Improving Skills in Missions, I must have missed something. Options

[suoq]

SR4A, pg 270

To learn or improve a skill or skill group, the character must succeed in an Extended Intuition + skill Test, with a threshold equal to the new skill rating x 2 and an interval of 1 week (1 month for skill groups). A teacher can add bonus dice to this test (see Using Instruction, p. 134).

Can someone walk me though this? For example, I don't see how a character with Intuition of 3 or less ever learns or improves a skill since I thought extended tests were done at the 4:1 buy instead of rolling.

At Intuition 3 and skill 0 you get, no hits so no new skill.
At intuition 3 and skill 1 you get 1 hit but need 4 hits for a new skill of 2.
At intuition 3 and skill 2, you get 2 hits after 2 weeks, but need 6 hits total.

I know I'm missing something, but I don't know what it is.

And correct me if I'm wrong but I can just keep pumping points into attributes and specializations with no extended tests, or did I miss something there as well?