Order 804857: Mathematics vs Music
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Childhood Education
ISSN: 0009-4056 (Print) 2162-0725 (Online) Journal homepage: http://www.tandfonline.com/loi/uced20
Music Makes Math Meaningful
R. Jill Edelson & Gretchen Johnson
To cite this article: R. Jill Edelson & Gretchen Johnson (2003) Music Makes Math Meaningful, Childhood Education, 80:2, 65-70, DOI: 10.1080/00094056.2004.10521259
To link to this article: https://doi.org/10.1080/00094056.2004.10521259
Published online: 04 Sep 2012.
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R. Jill Edetsan and Gretchen Johnson R. Jill Edelson is Assistant Professor, Teacher Education Department, SUNY College at Old Westbury, Old Westbury, New York, and a consultant and music specialist at Big Chief Nursery School and Kindergarten, East Meadow, New York. Gretchen Johnson is Associate Professor and Chair, Department of Child- hood Education, City College of the City University of New York.
t Music Makes Math Meaningful
T oday, everything seems to be interconnected. In the education community, "interdisciplinary" teaching is the latest buzzword. While good early childhood teachers have been teaching in an interdisciplinary manner for years, there is one combination that could be strengthened: math and music.
By integrating mathematics and music, teachers will be able to help children achieve national and state learning standards in mathematics as well as the creative arts. For example, the National Council of Teachers of Mathematics (NCTM) (2000) calls for teachers to help children make math- ematical connections in contexts outside of mathematics. Also, components of appropriate practice for young children, as defined by the National Association for the Education of Young Children (Bredekamp & Copple, 1997), state that math needs to be integrated with songs; children need to understand notation, rhythm, and explore their relationships; children need to have daily opportunities for aesthetic expressions and appreciation through art and music; and children need to learn from self-directed problem solving and experimentation.
The connections between music and math are ever-present. Brain re- searcher Eric Jensen, when asked about the arts and education, stated that "music is a part of all of us, and it's critical to us as learners to develop pattern-making," adding that math skills tend to be stronger in students who have a music background (D'Arcangelo, 1998, p. 25). Using music to enhance a curriculum, such as math, enriches the environment for children, creates an atmosphere free of undue pressure and stress and infused with a degree of pleasurable intensity, promotes exploration and the fun of learning, and allows the child to be an active participant rather than a passive observer (Diamond & Hobson, 1998).
Teachers can use music to enhance children's pleasure and understanding of difficult mathematics concepts and skills. Children need active, experi- ential learning experiences in meaningful contexts to develop complex thinking skills and problem solving. Grandin, Peterson, and Shaw (1998) state that music enhances spatial-temporal reasoning skills, which are cru- cial to learning proportional reasoning and geometry skills. Rauscher et al. (1997) found that music promotes the development of such thinking skills as recognizing patterns and using logic. This type of thinking is essential for mathematics and science.
While good
early childhood
teachers have
been teaching in
an interdisciplinary
manner for years,
there is one
combination that
could be
strengthened:
math and music.
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Pattern Activities The idea of pattern is a powerful one that not only is essential to mathematics and music, it also cuts across all other curriculum areas. Pattern work prepares children for the patterns they will encounter in the number system, such as alternating odd and even numbers. In music, children find patterns in the re- peated melodies, refrains, or rhythms of a song. A pattern is an arrangement of elements that repeats according to a rule. Work with patterns enhances children's thinking and reasoning skills, because they must: 1) analyze the pattern to figure out the rule, 2) communicate the rule in words, and 3 ) predict what will come next in the pattern. In addition, children also can learn to translate a pattern. When children trans- late a pattern, they refer to the same rule but express the pattern using a different medium or materials. Thus a one, two, one, two pattern can become a skip, jump, skip, jump pattern. The rule is the same-there are two elements that alternate-but the number pattern has been translated into a series of physical movements.
Name Patterns. Demonstrate how to use beats on a drum to represent the syllables in a first name, begin- ning with your own. Take the class attendance using the drum, and have the children listen carefully to each child's name to see who might share sound patterns.
"Hello, Jane" (strike once on the drum as you say the name). "Hello, Hen-ry" (strike twice on the drum). "Hello, Jen-ni-fer" (strike 3 times). "Hello, Al-ex-an- der" (strike 4 times). Beat one, two, three, or four beats on the drum and ask children to group themselves together when they hear the number of drum beats that corresponds to the number of syllables in their names. The children then can decide which group (or set) is the largest or the smallest.
