM
Music
Instruction
0
62
414.1
3.6
Total Test
1
49
419.0
4.0
Scale Score
2
54
428.5
3.7
3
75
438.3
3.7
0
62
432.0
4.8
Algebra/
1
49
425.0
4.8
Patterns
2
54
437.7
4.4
Subscore
3
75
441.4
4.3
0
62
413.2
4.6
Geometry/
1
49
417.1
4.3
Measurement
2
54
428.3
4.7
Subscore
3
75
440.5
4.3
0
62
415.2
5.2
Statistics/
1
49
416.7
4.9
Probability
2
54
434.5
4.9
Subscore
3
75
442.3
4.7
0
62
414.3
3.7
Number
1
49
421.1
4.7
Concepts/
Computation
2
54
423.9
5.0
Subscore
3
75
437.9
4.2
0
62
409.1
4.6
Process of
1
49
415.4
5.8
Mathematics
2
54
428.9
4.2
Subscore
3
75
435.8
4.0
Shown in Table 5 are the statistical results generated from the ANOVA calculations.
Based on the ANOVA at a 95% confidence interval, the null hypothesis that there was no
difference in the population means of the groups with different numbers of years of instrumental
music instruction was rejected. The ANOVA p-values for total test scale score and all subscores
were statistically significant which suggests that there were differences between all group mean
scores.
28
Table 5. One-way ANOVA Statistics for the Total Music Instruction Comparison of Years of
Instrumental Music Instruction Versus MSA Total Test Scale Score and Subscores
MSA Section
Source
SS
df
MS
F
p-value
Treatment (between columns)
22750
3
7585
8.770 <0.0001
Total Test
Residual (within columns)
204100
236
864.9
Scale Score
Total
226900
239
Treatment (between columns)
15730
3
5244
4.129
0.0071
Algebra/
Patterns
Residual (within columns)
299700
236
1270
Subscore
Total
315500
239
Treatment (between columns)
29950
3
9982
8.204 <0.0001
Geometry/
Measurement
Residual (within columns)
287100
236
1217
Subscore
Total
317100
239
Treatment (between columns)
34060
3
11350 7.655 <0.0001
Statistics/
Probability
Residual (within columns)
350100
236
1483
Subscore
Total
384100
239
Number
Treatment (between columns)
20450
3
6816
5.807
0.0008
Concepts/
Residual (within columns)
277000
236
1174
Computation
Total
297500
239
Subscore
Treatment (between columns)
28910
3
9638
7.647 <0.0001
Process of
Mathematics
Residual (within columns)
297500
236
1260
Subscore
Total
326400
239
The Tukey-Kramer method post hoc analysis was then used to compare all possible pairs
of means between student groups and determine if any specific pairs of group means were
significantly different from one another. The Tukey-Kramer results are shown in Table 6.
Figure 5 shows mean scores with significance reported based upon the Tukey-Kramer post hoc
comparison between students with one, two, or three of years of instrumental music instruction
versus students with no instrumental music instruction at a confidence interval of 95%.
29
Table 6. Tukey-Kramer Method Post Hoc Test Analysis for the Total Music Instruction
Comparison of Years of Instrumental Music Instruction Versus MSA Total Test Scale Score and
Subscores
Years of
Instrumental
MSA Section
Mean Difference
q
p-value
Music
Instruction
0 vs 1
-4.855
1.221
>0.05
0 vs 2
-14.34
3.704
<0.05
Total Test
0 vs 3
-24.13
6.762
<0.001
Scale Score
1 vs 2
-9.481
2.311
>0.05
1 vs 3
-19.28
5.047
<0.01
2 vs 3
-9.799
2.640
>0.05
0 vs 1
-1.996
0.4143
>0.05
0 vs 2
-14.68
3.130
>0.05
Algebra/
0 vs 3
-18.39
4.251
<0.05
Patterns
1 vs 2
-12.69
2.552
>0.05
Subscore
1 vs 3
-16.39
3.542
>0.05
2 vs 3
-3.707
0.8242
>0.05
0 vs 1
-3.860
0.8188
>0.05
0 vs 2
-15.04
3.275
>0.05
Geometry/
0 vs 3
-27.22
6.431
<0.001
Measurement
1 vs 2
-11.18
2.297
>0.05
Subscore
1 vs 3
-23.36
5.157
<0.01
2 vs 3
-12.19
2.769
>0.05
0 vs 1
-1.533
0.2944
>0.05
0 vs 2
-19.34
3.815
<0.05
Statistics/
0 vs 3
-27.13
5.804
<0.001
Probability
1 vs 2
-17.81
3.314
>0.05
Subscore
1 vs 3
-25.60
5.117
<0.01
2 vs 3
-7.793
1.603
>0.05
0 vs 1
-6.828
1.474
>0.05
0 vs 2
-9.633
2.136
>0.05
Number
0 vs 3
-23.65
5.686
<0.001
Concepts/
Computation
1 vs 2
-2.805
0.5869
>0.05
Subscore
1 vs 3
-16.82
3.779
<0.05
2 vs 3
-14.01
3.241
>0.05
0 vs 1
-6.283
1.309
>0.05
0 vs 2
-19.71
4.217
<0.05
Process of
0 vs 3
-26.69
6.195
<0.001
Mathematics
1 vs 2
-13.42
2.710
>0.05
Subscore
1 vs 3
-20.41
4.426
<0.05
2 vs 3
-6.988
1.560
>0.05
30
A.
