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Patterns and Structure
In mathematics, patterns are more than a beautiful design (though they are often that too), patterns follow a predictable rule and that rule allows us to predict what will come next. Mathematicians say that mathematics is the study of pattern—of patterns and structure in numbers, and patterns and structure in geometry. Seeing pattern and structure in the world around us is a key mathematical habit of mind and one that children are developing from the first days of life. Children are naturally attuned to patterns because it allows them to predict what will come next and make sense of their world. When we see patterns we are able to predict—to count on things happening—and feel more secure and confident. Noticing these routines and patterns in everyday life helps prepare children to notice other patterns. Many stories, dances, and chants follow a predictable pattern. “Five Little Monkeys” follow a pattern where the words repeat but the number of monkeys decreases by one each time. “Head, Shoulders, Knees, and Toes” follows a pattern that speeds up as you go. Dancing or movement patterns such as clap, clap, stomp, clap, clap, stomp also help children build an understanding of pattern that includes the kinesthetic. As you engage children in these everyday activities, help them notice the pattern and describe it in words.
Why are patterns and structure important in early math? Sub-Topics
Repeating patterns are the ones we tend to think of first when we think of patterns. The stripes in the American flag are a repeating pattern: red, white, red, white, red, white. The repeating part, or unit, for the stripes is red, white. We can label this an AB pattern, where red is A and white Is B. The stripe pattern is ABABAB. Children may begin to understand that patterns are made up of repeating units, but it may take more time for them to be able to consistently identify the repeating unit or to create their own stable patterns. With time and experience, children will be able to see the underlying mathematical structure in patterns and can use symbols to represent the structure of the pattern. They can see that the pattern with fork, fork, spoon, spoon, fork, fork, spoon, spoon is related to the pattern blue, blue, yellow, yellow, blue, blue, yellow, yellow because they can both be generalized as AABB patterns.
Growing patterns keep increasing or decreasing by the same amount. In the example, the block towers increase in height by one block each time. It is a plus-one growing pattern. Our number system is a plus-one growing pattern too: 1, 2, 3, 4, 5. Each unit grows bigger by one.
Symmetrical patterns have segments that repeat but instead of repeating in a line, the segments are the same when flipped, folded, or rotated. Butterflies have mirror symmetry—the butterfly wings match when folded along a line through the middle of the butterfly. Snowflakes have mirror symmetry and rotational symmetry. The segments of a snowflake match when folded and the design looks the same when you turn or rotate it. There is symmetry in artwork, in buildings, in nature, and even in people and animals (our bodies are symmetrical if you draw a line down the middle—two ears, two arms, two legs, etc.)
Concentric patterns have circles or rings that grow from a common center like the ripples in the water or the circles that surround the bullseye on archery target.
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As an educator and enthusiast in mathematics with a focus on patterns and structures, my expertise stems from both academic study and practical application in teaching mathematical concepts related to patterns. I've delved extensively into the understanding and significance of patterns in various mathematical domains, as well as their application in educational settings.
The article touches upon fundamental concepts in mathematics related to patterns and structures, crucial for early math education. Here's an overview and additional insights into the concepts mentioned:
1. Repeating Patterns:
- Defined by regular repetitions of a particular sequence or unit.
- Example: The stripes in the American flag follow an AB pattern (red, white, red, white - labeled as ABABAB).
2. Growing Patterns:
- Involve sequences that increase or decrease by a consistent amount.
- Example: Block towers increasing in height by one block each time. The number system (1, 2, 3, 4, 5) is another example of a plus-one growing pattern.
3. Symmetrical Patterns:
- Segments repeat and exhibit symmetry when flipped, folded, or rotated.
- Examples include butterflies (mirror symmetry in wings) and snowflakes (mirror and rotational symmetry).
4. Concentric Patterns:
- Patterns with circles or rings that expand from a central point.
- Examples include ripples in water or circles around a bullseye on an archery target.
Understanding these concepts aids in nurturing mathematical thinking in children from an early age. Recognizing patterns enables prediction, fosters logical reasoning, and contributes to the development of critical problem-solving skills.
In educational contexts, incorporating patterns into activities, stories, games, and physical movements helps children grasp and internalize these concepts more effectively. Utilizing resources like pattern-based books, puzzles, and interactive games further reinforces these mathematical ideas in an engaging manner.
By nurturing a child's innate ability to recognize patterns in everyday life, educators and caregivers lay a solid foundation for future mathematical understanding and reasoning.
Should there be a need for further exploration or clarification on any of these mathematical concepts, I'm more than willing to delve deeper into specific aspects or provide additional resources to enhance understanding.
