There is a frequent misperception that the move from behaviorism to cognitivism implies an abandonment of the possibilities of decomposing knowledge into its elements for the purposes of study and decontextualizing these elements for instruction. Cognitivism does not imply outright rejection of decomposition and decontextualization. Two movements based in part on this rejection--situated learning and constructivism--were analyzed. These two schools of thought are not identical: situated learning emphasizes that knowledge is maintained in the external, social world; constructivism argues that knowledge resides in an individual's internal state, perhaps unknowable to anyone else. However, both schools share the general philosophical positions that knowledge cannot be decomposed or"decontextualized" for purposes of either research or instruction, and each group often appeals to the writings of the other for support. Since rejection of decomposition and decontextualization appears to be the core common ground of this "new look" in mathematics education, this paper examines the degree to which modern cognitive psychology lends support to that rejection. (Contains 92 references.) (ASK)