She is known for her improvisations, and she played a slew of them. In fact, she devoted her whole second half to them — tunes were called out from the audience. But she played a “straight” first half: of Schumann and Ginastera.

Gabriela Montero, the Venezuelan pianist, appeared in recital at the Metropolitan Museum on Thursday night. She began with Schumann’s Op. 9, his “Carnaval,” a sprawling, delightsome work of about 20 sections. She had many things going for her: She was bold, confident, and accurate. But she had some things going against her.

She tended to be blunt, clangorous, and heavy. Many of the sections deserved more fleetness, and more lightness. And dynamics were insufficiently varied — the overall effect was too loud. For example, what should have been mezzo-piano tended to be mezzo-forte.

And Ms. Montero went in for many, many hesitations — rhythmic hesitations. Indeed, she was quasi-eccentric in her rhythm. “Carnaval” was filled with hesitations and hiccups — detracting from the general flow of the work.

Consider a couple of sections in particular: The Valse noble started well, but soon the hesitations kicked in, and then the music slowed down into absurdity. Why? And in the fabulous, stirring final section — Marche des Davidsbündler — Ms. Montero was impressively virtuosic. But, again, those hesitations and hiccups had to come and spoil things.

This was not a bad “Carnaval”; Ms. Montero does not give bad performances. But it was marred by bad habits, and not quite worth the price of admission.

Worthier was the pianist’s account of Ginastera’s Sonata No. 1. (Alberto Ginastera, you recall, was an Argentinian composer who lived between 1916 and 1983.) The sonata is in four movements, the first of which is marked Allegro marcato. From Ms. Montero, it was marcato indeed — that is no problem for her. It also had an appealing jazzy drive.

The next movement bears a most unusual marking: Presto misterioso. Normally, presto and misterioso don’t go together. But there are exceptions, such as the last movement of Chopin’s B-flat-minor sonata. And this second movement of the Ginastera. Ms. Montero brought it off well, imparting suitable mystery and ghostliness.

The next movement, the slow movement, is intricate and even ingenious. Here, Ms. Montero could have applied a tad more subtlety, more delicacy. And in the last movement, a kind of toccata, she unleashed her virtuosity. As before, she was heavier than necessary, but she still provided a thrill. And those octaves aren’t easy: Not only are they fast, they are trickily spaced.

Ms. Montero is to be thanked for bringing Ginastera’s sonata to the recital stage: a meritorious piece, from a meritorious composer.

After intermission, it was all improv. This is Ms. Montero’s shtick, and it is a good shtick. She has audience members name or sing a tune — and she goes to town on it. The first tune called out was “Twinkle, Twinkle.” Mozart had been there before. But Ms. Montero did admirably with it. Other tunes included a Bach fugue subject and “Für Elise.”

Ms. Montero’s improvisations tended to have structure and coherence — this was not mindless and formless noodling, as we often hear in jazz halls. Some of the improvisations had a Classical flavor, others a Romantic flavor, or an Impressionistic. At one point, we even heard some crazy Shostakovich-like circus music.

Mainly, Ms. Montero tended to Latinize the requested tunes. Just about anything could wind up a sort of tango.

The last tune named was the Allegretto from Beethoven’s Seventh Symphony — such great and transcendent music. Before improvising, Ms. Montero said, “I’m going to kind of destroy it” — a charming and apt remark. But she did unobjectionably.

She is a wonderful personality, this Gabriela Montero. Also a wonderful musician. And I will end with a question: Given her talent for improvisation, when is she going to branch into straight-out composition?