What I do to get ascendant materials its buy vanguard, crucible or factions legendary armor and then dismantel it. Obiusly after complete all de daily and weekly events :).
PD: You can also go onto [url=http://www.destinypublicevents.com/]Public events bounty[/url]
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That's what I do too. Or at least I did, since now I don't even get Crucible points (been giving up on Crucible more and more lately..). And with Vanguard cap its like that. Say you hoard marks for 2 weeks and get those 200 (which is max abyway). You go in and spend it on 3 pieces, which you the dismantle and get 2-3 ascendant shards (I am not sure if it matters, but I usually have bounty waiting to be finished, so I can unlock and buy first upgrade on each item - that method always gives me 3 shards). Do you get same amount with 0 upgrades, can someone confirm? But you can see how much of a grind that it still. Purple need 6 per upgrade, so that is 9 shards every 2 weeks, comes up to 3 slots upgraded every month. As to public events, I have yet to see a shard. I was under impression all the give is ascendant energies, though it may be just my luck acting up again LOL
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When I dismantel vanguard armor, i get 3 shards, and from faction armor 2 shards with 0 upgrades.
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No point in upgrading then! Good to know. Thank you kind sir!