Does Stone Blast deal Earth damage, and are Golems strong against it? ... Trying to get "Study Harder" at the earliest possible opportunity

Solution 1:

From Aselia wikia:

Stone Blast is a classic Earth-elemental spell in the Tales series, commonly appearing in the novice tier of damage.

And also from monster list:

So you are doing it right, apparently.

See this video for reference, and try to apply the same strategy with your golem. In the first battle there are 2 fire element enemies with Genis casting 10 Fire balls. The player keeps track with the usage counter on the lower-right side of the menu. At 2.31 Genis is rewarded with "Study Harder!" title.

EDIT:

According to TalesReserve forum, there are 3 different types of resistance:

Reduce (half damage): Lesser damage and the damage numbers tend to be slightly smaller.
Invalid (no damage): The attack does not produce any damage numbers at all and the enemy does not stagger.
Absorb (regains health): The damage numbers are green because the enemy restores HP instead of losing it.

Since you're trying only with the first one, maybe the simply reducted halving damage is not considered towards "has resistance to".

And also, from Playstation Trophies:

Genis must say something about the spells not being effective for it to count.

And this sounds more restrictive that just "has resistance to" stated elsewhere.