Eh. When I'm teaching, it depends on the student and the horse available. Within 6 weeks (typically 6 lessons), no.
When I was teaching full time, I was managing a farm where I had total access to 20 different lesson horses. I'd start kids out with the barebones balance exercises, lunge lessons, steering, independence of the extremities, etc for the first 8 or so lessons. If one student was picking it up really quickly and had the natural ability, I'd introduce trot poles and two point for leg strengthening and coordination. I only had two students that moved on to trotting low x's in the first 4 months, but they had been very natural riders, were conscious of their hands, and were able to control their body parts separately. Also, they were on excellent lesson horses.
With students that own their own horses, it was much different. Most of my students like these I was primarily teaching them how to get the most out of their own horse, and oftentimes how to train their own horse with my guidance. I really enjoy that, helping the person feel what is wrong and showing them how to fix it (via video sessions). I frequently get on the students horse mid lesson to show them how they are riding, and how they should be riding. It's very exciting to see that lightbulb go off in their head when I show them how they look and how it should be.... lol. Usually these people have too much to overcome to work as a team with their horse to start jumping at all in the first few months.
Owner and head trainer of SE-Wisconsin Horse Care
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