Make sure that your position is right, a lot of riding school horses will go slow, slow down or stop if you tip forward even a millimetre ... it's a safety thing and GREAT for absolute beginners but not so good if you're jumping
Lots of transitions, lots of circles, serpentines, shallow loops to get the horse 'switched on'. Some horses benefit from a canter fairly early on to get 'revved up'.
Why not ask your instructor what the 'buttons' are?
I used to ride a ploddy coloured cob. Some days the damn thing wouldn't move and would even park in the middle of the school with you flapping around like a fish out of water. My instructor told me that she could jump 4' and had done Medium dressage. Yeah, right, I thought.
One day though I went to ask for canter. Huh, the bloody animal never cantered first time so I was prepared for flapping around the school until she finally deigned to bother to go into canter. Anyway ... off the leg! Ok, fluke. Other rein, off the leg! What the?????? The instructor said to me afterwards that it was because my position was better and that I was more confident! She still had her ploddy days but if you 'got' her from the beginning and made her work (transitions, school figures etc) then she respected you, decided that perhaps you could ride a bit after all and could be a little star! She never was my favourite ned but my heart didn't sink when I was down to ride her any more!