The last time I saw Bert de Nemethy, the former U.S. Equestrian Team show jumping coach who died in January (see Feb. 22, p. 8), it was one of those magical moments you remember for a lifetime.

About 15 years ago, my horse was stabled upstairs in the huge USET headquarters in Gladstone, N.J., for the Essex Three-Day Event. Very early in the morning, as I was coming back from the trailer with a bucket of feed, I noticed, in the mist, a solitary horse and rider trotting around the huge, walled show jumping oval behind the stable.

Bert would have been in his mid-70s at that time. He was dressed, as always, quite formally in flared jodhpurs, polished brown boots, a riding jacket, gloves and a tweed cap. The horse he rode was a big, aggressive Thoroughbred named Sasquatch, which my friend David Hopper had brought east after Ira Schulman found him as a 4-year-old at a New Mexico racetrack.

Sasquatch’s scope and jumping prowess had enabled him to shoot through the jumper ranks several steps ahead of his intrinsic rideability. Now, here was de Nemethy, in his incredibly patient and systematic way, trying to build in the foundation that had never been fully established.

His jumping equipment consisted solely of four raised cavalletti, set at a trotting distance, and as Bert soothed Sasquatch into an increasingly measured and cadenced tempo, the horse’s nervous tendency to hurry through the gymnastic exercise diminished accordingly.

It was a classical’in the truest meaning of that word’display of soft, skilled and compassionate horsemanship. For me it was also an affirmation of the man’s status as the living legend who transformed American show jumping into something approaching an art form. Although I mainly admired Bert de Nemethy from afar, and never had the opportunity to ride with him, I’ve always considered him the perfect blend of teacher and coach.

I say “blend” because it strikes me that today there is often a widening disparity between those two roles. In FEI-level dressage, there’s a raging controversy going on right now about whether competitive dressage can ever truly be classical dressage. The jumping photographs we look at in Bill Steinkraus’ book Riding and Jumping or in de Nemethy’s The de Nemethy Method bear little resemblance to those we currently see in the equine press.

Just the other day, I was studying an old photograph of Neal Shapiro, a de Nemethy protégé. His heels were down, his eyes were up, his leg was underneath him, his back was flat, his hip and knee angles were correct, and there was a straight line from his elbow, through the rein, to his horse’s mouth.

Then I opened my current issue of the Chronicle. Most of the jumping pictures showed riders from all disciplines jumping ahead of the motion, looking down, with their backs hunched, their lower legs swinging back toward their horses’ hips, and their hands planted on the neck halfway up to their horse’s ears.

It’s difficult to escape the conclusion that we’ve strayed very far, very fast, from de Nemethy’s precepts. While today’s riders are being coached to win ribbons, they’re being insufficiently taught to ride in a classical fashion.

What, therefore, is the difference between a coach and a teacher, if there is one? And does it really matter if the end products, the riders and horses, are winning blue ribbons? Is it solely a matter of aesthetics, a kind of insubstantial ivory tower tempest in a teapot, or is classical riding (however defined) a fundamentally sounder approach?

Distinctions between someone who is primarily a coach and someone who is primarily a teacher are clear when we consider stereotypical polar opposites. The screaming, bombastic, tantrum-flinging, do-anything-to-win, in-your-face coach is far-removed from the pedantic, fussy, scholarly, introverted and meticulous classics professor. The one is pure energy, ego and desire; the other pure scholarship and love of learning for its own sake.

It’s true that some riding coaches are of the Bobby Knight mold, whereas H.L.M. Van Schaik, one of my first teachers, would probably have preferred that I learned to walk correctly before I trotted, cantered and jumped. It’s now 40 years later, and I would probably still be walking if it were up to him. In most cases, though, the distinctions are subtler.

I got together a group of riders, mostly girls in their late teens and early 20s, and asked them about the differences between coaches and teachers. Here are some of their answers:

“A coach is more of a cheerleader. She wants to make you believe in yourself.”

“A coach’s main goal is to win some competition. He doesn’t care so much if you understand all the reasoning or philosophy behind what you do, as long as you do it well.”

“A teacher is more patient. Her goal is your knowledge. A coach is more into short-term goals.”

“A riding teacher is less into gimmicks like draw reins and bits. A coach does what he has to do so you can win events, like, Groton House [Mass.]. If he has to take shortcuts or hide your problems, that’s his job.”

I’ve also sensed that some riding instructors change with the seasons. In the winter, when the competitive pressure is off, they become more teacher-like, more patient, more tolerant of mistakes. When the season heats up, though, so do they.

They might not have made a major issue of that insufficient lengthening when Pine Top (Ga.) was two months in the future. They might have even explained why correct lengthenings are the result the horse being more fully engaged, and that engagement, elevation and self-carriage cannot be rushed. Now, suddenly, with Pine Top looming large only two weeks away, philosophical considerations are cast aside in the urgency of the moment.

It’s always struck me that the very best riders are those for whom the correct ways seem to be their instinctive reactions. Those responses are usually examples of learned behavior, although they may look completely natural. If riders can recreate certain learned skills under competitive pressure, do we call the people from whom they’ve learned those skills teachers or coaches?

I don’t think it’s possible for someone to be a truly great coach unless that person has superior teaching skills as well. It isn’t just a matter of shouting, “Now go out there and win one for the Gipper,” unless the athletes have been taught the basic ingredients that allow them to win. I think it’s more likely that a coach must also be a teacher, than that a teacher must also be a coach.

I suppose that when someone has been both a great coach and a great teacher like Bertalan de Nemethy, it doesn’t really matter whether coaching or teaching was more true to his basic nature. It is enough that he was brilliant in both roles, and that he made all of us in America who ride horses that jump the beneficiaries of his legacy.