Direct Modeling: Parent Newsletter 3

Direct Modeling: A Window into Children’s Mathematical Thinking
By Linda Levi

Choose one of these problems to pose to your child. Remember to let your child use his or her own strategy to solve the problem.

A. Tylesha has 5 bags of marbles with 3 marbles in each bag. How many marbles does Tylesha have altogether?

B. Patrick has 12 peace cranes. How many more cranes would Patrick have to make to have 21 cranes altogether?

C. Mrs. Richards’ class is taking the bus on a field trip. They are riding in a min-bus that has 11 seats. Altogether 27 people are going on the trip. How many people can sit 2 to a seat and how many have to sit three to a seat?

D. Mr. Wu bought 22 animals for his students to take care. He knows he is getting some lizards, some chicks and some beetles. He also knows that altogether his creatures will have 100 legs. What might he have ordered? Is there anything else he might have ordered?

Children’s initial conceptions of mathematics are quite different than adults’. Adults would solve problem A by multiplication, problem B by subtraction, and, if they remember their high school algebra, problems C and D by using systems of linear equations. Children will first be able to solve these problems by direct modeling the situation in the problem. For example, for problem B they may draw 12 lines and keep drawing more lines until they get 21. They then will go back and count the extra lines they added. For problem D, they may take 100 pennies and make groups of 4, 2 and 6 until they end up with 22 groups.

Direct Modeling is a powerful strategy that provides a foundation for the more advanced strategies that follow. If you cannot model a problem, you cannot solve the problem. When your child struggles with a math problem, avoid referring to the operation (addition, subtraction, multiplication or division). Kids who are struggling should be reminded to think about what is happening in the story and find a way to show it. As children grow in their sophistication, they will no longer need to and should not be expected to directly model every problem. Adults use direct modeling to solve complex problems throughout our lives. Elementary school children naturally directly model problems they find challenging; we should encourage children’s use of this strategy.

Linda Levi is an Elementary School Mathematics Consultant and Researcher and Developer of Cognitively Guided Instruction. Dr. Levi has researched the factors that enable children to learn math with understanding and is currently studying how the teaching of mathematics in elementary school can prepare children for success in algebra.