Behaviorism had many successes, but there was growing evidence that as a theory it was too restrictive.  In other words, scientists starting finding results that could not be explained by behaviorism alone (i.e. in terms of, say, a history of reinforcements, or associations).  New theoretical ideas - like mental maps, or latent (unconscious, unreinforced) learning, etc. - seemed necessary.  These were among the first theoretical constructs of cognitive psychology and Cognitive Science.

“Latent”/”insight” learning

Tolman & Honzik (1930)

Rats allowed to wander a maze did better on subsequent tests of navigation (say finding food) in that maze.  This means they learned something during the wandering - but they were not being rewarded.  Behaviorism has difficulty accounting for this.  This should fit with your intuition though, e.g. you might have had a faster time finding our classroom if you had been in the building before.

Cognitive “maps”

Tolman, Ritchie, and Kalish (1946)

But what is being learned/stored from the latent learning?  Could it just be a series of responses, like whether to ‘automatically’ turn left at the end of a tunnel?  Or is the information more general, like a map?  To test this, this experiment had rats entering a maze from different locations to try to get to some food.  Rats found the food faster when it was in the same location in the maze, as opposed to being accessible by the same response (say, always turning left).  This means the rats are better at learning about ‘locations’/‘places’ than a sequence of movements; learning about something other than behavior in other words.  This was taken to mean that they had stored a ‘cognitive map’ so to speak, of the maze.  This is a kind of mental ‘represntation’ - we will talk more about this later.  This idea is inconsistent with behaviorism.

Plans, and Hierarchically organized behavior

Lashley (1951)

Behaviorism says that complex behaviors are built through ‘chaining’. One behavior leads to the next.  But in (most?) complex behaviors, the current response isn’t triggered by what has just happened but often what is going to happen later, or driven by what your overall goal is.  For instance, think about the actions you have to take when crossing the street:

                                                              Cross street

                                                                      /\

                             check safety                                                    move

                                    /\                                                                   /\

                    look left         look right                                left foot         right foot

Notice that “look right” does not lead to “left foot” movement.  The left foot movement is part of larger subtask to move, which in turn is part of the larger subtask of crossing the street in the first place.  So, what happens now (looking right) is because of what will happen later (moving). These results gave rise to hypothesis of subconscious processing (after all, you can’t/don’t keep track of all the subtasks you are performing) and the hypothesis of task analysis (notion of breaking down a task into subtasks).  These are ideas that are taken for granted now in Cognitive Science, but neither are easily accounted for by behaviorism.