Children come to school with a great deal of informal knowledge that we often don't take into account and we haven't really given them credit for...CGI is about attending to the kinds of knowledge children have, the informal strategies that they bring to school and trying to help the children build on those strategies.
Thomas Carpenter


The structure of a problem determines how difficult it is for children to solve and determines their initial solution strategies.
Children usually pass through three levels of solutions strategies
  1. Direct Modeling - children directly model the action or relationship described in the problem using objects or fingers to count all.

  2. Counting Strategies - children realize it is not necessary to physically construct and use counting strategies such as counting on. The counting strategies generally involve some sort of simultaneous double counting and the objects are used to keep track of counts rather than objects in the problem.

  3. Derived Facts - as children begin to understand relations between numbers they begin to use these relationships to use small sets of memorized facts to derive solutions for problems involving other numbers such as making a 10.


Addition and Subtraction word problems can be classified by ...
  1. focusing on the action or relationship described in the problems
  2. the placement of the unknown

Problem Structure Graphic
Addition and Subtraction Classification Table
Addition and Subtraction Blank Classification Table