Music Makes Math Meaningful
Edelson, R Jill
Today, 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 mathematical 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 j 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 researcher 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, experiential 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 crucial 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.
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 repeated 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 translate 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, beginning 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-ander” (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.
Translating 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 #1). 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 symbols-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 instrument makes a sound. Help the children to arrange 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 With Sound. A musical scale is an example of serial order, with sounds arranged according to pitch. Using a xylophone or piano, demonstrate the changes in pitch by going up or down a scale.
Serial Order From Lowest to 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 as a mouse
Deep down inside his
Little white house
Jack in the box
Still as can be
Will he pop out?
Yes! Let’s see!
Songs and Visuals To Reinforce the Concept of Serial Order. The song “The Old Lady Who Swallowed a Fly” illustrates 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 smallest 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 Chickadees,” 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 chickadees 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.
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 Activities/Venn 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 themselves into three groups according to the way their rhythm instrument makes a sound (by being hit, shaken, or rubbed). In some cases, an instrument can make a sound in more than one way (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 percussion 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 investigate all the ways they can make a whole note with quarter notes and half notes (and eighth notes, if appropriate). The partners then can tap out the resulting rhythm with sticks (see Figure 3).
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 recent research on thinking and learning. They will enable children to learn mathematical concepts more easily, while having lots of fun.
Copyright Association for Childhood Education International Winter 2003/2004
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