Hi I just started learning dancing. I was just wondering is there any point for me to go social dancing because I find that when I dance at original speed, my technique breaks down. Would I be better off using the time to practice dancing on my own
In most cases, the best way to learn things is to do them. And in this case, dancing with a partner, to music, at speed will do wonders for your dancing. Social dances are the perfect time to do that. You can certainly benefit from time spent practicing on your own, but if it were me, I wouldn't sacrifice time with a partner to do it.
Of course like mjnemeth pointed out, I'm assuming we're talking about ballroom dancing? Or at least partner dancing? If not, disregard all previous information.
I took private lessons (and even went to my first competition) for a full 5-6 months before I ever started going to dance socials. I just wasn't comfortable enough in my dancing until then. However, that said, if you're just starting out I would say that while practicing on your own is certainly important, practicing with a partner - any partner - is vital. If you can't afford regular private lessons with your teacher, do as much social dancing as you can - whether in group classes or socials. No one expects your technique to be perfect - or even close to it - if you're just starting. The most important thing is to get used to dancing with someone else.
It depends on how far along you are - if you can get through the steps, lead (or follow?) well enough, but some technique breaks down, I'd say it's time to attend social dances. No one is sitting around with a clipboard scoring your technique, you'll be able to practice connection, and eventually you'll find your technique coming back to you.
Slowing the music down is fine, but you should spend at least some time at each practice dancing to full speed music... there's no other way to train your muscles to do the technique (which you're perfecting by going slow) to full speed.
You might consider finding a practice partner, too, so you can practice dancing with someone to fully speed without the pressure of a social event - messing up is expected, because you're practicing and doing things out of your comfort level.