How do children solve real-life math problems?

    • Topic: Cognitive Development

    • Location: Discovery Center

    Sharing a group of objects is a math problem that children encounter regularly. Previous studies have shown that children do share, and that older children share more equally than younger children. We want to understand what strategies children use to make such decisions. For instance, children might take turns (“I get one, you get one” - a non-mathematical, rule-based strategy), they might look for symmetry (both groups should look the same - an approximation strategy), or they might think numerically (divide the number of objects by the number of people sharing).

    In this study, children (ages 3 – 5½ years) are introduced to a puppet and are asked to decide how to share stickers between the puppet, and themselves. They are asked to identify how many stickers they gave to the puppet, and how many they gave to themselves, as well as why they distributed the toys the way that they did. Then, they will play a card counting game with different animals on it - some children will be asked to count, whereas other children will not. After that, they will repeat the sharing game with another two puppets. Finally, children will play a game with rubber ducks and number words (e.g., “Can you make TWO ducks jump into the pond?”). We are interested in finding out if children’s familiarity with number words changes the way that they divide objects when sharing.

    We predict that children will use a numerical strategy to solve this simple math problem, if they are able to count the number of objects to share. We also predict children who practice counting cards will be more likely to share stickers equally. When the group is larger than they are able to count, we predict that children will use strategies involving either turn taking or symmetry instead.

    This research will help us better understand how children’s ability to count impacts how they solve math problems encountered in everyday life.

    This research is conducted at the Museum of Science, Boston by Sara Cordes with the Infant and Child Cognition Laboratory at Boston College

        » Infant and Child Cognition Lab at Boston College

    Activities to Try in the Discovery Center

    Dividing Dominoes

    In the physical science area of the Discovery Center, find the domino blocks and help your child count out 10 blocks. Ask your child to make two piles out of the blocks – one pile to keep and one pile to share with you. Does your child divide the blocks equally? What strategies does s/he use to divide the blocks (e.g. turn taking, symmetry)?

    Next, tell your child that another child is coming to the museum later today, and wants to play with the blocks too. Ask your child to make three piles this time – one for you, one for your child, and one for the “other child”. How does your child divide the blocks this time? Does s/he use the same strategies from before, or does s/he use different strategies?

    Activities to Try at Home

    Sharing Pennies

    Show your child a pile of ten pennies, and another pile of twenty pennies, and let him or her know that s/he will get to decide how to share the pennies with one of his or her toy animals, Without using number words (e.g. say “this many”) tell your child that s/he can share either five pennies from the pile of ten (one half), or that s/he can share ten pennies from the pile of twenty (also one half). Explain to your child that whichever pile s/he chooses to share from, s/he gets to keep the remainder of the pennies in that pile. Which pile does your child choose to share from?

    Try the same game, but use number words to emphasize the number of pennies your child needs to share from each pile. Does your child’s answer change? How does your child respond if you use number words to emphasize the total number of pennies in each pile?

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