Often they have an image of Ashtanga as fast paced, dynamic, frenetic, obsessive, impossible postures that are fixed in stone and must be practiced perfectly before you can progress (to the next posture), it's thought of as hot, sweaty and perhaps even a little... culty.
Often of course this is also an image of the practice that brings some to Ashtanga, but I digress.
Ashtanga can be approached like that perhaps, and hey if your young 9or even not so young) and are wanting a fast paced fitness practice then this approach may be just the thing for you, actually, in the beginning, it suited me for a while to practice Ashtanga this way myself.
But it is perhaps a mischaracterization of Ashtanga or at least the intention behind Ashtanga
Ashtanga can be practiced fast paced, we often see it demonstrated that way, but that perhaps is because it IS a demonstration, less time on the video tape or only half an hour to give an idea of as many postures as possible and perhaps also there is an aspect of trying to impress you, or at least show you what the body is capable of.
But it's what the body is capable of... through yoga asana practice, through, dedication, devotion, concentration, a focus on the breath....
Krishnamacharya, Pattabhi Jois' teacher stressed time and time again that the heart rate shouldn't increase ( if it does, take a mini savasana) and that the breath rate should slow, asana should be steady and comfortable.
In daily practice, Ashtanga tends to be practiced more slowly than is presented in demonstrations See my page on Mysore rooms around the world,.
Krishnamacharya indicates in his 1934 book Yoga Makaranda that it should be practiced even more slowly, the breaths are long, slow, full, 'like the pouring of oil', there are longer stays in many postures.
In recent Ashtanga the sequences are more fixed than Krishnamacharya seemed to have originally presented them but even here, in certain shalas, practice rooms around the world we find teachers giving modifications to postures, going with the intention and gesture of a posture and moving you forward with the advice to keep working on the posture your struggling with. Vinyasa Krama is perhaps the art of this approach.
I tend to breath quite slowly, my own practice is based on the original instruction Krishnamacharya gave for his 'Ashtanga' practice in Yoga Makaranda so I tend to only have time for half a 'series' before moving on to my finishing postures and some pranayama, perfectly acceptable.
Many are actually practising Ashtanga and don't realise it, in a gym or studio perhaps and going under a different name we can still find Krishnamacharya's influence. In fact many of the classes presented in some studios around the world have more in keeping with Krishnamacharya's original presentation than we find in some hard core exclusively 'Ashtanga' shala's.
The movements are linked to the breath, they follow the breath and the breath is intended to be slow, no fast paced practice here.... unless you feel like it, but then that's your approach, your practice and doesn't necessarily reflect the intention of the practice, it is though an option available.
There are crazy challenging postures but most of them are in the Advanced series intended for demonstration, not necessarily for daily practice unless that's an area you particularly wish to explore.
Some more challenging postures have found their way into the first series, personally I'd recommend dropping them and reintroducing them later. Marichiyasana D for example. Krishnamacharya put that posture in the Intermediate postures but it ended up finding it's way into Primary series, there are some good reasons for doing so, there are a lot of postures that prepare you for it but just as Pattabhi Jois would introduce the reverse triangle postures, the deep twists, back into the opening standing postures only once you had completed the series I'd recommend doing the same with Marchi D or any other particularly challenging posture.
Hot and sweaty? The room actually shouldn't actually be that hot, it should be comfortable, we want our body nicely warmed up and there will be some sweat but it shouldn't be excessive. I tend to turn the heat down in my practice room half way through my practice, no doubt many teachers do the same as a room fills up.
Ashtanga means eight limbs, it's become associated with asana practice but Krishnamacharya stressed the other limbs, the other aspects of yoga practice. Pranayama for example, the breathing practice. Krishnamacharya wasn't encouraging extream pranayama practices, holding the breath for excessive periods of time, we're not training to be free divers here, some of the pranayama practices don't include any retentions of breath, it's a gradual process, as with the asana, a building up of facility.
Krishnamacharya would also stress the meditative aspect of yoga.... Asana practice and pranayama clean the room ( the body ), what's the point if we don't then live in it, i.e. engage in some form of meditative practice. There are many kinds of meditative practice the familiar concentration practices in a meditative posture but it might also suggest chanting or the study of relevant and interesting texts, there are different options depending on our tastes and inclinations, and these of course may change as we continue with our practice,
Ashtanga is a yoga practice, it's seeking to prepare you for these mediative practices, to be able to concentrate, focus more effectively, there's no point having a frantic asana practice and then collapsing afterwards, we are aiming to be more satvic, more calm, peaceful, steady.
But of course, for now, a wilder practice might be what your looking for, perhaps your young with an excess of energy you wish to burn, Krishnamacharya did teach asana to the young boys of the mysore practice, perhaps he brought that aspect out somewhat, perhaps your approaching Ashtanga as a fitness practice, it's possible to do so, Yoga for the three stages of life, but that isn't the only aspect of the practice we should be aware of or indeed necessarily the original intention or the full scope of the possibilities of practice that Krishnamacharya left to us.
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This of course is only one Ashtangi's view of Ashtasnga, there are as many as there are those who practice it.