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# Child Development Tracker: Mathematics From Age 3 to 4 (page 5)

### Patterns, Reasoning, and Algebra

• Throughout this year, some children will still be developing a firm understanding of daily time sequence (e.g., time to eat, nap time, etc.). At the same time, some children will be just discovering basic patterns in the environment (e.g., day follows night, patterns in carpeting or clothing, etc.). They also use the terms, "tomorrow," and "yesterday." During the second half of the year, some children will understand a sequence of events when it is clearly explained (e.g., parent says, "First we plug the drain, then we run the water, and finally we take the bath.").
• Throughout this year, some children are just showing interest in patterns or sequence (e.g., attempts to follow patterns with stringing beads, magnetic shapes, peg boards). Children can also identify the "core" of simple repeating patterns (i.e., the basic sequence or building block that is repeated) and extend the pattern by replicating the core (e.g., for the pattern "red/blue/red/blue/red/blue," the child will add "red/blue"). Children show varying levels of progress with this skill through age six. This development is also true for when children imitate pattern sounds and physical movements (e.g., clap, stomp, clap, stomp...).
• During the second half of this year, a very small number of three-year-olds may recognize (from working concretely with small collections) the following general rules and may begin to summarize them with natural language: "additive identity" (e.g., says, "You did not add anything, so it is still the same"), "subtractive identity" (e.g., says, "You did not take anything away, so it is still the same"), and "subtractive negation" (e.g., says, "You took it all; there is nothing left.").
• Throughout the year, some three-year-olds will be able to use deductive reasoning (using what we know to logically reason out a conclusion about what we do not know) to solve everyday problems (e.g., figures out which child is missing by looking at children who are present).
• Throughout this year, some children will still be learning how to classify, label, and sort familiar objects by a known group (e.g., hard v. soft, large v. small, heavy v. light). A few children will also move beyond using arbitrary rules (e.g., creating a category for "because I like it") to complete an adult-imposed classification task. Instead, these children can stick with one feature (e.g., color, shape, size) in sorting objects into a class.
• During the second half of this year, some children will be able to reason "transitively" (e.g., if Abby is older than Betsy, and Betsy is older than Charlene, then Abby is also older than Charlene).

### Statistics and Probability

• Throughout this year, some children will recognize that some questions, issues, or areas of disagreement are "empirical questions" that cannot be answered without first collecting data. Also, children will be able to collect relevant data for addressing a question (e.g., What eye color is most common in the family?) or making a decision of personal importance (e.g., Which ice cream shop has the most flavors?).

For other child development articles, please see http://www.pbs.org/parents/childdevelopment/

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