Producers told about 90 pupils at Jordanhill Primary School in the west end of the city not to stare or wave at the former Doctor Who star as he performed scenes for Single Father, in which he plays a man left to bring up four children alone.
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In the scene, Tennant, 39, in his first major role since leaving the science fiction show, had to run from a car parked outside the gates as the real pupils emerged from the school.
One parent said: “They just couldn’t help it. They were all sneaking side glances at him and some had their hands tight to their bodies waving at him thinking the camera couldn’t see that. It took forever to do, they had to do it over and over again.”
A BBC spokeswoman said: “The Single Father cast and crew thoroughly enjoyed their time filming at Jordanhill Primary School. Our young extras proved enthusiastic and took well to directions about being in shot, how to act and why waving during filming is a TV no no.”