5th Grade Scale Score
B.
5th Grade Algebra/Patterns Subscore
450
450
***
440
Th
ne
s
Instrumental Music Instruction
5th Grade Geometry/Measurement Subscore
450
O
Ze
ro
Ye
re
e
o
Tw
O
Ye
ar
s
ar
s
Ye
Ye
ne
Ye
ro
Ze
Instrumental Music Instruction
Ye
ar
400
re
e
400
ar
s
410
ar
410
s
420
Th
420
Ye
ar
ns
ns
430
Tw
o
430
Ye
ar
MSA Score
*
ar
s
MSA Score
440
C.
*
ns
D.
5th Grade Statistics/Probability Subscore
***
450
***
440
*
440
ns
Ye
re
e
ne
Ye
ar
s
Th
Ze
Th
Instrumental Music Instruction
5th Grade Number Concepts/Computation Subscore
F.
5th Grade Process of Mathematics Subscore
450
450
***
ns
420
ar
s
Ye
ne
O
Ye
ro
Ze
Ye
ar
s
s
Ye
ar
re
e
Th
Tw
o
Ye
Ye
ar
O
ne
ar
s
Ye
ro
Instrumental Music Instruction
re
e
400
Th
400
ar
s
410
ar
s
410
Ye
420
*
430
o
ns
Tw
MSA Score
ns
430
Ze
***
440
ar
440
MSA Score
E.
O
ro
Ye
re
e
o
Tw
O
Ye
ar
s
ar
s
Ye
Ye
ne
Ye
a
ro
Ze
Instrumental Music Instruction
Ye
400
o
400
ar
s
410
ar
410
ar
s
420
Tw
420
430
ar
MSA Score
ns
rs
MSA Score
ns
430
Instrumental Music Instruction
Figure 5. 5th grade scale and subscores are reported, grouped by years of instrumental music
instruction. Significance is based on Tukey–Kramer post hoc p-values for no music versus one
year, two years and three years of instrumental music instruction (* p<0.05, ** p<0.01, ***
p<0.001). Total Test Scale Score (A), Algebra/Patterns subscore (B), Geometry/Measurement
subscore (C), Statistics/Probability subscore (D), Number Concepts/Computation subscore (E),
and Process of Mathematics subscore (F) by years of instrumental music instruction.
31
Based on the Tukey-Kramer post hoc analysis at a 95% confidence interval, the null
hypothesis stating that that the mean total test scale scores and subscores on the mathematics
portion of the MSA of students who received 0, 1, 2 and 3 years of instrumental music
instruction in elementary school would all be equal was rejected in the following comparisons:
total test scale score 0 vs. 2, 1 vs. 3 and 0 vs. 3 years of instrumental music instruction, all
subscores 0 vs. 3 years of instrumental music instruction, geometry/measurement subscore and
number concepts/computation subscore 1 vs. 3 years of instrumental music instruction, and
statistics/probability and processes of mathematics subscores 0 vs. 2 and 1 vs. 3 years of
instrumental music instruction. These results suggest that there is a statistically significant
difference in mathematics achievement in the aforementioned categories between students who
have received instrumental music instruction versus those who have not. In all other cases the
null hypothesis could not be rejected.
32
CHAPTER 5
DISCUSSION
The research hypothesis for this study theorized that students who received instrumental
music instruction were predicted to have a higher level of mathematics achievement as measured
by their performance on the MSA than those who did not receive instrumental music instruction.
The research hypothesis was tested using within grade comparisons to show the effect of
receiving instrumental music instruction in a given year on mathematics achievement and a total
music instruction comparison which related the total number of years of instrumental music
instruction in elementary school to fifth grade mathematics achievement. The research
hypothesis was supported by statistical analysis of the data.
According to the within grade comparison, the mean total test scale score or subscore
was higher in all cases for those students who received instrumental music instruction versus
those who did not. The statistical significance was most evident in grades 3 and 5 with less or no
statistically significant differences in the total test scale score and subscore means in grade 4.
Instrumental music instruction showed the greatest impact on the mathematics achievement of
students in the third grade.
