I use a method which I more invented than learned, albeit by watching videos. The singers have only ever said it is easy to follow and useful. Someone described it as "painting the neumes on the air" and I guess that's pretty accurate, since I direct a pretty close (if idiosyncratic) reading of them. The main thing is musical interest and sonic unity, and what I do works for that. The singers are young adult amateurs.

Your conducting of chant (and, frankly, of anything with singers) partly depends on the singers, their skill, interest and other factors. If you have a choir which can recognize arsis and thesis in what you do with your hands, well and good. If you're waving your hands as you were taught in the colloquium but your choir doesn't understand any of what you do all the technical perfection serves to make tired arms and agitated air and choir members, but not helpful conducting.

To reiterate what others have said, and what I think is the most important point: Chironomy is a means, not an end. Its purpose is to lead, guide, and provide direction to the singers. As far as I'm concerned, this means that there is not one single "right way" to conduct chant. It will depend on your interpretation, your comfort level, your singers' experience level, and what everyone is accustomed to. I've seen everything from pure, simple arsis/thesis to theatrical comically large motions to jarring jabs at each note to subtle and nuanced chironomy with a single finger.

With that said, I did a little introductory video a few months ago to provide some thoughts about how I conduct chant, which is definitely related to the methods and ideas discussed in Carroll's Technique of Gregorian Chironomy referenced above by @madorganist. Again - I'm not suggesting my way is the "right" way, but it gives you something to look at and think about in video form, which is often easier to relate to than just the written word when considering such motion-intensive tasks.

Video at https://youtu.be/aKypoLvnEfI

Beyond the basic introduction in the video, I do quite a lot more nuanced conducting in the real world. When the choir loft is full, I conduct chironomy with both hands. I'll often use my left hand for dynamic direction. I conduct adults and children the same way; I see no need to condescend or simplify for them... they often pick it up more intuitively than the adults! When I'm sitting at the organ, I'll occasionally through a hand up to conduct if needed, but more often just provide some subtle direction with my head as needed.

Once more, it all comes down to effectively and efficiently conveying the musical idea to the singers. Different methods are fine, as long as they achieve that end.

I, too, have seen the "trained" directors of chant wave their arms in circular motions. I wondered if their choirs just learned the music then ignored the director, who wasn't conveying much in the way of information. Standard conducting gestures would have provided much more actual direction for those choirs.

Don't wave arms in circles? But, but...Guido of Poughkeepsie said we will perish in the flames if we don't do it that way. Is outrage!

Charles,

Is there a Poughkeepsie outside of upstate New York? I ask because Guido would have a family name if he were from Poughkeepsie New York, but not, perhaps, if he were an itinerant musician, theoretician, mathematician and historian in some other Poughkeepsie.

https://en.wikipedia.org/wiki/Poughkeepsie,_Arkansas

Bonus point: the seat of the county in which it subsists is...Ash Flat. As in "men, your ash is flat".

As a resident of Dutchess County, NY I was shocked to find out there is another Poughkeepsie! By the way, we who live in Dutchess County do not consider ourselves as residing in "upstate" New York. We think of upstate as north of Albany. But Manhattanites think upstate is anything north of Yonkers.

Carol, Liam,

My apologies. As a native of Western New York,(growing up in the northern suburbs of Buffalo) I was taught somewhere along the way to treat everything that wasn't New York City or Westchester County as "Upstate" New York. I think it made sense because NYC was filled with crazy people, which left the rest of the state for sane folks.

I grew up on Long Island, but my sister was sent to a private school in Rhinebeck for a few years in the 1960s, where we learned that Rhinebeck was, pace our usage, definitely no where near Upstate*, which only began near Albany, and then my brother and his family have lived for decades in the Southern Tier and then Western NY, where this lesson was reinforced.

* Being along a commuter rail line to NYC, it by definition could not be, as it was well within the metro area - that includes all of the lower Hudson Valley. And Downstaters don't appreciate that Albany is 40 miles closer to NYC than to Canada....

Then again, if you live on Staten Island, all of the rest of NY State (including most of Long Island, save Brooklyn) is "upstate" (Montauk is north of White Plains and the Tappan Zee Bridge...and as far east as Napatree Point in RI*).

* Good geography trivia question: with how many other US states does New York State share a border? People almost always forget Rhode Island...the east end of ultra-exclusive Fishers Island is about 2 miles from formerly exclusive Napatree Point (the lovely former residences of which were washed out to sea in the Great Eastern Seaboard Hurricane of 1938).

I can drive for two hours and still be in Boston.

Mr. Elliot Livingston: "Why haven't we met before?"

Miss Charlotte Vale: "The world is small, but Boston is big."

I just came back from Texas a few weeks ago and I drove on I 35 from Dallas to south of Austin with 18 wheelers surrounding me on all sides. Driving less than 70 mph is not possible and it was terrifying!

A Texas rancher was researching farming practices in various European countries and was asking a German farmer about the size of his farm and its variety of produce. Then the little German farmer asked the Texan how big his ranch was. The Texan said boastfully, 'well, I get up at three o-clock in the morning and drive for three days and I'm still not across it'. The little German farmer smiled and said, 'Yes, I had a car like that once'.

.

Is there perhaps a conducting method that incorporates the gestures made when pushing overhanging branches out of the way and swatting gnats while hiking a rough trail through the Appalachians...?

...swatting gnats while...

I've seen some chironomy that was indistinguishable from swatting at gnats.