There are some things that are quite common in beginning cello pedagogy that I don't like much. The beginning bow hold with the thumb under the frog, for example, which teaches--for no good reason--a habit that has to be unlearned later. Another is the "left thumb as anchor," which teaches little hands to hit pitches chronically out of tune, and little ears to accept this poor intonation. I know why some otherwise good teachers are doing these things: because we all want to get a student set up with decent hand shaping so that they can advance to playing pieces quickly and not get bored and quit. But the fact is, poor setup leads to fundamental misunderstanding of how the body can be used to our advantage in playing the cello, and this in turn sets the student up for endless technical challenges later on.
It's not all doom and gloom, however. When I thought back to some of the exercises I was taught as a child, it seems that many of them make a lot of sense, even if children don't know what they're doing them for. When the teacher tests whether the student can stand up from a seated playing position without shuffling their feet or moving the chair, what they're actually doing is encouraging a balanced sitting position. You simply can't stand up directly from sitting if your legs are splayed out or wrapped around the chair legs, or if you're hunched up. This is a great "reset" for those children who grow faster than their cello technique can keep up with. (And a good reminder for teachers to keep checking whether the chair is at an ideal height!)
Another great "reset" is the "bow hold spider." This is universal among string teachers and it's actually a really great exercise. You hold your bow with the stick vertically, and "walk" your fingers up and down it, sometimes while singing "Incy Wincy Spider" (a song my American daughter assures me is called "Itsy Bitsy Spider" here in the United States). It's harder to spider back to the frog than it is to spider to the tip! Back when I taught children in Saturday morning Suzuki classes, they always complained if I forgot to include Spider in our preliminary warm-ups. (I may or may not have sometimes placed Life Saver candies on the tips of their bows...)
Spider is a fun game, but what's so great about it is that it's practically impossible to do it with a bad bow-hold. I know this, because I just tried to do it. I tried supinating my hand, and almost dropped the bow! I tried spreading my fingers in a widely-spaced, tense "claw," and I couldn't "walk" my fingers at all. I tried wedging my fingers together in a salute, and couldn't do it that way either. I tried "bracing" my fourth finger hard against the bow, and nearly whacked my bow into the wall. Holding the bow in a vice-grip? Neglecting to curve the fingers? Those don't work either.
Spider quite simply trains you to keep your fingers naturally spaced, curved, and relaxed on the bow, with thumb opposing the middle fingers, and the whole hand slightly pronated, playing-style. There's a reason for the hand shaping we have collectively deemed to be good for holding the bow--it's because our hands want to do it naturally.
The takeaway from this is that despite all the misinformation about cello technique, there are certain exercises that are never-fail "resets" for your technique. Of which the ever-helpful Spider is one.
Want to know more about these resets? Check out Chapter 2 and Chapter 4 of Cello Practice, Cello Performance.