Cognitively Guided Instruction
Cognitively Guided Instruction (CGI) is a professional development program that aims to improve teachers' understanding of how children develop arithmetic concepts. The professional development program was based on earlier research detailing various problem types and strategies that students employ while working on addition and subtraction word problems. The development of CGI and research by Carpenter, Fennema, Peterso, Chiang and Loef was influential for the way it integratedr research on student learning and research on teaching.
History
From 1979 to 1981, Carpenter, Hiebert and Moser conducted a study of approximately 100 first, second and third grade students in Madison, Wisconsin. They interviewed each student three times each year, observing them solve addition and subtraction word problems. Their aim was to investigate "the development of children's abilities to solve verbal addition and subtraction problems and particularly in the processes and strategies used by children." (http://eric.ed.gov/?id=ED188892)
Their earliest work identified a taxonomy of addition and subtraction word problem types. Different problem within this taxonomy are differently difficult for children even when the "arithmetic" remains constant. For example, "Tom had 11 apples, and then lost 3 of them" might be easier for a student to represent than "Tom has 11 apples and 3 of them are spoiled," as the former problem has an action that a student can act out using counters, paper or some other representation.
Another major result of this early study was the identification of a learning progression that children pass through on their way to more advanced procedures for solving addition/subtraction word problems. At early stages, they found that children solve word problems by directly representing the action in a problem, with counters or any other available physical object. (For this reason, word problems without clearly presented actions tend to be more difficult at these early stages.) Students then develop various counting strategies to make their work more efficient, and eventually come to abstract the structure of the word problem and use memorized facts to solve problems.
In Hiebert & Carpenter (1982), the researchers argued that Piagetian cognitive tasks are not good indicators of readiness for solving addition and subtraction word problems. In this way, the authors argue that cognitive development along Piagetian dimensions is not a strict prerequisite for engaging in mathematical problem solving. In essence, very young children can solve addition and subtraction word problems. The ability of children to solve problems became a major theme of their work. (See Carpenter & Moser (1982), "Young Children Are Good Problem Solvers.")