Problem Solving

When children are faced with an unfamiliar problem, they will often use their knowledge about a familiar problem to help them to solve the unfamiliar problem. We call this sort of reasoning analogical reasoning. Teachers and parents frequently use analogies when explaining things to young children. Over the past several years we have been trying to determine the types of analogies that young children can understand. In the first three experiments my students and I have been investigating if the amount of information a child can remember influences his or her analogical reasoning abilities. Generally, 2- to 4-year-old children are interested in discovering what makes things happen. As children mature they become better at figuring out more complicated relationships. For example, older children can figure out that the remote control changes the channel on your television set even though they cannot see any direct connection between these two items. As children age, the amount that they can easily remember at the same time also increases. In my research we are interested in answering three questions: (1) Do preschool aged children make use of analogical reasoning? (2) Are analogies that include a larger number of relationships more difficult than analogies that include fewer relationships for preschool aged children? (3) Does the amount a child can remember influence the types of analogies he or she can solve?

We investigated the kinds of problems that young children could solve using three games. In one game, Rachel Green showed 2- to 4-year-old children the solution to a simple problem. For example, some children saw that you could use a placemat to form a tube and move eggs into a basket. Some children were given the placemat after it had already been rolled into a tube, this made the problem a little less complicated to solve. Next she gave the children two similar problems. For example, children were asked to move fruit using a piece of cardboard or animals using a piece of plastic. We looked to see if children made use of the solution to the first problem in order to solve the second and third problems. If children did not spontaneously use the solution from the first problem to solve the later problems they were given two hints. In the first hint children were encouraged to think about how they had solved the previous problem. In the second hint they were shown an item that needed to be changed in order to solve the problem. Children received both simple problems (that required two actions to be solved) and complex problems (that required three actions to be solved).

Carina Fisher measured children’s analogical reasoning using a different game in which 2- to 3-year-old children were asked to complete a pattern. In this game showed children were shown two objects that underwent a change. For example, some children saw a lamb and then a sheep and a tiger cub and then a tiger. In this problem the objects were aging. Children then saw three new items (a panda cub, a baby giraffe and a calf). For each, they were asked to find the object that finished the pattern. Children received both simple problems (that required only one change such as aging) and complex problems (that required two changes such as aging and dressing).

Keli Small measured children’s analogical reasoning using a different game in which 3- to 5-year-old children were asked to complete a pattern with pictures instead of real objects. In this game children were shown a picture that underwent a change. For example, some children saw a picture of a boy and then a picture of a dirty boy. In this problem the objects were getting dirty. Children then saw a third picture (a pig). They were asked to find the picture that finished the pattern. As in the other research, children received both simple problems (that required only one change such as dirtying) and complex problems (that required two changes such as dirtying and wetting). In addition to asking children to complete analogies both Carina and Keli asked the children questions to determine if they understood the relations that were used in the analogies. For example, Keli asked the children what makes something get wet or dirty.

Working Memory Capacity

Working memory capacity reflects the maximum number of things children can think about at the same time. It has been hypothesized that increases in working memory capacity (which occur with age) might be responsible for allowing children to solve more complicated types of problems. Samantha Bering, Betsy Cohen, and Candy Nurse measured the size of children’s working memory capacity using 4 different games. In these games they looked at the total number of toys that children could correctly sort into two piles, the number of numbers or nonsense words they could recall, and the number of taps to 6 blocks they could recall in the correct order. We then looked to see how these different measures of working memory capacity related to each other and whether the size of a child’s working memory capacity influenced the types of analogies she would be able to solve.

What did we find?

Across all of the analogy experiments we found that 2- to 5-year-old children were making analogies in response to simple analogy questions. We also found that complex analogy questions were generally more difficult than simple questions. Despite the difficulty of complex questions, 3- to 5-year-olds solved many of these problems correctly. In most of the experiments older children were more able to solve complex problems than younger children were. One factor that may have helped the older children solve more problems correctly was their greater knowledge about the relations that were involved in the problems. For example, if 5-year-olds understand the process of dirtying in more detail than do 2-year-olds, this might explain why they are better able to solve analogies that involve dirtying. We also found that children who had larger working memory capacity were also able to solve more analogies. Because working memory capacity generally increases with age, this might also help to explain why older children answered more problems correctly than did younger children. Overall, the important implications of this research are that very young children can learn information using analogies. This suggests that analogies should be a tool for teaching during the preschool years.