Patterns and Patterning
In mathematics, a pattern represents a repeating series of any kind. We want to help children learn to recognize, replicate, represent, and extend visual, sound, and motor patterns. Many of the typical materials in Figure 10.2 are useful for learning about, copying, and creating patterns. To identify a pattern, children apply classification, comparison, and ordering concepts to establish where a pattern starts, ends, and repeats. Teachers help children “read” patterns by encouraging them to name the items in sequence, as in “blue, red, green, blue, red, green,” etc. (Taylor-Cox, 2003). Teachers label different kinds of patterns to indicate the level of complexity in a repeating segment, such as a/a, a/b, a/b/c, or ab/ac/bc, and so one.
A growing pattern increases the number of repetitions in each sequence, such as jump, squat, jump 1x/jump, squat , jump 2x/jump, squat, jump 3x . . . (Taylor-Cox, 2003). Many children find the inherent rhythm of patterns soothing. Some children may find it easier to identify one type of pattern than another. Patterns presented to children for identification should represent at least one repeat to help them determine what comes next (i.e., square, circle, rectangle/square, circle, rectangle/ square, circle . . . ) (Taylor-Cox, 2003).
Learning to recognize patterns is important not just for mathematics but for interpreting text in reading as well. Teachers can foster learning about patterns by:
- Displaying photographs of patterns in nature, such as a pine cone or nautilus shell
- Pointing out a pattern in the brickwork of a building
- Having a “pattern hunt” in the classroom or on the playground
- Clapping out the rhythm patterns in songs
- Making up motor games with actions that represent a pattern
- Decorating cupcakes with cutout patterns
- Filling in the days and weeks on a calendar
- Making patterns on paper with stamps or stickers
Geometry
“If mathematics is perceived as the search for order, pattern, and relationships to characterize ideas and experiences, then geometry and spatial sense should be central topics in a mathematics curriculum for young children” (Campbell, 1999, p. 124). Young children can begin to learn about geometry as they encounter a variety of shapes in play and daily life. Children play with and often recognize objects and symbols (including letters and words) by shape. As with other developmental sequences, children first match, then identify, name, and finally represent shapes (Charlesworth, 2005).
Spatial awareness develops as children learn prepositional and directional words such as on top of, below, next to, and so on. Teachers can help children learn the vocabulary of geometry, to develop a sense of two- and three-dimensional shapes and their respective characteristics as well as to think in terms of spatial relationships (Seefeldt & Galper, 2004).
Shapes
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Concepts about shape include the ideas that:
- There are different kinds of shapes
- Shapes can be found everywhere in different kinds of objects
- A single item can have different shapes (e.g., cookie or rock)
- A shape can be modified (made bigger or smaller, etc.)
- Combining shapes can create new or different shapes
Activities that promote learning about shapes include:
- Holding and feeling the edges of cutouts or models of different flat and three-dimensional shapes
- Tracing shapes
- Matching shapes with cutouts
- Making shapes with their bodies
- Using shape cookie cutters with play dough and for baking
- Making and cutting foods like a tray of brownies or pancakes into different shapes
- Folding paper to make simple origami
- Having a “shape hunt”
- Making mobiles with straight-sided shapes from objects like straws or toothpicks or making curved shapes with yarn or pipe cleaners
- Making silhouette cutouts of objects and matching them or having guessing games
- Making collections based on different shapes
- Using geoboards to make shapes with rubber bands
- Staking out “giant” shapes on the playground with crepe paper or string