1. If there has been so much research done on the success of the connection between music and math, why are we not seeing it more in the classrooms?
2. In my research, I discovered that having exposure to the arts such as music programs, gives you a chance of greater success in many of the mathematical areas. I wonder if the opposite is also true?
3. Since the connection between math and music goes back a long time- it makes you wonder what was considered more important, your music ability or your math comprehension?
Tuesday, April 3, 2007
Monday, March 26, 2007
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.
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/.
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.
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.
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
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
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
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