**David Fonda - Research Report for MUS 600 – Spring
2012 – Dr. Wang**

**Introduction**

** **As an elementary school music educator, I am very frequently looking for
ways to connect music across the curriculum to other areas of content. These connections have several positive
outcomes. The first one is the most important because it directly relates to
students. Connecting music to other content areas aids in strengthening the
understanding of those concepts by students. It can also be used to show your
fellow educators and administration the value of what is being offered in the
music classroom. Some of these connections to music are easier than others. It
seems to me, the easiest cross-curricular connection to music is with
mathematics.

Mathematics
and music connect on several different levels. By design, both subjects are
very structured. The time signature in music functions like a mathematical
formula to describe the expected contents of each measure of the piece of
music. The concept of intervals was discovered by Pythagoras, a brilliant
mathematician. The discovery of tuning with regards to the intervals of the
major scale can be related to mathematics. The structure of note values and how
they are subdivided is mathematical. It stands to reason that mathematical
understanding and musical understanding are related.

The question
this study attempts to explore is: does music instruction enhance mathematical
understanding?

**Review of Related
Literature**

Many
studies have been done on the topic of music’s connection to mathematical
understanding. Children develop an understanding of the structure of math long
before they can understand or use its vocabulary and symbols. For example,
recall the skills involved in the singing the childhood song *This Old Man*. “This simple song incorporates many basic
math skills, including matching and comparing (through changes in pitch,
volume, and rhythm); patterning and sequencing (through repetitions of
melodies, rhythms, and lyrics); and counting and addition (identifying cardinal
numbers and adding one more with each verse).”(Church, 2001) Many other songs
are used during early childhood to aid in children’s understanding of
mathematical concepts such as counting. A few of those that come to mind are; *1, 2, Buckle my Shoe* and *Engine, Engine #9*.

It may begin
with counting but the connection between music and mathematics blossoms into
much more as students start to learn other mathematical concepts. “Mathematics
is a major component of music. Music teaches and reinforces counting, number
recognition, fractions, symbols and their meanings in a concrete way. Rhythm
can also help students with memorization of math facts.” (Diamantes, 2002)

Research
studies have been conducted on the correlation between music and math for many
years. Interestingly, the results cover a broad spectrum of findings. One of
the studies “showed no significant statistical difference among students of
mathematics while listening to various forms of background music, it seems
likely that there is some association between music performance and development
of mathematical skills.” (Diamantes, 2002)
This clearly shows that it isn’t just the presence of music but the
actual study of and/or involvement in music is what has a positive impact on
mathematical learning. Even within students who are studying music the results
of these various studies have varied.

A study was conducted on high school
students, comparing those with some music credits to those with none. No
statistically significant difference was found in their mean math grade point
averages or their mean cumulative grade point averages. However, the students
were then separated into two groups based on the number of music credits.
Students who had earned at least two music credits per grade level were placed
into Group A. The remaining students were placed in group B. The Group A students performed better than the students in Group B.
“Lower GPAs were nonexistent as the music credits increased.” (Cox, 2006) This study would suggest that the
mathematical benefits of studying music come with time and repetition.

Another example of the varying
degrees of benefits among students of music was a study done using the results
of a standardized test known as the Iowa Tests of Basic Skills (ITBC). This
study compared the mathematics scores of eighth graders who had received music
instruction in a group setting or through private lessons. It also compared
students who took private lessons on the keyboard versus students who did not. “Analyses
indicated that students who had private lessons for two or more years performed
significantly better on the composite mathematics portion of the ITBS than the
students who did not have private lessons. In addition, students who received
lessons on the keyboard had significantly higher ITBS mathematics scores that
did students whose lessons did not involve the keyboard.” (Cheek, 1999)

Iowa is not the only state that has
used standardized testing results to measure the effects of musical learning on
mathematical understanding. Ohio has also used their test to explore the
connection between music and math. They compared the results of instrumental
music students and their non-instrumental classmates according to socioeconomic
status (SES) over time. “The results show that instrumental students
outperformed non-instrumental students in every subject and at every grade
level. Instrumental students at both levels of SES held higher scores than
their non-instrumental classmates from fourth grade, suggesting that
instrumental music programs attract higher scorers from the outset of
instruction.” (Fitzpatrick, 2006)

Some studies have even examined the impact of the quality of
the music program on mathematical understanding. One such study was conducted
utilizing scores from various parts of the United States. The findings were
clear after all the scores were standardized for comparison purposes. “Analysis
of elementary school data indicated that students in exemplary music education
programs scored higher on both English and mathematics standardized tests than
their counterparts who did not have this high-quality instruction; however, the
effect sizes were slight. Analysis of middle school data indicated that for
both English and math, students in both exceptional music programs scored
better than those in no music classes or deficient choral programs; however the
effect sizes were not large.” (Johnson, 2006) “Music participation, both inside
of school and outside of school, is associated with measures of achievement
among children and adolescents. (Southgate, 2009)

There have also been studies done in
regards to how the brain functions during mathematics and music instruction. One
study that was done based on the hemispheric laterality in music and math found
“a relatively strong correlation was found between music ability and
right-brain hemisphere preference. A relationship between math and left-brain
hemisphere preference or integrated brain processing scores was found to be
marginal.” (Szirony, 2008) Other studies findings indicated that “both
the right and left hemispheres of the brain are involved in processing the
music.” (Diamantes, 2002) Even on the physiological level the processing of
music and math are being studied because of their similar processing within the
brain.