TransIating a Pattern. This activity is designed to help children translate a pattern from one medium to another; for example, from sound to visual. Strike a name pattern on the drum; when the children with that name pattern stand up, give each child an index card on which his or her sound pattern is represented by "bumps"-one bump for a one-syllable name, two bumps for a two-syllable name, etc. Have the children arrange themselves into a one-bump, two-bump, one- bump, two-bump pattern. One child can strike the sound pattern with the drum while the other children clap their hands. Then, ask the children to suggest new patterns.
Graphing Sound Patterns. Children exchange their bump card for a colored Post-it note (e.g., yellow for one syllable, blue for two syllables, pink for three syllables, and green for four syllables), and place their Post-it notes on a large sheet of paper on the wall; thus, the children can prepare a graph from the data (see
photo #l). Ask the children to describe what they see on the graph.
Learning Symbols: Notes and Rests. Symbols are important in math, and this is a friendly, active way to introduce new symbols. Present two musical sym- bols-quarter notes and quarter rests-that can be displayed in a pattern on individual cards on a window sill, on the tray of a chalkboard, or on the floor (see photo #2). Have the children practice clapping when they see a note and spreading their arms wide for a rest. Subsequently, the children can arrange the symbol cards in various ways for the class to "play," using clapping and arm movements.
Two-element Pattern. Introduce two kinds of rhythm instruments. These rhythm instruments make their sounds either by being shaken (bells, maracas, tambourine) or by being hit (triangles, sticks, wood blocks). Hand out instruments to six children, asking each child to tell how his/her in- strument makes a sound. Help the children to ar- range themselves in a pattern of shake, hit, shake, hit. Repeat the activity with other children, and ask them to create new patterns.
Listening for Changes in a Musical Pattern. Have the children listen to music (e.g., "The Syncopated Clock" by Leroy Anderson). Demonstrate, with a wood block, the steady tick-tock of the clock, and then have the children raise their hands when they hear a change in the pattern of the music.
Serial Order Deepening the Concept of Serial Order Wi th Sound.
A musical scale is an example of serial order, with sounds arranged according to pitch. Using a xylo- phone or piano, demonstrate the changes in pitch by going up or down a scale.
Serial OrderFrorn Lowest t o Highest. Here's a game that children love, and it's a "magical" way to calm a class. Sing and play "The Jack in the Box," playing and/or singing a different tone for each line of the song. The children get down on the floor on all fours and curl up, hiding their eyes. At the highest note ("Yes"), they bounce up.
Jack in the box Still ns n iiioiise Deep dozoii inside liis Little zoliite house Jack in tlze box Still as can be Will lie pop out? Yes! LetS see!
Songs and Visuals To Reinforce the Concept of Serial Order. The song "The Old Lady Who Swal-
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lowed a Fly" illustratp serial order in two ways. The old lady swallows the animals in order, from first to second, to third, to fourth . . . all the way to eighth. Another pattern exists in that she swallows the small- est animal first and then swallows increasingly larger ones. If visuals such as posters are used, the children can discuss both kinds of serial order when the song is finished (see photo #3).
Comparing Cardinal and Ordinal Numbers Songs originally written to include cardinal numbers (one, two, three, four), such as "Five Little Chicka- dees," can be adapted to include ordinal numbers. Have five children come to the front of the room. Have the class sing the song with cardinal numbers. On the second line of the chorus, touch one child, who then "flies away." Deliberately mix up the order of the children you choose, to reinforce the idea that when using cardinal numbers, it doesn't matter which object we take away; we are still subtracting one and getting the same result. Then switch to the ordinal number version of the same song. This time, on the second line of the chorus, touch the first child in line, then the second child, etc. After the song is finished, discuss the difference between the two songs. With ordinal numbers, the order does matter. If the chicka- dees are lined up in a row, only one chickadee is the first in line, only one is the second in line, etc. The following song is the cardinal version, with the ordinal version in parentheses.
Five little chickadees sitting near the door, One (thefirst)flew away and then there were four.
CHORUS Chickadee, chickadee, happy and gay, Chickadee, chickadee, f ly, f l y away.
Four little chickadees sitting near a tree, One (the second) Jew away and then there were three.
CHORUS Three little chickadees looking at you. One (the third) flew away and then there were two.
