It’s hard to believe that Savion Glover, who first gained attention in the Broadway show “The Tap Dance Kid,” is almost forty. (He was only ten when, as an understudy, he took over the title role.) In the years since then, he’s appeared in other musicals (“Black and Blue,” “Jelly’s Last Jam”), won a Tony in his early twenties for choreographing “Bring in ’Da Noise, Bring in ’Da Funk,” and done films and TV shows, spreading his particular brand of urban tap to a wide audience. But perhaps his most lasting influence will be as a teacher. In Newark, his home town, he runs a tap school called HooFeRzCLuB, where he makes sure that pupils know who their tap forebears are and give them proper respect. His latest production, “Savion Glover’s STePz,” at the Joyce through July 6th, pays homage to some of the tap masters, and along the way cements Glover’s own place in its history.

Glover’s style is marked by unpredictability—it’s possible to be lulled by his fine control one moment and jarred by an involuntarily flung arm the next. There is nothing boring about his dancemaking, and watching his latest piece is like going on every ride at the carnival. Glover plunges us into the heart of tap right away, in a sequence called “Miles Mode.” As John Coltrane’s 1962 composition of the same name kicks in, Glover’s guests—Marshall Davis, Jr., Ayodele Casel, Robyn Watson, and Sarah Savelli, all highly regarded hoofers—begin tapping on a raised wooden platform. Dressed in street clothes, the dancers fit neatly into Coltrane’s jazz rhythms, setting the tone for what is to come: a primer in how the human body, and its tapping feet, can be a musical instrument in itself.

When Glover comes out, there is joyful applause. (His audiences are frequently filled with fans and aficionados.) In a black shirt and gray pants, his dreadlocks tied back, Glover’s rangy body responds to Coltrane’s music, plays with it, allowing it to sweep him along but also asserting his own mastery. For a few minutes, he parks himself in the downstage-right corner of the platform, showing us what speed and articulation are, then drifts to his left, and is replaced by Davis, whose movements are more contained, minimal, neater than Glover’s. Glover watches from the side, in the half-dark, and looks pleased by what his comrade is doing. Casel, Savelli, and Watson come on, one by one, and personalities emerge: Casel, petite, is lighthearted and warm; Savelli, a genial performer, is more stylized in her mannerisms; Watson moves gently, and is more reserved, but sneaks a grin in unexpectedly.