The oldest and most primitive pteraspidomorphs were the Astraspida and the Arandaspida. You'll notice that all three of these taxon names contain 'aspid', which means shield.
These early fishes and many of the Pteraspidomorphi possessed large plates of dermal bone at the anterior end of their bodies. This dermal armour was very common in early vertebrates, but it was lost in their descendants. Arandaspida is represented by two well-known genera: Sacabampaspis, from South America and Arandaspis from Australia. Arandaspis have large, simple, dorsal and ventral head shields. Their bodies were fusiform, which means they were shaped sort of like a spindle, fat in the middle and tapering at both ends. Picture a sausage that is a bit wider near the centre with a crisp outer shell. Image: Tamura (http://spinops.blogspot.com) - Own work, CC BY-SA 3.0, https://commons.wikimedia.org/w/index.php?curid=19460450