CHORUS Two little chickadees sitting in the sun, One (the fourth) flew away and then there was one.
CHORUS One little chickadee sitting all alone, Helshe (the fifth) flew away and then there were none.
CHORUS
Photo # 1: Graphing of names.
Photo #2: Musical notes infloor display.
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This song is an excellent one to sing throughout the year, as you can adapt it to suit seasonal themes (e.g., pumpkins that roll away, witches that fly away, or snowmen that melt away).
Sorting/Classifying ActivitieslVenn Diagram An understanding of sorting and classifying, an essential concept in mathematics, can be strengthened through the use of rhythm instruments. Have the children sort them- selves into three groups ac- cording to the way their rhythm instrument makes a sound (by being hit, shaken, or rubbed). In some cases, an
Photo #3: Children displaying serial order
instrument can make a sound in more than one way
Photo #4: Venn Diagram of musical instruments.
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(e.g., a tambourine can be hit or shaken), and this can be represented in a Venn Diagram (see photo #4). Then let the child choose which way to play the instrument. Have each group, in turn, make its sounds. Then, the children will describe each group's sound, and the teacher will write the descriptive words on a chart.
How Instruments in an Orchestra Are Sorted Symphony orchestras, no matter how large or small, are sorted into four groups: the strings (pluck), the woodwinds (whistle), the horns /brass (toot), and per- cussion instruments (boom) (see Figure 1). Have the children listen to selections from Benjamin Britten's "Young People's Guide to the Orchestra," examine pictures, or invite musicians to bring instruments to the class. The children then can place each instrument in a "pluck," "whistle," "toot," or "boom" group.
Learning Fractions by Creating Musical Arrangements Introduce the whole note, which gets four beats (counts), the half note, which gets two beats, and the quarter note, which gets one beat (see Figure 2). If some children are already familiar with notation, the eighth note, which gets one-half a beat, also can be introduced.
Have the children work with a partner and investi- gate all the ways they can make a whole note with quarter notes and half notes (and eighth notes, if ap- propriate). The partners then can tap out the resulting rhythm with sticks (see Figure 3).
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Conclusion Integrating music and mathematics activities does not require musical training or expensive equipment. All you need are a set of rhythm instruments (many of which can be made by the children), a phonograph, a tape recorder or CD player, a few musical selections, a baton, and some rules for following the “conductor.” The activities described here are consistent with the current focus on interdisciplinary curriculum and re- cent research on thinking and learning. They will enable children to learn mathematical concepts more easily, while having lots of fun.
References Bredekamp, S., & Copple, C. (Eds.). (1997). Developmentally
appropriate practice in early childhood programs (Rev. ed.). Washington, DC: National Association for the Education of Young Children.
DArcangelo, M. (1998). The brains behind the brain. Edu- cational Leadership, 56(3), 20-25.
Diamond, M., & Hobson, J. (1998). Magic trees ofthe mind: How to nurture your child‘s intelligence, creativity, and
healthy emotionsfrom birth through adolescence. New York Dutton.
Grandin, T., Peterson, M., & Shaw, G. L. (1998). Spatial- temporal versus language-analytic reasoning: The role of music training. Arts Education Policy Review, 99(6), 11-15.
Hoffman, M. (1997). The NPR classical musiccompanion: Terms and conceptsfrom A to Z. Boston/New York Houghton Mifflin.
National Council of Teachers of Mathematics. (2000). Prin- ciples and standards for school mathematics. Reston, VA: Author.
Rauscher,R.H.,Shaw,G.I.,Levine,I. J.,Wright,E.L.,Dennis, W. R., & Newcomb, R. I. (1997). Music training causes long-term enhancement of preschool children’s spatial- temporal reasoning. Neurological Research, 19, 2-8.
Westcott, N. B. (1980). I know an old lady who swallowed afly (retold and illustrated). Boston: Little, Brown.
Music References Anderson, Leroy. “The Syncopated Clock“ . . Britten, Benjamin. “Young People’s Guide to the Or-
chestra“
MUSICAL NOTATION
4 BEATS TO A MEASURE
0 d d
HOLD FOR 4 BEATS
EACH NOTE 2 BEATS
4 J J J J EACH NOTE 1 BEAT EACH QUARTER NOTE I GETS ONE BEAT EACH NOTE 1 /2 BEAT
1 and 2 and 3 and 4 and Say 1 and, 2 and, 3 and, 4 and
Figure 2
Figure 3
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