Well I will have to surmise a little about Derek's not-yet-in-training dogs from what I know of him and his family and what I have seen and read about at other collie places - and also from his book, and my own experience of bringing on a collie pup.
Most people want their collies to be well socialised with people and the majority get reared on a family farm. The kids usually make sure that the puppies know all about family life, children etc! It's probably quite typical that mum and kids walk and play with the pup(s) until it's time for training to start - but there will be some 'pre-training' if you like from a very early age. For instance, Derek likes to teach 'here here' for the pup to run straight (like an arrow) into your cupped hands as early as he can. (This is in the book but maybe not on the DVD, I can't remember.)
One of the problems with doing too much training before the sheep work begins is that the dog can become too focussed on looking at the handler. I do have a bit of this with my bitch Dot - if she can't see me the other side of the sheep she sometimes runs back around to check I'm there! Ideally you want them to work without ever needing to look at you - their eyes should be on the sheep and their
ears on you.
Of course they get exercised, they'd go mad if they weren't. Plus you want them fit when you start training them! I used a 'stender lead' with Dot, and 'here here' as a recall if she was running free (never in the same field as sheep, not until she had had some training with sheep.) I mostly exercised her with one or more other collies; they know the rules and the pup will mostly tag along with 'big bro' or 'unc'!
Many working collies are not house dogs, and some are. Mine live outside but are welcome in the house from time to time. As a pup, Dot spent time in the house with me - but never left alone, and she had no bed in the house - from early on. Before I became a farmer I would never have expected myself to keep dogs that lived outside, but for dogs that really work (and on the previous farm - 500+ sheep on 1000+ acres of moorland - they
really worked) it does seem to be best if they have their own homes where they can be themselves and make their own rules. They also absolutely need time on their own to reflect when they are learning.
Derek's home is a wonderful hill farm way out at the end of a long long country track - he has absolutely no passing traffic to worry about, and all the sheep in the immediate vicinity are his own. I guess he hasn't the same need to leash a dog the rest of us might!
Incidentally, one command I know that Derek would never teach before the dog is around sheep is 'Lie Down'. In fact he may not teach this until they have been training with sheep for 6 months. When he works his collies, 'Lie Down' isn't a single command it's practically a language. It always always means 'focus on the sheep' (hence why he won't teach it until they are working with sheep), and depending on the tone and the circumstances it may mean 'steady up and focus', or 'stop moving forwards and focus' or 'lie down and focus'. (Hence you may see me, or Derek, calling 'lie down' then 'Lie Down' then 'LIE DOWN' - it doesn't mean the dog isn't listening, it may be that the three stages of slowing up and stopping were required to manage the sheep. Or, of course, that the dog isn't listening...

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