Lesson Plans

Music Math:

Create a Clapping Symphony (Plus Fraction Math) This clapping symphony is a great way to introduce fractions. For as long as I can remember fractions has always been a topic that not all but many students struggle. I don't know whether it is the intimidation from what we hear or if it is just fear of the unknown. I think letting the children feel comfortable with participating in this little activity is a great beginning.


Link to lesson plan:
http://www.education-world.com/a_lesson/03/lp303-05.shtml

All these plan are simple enough to carry out with your students but also very valualble in teaching strategies that engage both the math and music skills. Having these resoursces in your classroom will help the child who struggles with math concepts and also the child who struggles with concepts in music. The following are links which go directly to the lesson plan.

A fun way to learn Shapes - sing Hokey Pokey with Shapes instead of body parts
Here's an idea for Shape "Hokey Pokey"
A fun way to learn math using the song, "Who Stole the Cookies"
A Math lesson plan that uses Music to help teach the Multiplication facts
"The Twelve Days of Math" Christmas song is the basis for this lesson idea
This Addition / Absolute Value lesson plan uses a song to help teach the concepts
This is just a brief song to help with teaching Circles, Diameter, and Radius
A fun way to learn math using the song, "Who Stole the Cookies
A Math lesson plan that uses Music to help teach the Multiplication facts
This Addition / Absolute Value lesson plan uses a song to help teach the concepts
This creative lesson teaches two-digit multiplication and the cha-cha
"Music Math" teaches order of operations using music note values
"Music Math" teaches order of operations using music note values


References:

"Hotchalks lessonplanpage.com." Choose your lesson plans. 1996 - 2007 . HotChalk, Inc. All Rights Reserved.. 26 Mar 2007 .



Hopkins, Gary. "LESSON PLANNING ARTICLE ." Education World. 02/26/2007. Copyright © 2007 Education World . 26 Mar 2007 .

Mathematics Songs

These songs bring math into childrens lives through playful interactive songs. Introducing math to children through this format will eliminate some of the fears and negative vives that seem to be associated with math.


Mathematics Songs Early Numbers Counting Lyrics CDs Downloads
Addition and Subtraction Lyrics CDs Downloads
Multiplication and Division Lyrics CDs Downloads
Middle/High School Math Song Lyrics CDs/Books


"Songs for Teaching." Songs for Teaching The Definitive Source for Educational Music. © 2002-2007 . Educators' Circle LLC.. 26 Mar 2007 http://www.songsforteaching.com/.

Mapping of Numbers to Tones

This information gives you better sense on how the note values used in music can be seen on a number graph. This information gives you a a good visual of what such a graph would look like.

Duration
All digits/numbers map to a specified note value. Digits or groups of digits map to specified note values. The number n of consecutive equal digits/numbers maps to a tied n multiple of a specified note value. The number of digits m of a number maps to the note value 1/m.

Pitch
Digits or groups of digits map to specified pitches, including a pause and change of octave. The number n maps to the pitch n scale steps relative to the pitch of the previously determined tone.

Structure
Digits of numbers of different powers map to separate parts. Parts are initiated later in a piece by numbers satisfying specified conditions.

Scholarly Journals: Math and Music - Harmonious Connections

Math and Music: Harmonious Connections

This journal concentrates on how mathematics can be used to analyze musical rhythms, to study the sound waves that produce musical notes, to explain why instruments are tuned, and to compose music. The relationship between mathematics and music is explained through proportions, patterns, Fibonacci numbers or the Golden Ratio, geometric transformations, trigonometric functions, fractals, and other mathematical concepts. A lot of associations are given which will allow readers a better chance to make the association clearer through prior knowledge.

Reference:

Garland, Trudi Hammel, and Kahn, Charity Vaughan. "Math and Music: Harmonious Connections.." ERIC (1995-00-00): 162.

Scholarly Journals: Integrate the Arts. Music by Numbers

Integrate the Arts - Music by Numbers

This article presents a group project that uses math, science, and art to help elementary school students explore the tones of music in their own world. The children make music out of their own telephone numbers, and graph their own telephone numbers. This article goes further to encourage children to use what they know about each subject and make associations that involve them using knowledge from each subject. The activities in this article are short, fun and non-intimating, which allow for lots of great learning.

