I have been told by many piano teachers to practice playing melodies slowly, ie using slow practice. I have never really been told by singing teachers to do slow practice.
Why is it common to use slow practice when learning melodies on the piano but less common when learning to sing them?
Probably a couple of simple reasons. We use breath when singing, and if we sang more slowly, it would run out sooner, so the breathing part of learning a particular part wouldn't reflect what ought to happen at the correct tempo. Most of us seem to have an inbuilt pitch control, which helps us find the note far quicker than we would on a piano, so there's little point in singing slowly.
Secondly, fingering is important on the piano, so playing slowly gives us time to move fingers to their correct positions, as well as probably having to read the dots and translate them into the correct notes played. Along with there's only ever one note to sing as opposed to often several to interpret while learning a piano piece.
I’m very sure it would depend on what you’re doing. Surely if you have a slow melody on piano there is no real benefit to practicing it even slower. And if you have a fast sung melody, such as fast coloraturas or very fast diction you’d usually start at a comfortable tempo and try to speed up from there.
It is of course much more common on piano to have fast notes, quirky shifts, multiple voices in one hand and such stuff, in which cases starting slow makes sense. In singing most literature is not particularly fast, and slowing down does not bring much benefit. In fact often slowing down makes things harder as holding notes and singing long, slow phrases is harder. But there are cases where you have to sing fast figures, fast diction or weird intervals, which profit from getting used to them slowly.
I think your question could be clearer or more meaningful if you gave some examples that you think are typical.
But, even without example, the first thing I would point out is most piano music involves playing two part simultaneously. One of the reasons to slow down at the piano is to work out the rhythmic timing of the parts. Additionally you can run into fingering issues, like two awkward position changes at the same time, and slowing down allows you to work out those problems.
In both cases what you are really doing is taking the two parts and figuring out what the composite rhythm and action is. The composite, once coordinated, can then be treated more like a single action. At least working up the composite happens in the beginning. After a while, when the parts are well practiced, and your playing skills improve overall, you can start feeling the performance as two separate parts. Slowing down practice facilitates the process.
Singing one part doesn't involve that kind of composite learning. The only thing you're really coordinating with is the accompaniment or the beat. If the singer were also playing the accompaniment, like sitting at the piano and accompanying yourself while singing a song, I imagine you might slow down the tempo a lot to workout the issues of coordinating multiple parts.
There are probably some vocal techniques that require slow practice. I don't really know, I'm not a singer. But something like yodeling might need slow practice to focus on when the voice changes register. Vibrato would be another one. That isn't really the slow practice I think you mean, because it isn't about singing a tune slowly, but it would involve slowing down.
It may depend on the choral director's philosophy re: learning new music. My current choral conductor in fact does take all new pieces (ie, sightreading) at a significantly reduced tempo, because she knows a significant number of our singers cannot read well. NOTE: this seems to be a major topic of interest re: learning instrumental solo music, and of particular interest to me as an "adult learner" of a string instrument. Can one master a piece faster / more efficiently by initially taking it slowly and speeding up as able, OR by playing very short bits (even just 2 notes, if necessary) at tempo, then extending the number of notes as able. The key to success in either case seems to be avoiding errors as you learn.
One website/podcast am finding helpful re: the latest thoughts about practice optimization / deliberate practice: Bulletproof Musician, with Noa Kageyama. One book on the same topic which I have found helpful: Practicing for Artistic Success, by Burton Kaplan (2004)
