ABSTRACT
This chapter describes Cognitively Guided Instruction in mathematics (CGI), a method within a subject, developed by Thomas Carpenter and Elizabeth Fennema. Research showed CGI students typically performed better on problem-solving than comparison students, but not necessarily on computation. Later students showed improvements on computation also. Very young children could participate successfully. The three-year follow-up showed modest continuing gains. Theoretical underpinnings were the principle that children could find their own strategies for solving problems. The structure of CGI covered basic word problem types, joining problems, separate problems, part-part-whole problems, comparing problems, multiplication and division problems, remainders, number of digits, solution strategies, direct modeling, joining to strategy, separating from strategy, separating to strategy, matching strategy, trial and error strategy, grouping strategy, measurement strategy, partitive strategy, counting and counting on strategy. Nine examples of various approaches are given. Training for CGI is described and extensions of CGI summarized. References and Bibliography conclude the chapter.
