Question: What adjective (single word) means 'having/using a willingness to learn'?

Answer: 
I understand you're looking for a single adjective, and I think "curious" fits the bill nicely (and from a pedagogical perspective curiosity is a key indicator of learner success) but I would like to add the following to the mix because I think it shows, if not willingness, at least readiness or capability, and it might be worth something to you:

**fertile mind**

From Collins:

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> *fertile mind:* One that is capable of sustaining, supporting, growing and developing mental thought interjection, especially among the very young.
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Three excellent non-idiomatic words have already been suggested, curious, inquisitive, and teachable, but my intuition is that English lacks a word with your precise definition.

**I believe that the idiom "thirst" is what you are seeking.** "Thirst for knowledge" is a borderline cliche, but it is still evocative and clear, and I think many people would define it as a "willingness (or desire) to learn". (For the close connection between "will" and desire" see the interesting discussion, [“Make of that what you will” – meaning of “will”](https://english.stackexchange.com/questions/161230/make-of-that-what-you-will-meaning-of-will).)