I do agree with Karl Kapp that different ways of learning are best explained by different theories and that teachers should not limit themselves to one theory but should be able to use an arsenal of methods (grounded in various theories) to educate students. Bill Kerr also considers each -ism to be valuable for various ways of understanding learning.
George Siemens connects the three first -isms to the three epistemological traditions or ways of looking at informations and knowledge.
Objectivism & Behaviorism
Pragmatism & Cognitivism
Interpretivism & Constructionism
Driscoll contends that Objectivism and Interpretivism are often considered as opposites and Pragmatism ties them together. (p. 13)
Piaget is a prominent cognitivist theorist who addressed the different developmental stages through which children grow. These stages are important to know for designing learning environments. Other cognitivist theorists have posited other useful ideas for teaching, like Vygotsky's ZPD, and Gardner's MI Theory. It should be noted that these theorists could fit into other theories as well. So while Kerr thinks -isms change, it may be better to change the -ism instead. The above mentioned posts are not so much about Cognitivism but about learning theories in general. All three men were involved in an an open course in 2008 called Connectivism & Connective Knowledge.
Driscoll, M. P. (2005). Psychology of learning for instruction (3rd ed.). Boston: Pearson Education, Inc.