Reference:

Integrate the Arts. Music by Numbers. Parks, Mary, Instructor, v105 n4 p33-34 Nov-Dec 1995. 1049-5851

Science Magazine: The Geometry of Musical Chords

The Geometry of Musical Chords - Dmitri Tymoczko

This magazine is a great source in establishing the history of how geometry got interlinked with the making of music. We are introduced to the music aspect of the association through the definition of what exactly a musical chord is. "A musical chord can be represented as a point in a geometrical space called an orbifold. Line segments represent mappings from the notes of one chord to those of another. Composers in a wide range of styles have exploited the non-Euclidean geometry of these spaces, typically by using short line segments between structurally similar chords. Such line segments exist only when chords are nearly symmetrical under translation, reflection, or permutation. Paradigmatically consonant and dissonant chords possess different near-symmetries and suggest different musical uses. Western music lies at the intersection of two seemingly independent disciplines: harmony and counterpoint. Harmony delimits the acceptable chords (simultaneously occurring notes) and chord sequences. Counterpoint (or voice leading) is the technique of connecting the individual notes in a series of chords so as to form simultaneous melodies. Chords are usually connected so that these lines (or voices) move independently (not all in the same direction by the same amount), efficiently (by short distances), and without voice crossings (along non intersecting paths). These features facilitate musical performance, engage explicit aesthetic norms, and enable listeners to distinguish multiple simultaneous melodies. The preceding ideas can be extended in several directions. First, one might examine in detail how composers have exploited the geometry of musical chords. Second, one could generalize the geometrical approach by considering quotient spaces that identify transpositionally and inversionally related chords. Third, because cyclical rhythmic patterns can also be modeled as points, one could use these spaces to study African and other non-Western rhythms. Fourth, one could investigate how distances in the orbifolds relate to perceptual judgments of chord similarity. Finally, understanding the relation between harmony and counterpoint may suggest new techniques to contemporary composers."

The information gathered in this magazine uses terms that both music and math students would be familiar with. I had to read this article several times to get an understanding of the links between geometry and musical chords, but I thought it was intriguing how simple the techniques seem when they are being used for a particular purpose. I'm sure I am qualified to review such an informative piece but I thought it was quite interesting because it really opens up the mind to make new associations with a topic such as geometry which has been introduced to us in our earlier years. Also , probably knowing the extent of such how geometry is used would help us put a bigger emphasis on its importance.

Reference:

Science 7 July 2006:Vol. 313. no. 5783, pp. 72 - 74DOI: 10.1126/science.1126287

Science Magazine: Exploring Musical Space

Exploring Musical Space

In this magazine we are introduced to musical score - a graph whose vertical axis represents pitch and whose horizontal axis represents time. We are brought back again to the time of Pythagoras where mathematical principles underlie many musical phenomena. In this article it goes on to say that it is even more surprising "that our understanding of the mathematical structure of the spaces in which musical phenomena operate remains fragmentary." I would never have thought how far back the roots of the connections between music and math were. This article points out that, music theorists classify chords in categories such as major triads, grouping chords together with their translations in some appropriate space. Western musicians are accustomed to a discrete view of pitch space, corresponding to the chromatic scale playable on the piano, but the general problem requires consideration of a larger space in which continuous pitch variation is possible. The various equivalence relations give rise to an assortment of quotient spaces.

In this article we are introduced to Tymoczko's work. He developed a project that characterizes these spaces in great generality and relates the geometry of the spaces to the musical behavior of the chords that inhabit them. Tymoczko's mathematical music theory stated that, "although Terra incognito to practicing musicians and even to many professional music theorists, has in recent years blossomed into a sizable and multifaceted industry." Tymoczko talks about the pitch-class set theory which is the study of a discrete 12-note quotient space, developed as a means of confronting the analytical challenges posed by "post-tonal" music of the 20th century. He included in his study the diatonic set theory which investigates the subtle and beautiful relationship between the 12-note chromatic scale and diatonic scales such as the C major scale, with seven unequally spaced notes per octave.


References:

Hook, Julian. "MATHEMATICS:Exploring Musical Space." Science Magazine Science 7 July 2006:Vol. 313. no. 5783, p7 July 2006: pp. 49 - 50. .

Relationship Between Math and Music SAT Scores

I thought it would be interesting to find out if there was a relationship between math and music SAT scores and sure enough, there was. I went back as far as 1994, and this is what I found out:

"In 1994, SAT takers with course work in music performance scored 49 points higher on the verbal portion of the test and 36 points higher on the math portion of the test than students with no course work or experience in the arts. Scores for those with course work in music appreciation were 59 points higher on the verbal portion and 42 points higher on the math portion. Longer arts study means even higher scores: In 1994, those who had studies the arts for more than four years scored 56 points higher on the verbal potion and 38 points higher on the math portion than students with no course work in the arts."

When I looked at more recent SAT scores, it was not surprising to see that students of the arts continue to outperform their non-arts peers on the SAT, according to reports by the College Entrance Examination Board. "In 2005, SAT takers with coursework/experience in music performance scored 56 points higher on the verbal portion of the test and 39 points higher on the math portion than students with no coursework or experience in the arts. Scores for those with coursework in music appreciation were 60 points higher on the verbal and 39 points higher on the math portion. Data for these reports were gathered by the Student Descriptive Questionnaire, a self-reported component of the SAT that gathers information about students' academic preparation."