The Anne Arundel County Public Schools elementary math curriculum was analyzed to
provide an interpretation of these results. The math curriculum in the elementary grades in Anne
Arundel County Public Schools is circular in nature, meaning that the topics are introduced early
on and then revisited each year in a more complex way. Several new topics are then introduced
in grade 5 to be revisited in the middle school years. Perhaps the greatest benefit of students
receiving instrumental music instruction occurs as they master the mathematical skills and
concepts when they are initially introduced and then there is an opportunity with successive
33
lessons on the same topics for students not receiving instrumental music instruction to narrow the
achievement gap. For example, students in grade 3 with instrumental music instruction might
receive the greatest benefit as new topics (multiplication, division, fractions, etc.) are fully taught
for the first time. In grade 4, students are seeing similar curriculum topics again, so instrumental
music instruction is not as beneficial as they might have mastered the skills necessary to be
successful in understanding these mathematics concepts. In grade 5, decimals, integers,
equations, and other novel topics are introduced and instrumental music instruction again
benefits students seeing a concept for the first time. It is theorized, then, that an analysis of
grade 6 instrumental music instruction might show trends similar to grade 4.
The total music instruction comparison shows that the mean fifth grade total test scale
score and all fifth grade subscores showed incremental improvement as total years of
instrumental music instruction increased. The mean scores of students who had three years of
instrumental music instruction by the fifth grade saw statistically significant differences of an
additional 18 to 27 points on their total test scale score or subscores over those who had zero
years of instrumental music instruction and an additional 19 to 25 points over those who had
only one year of instrumental music instruction. Though it was not statistically significant, zero
to one year, one to two years and two to three years of instrumental music instruction also
showed an increase in mean total test scale score and subscores. The results could become
statistically significant with an increase in sample size.
There are several possible threats to the internal validity of this study. The first possible
factor to consider is self-selection. The subjects and their families ultimately selected whether or
not they would receive instrumental music instruction. Therefore, it cannot be specified whether
the instrumental music instruction caused the outcomes observed or that pre-existing natural
34
differences in the subjects could have caused the variation in achievement. Random assignment
of individuals to treatment (instrumental music instruction) and control (no instrumental music
instruction) groups would be an effective solution to this validity concern. Unfortunately, this is
often not possible in an educational setting and might inadvertently cause more validity issues by
putting students in situations they would not otherwise choose. It is also possible that there were
maturation effects, meaning that the students’ mathematics achievement increased simply due to
the fact that they progressed physically and cognitively in their development from 3rd to 5th
grade. However, this effect is not significant because both students who received instrumental
music instruction and those who did not could exhibit this effect.
Additionally, there are concerns relating to the external validity of this study. One threat
to external validity is population. Generalizations of this study’s conclusions relating
mathematics achievement and instrumental music instruction may not translate to different
populations. The population of this study was an accessible population (those schools able to
gather historical instrumental musical instruction data) rather than a target population.
Therefore, the results may not even be able to be generalized to the district population as a
whole. The examined population was taught from two mathematics curricula where the same
academic topics were covered in a different sequence throughout the year. In order to eliminate
this concern, a standardized mathematics curriculum for all students should be implemented.
Finally, if a school has high mathematics achievement as well as high instrumental music
participation, the data could be skewed. An increase in both population sample size as well as
increasing the number of schools studied would be a solution to this problem. One ecological
threat to external validity of this study is the measurement of the dependent variable, where the
35
study’s results may not be generalized to other dependent standardized mathematics achievement
test measures besides the Maryland School Assessments.
Future work in the area of the relationship between mathematics achievement and
instrumental music instruction could examine the impact of this instruction disaggregated by
gender, race/ethnicity, special education, free and reduced meals and all other student groups. In
order to complete this study a significantly larger total sample size (both in terms of numbers of
students and numbers of schools participating) would be needed to have a significant number of
students in each subgroup. At least 100 students in each subgroup would be recommended for a
comparison at the level of this study. Also, increasing the number of class sets of students
(groups of students who were followed from grades 3 to 5) will give us a large enough school by
school sample size to determine whether individual school programs and their respective
instrumental music instruction programs bias the overall achievement results. In addition, future
work could include creating an experimental study where students are randomly selected and
assigned to control or treatment groups in order to eliminate several threats to validity.
This study is fundamental in its efforts to connect mathematics achievement and
instrumental music instruction, especially if it serves as a starting point from which to pursue the
future work discussed above. By completing studies such as this, the evidence for the
importance of elementary instrumental music programs increases and the loss of such critical
programs is prevented. The argument that instrumental music programs in elementary school
deprive a student of much needed core academic instruction is significantly weakened when the
benefits of the program are clearly articulated in terms of academic achievement. Therefore,
programs to produce increases in mathematics achievement should not be implemented at the
expense of instrumental music instruction. Rather, instrumental music instruction and other
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programs whose skill sets can be applied across disciplines should be supported and increased to
help maintain America’s status as a leader and innovator in mathematical fields.
37
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