Can children reason about unknown quantities?

    • Topic: Cognitive Development

    • Location: Discovery Center

    Previous research shows that children think about numbers long before entering school. For example: even infants know that when they see five objects and then see more objects added, the outcome should be a number of objects larger than five. We are interested in the limits of intuitive math abilities - in particular, whether preschoolers can do algebra. Children are usually taught how to do algebra in middle school, where they learn to solve equations by following specific rules. But, the ability to reason about unknown variables may develop much earlier.

    To determine if children have an intuitive understanding of algebra, we play games in which they must identify hidden numbers. For example, we introduce children to “Gator”, who has a cup that adds items (like buttons or pennies) to a pile. Gator’s cup always adds the same amount. Children see the pile before the cup adds its items, and they see the pile afterward, but they are not told how many items are in the cup. After a few rounds, we then ask children to choose Gator’s cup from two cups – one containg the number of items that where added to each pile and the other containing a different number of items Finally, we may ask children to choose which of two numbers completes a symbolic algebra problem (e.g., 9+☐= 17).

    We predict that children will find the Gator game easier than solving symbolic problems, and children who play the game with Gator first will more accurately complete the symbolic algebra problems than those who see the symbolic problems first then play the game with Gator.

    This study will us better understand children’s ability to reason abstractly and the kinds of mathematical reasoning children engage in.

    This research is conducted at the Museum of Science, Boston by Melissa Kibbe and the Developing Minds Lab at Boston University.

        » Developing Minds Lab

    Activities to Try in the Discovery Center

    Getting From Here to There

    Find the Ball Maze on the 2nd Floor of the Discovery Center. Help your child use the pipes to build a path that moves the balls from one side of the board to the other.

    How many pipes do you need to move one ball across the entire board? Can you find a way to use fewer pipes to accomplish this goal?

    How many balls can travel through your pipe maze at one time? Are there other ways your child is engaged in mathematical problem solving?

    Activities to Try at Home

    Play Estimation Games

    Gather some small items (e.g., cereal or raisins) and two cups. Have your child watch as you place five objects (one at a time) into one cup, and ten objects into the other cup. Ask the child to show you which cup has more. Then play again, but make the quantities more similar (e.g., five objects in one cup and seven in the other). Did changing the quantities affect your child’s estimation? How?

    Try some object arithmetic. Put five objects (one at a time) into one cup and ten objects into the other cup. Now, add ten more objects to the first cup and one object to the second cup. Ask your child to show you which cup has more and why. Did your child use number strategies like counting, or did s/he rely on his or her intuitive understanding of numbers?

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