The evidence of how each subject compliments the other is just phenomenal. From these scores, you cannot ignore the significance of how one compliments the other.


Reference:

"Scores of Students in the Arts." MENC. 2005. The National Association for Music Education. 26 Mar 2007 .

The Effect of Music on Spacial Reasoning

There is direct evidence, however, that music study does play a significant role in the improvement of spacial reasoning, the type most closely related to geometry and architecture. Research at the University of California at Irvine by Frances Rauscher has demonstrated a direct cause and effect relationship. She writes bluntly, "all other things being equal, if you look at two kids - one who studies music and one who doesn't - the child who studies music will have enhanced spacial reasoning" (Snyder, 1995, p. 40). This improvement, she writes, "generalizes as they get older and into better mathematical skills . . . a better understanding of those concepts that are required of research mathematicians" (Snyder, 1995, p. 41). This is the kind of spacial reasoning that is used when playing chess, for engineering, architecture, navigation and anything that requires a conceptual understanding of how things go together in space. She concludes, "I think the schools are really where music is going to make the most difference, and this connection to spacial reasoning is perhaps the place where music instruction is the most important and crucial for disadvantaged kids" (Snyder, 1995, p. 41). Every indication suggests that music will improve performance in the very areas that the educational reform movement would have us believe is important. But, by their actions, the reformers are removing the opportunities to achieve the very ends they set out for themselves.

Reference:

Snyder, , N., and Frances Rauscher. "Music and reasoning." ((1995). ): 40-41+50..

The Effect of Music Participation on Mathematical Achievement and Overall Academic Achievement of High School Students

During my research I stumbled upon a study that was conducted on high school students, comparing those with some music credits to those with none. The findings of this study was that no statistically significant difference was found between the two groups of students' mean math grade point averages (GPA) or their mean cumulative GPAs. Another study was conducted where 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 in Group A. This category included ninth graders with two or more music credits, tenth graders with four or more music credits, eleventh graders with six or more music credits, and twelfth graders with eight or more music credits. The remaining students were placed in Group B. The findings of this study indicated that students in Group A performed better than students in Group B. However, the differences were not statistically significant. This study did indicate a slight upward trend in GPAs as the number of music credits increased. Lower GPAs were nonexistent as the music credits increased.


Reference:

Cox, , H. A, and L. J.Stephens . "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 Volume 37, Number 7/(15 October 2006,on line date:Tuesday, November 07, 2006): 757-763.

First Person to Make the Connection

The first person to make the connection between math and music was Pythagoras of Samos, a famous philosopher and cult leader who lived most of the time in southern Italy in 5th century, BC. He is one of western civilization's strangest, but most influential thinkers and the first to believe in the idea that mathematics is everywhere. One bit of evidence of underlying rational numbers was in Greek music. At the time, music was not as complicated as it is today. The Greek octave had a mere five notes. Pythagoras pointed out that each note was a fraction of a string. He used the example of a string that played an A. The next note is 4/5 the length (or 5/4 the frequency) which is approximately a C. The rest of the octave has the fractions 3/4 (approximately D), 2/3 (approximately E), and 3/5 (approximately F), before you run into 1/2, which is the octave A. Pythagoras was excited by the idea that these ratios were made up of the numbers 1,2,3,4, and 5, and that there were five planets that moved along similar ratios and that all this meant something (ultimately the universe turned out to be irrational, which may explain a lot). Pythagoras imagined a "music of the spheres" that was created by the universe - a wonderful idea that inspired many composers. The 18th century music of J. S. Bach has mathematical undertones, as does the 20th century music of Philip Glass.


Reference:

Fauvel , John, Raymond Flood, and Robin Wilson. "Music and mathematics : from Pythagoras to fractals." Oxford University Press (2003): 189.

Welcome to the World of Math and Music

Mathematics and music have a strange connection. Music is the only art form where the form and the medium are the same. Mathematics is the only science where the methods and the subject are the same. During my research I have discovered that, as far back as 5th century, BC., math was accepted as a very natural part of music. Even though we do not really acknowledge the importance or should I say the connection between music and math in our classrooms, during my research I found many lesson plans readily available online for use. These lesson plans were designed so that each subject (math and music) compliment the other. There was an overwhelming amount of information about math and music connections . The more I researched their connections, the more I found out how much they complimented each other. This blog contains a summary of the information found and references in case you wish to read further. I hope through this research you will be able to see these connections more clearly and hopefully use this information in your future teachings.