The brain changes the way it is connected all the time. (Remember that when we say 'connected' we are treating the synapses as if they were connections between neurons even though there is a tiny gap). Anything we call learning, or experience, or memory, involves the brain adapting in some way; and this doesn't generally involve growing more neurons or changing shape or size. The adaptation of the brain, or 'neural plasticity', involves principally a change in the number or size or effectiveness of the synapses.
More later.