**Statement of Hypothesis**

** **Students who have music class before math class will score higher on
mathematical assessments than students who have music class after math class.

**Method**

The
participants in this study were chosen based on availability to the researcher.
Participants are 5^{th} grade students who attend an elementary school
in Mt. Sterling, KY. Socioeconomic status (SES) of students varies slightly;
most are lower class to lower-middle class and Caucasian. All students have
completed an instructional unit in music class that connected to various math
concepts one month prior to the study. None of the students have received
private instruction in music. They have music class for an entire week once
every four weeks. Four classes of 25 students each participated in this study.
Each class was made up of 20 students from the same homeroom and five students
from a 5^{th} homeroom.

This experimental
study was conducted with the cooperation of the homeroom teachers of the 5^{th}
grade team. Two of the homeroom teachers were asked to move their math block to
occur right before music class (Group A). Two homeroom teachers were asked to
move their math block to right after music class (Group B). The remaining
homeroom that was split up when attending my class will be analyzed separately
as SubGroup C.

The
assessment was a standardized math assessment that the entire grade level
across the district was using to assess the content of the current unit of
study. It was an open response assessment that consisted of four word problems
that included the content from the unit of study. It was administered on the fifth
day (Friday) of music class.

**Time Schedule**

This study
was completed over a four week period in March/April 2012. Each class attended
music class for five consecutive days for 50 minutes, per our school schedule.

**Results**

Significant
differences were found when comparing these two groups. The two and a half classes making up Group A,
which attended music class after their math block, scored lower on the math
assessment than the two and a half classes making up Group B, which attended
music class before their math block.

Group Involved in Study |
Math Assessment Results
- mean assessment score, percentage out of 100 |

Group A (50 students)
Math before Music |
82% |

Group B (50 students)
Music before Math |
87% |

SubGroup C (20 students) |
84% |

Group B scored an average of 5%
higher on the math assessment when compared to Group A. Subgroup C scored 2%
higher than Group A, and 3% lower than Group B on the assessment.

**Conclusion**

This study
showed that students who attended music class prior to their math block scored
higher on mathematical assessments when compared to students who attended music
class after their math block. It is interesting to note that members of SubGroup C still scored high enough to raise their mean
score over Group A. This study did not take into account that the homeroom
teachers involved have different strengths as well. Some of them teach math
more often than the others. Another potential variable to might have affected
the results was the occurrence of Spring break during the duration of the
study. Three of the classes were assessed prior to Spring break the other class
was assessed after Spring break.

A possible
limitation to the findings of this study is that the scope is broad. The
mathematical concepts that were being assessed were chosen by the researcher so
there weren’t necessarily any intentional specific connections to the
mathematical content during the duration of the study. With results this
favorable without any intentional specific connections to the math content, one
can hope that if it musical/mathematical connections are specific than there
could be an even greater positive correlation between music learning and
mathematical understanding.

**References:**

Cheek, Joyce M., Smith, Lyle R. (1999). Music Training and Mathematical
Achievement, *Adolescence*, Winter 1999, Vol. 34 Issue 136, p.759-761, 3p

Church,
Ellen Booth (2001). The Math in Music & Movement, *Early Childhood Today*, January 2001, Vol. 15 Issue 4, p.38-45, 8p

Church,
Ellen Booth (2006). Add Some Music & Math to Group Time, *Early Childhood Today,* October 2006,
Vol. 21 Issue 2, p.33-34, 2p

Cox, H.A., Stephens, L.J. (2006). The Effect of Music Participation on Mathematical
Achievement and Overall Academic Achievement of High School Students, *International Journal of Mathematical
Education in Science and Technology, *October 15 2006, Vol. 37 Issue 7,
p.757-763, 7p

Diamantes, Thomas, Young, Karen M., McBee,
Kimberly (2002).
An Analysis of Reading and Content Area Skills Improvement through Music
Instruction, *Reading Improvement*,
Fall 2002, Vol. 39 Issue 3, p.114-118, 5p

Fitzpatrick,
Kate R. (2006). The Effect of Instrumental Music Participation and
Socioeconomic Status on Ohio Fourth-, Sixth-, and Ninth-Grade Proficiency Test
Performance, *Journal of Research in Music
Education,* Spring 2006, Vol. 54 Issue 1, p.73-84, 12p

Geist, Kamile, Geist, Eugene A. (2008). Do Re Mi,
1-2-3: That’s How Easy Math Can Be: Using Music to Support Emergent
Mathematics, *YC: Young Children,*
March 2008, Vol. 63 Issue 2, p.20-25, 6p

Johnson,
Christopher M., Memmott, Jenny E. (2006). Examination
of Relationships between Participation in School Music Programs of Differing
Quality and Standardized Test Results, *Journal
of Research in Music Education*, Winter 2006, Vol. 54 Issue 4, p.293-307,
15p

Olson,
Catherine Applefield (2008). Test Scores Linked to
Music Program Quality, *Teaching Music*;
April 2008, Vol. 15 Issue 5, p.23-23, 1p

Southgate,
Darby E., Roscigno, Vincent J. (2009). The Impact of
Music on Childhood and Adolescent Achievement, *Social Science Quarterly*, March 2009, Vol. 90 Issue 1, p.4-21, 18p

Szirony,
Gary Michael, Burgin, John S., Pearson, L. Carolyn (2008). Hemispheric
Laterality in Music and Math, *Learning
Inquiry*, December 2008, Vol.2 Issue 3, p.169-180, 12p