A few years ago, some friend's kids came away with us on holidays and I promised them I would teach them to ride. Their names were T. and D. and they were about 6 & 5 respectively. T., being the boy, was right into it and took off like a flash. After barely an hour of running behind him, he was off like a pro. But D. took a bit more work. After the first fall or two, she was ready to give up. It seemed that everytime she got going, she fell off. To her, riding was pain and not something worth pursuing. I could see that I needed to change my approach.
So instead of teaching her to ride, I started teaching her to stop. We did a few practice stops where I held her on the bike and without it moving forwards, I got her to take her foot off the pedals and place it on the ground as the bike fell to the side. Once she mastered that simple skill, integrating it with moving forward was just a matter of practice. After a day, she was up and doing laps alongside her brother. By taking the fear out of the fall, she was suddenly free to succeed.