Final answer:
The most important development contributing to the rise of the cognitive approach was the interdisciplinary collaboration across fields such as linguistics, computer science, and neuroscience, combined with influential work by figures like Noam Chomsky and Jean Piaget.
Step-by-step explanation:
The cognitive approach in psychology highlights the significance of mental processes like thinking, remembering, and problem-solving. This approach emerged as a counter to the behaviorist perspective, which essentially ignored internal mental states as drivers of behavior. Instead, the cognitive revolution directed psychology's focus back to the mind. Several factors contributed to its rise, but one of the most important was the intermingling of various disciplines, such as anthropology, linguistics, computer science, and neuroscience, which encouraged a more holistic exploration of human cognition and behavior. Moreover, influential figures like Noam Chomsky and Jean Piaget played pivotal roles; Chomsky's critique of behaviorism and Piaget's work on cognitive development were particularly instrumental in shaping the cognitive paradigm.