no, Don't rinse with water straight after toothbrushing
After brushing, spit out any excess toothpaste. Don't rinse your mouth immediately after brushing, as it'll wash away the concentrated fluoride in the remaining toothpaste. This dilutes it and reduces its preventative effects.
Explanation: Certain theories postulates that after each day, the events of the day and activities that went on during the can be replayed in our subconscious as dreams.