Frost sounds like it's good for making things cold; what else is it good for? And what does arcane do?

Frost, fire, and nature are referred to as the elemental schools. They deal mostly with conjuration and manipulation of their subject and have primarily offensive applications. At high levels of mastery, one can also call forth elementals, which are low-intelligence semi-autonomous servitors.

The arcane school is the magic of purposeful creation. It is the purest school and the most versatile. It was arcane magic that the Titans used to sculpt Azeroth, and it is arcane magic that blue dragonflight uses to maintain the Nexus. Enchantment, teleportation, scrying; all these are of arcane magic.

She wants to learn everything about all of the kinds of magic but arcane is definitely the best one (she whispers this opinion to her nearest siblings). Do all of the kinds use runes? 

They can, but runes are most often used for long-term effects or for things that require more intricate specification than a reasonable amount of active casting would allow.

What else goes into active casting? What kind of magic lets their mother turn into an elf and back? How long until they can cast their first spells?

Active casting is the process of taking one's personal mana and forming it to the proper shape required by the spell. Every being has a certain amount of mana and this determines how much magic they can do at one time. As whelps, their mana pool is currently too small to cast any spells. As they grow, the amount of mana available to them will increase and they can start casting spells.

Shapeshifting is a form of instinctive magic that does not fit neatly within the paradigm of the schools. When they're older, they'll be introduced to how it works. Certain mortals who are deeply in touch with the rhythm of the world, usually druids, are also capable of shapeshifting.

That's a lot of waiting. But they can learn all the theory while they wait, so when they have enough mana they can be ready to do all sorts of things with it!

That's the idea!

Magical theory is, it turns out, a tricky thing to grapple with when you get down to the gritty details. Most whelps don't have the patience or the ability to concentrate for so long, so a significant portion of each day is also devoted to time spent flying around, exploring, and playing.

Maragosa can concentrate for quite a long time, for a whelp. She enjoys the other activities too, though. And she can think about what she's learning as she flies around, and talk about it with her brothers and sisters who might have thought of something she missed. All in all, an excellent set of ways to spend time! The gritty details slowly get less confusing as she builds up conceptual frameworks to fit them into. 

Eventually they're ready to cast their first spell, a simple ice lance. Kharmeena demonstrates how to pull the ice out and sharpen it and send it flying a few times. There's a line of target dummies set up for them to practice with.

Magic! Is so great! She experiments with pulling different amounts of ice, and sharpening it more or less or differently, and practices aiming at the target dummies.

It's easiest to cast using close to the same specifications demonstrated.

Using more ice costs more mana, using less lowers the cost. It seems like the cost increases more steeply than it decreases.

Changing the shape is fairly trivial, as long as a constant volume of ice is maintained.

Aiming is more about concentrating on the right spot at the right moment; the lance will hit whatever she's looking at.

Can she make it change direction in midair? Can she do two at once?

She can't make it change direction unless she keeps an active connection, which is a significant drain on her present mana.

To do two at once, she'll have to split her attention and magic. If she wavers, she could lose one or both lances.

Once she manages to get it to change direction once she moves on; she doesn't have enough mana to give that the effort it deserves yet. Doing two at once is much more interesting; she works diligently and gets better at concentrating on multiple things at the same time.

It takes a couple days of practice before she's reliably able to get two ice lances to hit the target without one evaporating or melting into a puddle or shattering mid-air. Everyone's very impressed, especially her siblings. They all clamor for her to teach them the trick.

She does her best to explain it! "You have to think about everything you need to think about for one lance, but twice. Practicing helps, because eventually you can sort of bundle up everything you need for one lance up into a single thought, and then just have that thought twice."

Hm! The whelps set to practicing this.

Kharmeena sets Maragosa a new challenge. Can she make two ice lances, fire only one of them, and then keep the extra hanging around while she makes two more?

She can sure try it! There's going to be a fair bit of accidentally firing both of them first, and also some dropping the second one while working on the third and forth, but she keeps at it.

Good, very good.

This is the key to the school of frost, Kharmeena explains. Fire propagates itself, it's the way of nature to grow, but frost does not self-sustain. Frost requires attention, maintenance. A mage who studies frost understands the value of careful management of power. You get out what you put in. If the mage is clever, they will find ways to make the most of what they can do.

Hearing the general principles laid out like that helps bring some clarity to her nonverbal intuitions, which is really nice. She starts trying more explicitly to find out exactly how much attention she has to put into each lance, and how much can be held back for the next one.

That does help her progress on the challenge.

They also get history lessons, starting with the ascension of the five Dragon Aspects. In the early days of the world, while the Titans were still molding it to their desire, they faced much opposition. Their primary foe was the Black Empire of the Old Gods, beings of pure shadow and darkness imprisoned within the crust of the world. But there were also natural threats. Among these was the great proto-drake Galakrond, Grandfather of Dragons. He wreaked havoc across the northern half of the world, destroying the Titans' servants and creations with impunity. Of his children, five stood up to end his depredations. These were Alexstrasza the red, Neltharion the black, Nozdormu the bronze, Ysera the green, and Malygos the blue. A mighty battle was fought, and at the end, the five stood victorious with Galakrond dead below them. In recognition of their service, the Titans imbued them with great power and charged each with the management of a facet of Azeroth. To Alexstrasza was given life, to Neltharion the earth, to Nozdormu the timeways, to Ysera nature and the Emerald Dream, and to Malygos was given magic.

"Wow!" Maragosa mumurs to a sibling. "The five were so brave and heroic!"

"Yeah! And then they got cool powers and now we have cool powers!"

"Such cool powers. And the blue powers are the best ones! We'll be able to do all kinds of stuff someday."